Great books of the Western world, vol. 8 [8]

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')'

WSmiw lllli will

111

W6m

will fl$>-^^^^$'^)^(c related in the same way, and A follows C but the relation cannot be reversed, then

mal

either

B and the relation cannot be reAnd A and D may belong to the same but B and C cannot. First it is clear

must follow versed.

thing,

is

D

D

D D necessarily

from the following consideration that

[5]

C

follows B. For since either

or

belongs to everything; and since C cannot belong to that to which B belongs, because it carries A along with it and A and B cannot belong to the same thing; it is clear that must follow B. Again since C does not reciprocate with A, but C or belongs to everything, should belong [10] it is possible that A and to the same thing. But B and C cannot belong

D

D

D

same

to the

thing, because

that

B does not

it is

possible that

same time

A

follows C; and so

results. It

reciprocate with

is

clear then

D either, since

D and A should belong at the

same thing. sometimes even in such an arrange[75] ment of terms that one is deceived through not apprehending the opposites rightly, one of which must belong to everything, e.g. we may reason that 'if A and B cannot belong at the same time to the same thing, but it is necessary that one of them should belong to whatever the other does not belong to: and again C and are related in the same way, It

In many things also, to some of which something belongs which does not belong to others, the negation may be true in a similar way, viz. [20] that all are not white or that each is not white, while that each is not-white or all are not-white is false. Similarly also 'every animal

mal

71

something impossible

[75] Privative terms are similarly related to positive terms in respect of this arrangement.

Let

45-46

to the

results

D

and

A

follows everything which

C

follows:

it

B

belongs necessarily to everything to which belongs': but this is false. [20] 'Assume that F stands for the negation will result that

D

H

A and B, and again that stands for the negation of C and D. It is necessary then that either A or F should belong to everything: for of

either the affirmation or the denial

must

be-

H

And

must belong to again either C or everything: for they are related as affirmation and denial. And ex hypothesi A belongs to everything to which C belongs. Therefore [25] belongs to everything to which F belongs. Again since either F or B belongs to long.

H

since

know

H

follows F,

this.

1

If

D'. But this

quence

is

then

is

H

or D, and follow D: for we follows C, B must follow

everything, and similarly either

B must

A

false: for as

we proved 2

the se-

reversed in terms so constituted.

The

perhaps it is not neces[50] sary that A or F should belong to everything, or that F or B should belong to everything: for F is not the denial of A. For notgood is the negation of good: and not-good is not identical with 'neither good nor not-good'. Similarly also with C and D. For two negations have been assumed in respect to one term. fallacy arises because

1

From

ft

39-b 13.

a

39

J 3*

PRIOR ANALYTICS

72

BOOK

53 b

II

B 52b

We have already explained

the figures, the character

[40] premisses,

number of and number of the

when and how

the

a syllogism

is

formed; further what we must look for when 53a refuting and establishing propositions, and how we should investigate a given problem in any branch of inquiry, also by what

belongs to no C, it has been assumed without proof that B does not belong to A, consequently it does not result through the syllogism

means we

shall obtain principles appropriate to

each subject. 2 Since some syllogisms are univer[5]

sal,

others particular,

all

the universal syl-

logisms give more than one result, and of particular syllogisms the affirmative yield more than one, the negative yield only the stated conclusion. For all propositions are convertible save only the particular negative: and the conclusion states one definite thing about another definite thing. Consequently all syllogisms save the particular negative yield

more than

one conclusion, e.g. if A has been proved to be[10] long to all or to some B, then B must belong to some A: and if A has been proved to belong to no B, then B belongs to no A. This is a different conclusion from the former. But if A does not belong to some B, it is not necessary that B should not belong to some A: for it may possibly belong to all A. [75] This then is the reason common to all syllogisms whether universal or particular. But it is possible to give another reason concerning those which are universal. For all the things that are subordinate to the middle term or to the conclusion may be proved by the same syllogism, if the former are placed in the middle, the latter in the conclusion; e.g.

[20] sion

AB

is

subordinate to

D

if

the conclu-

proved through C, whatever

B

or

C must

is

accept the predi-

included in B as in a whole, and B is included in A, then will be included in A. Again if E is included in C as in a whole, and C is included in A, then E will be included in A. Similarly if the syllogism is negative. In the second figure it will be possible [25] to infer only that which is subordinate to the conclusion, e.g. if A belongs to no B and to all C; we conclude that B belongs to no C. If then is subordinate to C, clearly B does not belong to it. But that B does not belong to what is subordinate to A, is not clear by means [30] of the syllogism. And yet B does not belong to E, if E is subordinate to A. But while it has been proved through the syllogism that

cate

A:

for

if

is

D

D

1.

1-26.

27-31.

B

that

But

1

does not belong to E. in particular syllogisms there will be

no

[35] necessity of inferring what is subordinate to the conclusion (for a syllogism does not re-

when

this premiss is particular), but whatsubordinate to the middle term may be inferred, not however through the syllogism, e.g. if A belongs to all B and B to some C. Nothing can be inferred about that which is subordinate to C; something can be inferred about that which is subordinate to B, but not sult

ever

is

[40] through the preceding syllogism. Simother figures. That which is subordinate to the conclusion cannot be proved; ilarly in the

53b the other subordinate can be proved, only not through the syllogism, just as in the universal syllogisms what is subordinate to the midis proved (as we saw) from a premiss not demonstrated: consequently either a conclusion is not possible in the case of uni-

dle term

which

is

versal syllogisms or else

it

is

possible also in

the case of particular syllogisms.

possible for the premisses of the syllogism

It is

[5] to be true, or to be false, or to be the one true, the other false. The conclusion is either

From true premisses it not possible to draw a false conclusion, but a true conclusion may be drawn from false premtrue or false necessarily. is

true

however only

in respect to the fact, reason cannot be established from false premisses: why this is so will isses,

not to the reason.

The

3 [10] be explained in the sequel. First then that it is not possible to

conclusion from true premisses,

false

draw is

a

made

by this consideration. If it is necessary should be when A is, it is necessary that A should not be when B is not. If then A is true, B must be true: otherwise it will turn out [15] that the same thing both is and is not at the same time. But this is impossible. Let it clear

B

that

not, because

A

is

laid

be supposed that

it is

fact

down

as a single term,

possible,

when

a single

given, that something should necessarily

is

not possible. For what rethe conclusion, and the means by which this comes about are at the least three terms, and two relations of subject result.

8

57

For that

necessarily

sults

a

4°- b *7-

is

is

BOOK

54b

[20] and predicate or premisses.

II,

If .then

it

CHAPTERS is

A

belongs to all that to which B beB belongs to all that to which C belongs, it is necessary that A should belong to all that to which C belongs, and this cannot be false: for then the same thing will belong true that

longs,

and that

and not belong at the same time. So A is posited as one thing, being two premisses taken together. The same holds good of negative [25] syllogisms:

it

is

not possible to prove a

from true premisses. But from what is false a true conclusion may be drawn, whether both the premisses are false

false conclusion

or only one, provided that this the premisses indifferently, if wholly false: but if the premiss

is it

is

not either of is taken as not taken as

does not matter which of the [jo] two is false. (1) Let A belong to the whole of C, but to none of the 5s, neither let B belong to C. This is possible, e.g. animal belongs to no stone, nor stone to any man. If

wholly

false, it

taken to belong to all B and B to all belong to all C; consequently though both the premisses are false the conclusion is [35] true: for every man is an animal. Simthen C,

A

A

is

will

with the negative. For it is possible that A nor B should belong to any C, although A belongs to all B, e.g. if the same terms are taken and man is put as middle: for neither animal nor man belongs to any stone, but animal belongs to every man. Consequently if one term is taken to belong to none ilarly

neither

[40] of that to which it does belong, and the other term is taken to belong to all of that to which it does not belong, though both the premisses are false the conclusion will be true. 54a (2) similar proof may be given if each

A

premiss

is

partially false.

(3) But if one only of the premisses is false, when the first premiss is wholly false, e.g. AB, the conclusion will not be true, but if the premiss BC is wholly false, a true conclusion will be possible. I mean by 'wholly false' the contrary [5] of the truth, e.g. if what belongs to none is assumed to belong to all, or if what belongs to

assumed to belong to none. Let A belong no B, and B to all C. If then the premiss BC which I take is true, and the premiss AB is

all is

to

false, viz. that A belongs to all B, it is impossible that the conclusion should be true: for A belonged to none of the Cs, since A be[10] longed to nothing to which B belonged,

wholly

B belonged to all C. Similarly there cannot be a true conclusion if A belongs to all B, and B to all C, but while the true premiss BC is assumed, the wholly false premiss AB is also

and

1-2

73

A

belongs to nothing to which B belongs: here the conclusion must be [75] false. For A will belong to all C, since A belongs to everything to which B belongs, and B to all C. It is clear then that when the first premiss is wholly false, whether affirmative or negative, and the other premiss is true, the conclusion cannot be true. (4) But if the premiss is not wholly false, a true conclusion is possible. For if A belongs to all C and to some B, and if B belongs to all C, [20] e.g. animal to every swan and to some white thing, and white to every swan, then if we take as premisses that A belongs to all B, and B to all C, A will belong to all C truly: for every swan is an animal. Similarly if the state-

assumed,

AB

ment

viz. that

is

negative. For

it

A

possible that

is

[25] should belong to some B and to no C, and that B should belong to all C, e.g. animal to

some white thing, but

to

no snow, and white

then one should assume that A belongs to no B, and B to all C, then A will belong to no C. (5) But if the premiss AB, which is assumed, is wholly true, and the premiss BC is wholly false, a true syllogism will be possible: [jo] for nothing prevents A belonging to all B and to all C, though B belongs to no C, e.g. these being species of the same genus which are not subordinate one to the other: for animal belongs both to horse and to man, but horse to no man. If then it is assumed that A belongs to all B and B to all C, the conclusion will be [55] true, although the premiss BC is wholly false. Similarly if the premiss AB is negative. For it is possible that A should belong neither to any B nor to any C, and that B should not belong to any C, e.g. a genus to species of another genus: for animal belongs neither to to all

snow.

If

music nor to the art of healing, nor does mubelong to the art of healing. If then it is assumed that A belongs to no B, and B to all

54t> sic

C, the conclusion will be true. (6) And if the premiss BC is not wholly but in part only, even so the conclusion

false

may

be true. For nothing prevents

[5] to the whole of B longs to some C, e.g. a

and

A belonging B

of C, while

genus

to

its

species

difference: for animal belongs to every

and

to every footed thing,

and man

footed things though not to

assumed that C,

A

A

belongs to

will belong to all

all.

all

C: and

If

this

man some

to

then

B, and

be-

and

B

it

is

to all

ex hypothesi

AB

is [10] is true. Similarly if the premiss negative. For it is possible that A should

neither belong to any

B

nor to any C, though

PRIOR ANALYTICS

74

B

belongs to some C,

e.g. a genus to the species and its difference: for animal neither belongs to any wisdom nor to any in-

of another genus

stance of 'speculative', but

some

wisdom belongs

instance of 'speculative'. If then

it

to

should

A belongs to no B, and B belong to no C: and this ex

[75] be assumed that to all C,

hy pot he si

A is

will true.

In particular syllogisms

it

is

possible

when

premiss is wholly false, and the other true, that the conclusion should be true; also when the first premiss is false in part, and the the

first

[20] other true; and when the first is true, and the particular is false; and when both are false.

(7) For nothing prevents A belonging to no B, but to some C, and B to some C, e.g. animal belongs to no snow, but to some white thing, and snow to some white thing. If then snow [25] is taken as middle, and animal as first term, and it is assumed that A belongs to the whole of B, and B to some C, then the premiss AB is wholly false, the premiss BC true, and the conclusion true. Similarly if the premiss AB is negative: for it is possible that A should belong to the whole of B, but not to some C, [jo] although B belongs to some C, e.g. animal belongs to every man, but does not follow some white, but man belongs to some white; consequently if man be taken as middle term and it is assumed that A belongs to no B but B belongs to some C, the conclusion will be true although the premiss AB is wholly false. W tne premiss AB is false in part, the [35] conclusion may be true. For nothing prevents A belonging both to B and to some C, and B belonging to some C, e.g. animal to something

W

and to something great, and beautiful belonging to something great. If then A is assumed to belong to all B, and B to some C, the 55a premiss AB will be partially false, the premiss BC will be true, and the conclusion true. Similarly if the premiss AB is negative. For the same terms will serve, and in the same positions, to prove the point. (9) Again if the premiss AB is true, and the [5] premiss BC is false, the conclusion may be true. For nothing prevents A belonging to the whole of B and to some C, while B belongs to no C, e.g. animal to every swan and to some black things, though swan belongs to no black thing. Consequently if it should be assumed that A belongs to all B, and B to some C, the [10] conclusion will be true, although the statement BC is false. Similarly if the premiss AB is negative. For it is possible that A should belong to no B, and not to some C, while B be-

beautiful

55 b

longs to no C, e.g. a genus to the species of another genus and to the accident of its own [75] species: for animal belongs to no number and not to some white things, and number belongs to nothing white. If then number is taken as middle, and it is assumed that A belongs to no B, and B to some C, then A will not belong to some C, which ex hypothesi is true. And the premiss AB is true, the premiss BC false. ( 10) Also if the premiss AB is partially false, [20] and the premiss BC is false too, the conclusion may be true. For nothing prevents A belonging to some B and to some C, though B belongs to no C, e.g. if B is the contrary of C, and both are accidents of the same genus: for animal belongs to some white things and to some black things, but white belongs to no [25] black thing. If then it is assumed that A belongs to all B, and B to some C, the conclusion will be true. Similarly if the premiss AB is negative: for the same terms arranged in the

same way

will serve for the proof.

(11) Also though both premisses are false the conclusion may be true. For it is possible that A may belong to no B and to some C, [50] while B belongs to no C, e.g. a genus in relation to the species of another genus,

own

and

to

animal belongs to no number, but to some white things, and number to nothing white. If then it is assumed that A belongs to all B and B to some the accident of

its

species: for

[35] C> tne conclusion will be true, though both premisses are false. Similarly also if the premiss AB is negative. For nothing prevents A belonging to the whole of B, and not to some C, while B belongs to no C, e.g. animal belongs to every swan, and not to some black things, and swan belongs to nothing black. [40] Consequently if it is assumed that A be55 b longs to no B, and B to some C, then A does not belong to some C. The conclusion then is true, but the premisses are false.

In the middle figure

it is

possible in every

to reach a true conclusion isses,

through

false

way

prem-

whether the syllogisms are universal or when both premisses are wholly

particular, viz.

[5] false; when each is partially false; when one is true, the other wholly false (it does not matter which of the two premisses is false); if both premisses are partially false; if one is quite true, the other partially false; if one is wholly [70] false, the other partially true. For (1) if A belongs to no B and to all C, e.g. animal to no stone and to every horse, then if the prem-

BOOK

56b isses

II,

CHAPTERS

and it is assumed and to no C, though the

are stated contrariwise

that A belongs to all B premisses are wholly false they will yield a true [75] conclusion. Similarly if A belongs to all

B

and

to

no C:

for

we

shall

have the same

syllogism.

(2) Again if one premiss is wholly false, the other wholly true: for nothing prevents A belonging to all B and to all C, though B belongs to no C, e.g. a genus to its co-ordinate species. For animal belongs to every horse and man, [20] and no man is a horse. If then it is assumed that animal belongs to all of the one, and none of the other, the one premiss will be wholly false, the other wholly true, and the conclusion will be true whichever term the

negative statement concerns. (3) Also if one premiss is partially other wholly true. For

it

is

false,

possible that

the

A

should belong to some B and to all C, though [25] B belongs to no C, e.g. animal to some white things and to every raven, though white belongs to no raven. If then it is assumed that A belongs to no B, but to the whole of C, the premiss AB is partially false, the premiss AC wholly true, and the conclusion true. Similarly [jo] if the negative statement is transposed: the proof can be made by means of the same terms. Also if the affirmative premiss is partially false, the negative wholly true, a true conclusion is possible. For nothing prevents A belonging to some B, but not to C as a whole, while B belongs to no C, e.g. animal belongs to some white things, but to no pitch, and [35] white belongs to no pitch. Consequently if it is assumed that A belongs to the whole of B, but to no C, the premiss AB is partially false, the premiss AC is wholly true, and the conclusion is true. (4) And if both the premisses are partially false, the conclusion may be true. For it is possible that A should belong to some B and to [40] some C, and B to no C, e.g. animal to some white things and to some black things, 56 a though white belongs to nothing black. If then it is assumed that A belongs to all B and to no C, both premisses are partially false, but the conclusion is true. Similarly, if the negative premiss is transposed, the proof can be made by means of the same terms. [5] It is clear also that our thesis holds in particular syllogisms. For (5) nothing prevents A belonging to all B and to some C, though B does not belong to some C, e.g. animal to every man and to some white things, though man will not belong to some white things. If

2-4

75

A

belongs to no B and to [10] some C, the universal premiss is wholly false, the particular premiss is true, and the conclusion is true. Similarly if the premiss AB

then

stated that

it is

affirmative: for it is possible that A should belong to no B, and not to some C, though B does not belong to some C, e.g. animal belongs to nothing lifeless, and does not belong to some [75] white things, and lifeless will not belong to some white things. If then it is stated that A belongs to all B and not to some C, the premiss AB which is universal is wholly false, the premiss AC is true, and the conclusion is true. Also a true conclusion is possible when the universal premiss is true, and the particular is false. For nothing prevents A following neither B [20] nor C at all, while B does not belong to some C, e.g. animal belongs to no number nor to anything lifeless, and number does not follow some lifeless things. If then it is stated that A belongs to no B and to some C, the conclusion will be true, and the universal premiss [25] true, but the particular false. Similarly if the premiss which is stated universally is affirmative. For it is possible that A should belong both to B and to C as wholes, though B does not follow some C, e.g. a genus in relation to its species and difference: for animal follows every man and footed things as a whole, but man does not follow every footed thing. Consequently if it is assumed that A belongs [jo] to the whole of B, but does not belong to some C, the universal premiss is true, the paris

ticular false,

and the conclusion

true.

(6) It is clear too that though both premisses are false they may yield a true conclusion, since

possible that

it is

B and

to

C

A

should belong both

though B does not fol[^5] low some C. For if it is assumed that A belongs to no B and to some C, the premisses to

as wholes,

are both false, but the conclusion larly if the universal

premiss

the particular negative. For

A should

follow no

B and

all

is

true. Simi-

is

affirmative

it

is

and

possible that

C, though

B

does

[40] not belong to some C, e.g. animal follows no science but every man, though science does

not follow every man. If then A is assumed to 56 b belong to the whole of B, and not to follow some C, the premisses are false but the conclusion

In

the

is

last

true.

figure

come through what

a is

true

may when both when each is

conclusion

false, alike

[5] premisses are wholly false, partly false, when one premiss is wholly true,

PRIOR ANALYTICS

7* the other false,

when one

premiss

is

partly

and vice versa, and in every other way in which it is possible to alter the premisses. For (i) nothing prevents [10] neither A nor B from belonging to any C, while A belongs to some B, e.g. neither man nor footed follows anything lifeless, though man belongs to some footed things. If then it is assumed that A and B belong to all C, the false,

the other wholly true,

premisses will be wholly false, but the conclusion true. Similarly if one premiss is negative, the other affirmative. For

it

possible that

is

B

A

to all C, [75] should belong to no C, but should not belong to some B, e.g. and that

A

black belongs to no swan, animal to every swan, and animal not to everything black. Con-

57-

belongs to every swan, black to no swan, and [5] black to some animals. Consequently if it is assumed that A and B belong to every C, the premiss BC is wholly true, the premiss AC is wholly false, and the conclusion is true. Similarly if the premiss AC which is assumed is true: the proof can be made through the same

terms.

(4) Again if one premiss is wholly true, the [10] other partly false, the conclusion may be true. For it is possible that B should belong to C, and A to some C, while A belongs to some B, e.g. biped belongs to every man, beautiful not to every man, and beautiful to some bipeds. If then it is assumed that both A and B belong to the whole of C, the premiss BC is all

AC

if it is

assumed that B belongs to all no C, A will not belong to some [20] B: and the conclusion is true, though the

wholly

to

[75] conclusion true. Similarly if of the premisses assumed is true and BC partly false,

premisses are

a true conclusion

sequently C, and

A

false.

(2) Also if each premiss is partly false, the conclusion may be true. For nothing prevents both A and B from belonging to some C while

A

belongs to some B, e.g. white and beautiful belong to some animals, and white to some beautiful things. If then it is stated that A and [25] B belong to all C, the premisses are partially false, but the conclusion is true. Similarly is stated as negative. For if the premiss nothing prevents A from not belonging, and B from belonging, to some C, while A does not belong to all B, e.g. white does not belong to

AC

some animals, beautiful belongs to some ani[jo] mals, and white does not belong to everything beautiful. Consequently if it is assumed that A belongs to no C, and B to all C, both premisses are partly

false,

but the conclusion

is

true.

is

one of the premisses assumed

(3)Similarly

if

wholly

the other wholly true. For

false,

it is

premiss

true, the

partly false, the

AC

is

possible: this can be proved,

same terms

the

if

Also the conclusion is

as before are

may

be true

if

negative, the other affirmative.

transposed.

one premiss

For

since

it

B

should belong to the whole of C, and A to some C, and, when they are so, [20] that A should not belong to all B, therefore it is assumed that B belongs to the whole of C, and A to no C, the negative premiss is partly false, the other premiss wholly true, and the conclusion is true. Again since it has been proved that if A belongs to no C and B to some C, it is possible that A should not belong to [25] some C, it is clear that if the premiss AC is wholly true, and the premiss BC partly false, it is possible that the conclusion should be true. For if it is assumed that A belongs to no C, and B to all C, the premiss AC is wholly true, and the premiss BC is partly false. is

possible that

(5) It is clear also in the case of particular syllogisms that a true conclusion may come

A and B should follow all C, does not belong to some B, e.g. animal and white follow every swan, though animal does not belong to everything white. Taking these then as terms, if one assumes that B belongs to the whole of C, but A does not belong to C at all, the premiss BC will be wholly true, the premiss wholly false, and

[50] through what is false, in every possible way. For the same terms must be taken as have been taken when the premisses are universal, positive terms in positive syllogisms, negative terms in negative. For it makes no difference to the setting out of the terms, whether one assumes that what belongs to none belongs to all

the conclusion true. Similarly

all.

possible that both [

35] though

A

AC

if

the statement

AC

true, the [40] BC is false, the statement conclusion may be true. The same terms will

57 a

both the premisses assumed are affirmative, the conclusion may be true. For nothing prevents B from following all C, and A from not belonging to C at all, though A belongs to some B, e.g. animal serve for the proof. Also

if

[^5] or that

The same

It is

what belongs

to

some belongs

to

applies to negative statements.

clear then that

if

the conclusion

the premisses of the argument either all or some of them; but

is false,

must be

when

false,

the con-

is true, it is not necessary that the premshould be true, either one or all, yet it is

clusion isses

possible,

though no part of the syllogism is may none the

[40] true, that the conclusion

BOOK

58*

II,

CHAPTERS

be true; but it is not necessitated; The rea57 b son is that when two things are so related to one another, that if the one is, the other necessarily is, then if the latter is not, the former will not be either, but if the latter is, it is not necessary that the former should be. But it is impossible that the same thing should be necessitated by the being and by the not-being of the same thing. I mean, for example, that it is impossible that B should necessarily be great [5] since A is white and that B should necessarily be great since A is not white. For whenever since this, A, is white it is necessary that that, B, should be great, and since B is great that C should not be white, then it is necessary if A is white that C should not be white. And whenever it is necessary, since one of two [10] things is, that the other should be, it is necessary, if the latter is not, that the former (viz. A) should not be. If then B is not great A cannot be white. But if, when A is not white, it is necessary that B should be great, it necessarily results that if B is not great, B itless

self is great.

(But

this

is

impossible.) For

if

B

not great, A will necessarily not be white. If [75] then when this is not white B must be great, it results that if B is not great, it is great, is

just as if

it

were proved through three terms.

Circular and reciprocal proof means proof by means of the conclusion, i.e. by converting one of the premisses simply and inferring the [20] other premiss which was original syllogism: e.g. suppose essary to prove that

A

assumed it

belongs to

in the has been necall

C, and

it

has been proved through B; suppose that A should now be proved to belong to B by assuming that A belongs to C, and C to B so A belongs to B: but in the first syllogism the

—

[25] converse was assumed, viz. that B belongs to C. Or suppose it is necessary to prove

B belongs to C, and A is assumed to belong to C, which was the conclusion of the first syllogism, and B to belong to A: but the con-

that

verse

was assumed

in the earlier syllogism, viz.

A

belongs to B. In no other way is reciprocal proof possible. If another term is taken as middle, the proof is not circular: for neither that

[50] of the propositions assumed is the same one of the accepted terms is taken

as before: if

one of the premisses of the first syllogism can be assumed in the second: for if both of them are taken the same conclusion as

as middle, only

before will result: but it must be different. If the terms are not convertible, one of the prem-

isses

4-5

77

from which the syllogism

results

must be to dem-

undemonstrated: for it is not possible onstrate through these terms that the third belongs to the middle or the middle to the first. [35] If the terms are convertible, it is possible to demonstrate everything reciprocally, e.g. if A and B and C are convertible with one another. Suppose the proposition AC has been demonstrated through B as middle term, and again the proposition AB through the conclusion and the premiss BC converted, and simi[40] larly the proposition BC through the conclusion and the premiss AB converted. But it 58 a is necessary to prove both the premiss CB, and the premiss BA: for we have used these alone without demonstrating them. If then it is

assumed that B belongs to all C, and A, we shall have a syllogism relating [5] all

Again if A, and A

it

to

C B

to all

to A. assumed that C belongs to all B, C must belong to all B. is

In both these syllogisms the premiss

CA

has

been assumed without being demonstrated: the other premisses had ex hypothesi been proved. Consequently if we succeed in demonstrating this premiss, all the premisses will have been [10] proved reciprocally. If then it is assumed that C belongs to all B, and B to all A, both the premisses assumed have been proved, and C must belong to A. It is clear then that only if the terms are convertible is circular and reciprocal demonstration possible (if the terms are not convertible, the matter stands as we said [75] above). But it turns out in these also that we use for the demonstration the very thing that is being proved: for C is proved of B, and B of A, by assuming that C is said of A, and C is proved of A through these premisses, so that [20] we use the conclusion for the demonstration.

In negative syllogisms reciprocal proof

is

as

belong to all C, and A to none of the Bs: we conclude that A belongs to none of the Cs. If again it is necessary to prove that A belongs to none of the Bs (which was pre[25] viously assumed) A must belong to no C, and C to all B: thus the previous premiss is reversed. If it is necessary to prove that B befollows. Let

B

longs to C, the proposition

AB

must no longer

be converted as before: for the premiss 'B belongs to no A' is identical with the premiss 'A

belongs to no B\ But we must assume that B belongs to all of that to none of which A be[30] longs. Let A belong to none of the Cs (which was the previous conclusion) and assume that B belongs to all of that to none of which A belongs. It is necessary then that B

PRIOR ANALYTICS

78

should belong to

all

C. Consequently each of

the three propositions has been sion,

and

sume

the conclusion

this

is

made

a conclu-

circular demonstration,

[35] the premisses, premiss.

to as-

and the converse of one of and deduce the remaining

In particular syllogisms

it is

not possible to

demonstrate the universal premiss through the other propositions, but the particular premiss can be demonstrated. Clearly it is impossible to demonstrate the universal premiss: for what is proved through propositions is universal [40] which are universal, but the conclusion is not universal, and the proof must start from the conclusion and the other premiss. Further a syllogism cannot be made at all if the other 58 b premiss is converted: for the result is that both premisses are particular. But the particular premiss may be proved. Suppose that A has been proved of some C through B. If then it is assumed that B belongs to all A, and the con[5] elusion is retained. B will belong to some C: for we obtain the first figure and A is middle.

But

if

the syllogism

is

negative,

it

is

not

possible to prove the universal premiss, for the

reason given above. But it is possible to prove the particular premiss, if the proposition AB is

converted as in the universal syllogism,

[10] 'B belongs to some of that to which does not belong': otherwise

A

gism

i.e.

some of no syllo-

results because the particular premiss

is

negative.

6 second figure it is not possible to prove an affirmative proposition in this way, but a negative proposition may be proved. An [75] affirmative proposition is not proved because both premisses of the new syllogism are not affirmative (for the conclusion is negative) but an affirmative proposition is (as we saw) proved from premisses which are both affirmative. The negative is proved as follows. Let A belong to all B, and to no C: we conclude that [20] B belongs to no C. If then it is assumed that B belongs to all A, it is necessary that A should belong to no C: for we get the second figure, with B as middle. But if the premiss In the

AB

was negative, and the other affirmative, have the first figure. For C belongs to all A, and B to no C, consequently B belongs [25] to no A: neither then does A belong to B. Through the conclusion, therefore, and one premiss, we get no syllogism, but if another premiss is assumed in addition, a syllogism will be possible. But if the syllogism is not uni-

we

shall

59a

premiss cannot be proved, we gave above, but the [?o] particular premiss can be proved whenever the universal statement is affirmative. Let A belong to all B, and not to all C: the conclusion is BC. If then it is assumed that B belongs to all A, but not to all C, A will not belong to some C, B being middle. But if the universal premiss is negative, the premiss will not be demonstrated by the conversion of AB: for it [^5] turns out that either both or one of the premisses is negative; consequently a syllogism will not be possible. But the proof will proceed as in the universal syllogisms, if it is assumed that A belongs to some of that to some of which B does not belong. versal, the universal

for the

same reason

1

as

AC

In the third figure, [40]

when both

taken universally,

is

it

premisses are not possible to

prove them reciprocally: for that which is universal is proved through statements which are 59 a universal, but the conclusion in this figure is always particular, so that it is clear that it is not possible at all to prove through this figure the universal premiss. But if one premiss is universal, the other particular, proof of the latter will sometimes be possible, sometimes not. When both the premisses assumed are affirma[5] tive, and the universal concerns the minor extreme, proof will be possible, but when it concerns the other extreme, impossible. Let A belong to all C and B to some C: the conclusion is the statement AB. If then it is assumed that C belongs to all A, it has been proved that C belongs to some B, but that B belongs to some C has not been proved. And yet it is nec[10] essary, if C belongs to some B, that B should belong to some C. But it is not the same that this should belong to that, and that to this: but we must assume besides that if this belongs to some of that, that belongs to some of this.

But

if

this

is

assumed the syllogism no

longer results from the conclusion and the oth[75] er premiss. But if B belongs to all C, and to some C, it will be possible to prove the

A

proposition

AC, when

it is

assumed

that

C

be-

A

to some B. For if C belongs to all B, and longs to all B and A to some B, it is necessary that A should belong to some C, B being middle. And whenever one premiss is affirmative,

the other negative,

and the

affirmative

is

uni-

premiss can be proved. Let B [20] belong to all C, and A not to some C: the conclusion is that A does not belong to some

versal, the other

lft

3 8.

BOOK

60*

II,

CHAPTERS 5-8 A will belong, not to

then it is assumed further that C belongs to all B, it is necessary that A should not belong to some C, B being middle. But when the negative premiss is universal, the other prem1 ie] iss is not proved, except as before, viz. if it is assumed that that belongs to some of that, to some of which this does not belong, e.g. if A belongs to no C, and B to some C: the conclusion is that A does not belong to some B. If then it is assumed that C belongs to some of that to some of which A does not belong, it is necessary that C should belong to some of the Bs. In no other way is it possible by converting [50] the universal premiss to prove the other: for in no other way can a syllogism be formed. It is clear then that in the first figure reciprocal proof is made both through the third and through the first figure if the conclusion is affirmative through the first; if the conclusion [35] is negative through the last. For it is assumed that that belongs to all of that to none of which this belongs. In the middle figure, when the syllogism is universal, proof is possible through the second figure and through the first, but when particular through the second and the last. In the third figure all proofs are B.

If

—

made through

itself. It is

clear also that in the

[40] third figure and in the middle figure those syllogisms which are not made through

those figures themselves either are not of the nature of circular proof or are imperfect. 8

59 b To convert a syllogism means to alter the conclusion and make another syllogism to prove that either the extreme cannot belong to the middle or the middle to the last term. For if the conclusion has been it is necessary, changed into its opposite and one of the premisses stands, that the other premiss should be [5] destroyed. For if it should stand, the con-

must

stand.

It

whether the conclusion

is

clusion also

contradictory or into

its

makes

a difference

converted into

its

same whichever form the

contrary. For the

syllogism does not result

conversion takes. This will be made clear by the sequel. By contradictory opposition I mean the opposition of 'to all' to 'not to all', and of 'to some' to 'to none' ; by contrary opposition I

mean

[10]

the opposition of

'to all' to 'to

none',

some' to 'not to some'. Suppose that A has been proved of C, through B as middle term. If then it should be assumed that A belongs to no C, but to all B, B will belong to no C. And if A belongs to no C, and B to all C,

and of

*

b

58

'to

9.

[75] B. For (as

79

no B at all, but not to all we saw) the universal is not

2 last figure. In a word it is not possible to refute universally by conversion the premiss which concerns the major extreme: for the refutation always proceeds through the third figure; since it is necessary to take both fremisses in reference to the minor extreme. 20] Similarly if the syllogism is negative. Suppose it has been proved that A belongs to no C through B. Then if it is assumed that A belongs to all C, and to no B, B will belong to none of the Cs. And if A and B belong to all C, A will belong to some B: but in the original premiss it belonged to no B. [25] If the conclusion is converted into its contradictory, the syllogisms will be contradictory and not universal. For one premiss is particular, so that the conclusion also will be particular. Let the syllogism be affirmative, and let it be converted as stated. Then if A belongs not to all C, but to all B, B will belong not to all [jo] C. And if A belongs not to all C, but B belongs to all C, A will belong not to all B. Similarly if the syllogism is negative. For if A belongs to some C, and to no B, B will belong, not to no C at all, but not to some C. And if A belongs to some C, and B to all C, as was [55] originally assumed, A will belong to some B. In particular syllogisms when the conclusion is converted into its contradictory, both premisses may be refuted, but when it is converted

proved through the

—

into

its

contrary, neither. For the result

is

no

3 [40] longer, as in the universal syllogisms, a refutation in which the conclusion reached by

60 a conversion

lacks universality, but no refuSuppose that A has been proved of some C. If then it is assumed that A belongs to no C, and B to some C, A will not belong to some B: and if A belongs to no C, but to all B, B will belong to no C. Thus both premisses are refuted. But neither can be refuted if the tation at

all.

is converted into its contrary. does not belong to some C, but to all B, then B will not belong to some C. But the original premiss is not yet refuted: for it is possible that B should belong to some C, and should not belong to some C. The universal premiss AB cannot be affected by a syllogism at all: for if A does not belong to some of the [10] Cs, but B belongs to some of the Cs, neither of the premisses is universal. Similarly if the syllogism is negative: for if it should be assumed that A belongs to all C, both prem-

[5] conclusion

For

if

« 1. 6.

A

'11.

[3-20, 23-4.

PRIOR ANALYTICS

8o isses

sumed

A

to all

are refuted: but if the assumption is that belongs to some C, neither premiss is refuted. The proof is the same as before.

to

60 b

belong to some C. Again

C and A

to

some C,

whichever form the conversion of the conmay take. For the conclusion of the refutation will always be in the third figure, and it,

clusion

in this figure (as sal

syllogism.

in a if

manner

The

we saw

1

)

there

is

no univer-

other premiss can be refuted

similar to the conversion:

the conclusion of the

first

I

syllogism

mean, is

con-

[20] verted into its contrary, the conclusion of the refutation will be the contrary of the minor

premiss of the

first,

no C: conclusion BC.

B

belongs to

A

all

into

if

A

the contradictory. Let

If

its

contradictory,

belong to all B and to then it is assumed that

C, and the proposition

AB

belong to all C, since the first figure is produced. If B belongs to all C, and [25] A to no C, then A belongs not to all B: the figure is the last. But if the conclusion BC is converted into its contradictory the premiss AB will be refuted as before, the premiss AC by its contradictory. For if B belongs to some C, and A to no C, then A will not belong to some B. Again if B belongs to some C, and [jo] A to all B, A will belong to some C, so stands,

will

,

that the syllogism results in the contradictory

minor premiss.

of the

given

if

A

similar proof can be

the premisses are transposed in respect

of their quality. If

the syllogism

is

particular,

when

1

1.

6.

is

2

b 59 39-60*

1.

6oa 5-14.

B

belongs

is

if

the

affirmative.

10

In the third figure when the conclusion is converted into its contrary, neither of the premisses can be refuted in any of the syllogisms, but when the conclusion is converted into its contradictory, both premisses may be

refuted and in all the moods. Suppose it has been proved that A belongs to some B, C being [10] taken as middle, and the premisses being universal. If then it is assumed that A does not belong to some B, but B belongs to all C, no syllogism is formed about A and C. Nor if A does not belong to some B, but belongs to all C, will a syllogism be possible about B and C. A similar proof can be given [75] if the premisses are not universal. For either both premisses arrived at by the conversion must be particular, or the universal premiss must refer to the minor extreme. But we

found that no syllogism is possible thus either 3 in the first or in the middle figure. But if the conclusion

is

converted into

its

contradictory,

[20] both the premisses can be refuted. For if belongs to no B, and B to all C, then be-

A

A

longs to no C: again if A belongs to no B, and to all C, B belongs to no C. And similarly if

one of the premisses is not universal. For if A belongs to no B, and B to some C, A will not belong to some C: if A belongs to no B, and to [25] all C, B will belong to no C.

the con-

converted into its contrary neither premiss can be refuted, as also happened in the 2 first figure, but if the conclusion is converted into contradictory, both premisses can its [35] be refuted. Suppose that A belongs to no B, and to some C: the conclusion is BC. If then it is assumed that B belongs to some C, and the statement AB stands, the conclusion will be that A does not belong to some C. But the original statement has not been refuted: for it is possible that A should belong to some C and also not to some C. Again if B belongs to some [40] C and A to some C, no syllogism will be possible: for neither of the premisses taken is 60 b universal. Consequently the proposition AB is not refuted. But if the conclusion is converted into its contradictory, both premisses can be refuted. For if B belongs to all C, and A to no B, A will belong to no C: but it was as-

clusion

if

will belong to

some B. The same proof can be given [5] universal statement

[75] In the second figure it is not possible to refute the premiss which concerns the major extreme by establishing something contrary to

A

Similarly

if

the original syllogism

is

nega-

Suppose it has been proved that A does not belong to some B, BC being affirmative, tive.

AC

being negative: for it was thus that, as we saw, 4 a syllogism could be made. Whenever then the contrary of the conclusion is assumed a syllogism will not be possible. For if A be[30] longs to some B, and B to all C, no syllogism is possible (as we saw 5 ) about A and C. Nor, if A belongs to some B, and to no C, was a syllogism possible concerning B and C.

Therefore the premisses are not refuted. But

when

the contradictory of the conclusion

is

as-

sumed, they are refuted. For if A belongs to [55] all B, and B to C, A belongs to all C: but A was supposed originally to belong to no C. Again if A belongs to all B, and to no C, then B belongs to no C: but it was supposed to belong to

all

C.

A

similar proof

26a 17-21, 27* 4-12. 5 2 6a 30-6.

3

4

28 b

is

1-4,

possible 11

I5-29

10.

if

the

61 b premisses are not universal.

BOOK II, CHAPTERS 8-11 For AC becomes true. Similarly

and negative, the other premiss parand affirmative. If then A belongs to all [40] B, and B to some C, it results that A belongs to some C: but it was supposed to belong to no C. Again if A belongs to all B, and to no 61 a C, then B belongs to no C: but it was assumed to belong to some C. If A belongs to some B and B to some C, no syllogism results: nor yet if A belongs to some B, and to no C. Thus in one way the premisses are refuted, in

81 in the other figures: for

moods admit

ever

the reduction per impossibile.

way

they are not. has been said it is clear how a syllogism results in each figure when the conclusion is converted; when a result contrary to the other [5]

From what

the premiss, the premiss,

and when is

a result contradictory to

obtained.

It is clear

that in the

figure the syllogisms are formed through the middle and the last figures, and the premiss which concerns the minor extreme is always [10] refuted through the middle figure, the

first

premiss which concerns the major through the last figure. In the second figure syllogisms proceed through the first and the last figures, and the premiss which concerns the minor extreme is always refuted through the first figure, the premiss which concerns the major extreme

admit

of conversion

universal

ticular

whatalso of

All the problems can be proved per impos-

excepting the universal

sibile in all the figures,

[35] affirmative, which is proved in the middle and third figures, but not in the first. Sup-

pose that A belongs not to all B, or to no B, and take besides another premiss concerning either of the terms, viz. that C belongs to all A, or that B belongs to all D; thus we get the [40] first figure. If then it is supposed that A does not belong to all B, no syllogism results whichever term the assumed premiss concerns; 61 b but if it is supposed that A belongs to no B, when the premiss is assumed as well we shall prove syllogistically what is false, but not the problem proposed. For if A belongs to no B, and B belongs to all D, A belongs to no [5] D. Let this be impossible: it is false then that A belongs to no B. But the universal affirmative is not necessarily true if the universal negative is false. But if the premiss CA is as-

BD

sumed

no syllogism

[75] is always refuted through the first figure, the premiss which concerns the minor through

results, nor does it supposed that A does not belong to all B. Consequently it is clear that the universal affirmative cannot be proved in the first figure per impossibile. [10] But the particular affirmative and the universal and particular negatives can all be proved. Suppose that A belongs to no B, and let it have been assumed that B belongs to all

the middle figure.

or to

through the

last.

tion proceeds

In the third figure the refutafirst and the middle

through the

figures; the premiss

which concerns the major

n then what conversion is, how it is effected in each figure, and what syllogism results. The syllogism per impossible is proved when the contradictory of the conclusion is [20] stated and another premiss is assumed; it can be made in all the figures. For it resembles conversion, differing only in this: conversion takes place after a syllogism has been formed and both the premisses have been taken, but a reduction to the impossible takes place not because the contradictory has been already, but because it is clear 2 [ 5] agreed to that it is true. The terms are alike in both, and the premisses of both are taken in the same way. For example if A belongs to all B, C being middle, then if it is supposed that A does not belong to all B or belongs to no B, but to all C (which was admitted to be true), it fol[50] lows that C belongs to no B or not to all B. But this is impossible: consequently the supposition is false: its contradictory then is It is clear

do

so

as well,

when

it is

some C. Then

should belong to no is

A

impossible (for

C

it

is

necessary that

or not to

let it

all

A

C. But this

be true and clear that

C): consequently if this is [75] false, it is necessary that A should belong to some B. But if the other premiss assumed belongs to

all

relates to A, no syllogism will be possible. Nor can a conclusion be drawn when the contrary of the conclusion is supposed, e.g. that A does not belong to some B. Clearly then we must suppose the contradictory. Again suppose that A belongs to some B, and let it have been assumed that C belongs to [20] all A. It is necessary then that C should belong to some B. But let this be impossible, so

that the supposition

A

is

false: in that case

We

it

is

belongs to no B. may proceed in the same way if the proposition CA has been taken as negative. But if the premiss assumed concerns B, no syllogism will be possible. If the contrary is supposed, we shall have a syllogism and an impossible conclusion, but [25] the problem in hand is not proved. Suppose that A belongs to all B, and let it have true that

PRIOR ANALYTICS

82

been assumed that essary then that this

is

C

C

belongs to all A. It is necshould belong to all B. But

impossible, so that

longs to

all

B. But

it

is

false that

A

concerns B, nothing is proved. is that A belongs not to all [40] but to some B, it is not proved that A belongs not to all B, but that it belongs to no B. For if A belongs to some B, and C to all A, then C will belong to some B. If then this is impossible, it is false that A belongs to some 62a B; consequently it is true that A belongs to no B. But if this is proved, the truth is refuted as well; for the original conclusion was that A belongs to some B, and does not belong to some B. Further the impossible does not result from the hypothesis: for then the hypothe[5] sis would be false, since it is impossible to draw a false conclusion from true premisses: but in fact it is true: for A belongs to some B. Consequently we must not suppose that A belongs to some B, but that it belongs to all B. Similarly if we should be proving that A does not belong to some B: for if 'not to belong to some' and 'to belong not to all' have the same [10] meaning, the demonstration of both will be identical. It is clear then that not the contrary but the contradictory ought to be supposed in all the syllogisms. For thus we shall have necessity of inference, and the claim we make is one that will be generally accepted. For if of everything one or other of two contradictory statements holds good, then if it is proved that the negation does not hold, the affirmation must be [75] true. Again if it is not admitted that the affirmation is true, the claim that the negation is true will be generally accepted. But in neither way does it suit to maintain the contrary: for it is not necessary that if the universal negtive is false, the universal affirmative should be the hypothesis

is it

generally accepted that

if

the one

be-

must suppose that it belongs to all B: for if A belongs to all B, and C to all A, then C belongs [^5] to all B; so that if this is impossible, the hypothesis is false. Similarly if the other premiss assumed concerns B. The same results if the original proposition CA was negative: for thus also we get a syllogism. But if the negaIf

nor

false the other is true.

is

12

we have not yet shown it to be

necessary that A belongs to no B, if it does not [jo] belong to all B. Similarly if the other premiss taken concerns B; we shall have a syllogism and a conclusion which is impossible, but the hypothesis is not refuted. Therefore it is the contradictory that we must suppose. To prove that A does not belong to all B, we

tive proposition

true,

62 b

[20]

It is

clear then that in the first figure all

problems except the universal affirmative are proved per impossibile. But in the middle and the last figures this also is proved. Suppose that A does not belong to all B, and let it have been assumed that A belongs to all C. If then [25]

A

belongs not to

will not belong to all B.

all

all C, C impossible

B, but to

But

this

is

(for suppose it to be clear that C belongs to all B): consequently the hypothesis is false. It is true then that A belongs to all B. But if the contrary is supposed, we shall have a syllogism

and a

result which is impossible: but the probjo] lem in hand is not proved. For if A belongs to no B, and to all C, C will belong to no B. This is impossible; so that it is false that [

A

belongs to no B. But though this is false, it does not follow that it is true that A belongs to all B.

When A belongs to some B, suppose that A belongs to no B, and let A belong to all C. It is necessary then that C should belong to no [35] B. Consequently, if this is impossible, A must belong to some B. But if it is supposed that A does not belong to some B, we shall have the same results as in the first figure. 1 Again suppose that A belongs to some B, and let A belong to no C. It is necessary then that C should not belong to some B. But originally it belonged to all B, consequently the hy[40] pothesis is false: A then will belong to

no

B.

When A

does not belong to all B, suppose it to all B, and to no C. It is necessary then that C should belong to no B. But this is impossible: so that it is true that A does not belong to all B. It is clear then that all the syllogisms can be formed in the middle figure.

62 b does belong

[5] Similarly they can all be formed in the last does not belong to some figure. Suppose that

A

belongs to all B: then A does not beIf then this is impossible, it is long to some false that A does not belong to some B; so that it is true that A belongs to all B. But if it is supposed that A belongs to no B, we shall have a syllogism and a conclusion which is impossible: but the problem in hand is not proved: [10] for if the contrary is supposed, we shall B, but

C

C

have the same 1

6i b 39-62* 8.

results as before. 2 a

28-32.

2

BOOK

63 b

CHAPTERS

II,

prove that A belongs to some B, this hypothesis must be made. If A belongs to no B, and C to some B, A will belong not to all C. If then this is false, it is true that A belongs to some B. [75] When A belongs to no B, suppose A belongs to some B, and let it have been assumed that C belongs to all B. Then it is necessary that A should belong to some C. But ex hy~ pothesi it belongs to no C, so that it is false that A belongs to some B. But if it is supposed that A belongs to all B, the problem is not proved. But this hypothesis must be made if we are [20] to prove that A belongs not to all B. For if A belongs to all B and C to some B, then A

But

to

belongs to some C. But this we assumed not to be so, so it is false that A belongs to all B. But in that case it is true that A belongs not to all B. If however it is assumed that A belongs

some B, we

to

fore.

shall

have the same

result as be-

clear then that in all the syllogisms

It is

which proceed per impossibile the contradictory must be assumed. And it is plain that in the middle figure an affirmative conclusion, and in the last figure a universal conclusion, are proved in a way.

M Demonstration per impossibile

differs

from

os-

[30] tensive proof in that it posits what it wishes to refute by reduction to a statement ad-

mitted to be false; whereas ostensive proof starts from admitted positions. Both, indeed, take two premisses that are admitted, but the latter takes the premisses from which the syl-

logism starts, the former takes one of these, along with the contradictory of the original [35] conclusion. Also in the ostensive proof it is not necessary that the conclusion should be known, nor that one should suppose before-

hand

that

it is

true or not: in the other

necessary to suppose beforehand that true. It

makes no

clusion

is

it

it is

is

not

difference whether the con-

affirmative or negative; the

method

Everything which is concluded ostensively can be proved per impos[40] sibile, and that which is proved per impossibile can be proved ostensively, through is

the

the

same

in both cases.

same terms. Whenever the syllogism

is

63 a formed in the first figure, the truth will be found in the middle or the last figure, if negative in the

Whenever 1

14

83

whatever the problem

may

found be.

in the first,

Whenever

the

[5] syllogism is formed in the last figure, the truth will be found in the first and middle fig-

affirmative in the

negative in has been proved to belong to no B, or not to all B, through the first figure. Then the hypothesis must have been that A belongs to some #, and the original ures,

if

the middle. Suppose that

first, if

A

[jo] premisses that C belongs to all A and to no B. For thus the syllogism was made and the impossible conclusion reached. But this is the middle figure, if C belongs to all A and to no B. And it is clear from these premisses that A belongs to no B. Similarly if A has bsen proved [75] not to belong to all B. For the hypothesis is that A belongs to all B; and the original

premisses are that C belongs to all A but not to all B. Similarly too, if the premiss CA should be negative: for thus also we have the middle

Again suppose it has been proved that belongs to some B. The hypothesis here is [20] that A belongs to no B; and the original premisses that B belongs to all C, and A either figure.

A

1

[25]

11

die figure, the truth will be

middle,

if

affirmative in the

the syllogism

6i b 39-62* 8.

is

formed

in the

last.

mid-

to all or to

get

what

to all C,

is

some C:

for in this

we have

way we

A

and

the last figure.

And

impossible. But

if

B

shall

belong

it is

clear

from these premisses that A must belong to some B. Similarly if B or A should be assumed to belong to some C. [25] Again suppose it has been proved in the middle figure that A belongs to all B. Then the hypothesis must have been that A belongs not to all B, and the original premisses that A belongs to all C, and C to all B: for thus we shall get what is impossible. But if A belongs to all C, and C to all B, we have the first figure. Similarly [30] to

if it

has been proved that

some B:

A

belongs

for the hypothesis then

must

A

belongs to no B, and the original premisses that A belongs to all C, and C to some B. If the syllogism is negative, the hypothesis must have been that A belongs to some B, and the original premisses that A belongs to no C, and C to all B, so that the first [35] fig ure results. If the syllogism is not universal, but proof has been given that A does not belong to some B, we may infer in the same way. The hypothesis is that A belongs to all B, the original premisses that A belongs to no C, and C belongs to some B: for thus we

have been that

get the

first figure.

[40] Again suppose it has been proved in the third figure that belongs to all B. Then the

A

hypothesis must have been that A belongs not 63 b to all B, and the original premisses that

PRIOR ANALYTICS

84

C

belongs to

thus

we

original

all

A

B, and

belongs to

C; for

all

what is impossible. And the premisses form the first figure. Simshall get

demonstration establishes a particular proposition: the hypothesis then must have been that A belongs to no B, and the origin] inal premisses that C belongs to some B,

ilarly if the

64

possible because opposites affirm

is

same predicate of the same the middle term in the first figure the

a

and deny and

subject,

is not predicated of both extremes, but one thing is denied of it, and it is affirmed of something else: but

such premisses are not opposed.

the hypothesis

[40] In the middle figure a syllogism can be of contradictories and of contraries. Let stand for good, let B and C stand for

to

64 a

and

A

to all C. If the syllogism

is

negative,

must have been that A belongs some B, and the original premisses that C belongs to no A and to all B, and this is the

middle is

figure. Similarly

the demonstration

if

not universal. The hypothesis will then be A belongs to all B, the premisses that

[10] that

C

belongs to no

A

and

to

some B: and

this

is

the middle figure. It is

clear then that

same terms

possible

it is

to prove each of the

tensively as well. Similarly if

it

through the problems os-

will be possible

the syllogisms are ostensive to reduce

them

[75] ad impossibile in the terms which have been taken, whenever the contradictory of the

conclusion of the ostensive syllogism is taken as a premiss. For the syllogisms become identical with those which are obtained by means of conversion, so that

the figures through

be solved.

It is

we

obtain immediately

which each problem

will

clear then that every thesis can

be proved in both ways,

per impossibile is not possible to

i.e.

[20] and ostensively, and it separate one method from the other.

made both

A

is

longs to

good, and no science

B and

all

no C: no

to

no C,

science then

is

is

so that

good, A bebelongs to

B

a science. Similarly

after taking 'every science

if

good' one took [5] 'the science of medicine is not good'; for A belongs to all B but to no C, so that a particular science will not be a science. Again, a particular science will not be a science if A belongs to all C but to no B, and B is science, C medicine, and A supposition: for after taking 'no science is supposition', one has assumed is

[10] that a particular science is supposition. differs from the preceding be-

This syllogism

cause the relations between the terms are reversed: before, the affirmative statement concerned B, now it concerns C. Similarly if one premiss is not universal: for the middle term is

always that which is stated negatively of one extreme, and affirmatively of the other. Conse[75] quently it is possible that contradictories

may

lead to a conclusion,

in every

15

one assumes that every

science. If then

science

mood, but only

though not always or the terms subordi-

if

nate to the middle are such that they are either

In what figure it is possible to draw a conclusion from premisses which are opposed, and in what figure this is not possible, will be made clear in this way. Verbally four kinds of opposition are possible, viz. universal affirmative to

identical or related as

whole

to part.

Otherwise

impossible: for the premisses cannot any-

it is

how

be either contraries or contradictories.

[20] In the third figure an affirmative syllogism can never be made out of opposite prem-

[25] universal negative, universal affirmative

isses,

to particular negative, particular affirmative to

first

for the reason given in reference to the 1

figure; but a negative syllogism

is

possible

universal contraries, the universal affirmative

whether the terms are universal or not. Let B and C stand for science, A for medicine. If [25] then one should assume that all medicine is science and that no medicine is science, he has asumed that B belongs to all A and C to no A, so that a particular science will not be a

and the universal negative,

science. Similarly

universal negative,

and particular

affirmative

to particular negative: but really there are only

three:

for the

particular affirmative

is

only

verbally opposed to the particular negative.

the genuine opposites

I

[30] is good', 'no science call contradictories.

call

is

Of

those which are

e.g. 'every science

good'; the others

I

In the first figure no syllogism whether affirmative or negative can be made out of op-

posed premisses: no affirmative syllogism is possible because both premisses must be affirmative, but opposites are, the one affirmative, [35] tne other negative:

no negative syllogism

sumed

if

the premiss

BA

is

not

as-

For if some medicine is science and again no medicine is science, it [30] results that some science is not science.

The

universally.

premisses are contrary

en universally;

if

one

is

if

the terms are tak-

particular, they are

contradictory.

We must x

6 3b 33-

recognize that

it is

possible to take

BOOK

65* opposites in the

way we

II,

CHAPTERS

escape notice. But it is possible to establish one part of a contradiction through other premisses, or to assume it in the way suggested 1

ways;

versal affirmative

of the other; here too the

[10] contrary to the fact, e.g. if a thing is good, it is proved that it is not good, if an animal, that it is not an animal, because the syllogism springs out of a contradiction and the terms presupposed are either identical or related as whole and part. It is evident also that in fallacious reasonings nothing prevents a contradiction to the hypothesis from resulting, e.g. if something is odd, it is not odd. For the [75] syllogism owed tradictory premisses;

its

contrariety to

its

con-

we assume

such premisses we shall get a result that contradicts our hypothesis. But we must recognize that contraries cannot be inferred from a single syllogism in such a way that we conclude that what is not good is good, or anything of that sort, [20] unless a self-contradictory premiss is at once asumed, e.g. 'every animal is white and not white', and we proceed 'man is an animal'. Either we must introduce the contradiction by an additional assumption, assuming, e.g., that every science is supposition, and then assuming 'Medicine is a science, but none of it is suppois

the

if

mode

[25] tions are made), or we two syllogisms. In no other

was

said before,

is it

viii. 1.

2

which refutamust argue from

in

way than

this, as

possible that the premisses

should be really contrary. 1

[50] proposed; but this happens in many ways. reason syllogistically at all, or

A man may not

is

between the terms may be reversed. Similarly in the third figure. So it is clear in [5] how many ways and in what figures a syllogism can be made by means of premisses which are opposed. It is clear too that from false premisses it is possible to draw a true conclusion, as has been 2 said before, but it is not possible if the premisses are opposed. For the syllogism is always

(which

a

and negative, or universal

relation

sition'

is

problem

lish the antecedent by means of its consequents; for demonstration proceeds from what

and the relations between the terms may be 64 b reversed; e.g. A may belong to all B and to no C, or to all C and to no B, or to all of all

the original question

species of failure to demonstrate the

may be assumed as premwe may have either uni-

it

[40] affirmative and particular negative, or particular affirmative and universal negative,

the one, not to

To beg and assume

may argue from premisses which are less known or equally unknown, or he may estab-

to affirmative statements,

in six

16

follows that op-

in the Topics. Since there are three oppositions

isses

85

said, viz. 'all science

[35] 1S g°°d' and 'no science is good' or 'some science is not good'. This does not usually

posite statements

14-16

Chapters 2-4.

he

and is prior. Now begging the none of these: but since we get to know some things naturally through themselves, and other things by means of sonnets] thing else (the first principles through themselves, what is subordinate to them through something else), whenever a man tries to prove what is not self-evident by means of

more

certain

question

is

then he begs the original question. This be done by assuming what is in question at once; it is also possible to make a transits] tion to other things which would naturally be proved through the thesis proposed, and itself,

may

65 a demonstrate it through them, e.g. if A should be proved through B, and B through C, though it was natural that C should be proved through A: for it turns out that those who reason thus are proving A by means of itself. This is what those persons do who suppose that they [5] are constructing parallel straight lines: for fail to see that they are assuming facts

they

which

it

is

impossible to demonstrate unless it turns out that those

the parallels exist. So

who

reason thus merely say a particular thing in this way everything will be self-

is, if it is:

evident. But that

is

impossible.

A

belongs [10] If then it is uncertain whether to C, and also whether belongs to B, and if

A that A

one should assume does belong to B, it is not yet clear whether he begs the original question, but it is evident that he is not demon-

what is as uncertain as the quesanswered cannot be a principle of a demonstration. If however B is so related to C strating: for

tion to be

that they are identical, or

if

they are plainly

[75] convertible, or the one belongs to the other, the original question is begged. For one

might equally well prove that A belongs to B through those terms if they are convertible. But if they are not convertible, it is the fact that they are not that prevents such a demonstration, not the method of demonstrating. But if one were to make the conversion, then he would be doing what we have described 3 a

In

11.

1-4.

PRIOR ANALYTICS

86

and

effecting a

reciprocal

proof with

three

66

sive proofs: since

an assumption

if

propositions.

syllogism can no longer be

Similarly if he should assume that B be[20] longs to C, this being as uncertain as the belongs to C, the question question whether

to

A

is

not yet begged, but no demonstration

made.

If

however

A

and B are

is

identical either

because they are convertible or because A follows B, then the question is begged for the same reason as before. For we have explained the

meaning

of begging

[25] proving that means of itself.

which

the question, viz.

is

not self-evident by

then begging the question is proving what not self-evident by means of itself, in other words failing to prove when the failure is due to the thesis to be proved and the premiss If

is

through which

it is proved being equally unbecause predicates which are identical belong to the same subject, or because the same predicate belongs to subjects which are identical, the question may be begged in [50] the middle and third figures in both ways, though, if the syllogism is affirmative, only in the third and first figures. If the syllogism is

certain, either

it.

drawn

is

s

refuted, a

in reference

clear then that the expression 'false

It is

[10] cause' can only be used in the case of a reductio ad impossibile, and when the original

hypothesis

is

so related to the impossible con-

clusion, that the conclusion results indifferent-

whether the hypothesis is made or not. The most obvious case of the irrelevance of an assumption to a conclusion which is false is when a syllogism drawn from middle terms to an [75] impossible conclusion is independent of the hypothesis, as we have explained in the Topics. For to put that which is not the cause as the cause, is just this: e.g. if a man, wishing ly

1

to

prove that the diagonal of the square

is

in-

commensurate with the side, should try to prove Zeno's theorem that motion is impossible, and so establish a reductio ad impossi[20] bile: for Zeno's false theorem has no connexion at all with the original assumption. Another case is where the impossible conclusion is

terms in negative syllogisms are not converti[^5] ble. In scientific demonstrations the question is begged when the terms are really related in the manner described, in dialectical arguments when they are according to common

connected with the hypothesis, but does not result from it. This may happen whether one traces the connexion upwards or downwards, [ 2 5] e -g- if it i s laid down that A belongs to B, B to C, and C to D, and it should be false that B belongs to D: for if we eliminated A and assumed all the same that B belongs to C and C to D, the false conclusion would not depend on the original hypothesis. Or again trace the connexion upwards; e.g. suppose that A [30] belongs to B, E to A, and F to E, it being false that F belongs to A. In this way too the impossible conclusion would result, though the

opinion so related.

original hypothesis

begged when identical same subject; and both premisses do not beg the question indif-

negative, the question

is

predicates are denied of the ferently (in a similar

way

the question

may

be

begged in the middle figure), because the

were eliminated. But the

impossible conclusion ought to be connected

not the reason why the result is false', which we frequently make in argument, is made primarily in the case of [40] a reductio ad impossible, to rebut the

The

objection that 'this

is

proposition which was being proved by the re65 b duction. For unless a man has contradicted

he will not say, 'False cause', but urge that something false has been assumed in the earlier parts of the argument; nor will he use the formula in the case of an ostensive proof; for here what one denies is not assumed as a premiss. Further when anything is refuted ostensively by the terms ABC, it can[5] not be objected that the syllogism does not

this proposition

depend on the assumption

laid

use the expression 'false cause',

gism

is

down. For we

when

the syllo-

concluded in spite of the refutation of but that is not possible in osten-

this position;

with the original terms: in this way it will depend on the hypothesis, e.g. when one traces the connexion downwards, the impossible Cottle ] elusion must be connected with that term

which

is

predicate in the hypothesis: for

if it

A

should belong to D, the false conclusion will no longer result after A has been eliminated. If one traces the connexion upwards, the impossible conclusion must be connected with that term which is

impossible that

is

subject in the hypothesis: for

if it is

impossi-

F

should belong to B, the impossible conclusion will disappear if B is eliminated. [40] Similarly when the syllogisms are nega-

ble that

tive. It is clear then that when the impossibility not related to the original terms, the false conclusion does not result on account of the

66 a is

1

On

h Sophistical Refutations, i6j 21-36.

BOOK

66 b

II,

CHAPTERS

assumption. Or perhaps even so it may sometimes be independent. For if it were laid down bethat A belongs not to B but to K, and that [5] longs to C and C to D, the impossible con-

K

would

one takes the terms in an ascending series. Consequently since the impossibility results whether the first assumption is suppressed or not, it would appear to be independent of that assumption. Or perhaps we ought not to understand the stateclusion

ment

still

stand. Similarly

if

conclusion results independently of the assumption, in the sense that if something else were supposed the impossithat the false

[10] bility

when

would

result; but rather

we mean

assumption is eliminated, the same impossibility results through the remaining premisses; since it is not perhaps absurd that the same false result should follow that

from

the

several

first

hypotheses, e.g.

that

two right

ought in attack to try This will be possible first, if, instead drawing the conclusions of preliminary [ ^5] of

their admissions, they to conceal.

syllogisms, they take the necessary premisses

and leave the conclusions ondly tions

angles.

18 false

argument depends on the

if

first

false

it. Every syllogism is made out of two or more premisses. If then the false conclusion is drawn from two premisses, one or both of them must be false: for (as we proved ) a false syllogism cannot be drawn from true [20] premisses. But if the premisses are more than two, e.g. if C is established through A and B, and these through D, E, F, and G, one of these higher propositions must be false, and on this the argument depends: for A and B are inferred by means of D, E, F, and G. Therefore the conclusion and the error results from

statement in

1

which are

against us

we must

take care, whenever

an opponent asks us to admit the reason without the conclusions, not to grant him the same term twice over in his premisses, since we know that a syllogism cannot be drawn without a middle term, and that term which is stated more than once is the middle. How we ought to watch the middle in reference to each [30] conclusion, is evident from our knowing what kind of thesis is proved in each figure. This will not escape us since we know how we are maintaining the argument. That which we urge men to beware of in l

b 53 11-25.

closely connected they take as

connected by middle terms. For example suppose that A is

to be inferred to be true of F; B, C,

D, and

E

being middle terms. One ought then to ask whether A belongs to B, and next whether belongs to E, instead of asking whether B be[40] longs to C; after that he may ask whether 66 b B belongs to C, and so on. If the syllogism is drawn through one middle term, he ought to begin with that: in this way he will most likely deceive his opponent.

D

20 Since

we know when

[5]

formed and how

it is

clear

when

its

a syllogism can be terms must be related,

refutation will be possible

impossible.

A

refutation

is

and

possible

whether everything is conceded, or the answers I mean, being affirmative, the other negative). For as has been shown a syllogism is possible whether the terms are related in affirmative propositions or one propoalternate (one,

sition

is

affirmative, the other negative: con-

[10]

what

down

is

contrary to

the conclusion, a refutation

must take which es-

sequently,

if

is

laid

place: for a refutation

is

a syllogism

tablishes the contradictory. But if nothing is conceded, a refutation is impossible: for no 2 syllogism is possible (as we saw ) when all the terms are negative: therefore no refutation is possible.

For

refutation

In order to avoid having a syllogism

drawn

the dark; sec-

if

a refutation

were

possible, a

[75] syllogism must be possible; although if a syllogism is possible it does not follow that a

one of them.

[25]

in

instead of inviting assent to proposi-

far as possible those that are not

when

A

87

parallels

meet, both on the assumption that the interior angle is greater than the exterior and on the assumption that a triangle contains more than [75]

16-21

is

not possible

if

possible. Similarly refutation

nothing

is

is

conceded universally:

since the fields of refutation

and syllogism are

defined in the same way. 21

sometimes happens that just as we are deceived in the arrangement of the terms, so error may arise in our thought about them, It

same predimore than one subject immediately, but although knowing the one, a [20] e.g.

if it is

possible that the

cate should belong to

man may

forget the other

posite true.

C

Suppose that

A

and think the opbelongs to B and to

in virtue of their nature, 2

4I

b 6.

and that

B and C

PRIOR ANALYTICS

88

belong to

all

thinks that

A

to

D in the same way.

A

belongs to

no C, and

C

to all

all

If

B, and

D, he

then a

B

to

will both

man

D, but

know

67 b

biguous, meaning to have the knowledge either of the universal or of the particulars. Thus then he knows that C contains two right

[25] and not know the same thing in respect of the same thing. Again if a man were to make a mistake about the members of a single

angles with a knowledge of the universal, but

series; e.g.

suppose A belongs to B, B to C, and D, but some one thinks that A belongs to all B, but to no C: he will both know that A [30] belongs to D, and think that it does not. Does he then maintain after this simply that what he knows, he does not think? For he knows in a way that A belongs to C through

trary to his ignorance.

C

Meno

to

included in the whole; so in a way, this he maintains he does not think at all: but that is imB, since the part

that

is

what he knows

possible.

[35] In the former case, where the middle term does not belong to the same series, it is not possible to think both the premisses with reference to each of the two middle terms: e.g. that A belongs to all B, but to no C, and both B and C belong to all D. For it turns out that the first premiss of the one syllogism is either wholly or partially contrary to the first premiss of the other. For if he thinks that A belongs to [40] everything to which B belongs, and he that B belongs to D, then he knows belongs to D. Consequently if again he thinks that A belongs to nothing to which C belongs, he thinks that A does not belong to some of that to which B belongs; but if he thinks that A belongs to everything to which B belongs, and again thinks that A does not be-

67 a knows that

A

long to some of that to which B belongs, these [5] beliefs are wholly or partially contrary. In this way then it is not possible to think; but nothing prevents a man thinking one premiss of each syllogism or both premisses of one of the two syllogisms: e.g. A belongs to all B, and B to D, and again A belongs to no C. An error of this kind is similar to the error into which we fall concerning particulars: e.g. if A [10] belongs to all B, and B to all C, A will belong to all C. If then a man knows that A belongs to everything to which B belongs, he knows that A belongs to C. But nothing prevents his being ignorant that C exists; e.g. let A stand for two right angles, B for triangle,

C for a particular diagram man might think that C did

of a triangle.

A

though [75] he knew that every triangle contains two right angles; consequently he will know and not know the same thing at the same time. For the expression 'to know that every triangle has its angles equal to two right angles' is amnot

exist,

[20] not with a knowledge of the particulars; consequently his knowledge will not be con1

learning

that

is

The argument in the recollection may be

way. For it never hapwith a foreknowledge of the particular, but along with the process of being led to see the general principle he receives a knowledge of the particulars, by an act (as it were) of recognition. For we know some criticized in a similar

pens that a

man

starts

things directly; e.g. that the angles are equal

know

[25] to two right angles, if we figure is a triangle. Similarly in

By

a

knowledge

that the

other cases.

we see know them by

of the universal then

the particulars, but the kind of

all

we do

not

knowledge which

proper to

is

them; consequently it is possible that we may make mistakes about them, but not that we should have the knowledge and error that are contrary to one another: rather we have the

knowledge

of the universal but

make

a mis-

[30] take in apprehending the particular. Sim2 ilarly in the cases stated above. The error in respect of the middle term

the

is

not contrary to

knowledge obtained through the syllogism,

nor is the thought in respect of one middle term contrary to that in respect of the other.

Nothing prevents a man who knows both that A belongs to the whole of B, and that B again belongs to C, thinking that A does not belong [^5] to C, e.g. knowing that every mule is sterile and that this is a mule, and thinking that this animal is with foal: for he does not

know

that

A

belongs to C, unless he considers

two propositions together. So it is evident that if he knows the one and does not know the

the other, he will

fall

into error.

And this

is

the

relation of knowledge of the universal to 67 b knowledge of the particular. For we know

no

sensible thing, once

it

has passed beyond

the range of our senses, even

have perceived versal

and

it,

except by

if

we happen

means

the possession of the

to

of the uni-

knowledge

proper to the particular, but without the actual exercise of that knowledge. For to know is used in three senses: it may mean either to have knowledge of the universal or to [5] have knowledge proper to the matter in hand or to exercise such knowledge: consequently three kinds of error also are possible. Nothing then prevents a man both knowing

which

1

is

Plato,

Meno,

81.

2

66 b 20-6, 26-30

BOOK

68'

CHAPTERS

II,

and being mistaken about the same thing, provided that his knowledge and his error are not contrary. And this happens also to the man whose knowledge is limited to each of the premisses and who has not previously considered the particular question. For when he thinks that the mule is with foal he has not the knowledge in the sense of its actual ex[10] ercise, nor on the other hand has his thought caused an error contrary to his knowledge: for the error contrary to the knowledge of the universal would be a syllogism. But he who thinks the essence of good is the essence of bad will think the same thing to be the essence of good and the essence of bad. Let A stand for the essence of good and B for the essence of bad, and again C for the essence of [75] good. Since then he thinks B and C identical, he will think that C is B, and similarly that B is A, consequently that C is A. For just as we saw that if B is true of all of which C is true, and A is true of all of which B is true, A is

true of C, similarly with the

word

'think'.

[20] Similarly also with the word 'is'; for we saw that if C is the same as B, and B as A, C is the same as A. Similarly therefore with 'opine'.

Perhaps then

this

will grant the first point. is

false,

that

is

necessary

if

a

man

But presumably that

any one could suppose the

es-

sence of good to be the essence of bad, save [25] incidentally. For it is possible to think this in

many

different ways.

But we must con-

sider this matter better.

22

Whenever

the extremes are convertible

it

is

A

A

and C are convertible and C bethen if longs to everything to which A belongs, B is [jo] convertible with A, and B belongs to everything to which A belongs, through C as middle, and C is convertible with B through A as middle. Similarly if the conclusion is negative, e.g. if B belongs to C, but A does not belong to B, neither will A belong to C. If then B is convertible with A, C will be convertible [35] with A. Suppose B does not belong to A; neither then will C: for ex hypothesi B belonged to all C. And if C is convertible with B, B is convertible also with A: for C is said of

which

B

is

vertible in relation to

said.

A

convertible in relation to

68 a

that to

which

B

And

if

C

is

con-

and to B, B also A. For C belongs

belongs: but

belong to that to which

89

alone starts from the conclusion; the preceding moods do not do so as in the affirmative syllo-

A and B are convertible, and C and D, and if A or C must beanything whatever, then B and D will

gism. Again

if

[5] similarly

long to be such that one or other belongs to anything whatever. For since B belongs to that to which A belongs, and belongs to that to which C belongs, and since A or C belongs to everything, but not together, it is clear that B or belongs to everything, but not together. For example if that which is uncreated is incorruptible and that which is incorruptible is un-

D

D

created,

it

is

necessary that

what

is

created

[10] should be corruptible and what is corruptible should have been created. For two syl-

logisms have been put together. Again if A or belongs to everything and if C or belongs to everything, but they cannot belong together,

D

B

and C are convertible B and D For if B does not belong to something to which D belongs, it is clear that [75] A belongs to it. But if A then C: for they are convertible. Therefore C and D belong together. But this is impossible. When A belongs to the whole of B and to C and is affirmed of nothing else, and B also belongs to all C, it is necessary that A and B should be convertible: for since A is said of B and C only, and B [20] is affirmed both of itself and of C, it is clear that B will be said of everything of which A is said, except A itself. Again when A and B belong to the whole of C, and C is convertible then

when

A

are convertible.

with B, it is necessary that A should belong to B: for since A belongs to all C, and C to B by conversion, A will belong to all B.

all

necessary that the middle should be convertible belongs to C through B, with both. For if

that of all of

21-22

A

C

belongs.

is

to

does not

And

this

two opposites A and B, A is and similarly D is preferable to C, then if A and C together are preferable to B and D together, A must be preferable to D. For A is an object of desire to the same extent as B is an object of aversion, since they are opposites: and C is similarly related to D, [25] When, of preferable to B,

since they also are opposites. If then

A

is

an

same extent as D, B is an object of aversion to the same extent as C (since each is to the same extent as each the one an object of aversion, the other an object of desire). Therefore both A and C together, and B and D together, will be equally objects of desire or aversion. But since A and C are preferable to B and D, A cannot be equal[jo] object of desire to the

D

with D; for then B along with desirable with A along with is preferable to A, then B [55] C. But if must be less an object of aversion than C: for ly desirable

would be equally

D

PRIOR ANALYTICS

9o the less

is

opposed

to the less.

But the greater

good and lesser evil are preferable to the lesser good and greater evil: the whole BD then is preferable to the whole AC. But ex hypothesi this is not so. A then is preferable to C consequently is less an object of aversion than B. If then every lover in virtue of his

D, and

[40] love would prefer A, viz. that the beloved should be such as to grant a favour, and yet should not grant it (for which C stands), the beloved's granting the favour (repre-

to

68 b sented by D) without being such

as to

grant it (represented by 5), it is clear that A (being of such a nature) is preferable to granting the favour. To receive affection then is

Love more dependent on friendship than on

preferable in love to sexual intercourse.

then

is

intercourse. [5]

And

if

is

it

Intercourse then either

is

is

not an end at

its

all

end. or

is

relative to the further end, the receiv-

ing of affection.

And

of the other desires

indeed the same

and

is

true

clear then

how

the terms are related in

conversion, and in respect of being in a higher

degree objects of aversion or of desire. We [10] must now state that not only dialectical and demonstrative syllogisms are formed by means of the aforesaid figures, but also rhetorical syllogisms and in general any form of persuasion, however it may be presented. For every belief comes either through syllogism or

from induction. [75]

Now

induction, or rather the syllogism

which springs out

of induction, consists in es-

tablishing syllogistically a relation between one extreme and the middle by means of the other extreme, e.g. if B is the middle term between A and C, it consists in proving through C that

A

belongs to B. For this is the manner in which we make inductions. For example let A stand for long-lived, B for bileless, and C [20] for the particular long-lived animals, e.g. horse, mule. then belongs to the whole

A

man,

of C: for whatever

B

is

bileless is long-lived.

But

also ('not possessing bile') belongs to all C.

C

is convertible with B, and the middle not wider in extension, it is necessary that A should belong to B. For it has already 1 [25] been proved that if two things belong to

If

then

term

is

same thing, and the extreme is convertible with one of them, then the other predicate will belong to the predicate that is converted. the

la 21-25.

clearer to us.

is

24

We

have an 'example' when the major term is proved to belong to the middle by means of a term which resembles the third. It ought to be known both that the middle belongs to the [40] third term, and that the first belongs to that which resembles the third. For example

arts.

23 It is

induction

most dependent on

receiving affection, then this

an end

69*

But we must apprehend C as made up of all the particulars. For induction proceeds through an enumeration of all the cases. [30] Such is the syllogism which establishes the first and immediate premiss: for where there is a middle term the syllogism proceeds through the middle term; when there is no middle term, through induction. And in a way induction is opposed to syllogism: for the latter proves the major term to belong to the third term by means of the middle, the former proves the major to belong to the middle [55] by means of the third. In the order of nature, syllogism through the middle term is prior and better known, but syllogism through

let A be evil, B making war against neigh69 a bours, C Athenians against Thebans, D Thebans against Phocians. If then we wish to prove that to fight with the Thebans is an evil, we must assume that to fight against neighbours is an evil. Evidence of this is obtained from similar cases, e.g. that the war against [5] the Phocians was an evil to the Thebans.

Since then to fight against neighbours is an and to fight against the Thebans is to fight

evil,

against neighbours,

it

Thebans

is

against the that

B

belongs to

C

is

an and

clear that evil.

to

D

Now

to fight it is

clear

(for both are

making war upon

one's neighbours) belongs to (for the war against [jo] the Phocians did not turn out well for the Thebans): but that A belongs to B will be

cases of

and

that

D

A

proved through D. Similarly if the belief in the relation of the middle term to the extreme should be produced by several similar cases. Clearly then to argue by example is neither like reasoning from part to whole, nor like reasoning from whole to part, but rather rea[75] soning from part to part, when both par-

same term, and from induction, because induction starting from all the 2 particular cases proves (as we saw ) that the major term belongs to the middle, and does not apply the syllogistic conclusion to the minor term, whereas argument by example does ticulars are subordinate to the

one of them

2

Chapter

23.

is

known.

It differs

BOOK

70*

make

this application

proof from

all

II,

and does not draw

CHAPTERS its

22-26

we

are opposites, so that that the

the particular cases.

9*

gel the

not subjects of a single science: this proof the third figure: for

[20] By reduction we mean an argument in which the first term clearly belongs to the middle, but the relation of the middle to the last term is uncertain though equally or more

probable than the conclusion; or again an argument in which the terms intermediate between the last term and the middle are few. For in

any of these cases it turns out that we approach more nearly to knowledge. For example let A [25] stand for what can be taught, B for knowledge, C for justice. Now it is clear that

knowledge can be taught: but it is uncertain whether virtue is knowledge. If now the statement BC is equally or more probable than

AC, we have

a reduction: for

we

are nearer to

knowledge, since we have taken a new term, being so far without knowledge that A belongs to C. Or again suppose that the terms intermediate between B and C are few: for [30] thus too we are nearer knowledge. For example let D stand for squaring, E for rectilinear figure, F for circle. If there were only one term intermediate between E and F (viz. that the circle

made equal

is

to a rectilinear

help of lunules), we should be near to knowledge. But when BC is not [35] more probable than AC, and the intermediate terms are not few, I do not call this re-

figure by the

duction: nor again is

when

the statement

immediate: for such a statement

is

BC

knowl-

edge.

objection

An

brought in two ways and

is

through two figures; in two ways because every objection

is

either universal or particular,

by two figures because objections are brought in opposition to the premiss, and opposites can [5] be proved only in the first and third figures. If a man maintains a universal affirmative, we reply with a universal or a particular negative; the former is proved from the first figure, the latter from the third. For example let A stand for there being a single science, B for contraries.

If

a

man

premises that con-

traries are subjects of a single science, the ob-

[10] jection may be either that opposites are never subjects of a single science, and contraries

C

(the

is

in

know-

of a single science.

[75] Similarly if the premiss objected to is negative. For if a man maintains that con-

we

traries are not subjects of a single science,

reply either that contraries, e.g.

opposites or that certain

all

what

is

healthy and what

same from the

is

sickly, are subjects of the

science: the

former argument issues

first,

ter

from the third

In general

if

a

the

lat-

figure.

man

urges a universal objec-

[20] tion he must frame his contradiction with reference to the universal of the terms taken by

opponent,

his

e.g.

if

a

man

maintains that

same science, opponent must reply that there is a single science of all opposites. Thus we must have the first figure: for the term which embraces the original subject becomes the middle term. contraries are not subjects of the his

the objection

If

must frame a

term

is

particular, the objector

his contradiction

relatively to

ponent's premiss

is

with reference to

which the subject of

his op-

universal, e.g. he will point

[25] out that the knowable and the unknowable are not subjects of the same science: 'contraries' is universal relatively to these.

And we

have the third figure: for the particular term assumed is middle, e.g. the knowable and the unknowable. Premisses from which it is possi-

draw the contrary conclusion are what from when we try to make objec-

start

[30] tions. Consequently

ticular at all or not in universal syllogisms.

69 b

true of

traries,

we 26

it is

and the unknowable) that they are conand it is false that they are the subjects

able

ble to

An objection is a premiss contrary to a premiss. It differs from a premiss, because it may be particular, but a premiss either cannot be par-

or

first figure,

knowable and the unknowable are

we

bring objections them only are opposite syllogisms possible, since the second figure cannot produce an affirmative concluin these figures only: for in

sion.

Besides, an objection in the middle figure

would require

a fuller

argument,

e.g.

if

it

should not be granted that A belongs to B, because C does not follow B. This can be made [55] clear only by other premisses. But an objection ought not to turn off into other things, but have its new premiss quite clear immediately. For this reason also this is the only figure from which proof by signs cannot be obtained. We must consider later the other kinds of

namely the objection from contrafrom similars, and from common opinion, 70* and inquire whether a particular objection cannot be elicited from the first figure or a negative objection from the second. objection, ries,

PRIOR ANALYTICS

92

70 b

essary that she should be with child.

27

A

and a sign are not identical, is a generally approved proposition: what men know to happen or not to [5] happen, to be or not to be, for the most part thus and thus, is a probability, e.g. 'the enprobability

but a probability

vious hate', 'the beloved

means

show

A sign

affection'.

a demonstrative proposition necessary

or generally approved: for anything such that when it is another thing is, or when it has into being the other has come into being before or after, is a sign of the other's being or an enthymeme having come into being.

come

Now

[10] is a syllogism starting from probabilities or signs, and a sign may be taken in three ways, corresponding to the position of the middle

term the

in the figures.

first

For

it

may

be taken as in

figure or the second or the third. For

example the proof that a woman is with child because she has milk is in the first figure: for [75] to have milk is the middle term. Let A represent to be with child, B to have milk, C that wise men are good, good, comes through the last figure. Let A stand for good, B for wise men, C for Pittacus. It is true then to affirm both A and B of C: only men do not say the latter, because they know it, though they state the for[20] mer. The proof that a woman is with

woman. The proof

since Pittacus

is

child because she

is

pale

is

meant

to

come

through the middle figure: for since paleness follows women with child and is a concomitant of this woman, people suppose it has been proved that she is with child. Let A stand for paleness, B for being with child, C for woman. Now if the one proposition is stated, we have [25] only a sign, but

if

the other

well, a syllogism, e.g. 'Pittacus

is

stated as

generous,

is

men are generous and Pittacus Or again 'Wise men are good,

since ambitious is

ambitious.'

since Pittacus

is

not only good but wise.' In this

way then syllogisms are formed, only that which proceeds through the if it is

true (for

it

is

first

figure

is

irrefutable

universal), that

[jo] proceeds through the last figure

is

which refuta-

ble even

if the conclusion is true, since the syllogism is not universal nor correlative to the matter in question: for though Pittacus is good, it is not therefore necessary that all other wise men should be good. But the syllogism which proceeds through the middle figure is always

refutable in any case: for a syllogism can never

[35] be formed

when

the terms are related in

way: for though a woman with child is pale, and this woman also is pale, it is not necthis

Truth

then may be found in signs whatever their kind, but they have the differences we have stated. b

70

We

stated,

must either divide signs in the way and among them designate the middle

term as the index (for people call that the index which makes us know, and the middle term above all has this character), or else we must call the arguments derived from the extremes signs, that derived from the middle term the index: for that which is proved [5] through the first figure is most generally accepted and most true. It is possible to infer character from features, if it is granted that the body and the soul are changed together by the natural affections: I say 'natural', for though perhaps by learning music a man has made some change in his [10] soul, this is not one of those affections

which are natural to us; rather I refer to pasand desires when I speak of natural emotions. If then this were granted and also that for each change there is a corresponding sign, and we could state the affection and sign proper to each kind of animal, we shall be able to infer character from features. For if there is an affection which belongs properly to an individsions

[75] ual kind, e.g. courage to lions, it is necessary that there should be a sign of it: for ex

hypothesi body and soul are affected together.

Suppose

this sign

is

the possession of large ex-

may

belong to other kinds also though not universally. For the sign is proper in the sense stated, because the affection is proper to the whole kind, though not proper to it alone, according to our usual manner of [20] speaking. The same thing then will be found in another kind, and man may be brave, and some other kinds of animal as well. They will then have the sign: for ex hypothesi there is one sign corresponding to each affection. If then this is so, and we can collect signs of this sort in these animals which have only one afbut each affection has fection proper to them its sign, since it is necessary that it should have [25] a single sign we shall then be able to infer character from features. But if the kind as a whole has two properties, e.g. if the lion is both brave and generous, how shall we know which of the signs which are its proper concomitants is the sign of a particular affection? Perhaps if both belong to some other kind though not to the whole of it, and if, in those kinds in which each is found though not in the tremities: this

—

—

whole of

their

members, some members pos-

BOOK

70 b sess

II,

CHAPTER

one of the affections and not die other:

man

brave but not generous, but two signs, large extremities, it is clear that this is the sign of courage in the lion also. To judge character from fea-

e.g. if a

is

[jo] possesses, of the

tures, then,

is

middle term treme, but

is

possible in the first figure

if

the

convertible with the first exwider than the third term and

is

27

not convertible with courage,

93 it:

e.g. let

A

stand for

B for large extremities, and C for lion,

[55] B then belongs to everything to which C belongs, but also to others. But A belongs to

everything to which B belongs, and to nothing besides, but is convertible with B: otherwise, there would not be a single sign correlative with each affection.

CONTENTS: POSTERIOR ANALYTICS BOOK

timate subject fixed? (3) supposing both priattribute and ultimate subject fixed?

I

mary BERLIN NOS.

CHAP. i.

The

knowledge; 2.

7i a

student's need of pre-existent its

yi b 8

meaning

Enunciation,

Contradiction,

82 s 36 demonstration cannot develop an indefinite regress, then negative

21. If affirmative

demonstration cannot

Proposition,

Axiom, Hypothesis,

Basic truth, Thesis,

Defi-

Two

erroneous views of

72 b 5

scientific

futility of circular

attribute: 'True in every in-

73 s 21 25.

Causes through which

we

ously suppose a conclusion

when

universal

it

is

not;

errone-

74

s

26.

4

commensurate and

how

to avoid this

27.

The

premisses of demonstration must

74 b 5

28.

be necessary and essential 7.

The

premisses and conclusion of a

demonstration must

fall

75

s

38

86 a 31

and nega- 87 s

The

superiority of affirmative

live

demonstration to reductio ad itnpossibile

The more

abstract science

What

is

the prior

1

87 s 31

science

constitutes the unity of a

87 s 38

Chance conjunctions are not demon-

there

tions of

may

be several demonstra-

8715 5

one connexion 87b 18

strable

Only

eternal connexions can be demonstrated Demonstration must proceed from

The The

superiority of affirmative to nega-

30.

within a single genus;

b 2i

31.

75 b 36

32.

75

different sorts of basic truth

function of the

common

axioms

There can be no demonstration through sense-perception Different sciences must possess differ-

87b 27 88 a 17

ent basic truths

cept in the case of subalternate sciences

11.

The

How

the basic premisses peculiar to each science, ex-

10.

12

demonstration

29.

tion

9.

84 b 3 85**

science

the three constituent elements of demonstra-

8.

82 b 36

in the nega-

superiority of universal to particu-

and the more accurate

error 6.

is

dvc demonstration

versal', 'Accidental' 5.

The lar

'Commensurate and uni-

'Essential',

(2)

23. Corollaries 24.

Types of

and

tive

demonstra-

tion

stance',

analytic proofs that

the answer to both (1)

knowledge; the 4.

and

22. Dialectical

nition 3.

(2) are

tive

nature of scientific knowledge;

of

tively,

I

nature

the conditions of demonstration; the

The

82 a 2i answered negabe in the negathe answer to (3) must

and

20. If (1)

33.

76 s 31 a

34.

77 5

The

relation of opinion to

knowledge

Quick wit: the faculty of instantaneously hitting upon the middle term

88 b 30

89b 10

in demonstration s 77 36

12.

The

13.

form; formal fallacy; the growth of a science The difference between knowledge 78 s 22

scientific

of the fact 14.

The

first

scientific

premiss in interrogative

and knowledge

figure

is

2.

s 16

3.

The four possible forms of inquiry 89b 21 They all concern the middle term 89 b 36 The difference between definition and 90 s 35

4.

Essential nature cannot be

the true type of

79

1.

demonstration

syllogism a

Immediate negative propositions

16.

Ignorance as erroneous inference

17.

Ignorance as erroneous inference when the premisses are mediate Ignorance as the negation of knowl-

the premisses are

when

79 33 b 79 23

immediate

5.

8ob 16 6.

8i a 37

(1)

indefi-

Attempts

to

definition of

8i b 10

supposing the

primary attribute fixed? (2) supposing the

Essential nature cannot be inferred by

9i b

1

prove a thing's essential

92 s 6

nature either hypothetically or through the

7.

Can demonstration develop an

91 s 12

division

edge, e.g. such as must result from the lack of

nite regress of premisses,

demon-

strated

a sense 19.

II

of the reasoned fact

15.

18.

BOOK

ul-

8.

95

its

contrary beg the question

Definition does not touch the question 92 s 33 of existence; demonstration proves existence;

hence definition cannot demonstrate Yet only demonstration can reveal the

93 s

1

CONTENTS

96 essential nature of things

other than themselves 9-

That which premisses

10. 1

1.

12.

—

is is

—

which have

i.e.

self-caused

15

— the

basic

several causes as

93 21

16.

question of time in causal infer-

a 94 20

17.

a 95 io

How How

98 s 24

the effect

is

present,

is

the cause

where cause and

effect are

Different causes

may produce

effect,

is

s

98 35 impossible

commensurate s

the 99 1 but not in things specifically iden-

tical

to obtain the definition of a sub-

96 a 2o

18.

stance; the use of division for this purpose 14.

If

same

ence 13-

will often serve to prove

also present? Plurality of causes

93b 28

middle terms

One middle

several connexions

grasped immediately

Types of definition

The The

cause

attributes

to select a

demonstration

connexion for

98

19.

99b true cause of a connexion is the 7 proximate and not the more universal cause How the individual mind comes to 99b i5

The

know

the basic truths

POSTERIOR ANALYTICS BOOK

I

are not predicable of anything else as subject)

7l a

All

instruction given or received by

way

are only learnt in this way,

all

matical sciences and

all

as subject to a major. Before

The mathe-

the species of such instruction.

other speculative disci-

[25] elusion,

known

the clearly

enthymeme,

sume

particular.

a

[75] of the

means to

so

make

meaning

and

so;

as

you says

regards

the double assumption

of the

word and

the ex-

The

Recognition of a truth

may

in

tain as factors both previous also

some cases conknowledge and

knowledge acquired simultaneously with

that recognition

—knowledge,

that he

came

to

know

the semicircle' to

'this figure

be a

triangle.

not.

how

1

in the

A man is asked, 'Do you, or do know that every pair is even?' He he does know it. The questioner then pronot,

form

'every

number which you know

[5] construed as applicable to

instance of the thing.

to

On

any and every

the other hand,

I imnothing to prevent a man in one sense knowing what he is learning, in another not knowing it. The strange thing would be, not if in some sense he knew what he was learning, but if he were to know it in that precise sense and manner in which he was learning it.

agine there

him

inscribed in

For some

Note: The bold face numbers and letters are approximate indications of the pages and columns of the standard Berlin Greek text; the bracketed numbers, of the lines in the Greek text; they are here assigned as they Oxford

manner

be such', or 'every rectilinear figure which you know to be such': the predicate is always

things (viz. the singulars finally reached which

are assigned in the

in a

the existence of this triangle,

dilemma

in the

this latter, of the

under the universal and therein already virtually known. For example, the student knew beforehand that the [20] angles of every triangle are equal to two right angles; but it was only at the actual moment at which he was being led on to recogparticulars actually falling

nize this as true in the instance before

a con-

duces a particular pair, of the existence, and so a fortiori of the evenness, of which he was unaware. The solution which some people offer is to assert that they do not know that every pair is even, but only that everything which they 71 b know to be a pair is even: yet what they know to be even is that of which they have demonstrated evenness, i.e. what they made the subject of their premiss, viz. not merely every triangle or number which they know to be such, but any and every number or triangle without reservation. For no premiss is ever couched

reason is that these several objects are not equally obvious to us. istence of the thing.

drew

should perhaps say that in a

people offer.

that every predicate can be either truly

we have

he was led on to

Meno: either a man will learn nothing or what he already knows; for [50] we cannot accept the solution which some the

affirmed or truly denied of any subject, and 'unit'

here no

could he know without qualification that its angles were equal to two right angles? No: clearly he \nows not without qualification but only in the sense that he \nows universally. If this distinction is not drawn, we are faced with

pre-existent

that 'triangle'

\now

term

form of syllogism. knowledge required is of two kinds. In some cases admission of the fact must be assumed, in others comprehension of the meaning of the term used, and sometimes both assumptions are essential. Thus, we as-

The

is

he did not in an unqualified sense of the

If

Again, the persuasion exerted by rhetorical arguments is in principle the same, since they [10] use either example, a kind of induction, or

we

manner he knew,

premisses, induction exhibiting the universal in

there

recognition or before he actually

plines are acquired in this way, and so are the two forms of dialectical reasoning, syllogistic [5] and inductive; for each of these latter make use of old knowledge to impart new, the syllogism assuming an audience that accepts its as implicit

i.e.

recognition through a middle of a minor term

argument proceeds from pre-existent knowledge. This becomes evident upon a survey of

of

We

is

suppose ourselves to possess unqualified knowledge of a thing, as opposed to

scientific 1

translation.

97

Plato,

Meno, 80

POSTERIOR ANALYTICS

98

knowing

it

in the accidental

way

in

which the

[10] sophist knows, when we think that we know the cause on which the fact depends, as

the cause of that fact and of no other, and, further, that the fact could not be other than it

Now

is.

that scientific

—

knowing

is

something

evident witness both those who and those who actually possess it, since the former merely imagine themselves to be, while the latter are also actually, in the condition described. Consequently the proper of this sort

is

claim

falsely

it

[75] object of unqualified scientific knowledge something which cannot be other than it is.

is

There may be another manner of knowing as well

—that

What I we do know by

will be discussed later.

now

1

assert is that at all events demonstration. By demonstration I mean a syllogism productive of scientific knowledge, a syllogism, that is, the grasp of which is eo ipso such knowledge. Assuming then that my the-

the nature of scientific

sis as to

knowing

is

cor-

premisses of demonstrated knowledge must be true, primary, immediate, better known than and prior to the conclusion, [20]

which

the

rect,

further related to

is

them

as effect to

cause. Unless these conditions are satisfied, the basic truths will not be 'appropriate'

to the

Syllogism there may indeed be without these conditions, but such syllogism, not being productive of scientific knowledge, will not be demonstration. The premisses must conclusion.

[25] be true: for that

known

non-existent

—we cannot know,

demonknowledge must be primary, I mean that they must be the 'appropriate' basic truths, for I identify primary premiss and basic

other. In saying that the premisses of strated

A 'basic truth' in a demonstration is an immediate proposition. An immediate proposition is one which has no other proposition prior to it. A proposition is either part of an

truth.

enunciation,

i.e. it

predicates a single attribute

of a single subject. If a proposition

[10]

dialecti-

is

assumes either part indifferently demonstrative, it lays down one part to

cal,

if it is

it

the definite exclusion of the other because that part

The term

'enunciation' denotes

ei-

ther part of a contradiction indifferently.

A

true.

is

contradiction

is

an opposition which of

its

own

nature excludes a middle. The part of a contradiction which conjoins a predicate with a

an affirmation; the part disjoining I call an immediate basic [75] truth of syllogism a 'thesis' when, though it is not susceptible of proof by the teacher, yet subject

them

is

is

a negation.

ignorance of it does not constitute a total bar to progress on the part of the pupil: one which the pupil must know if he is to learn anything

whatever

is

an axiom.

I

call it

cause there are such truths and the

name

an axiom be-

we

give

them

of axioms par excellence. If a thesis

e.g. that

assumes one part or the other of an enuncia[20] tion, i.e. asserts either the existence or the non-existence of a subject, it is a hypothesis; if

the diagonal of a square side.

is

are those further from sense. Now the most universal causes are furthest from sense and particular causes are nearest to sense, and [5] they are thus exactly opposed to one an-

known

commensurate with The premisses must be primary and

cannot be its

which

72*

is

indemonstrable; otherwise they will require demonstration in order to be known, since to have knowledge, if it be not accidental knowledge, of things which are demonstrable, means precisely to have a demonstration of them. The premisses must be the causes of the conclusion, better known than it, and prior to it; its causes,

it

does not so assert,

tion

is

it is

a definition. Defini-

a 'thesis' or a 'laying

since the arithmetician lays

a unit

is

something down', it

down

that to be

to be quantitatively indivisible; but

it

this

not a hypothesis, for to define what a unit is is not the same as to affirm its existence. [25] Now since the required ground of our knowledge i.e. of our conviction of a fact is the possession of such a syllogism as we call demonstration, and the ground of the syllo-

antecedent knowledge being not our mere understanding of the meaning, but knowledge of

gism is the facts constituting its premisses, we must not only know the primary premisses

Now 'prior' and 'better known* ambiguous terms, for there is a difference between what is prior and better known in the 72 a order of being and what is prior and better known to man. I mean that objects nearer to sense are prior and better known to man; objects without qualification prior and better

some if not all of them beforehand, but know them better than the conclusion: for the cause

[30] since we possess scientific knowledge of a thing only when we know its cause; prior, in order to be causes; antecedently

known,

the fact as well. are

1

Cf. the following chapter and

ch. 19.

more

particularly

11,

is

—

—

—

of an attribute's inherence in a subject always itself

inheres in the subject

more firmly than

that attribute; e.g. the cause of our loving anyis dearer to us than the object of our [50] love. So since the primary premisses are i.e. of our convicthe cause of our knowledge

thing

tion

—

—

it

follows that

we know them

better

BOOK

7V that

more convinced

are

is,

of

them

I,

CHAPTERS

—than

their consequences, precisely because of our

knowledge knowledge

of the latter

is

the effect of our

of the premisses. Now a man cannot believe in anything more than in the things he knows, unless he has either actual

knowledge of

it

or something better than ac-

knowledge. But we are faced with this [35] paradox if a student whose belief rests on demonstration has not prior knowledge; a man must believe in some, if not in all, of the basic truths more than in the conclusion. Moreover, tual

a

if

man

sets

out to acquire the scientific

knowledge that comes through demonstration, he must not only have a better knowledge of the basic truths and a firmer conviction of them than of the connexion which is being 72 b demonstrated: more than this, nothing must be more certain or better known to him than these basic truths in their character as fundamental premisses the contradicting which lead to the opposed and erroneous conclusion. For indeed the conviction of pure science must be unshakable.

[5] Some hold that, owing to the necessity of knowing the primary premisses, there is no sci-

knowledge. Others think there is, but that all truths are demonstrable. Neither doctrine is either true or a necessary deduction from the premisses. The first school, assuming that there is no way of knowing other than by demonstration, maintain that an infinite regress is involved, on the ground that if behind the prior stands no primary, we could not [10] know the posterior through the prior (wherein they are right, for one cannot traverse an infinite series): if on the other hand they the series terminates and there are primary say entific

—

—

unknowable because incapable of demonstration, which according to them is the only form of knowledge. And since premisses, yet these are

thus one cannot know the primary premisses, knowledge of the conclusions which follow

from them properly

is

not pure scientific knowledge nor at all, but rests on the mere

knowing

supposition that the premisses are true.

The

[75] other party agree with them as regards knowing, holding that it is only possible by

demonstration, but they see no difficulty in holding that all truths are demonstrated, on the ground that demonstration may be circular

and

reciprocal.

Our own is

knowledge demonstrative: on the contrary, knowledge doctrine

is

that not

all

of the

2-3

99

immediate premisses

is

independent of

[20] demonstration. (The necessity of this is obvious; for since we must know the prior premisses from which the demonstration is drawn, and since the regress must end in im-

mediate truths, those truths must be indemonSuch, then, is our doctrine, and in addition we maintain that besides scientific

strable.)

knowledge there is its originative source which enables us to recognize the definitions. demonstration must be based on [25]

Now

premisses prior to and better known than the conclusion; and the same things cannot simultaneously be both prior and posterior to one another: so circular demonstration

is

clearly

not possible in the unqualified sense of 'demonstration', but only possible if 'demonstration' be extended to include that other method of

argument which

on a distinction between and truths without qualification prior, i.e. the method by which induction [jo] produces knowledge. But if we accept this extension of its meaning, our definition of unqualified knowledge will prove faulty; for there seem to be two kinds of it. Perhaps, however, the second form of demonstration, that which proceeds from truths better known to rests

truths prior to us

us,

is

not demonstration in the unqualified

sense of the term.

The advocates of circular demonstration are not only faced with the difficulty we have just stated: in addition their theory reduces to the mere statement that if a thing exists, then it does exist an easy way of proving anything.

—

That

this is so can be clearly shown by taking three terms, for to constitute the circle

[55]

makes no difference whether many terms or few or even only two are taken. Thus by direct proof, if A is, B must be; if B is, C must be; therefore if A is, C must be. Since then by the circular proof if A is, B must be, and if 73 a B is, A must be, A may be substituted for C above. Then 'if B is, A must be' 'if B is, C must be', which above gave the conclusion 'if A is, C must be': but C and A have been identified. Consequently the upholders of cirit

—

—

=

cular demonstration are in the position of sayis, must be a simple way [5] ing that if

A

A

—

of proving anything. Moreover, even such cir-

cular demonstration

is

impossible except in the

case of attributes that imply one another, viz. 'peculiar' properties.

Now, it has been shown that the positing of one thing be it one term or one premiss never involves a necessary consequent: two

—

1

1

Prior Analytics,

I,

25.

POSTERIOR ANALYTICS

100

[10] premisses constitute the first and smallest foundation for drawing a conclusion at all and therefore a fortiori for the demonstrative syllogism of science. If, then, A is implied in B and C, and B and C are reciprocally implied in one another and in A, it is possible, as has been

shown prove

all

my

1

writings on the syllogism, to the assumptions on which the original

in

conclusion rested, by circular demonstration in [75] the first figure. But it has also been shown that in the other figures either no conclusion

is

possible,

or at

none which

least

2 proves both the original premisses. Proposinot convertible which are the terms of tions

73 b

which they belong

tain subjects, the subjects to

are contained in the attribute's

Thus

own

defining

and curved belong to [40] line, odd and even, prime and compound, square and oblong, to number; and also 73 b the formula defining any one of these at-

formula.

straight

tributes contains

ber as the case

Extending tributes,

its

may

subject

—

e.g. line or

num-

be.

this classification to all other at-

distinguish those that answer the

I

above description as belonging essentially to their respective subjects; whereas attributes re-

two ways

lated in neither of these jects

I call

to their sub-

accidents or 'coincidents'; e.g. musi-

cannot be circularly demonstrated at all, and since convertible terms occur rarely in actual demonstrations, it is clearly frivolous and impossible to say that demonstration is reciprocal [20] and that therefore everything can be

cal or

demonstrated.

as substance, in the sense of

white

is

a 'coincident' of animal.

[5] Further (a) that is essential which is not predicated of a subject other than itself: e.g. 'the

walking [thing]' walks and

is

white in

virtue of being something else besides; where-

whatever signifies somewhat', is not what it is in virtue of being something else besides. Things, then, not a 'this

Since the object of pure scientific knowledge cannot be other than it is, the truth obtained by demonstrative knowledge will be necessary. And since demonstrative knowledge is only present when we have a demonstration, it follows that demonstration is an inference from necessary premisses. So

we must

consider

are the premisses of demonstration

[25] is their character: let us define what we

and

—

i.e.

what what

as a preliminary,

mean by an

attribute

an 'essenand a 'commensurate and uni-

'true in every instance of its subject', tial'

attribute,

versal' attribute.

what one

is

I call

'true in every instance'

truly predicable of all instances

to the exclusion of others

—and

—not of

at all times,

not at this or that time only; e.g. if animal is [_?o] truly predicable of every instance of man, then if it be true to say 'this is a man', 'this is an animal' is also true, and if the one be true now the other is true now. corresponding account holds if point is in every instance predicable as contained in line. There is evidence for

A

this

in the

fact that the objection

we

raise

against a proposition put to us as true in every instance is either an instance in which, or an occasion on which, it is not true. Essential attributes are (1) such as belong to their subtil ) ect as elements in its essential nature (e.g.

predicated of a subject predicated of a subject

call essential;

things

call accidental

or 'co-

I I

incidental'.

[10] In another sense again (b) a thing consequentially connected with anything is essential; one not so connected is 'coincidental'. An example of the latter is 'While he was walking it lightened': the lightning was not due to his walking; it was, we should say, a coincidence. If, on the other hand, there is a consequential

connexion, the predication

when

is

essential; e.g.

if

a

being cut, then its death is also essentially connected with the cut[75] ting, because the cutting was the cause of death, not death a 'coincident' of the cutting. So far then as concerns the sphere of connexions scientifically known in the unqualified sense of that term, all attributes which (within that sphere) are essential either in the sense that their subjects are contained in them, or in the sense that they are contained in their sub-

beast dies

jects,

its

throat

is

are necessary as well as consequentially

connected with their subjects. For it is impossible for them not to inhere in their subjects either simply or in the qualified sense that one or other of a pair of opposites must inhere in [20] the subject; e.g. in line must be either straightness or curvature, in

number

either

the very being or 'substance' of triangle

oddness or evenness. For within a single identical genus the contrary of a given attribute is

is

either

line): (2) such that, while they

not odd is even, inasmuch as within this sphere even is a necessary consequent of not-odd. So, since any given

line thus belongs to triangle, point to line; for

and line composed of these elements, which are contained in the formulae defining triangle and 1

Ibid., 11, 5.

2 Ibid., 11,

5 and 6.

belong to cer-

within

its

privative or

number what

is

its

contradictory; e.g.

BOOK

74*

must be

predicate

any

I,

CHAPTERS

either affirmed or. denied of

subject, essential attributes

must inhere

in

their subjects of necessity.

we have established the disbetween the attribute which is 'true in every instance' and the 'essential' attribute. I term 'commensurately universal' an attribute which belongs to every instance of its subject, and to every instance essentially and as such; from which it clearly follows that all commensurate universals inhere necessarily in their subjects. The essential attribute, and the [25] Thus, then,

tinction

attribute that belongs to identical. E.g. point

and

its

subject as such, are

straight belong to line

[30] essentially, for they belong to line as such; and triangle as such has two right angles, for

equal to two right angles. An attribute belongs commensurately and universally to a subject when it can be shown to belong to any random instance of that subject and when the subject is the first thing to which it can be shown to belong. Thus, e.g. it is

essentially

(1) the equality of its angles to two right anis not a commensurately universal attri-

gles

bute of figure. For though it is possible to [35] show that a figure has its angles equal to two right angles, this attribute cannot be demonstrated of any figure selected at haphazard,

nor in demonstrating does one take a figure at random a square is a figure but its angles are not equal to two right angles. On the other hand, any isosceles triangle has its angles equal

—

to

two right

angles, yet isosceles triangle

is

not

the primary subject of this attribute but triangle

is

prior.

So whatever can be shown

to

have

[40] its angles equal to two right angles, or to possess any other attribute, in any random in-

—

and primarily that is the first which the predicate in question belongs commensurately and universally,

stance of itself subject to

74 a and the demonstration, in the essential sense, of any predicate is the proof of it as belonging to this first subject commensurately and universally:

while the proof of

the other subjects to

which

it

as

belonging to

is demand unessential equality to two right it

attaches

onstration only in a secondary sense.

Nor

again (2)

is

angles a commensurately universal attribute of isosceles;

We fall

it is

of wider application.

must not

fail

that

we

the sense in

We

is

often not in

primary and commensurately univerwhich we think we prove it make this mistake ( 1 ) when the subject

[5] fact sal in so.

to observe

into error because our conclusion

3-5

101

an individual or individuals above which there is no universal to be found: (2) when the subjects belong to different species and there is a higher universal, but it has no name: (3) when the subject which the demonstrator takes as a whole is really only a part of a larger whole; for then the demonstration will be true is

[10] of the individual instances within the part and will hold in every instance of it, yet the demonstration will not be true of this subject

primarily and commensurately and uni-

versally.

subject

When

universally, that is

a demonstration

primarily and is

is

true of a

commensurately and

to be taken to

true of a given subject primarily

mean and

that

it

as such.

Case (3) may be thus exemplified. If a proof were given that perpendiculars to the same line are parallel, it might be supposed that lines thus perpendicular were the proper subject of the demonstration because being parallel is true of every instance of them. But it is not so, [75] for the parallelism depends not on these angles being equal to one another because each is a right angle, but simply on their being equal to one another. An example of ( 1 ) would be as follows: if isosceles were the only triangle, it would be thought to have its angles equal to

two right angles qua isosceles. An instance of (2) would be the law that proportionals alternate. Alternation used to be

demonstrated sepnumbers, lines, solids, and durations, though it could have been proved of [20] them all by a single demonstration. Be-

arately of

was no single name to denote that which numbers, lengths, durations, and solids are identical, and because they differed specifically from one another, this property was proved of each of them separately. To-day, however, the proof is commensurately universal, for they do not possess this attribute qua lines or qua numbers, but qua manifesting this generic character which they are postulated as cause there in

[25] possessing universally. Hence, even if one prove of each kind of triangle that its angles are equal to two right angles, whether by

means

of the

same or

different proofs;

still,

as

long as one treats separately equilateral, scalene, and isosceles, one does not yet know, except sophistically, that triangle has its angles equal to two right angles, nor does one yet know that triangle has this property commensurately and universally, even if there is no other species of triangle but these. For one does [50] not know that triangle as such has this property, nor even that 'all' triangles have it unless 'all' means 'each taken singly': if 'all'

—

POSTERIOR ANALYTICS

102

means 'as a whole class', none in which one does not recognize

then, though there be

property, one does not

When,

know

it

of

'all

this

triangles'.

knowledge fail of commensurate universality, and when it is unqualified knowledge? If triangle be identical in then, does our

with each or

essence with equilateral,

i.e.

equilaterals, then clearly

we have

knowledge:

if

on the other hand

all

75*

necessary premisses. For though you may reason from true premisses without demonstrat-

your premisses are necessary you demonstrate in such necessity you have at once a distinctive character of demonstration. That demonstration proceeds from necessary premisses is also indicated by the ing, yet

if

—

will assuredly

unqualified

fact that the objection

be not, and

fessed demonstration

it

the attribute belongs to equilateral qua trianle; then our knowledge fails of commensurate

55] universality. 'But', it will be asked, 'does belong to the subject of which it

we

is

raise against a pro-

that a premiss of

so far as our opponent's previous

shows how naive

this attribute

goes. This

has been demonstrated qua triangle or qua isosceles? What is the point at which the sub-

one's basic truths rightly chosen

ject to

what

which

belongs

it

subject can

it

primary?

is

(i.e.

to

be demonstrated as belong-

ing commensurately and universally?)' Clearly this point is the first term in which it is found to inhere as the elimination of inferior differentiae proceeds. Thus the angles of a

brazen

equal to two right

isosceles triangle are

and isosceles and the attribute remains. 'But' you may say 74 b 'eliminate figure or limit, and the attribute vanishes.' True, but figure and limit are not the first differentiae whose elimination destroys the attribute. 'Then what is the first?' If angles: but eliminate brazen

—

it is

triangle,

it

will be in virtue of triangle that

the attribute belongs to

which

it is

predicable,

the other subjects of

all

and

triangle

is

the sub-

which it can be demonstrated as belonging commensurately and universally.

ject to

it is

—

whether we think [20] not a necessary truth it altogether devoid of necessity, or at any rate it

is

argument to suppose

if one starts with a proposition which is (1) popularly accepted and (2) true, such as the sophists' assumption that to know is the same as to possess knowledge. For (1) popular acceptance or re1

jection

is

no

criterion of a basic truth,

which

can only be the primary law of the genus constituting the subject matter of the demonstra[25] tion; and (2) not all truth is 'appropriate'. further proof that the conclusion must be

A

the development of necessary premisses follows.

Where demonstration

is

is

possible,

as

one

who can give no account which includes the cause has no scientific knowledge. If, then, we suppose a syllogism in which, though essarily inheres in C, yet B, the

the demonstration,

is

A

nec-

middle term of

not necessarily connected

A

and C, then the man who argues thus [jo] has no reasoned knowledge of the conclu-

with

sion, since this conclusion does not

owe

its

ne-

middle term; for though the conclusion is necessary, the mediating link is a contingent fact. Or again, if a man is without knowledge now, though he still retains the steps of the argument, though there is no change in himself or in the fact and no lapse of memory on his part; then neither had he knowledge previously. But the mediating link, not being necessary, may have perished in the [^5] interval; and if so, though there be no change in him nor in the fact, and though he will still retain the steps of the argument, yet he has not knowledge, and therefore had not knowledge before. Even if the link has not accessity to the

[5]

Demonstrative knowledge must

rest

on

necessary basic truths; for the object of scientific knowledge cannot be other than it is.

Now

attributes attaching essentially to their subjects

attach necessarily to them: for essential attributes are either elements in the essential nature of their subjects, or contain their subjects as

elements in their pairs of opposites

own

essential nature.

which the

are necessary because one

(The

latter class includes

member

or the other

[10] necessarily inheres.) It follows from this that premisses of the demonstrative syllogism

must be connexions plained: for tially or else

all

essential in the sense ex-

attributes

be accidental,

must inhere essenand accidental attri-

butes are not necessary to their subjects.

We

must

either state the case thus, or else

premise that the conclusion of demonstration is necessary and that a demonstrated conclusion cannot be other than it is, and then infer that [75] the conclusion must be developed from

tually perished but

is

liable to perish, this situ-

and might occur. But such a condition cannot be knowledge. 75 a When the conclusion is necessary, the middle through which it was proved may yet ation

is

possible

You can in fact even from a non-necessary you can infer the true from the

quite easily be non-necessary. infer the necessary

premiss, just as 1

Plato, Euthydemus, 277.

BOOK

75 b not true. is

On

the other hand,

necessary the conclusion

when

I,

CHAPTERS

the middle

must be necessary;

[5] just as true premisses always give a true is necessarily predicated conclusion. Thus, if

A

of

B and B

of C, then

cated of C. But

when

A

is

necessarily predi-

the conclusion

is

non-

necessary the middle cannot be necessary eibe predicated non-necessarily ther. Thus: let

A

[10] of C but necessarily of B, necessary predicate of C; then

necessary predicate of C, it is

and

let

B

be a

which

too will be a by hypothesis

up, then: demonstrative knowledge must be knowledge of a necessary nexus, and therefore must clearly be obtained through a

To sum

necessary middle term; otherwise its possessor will know neither the cause nor the fact that a necessary connexion.

Either he will mistake the non-necessary for and believe the necessity of the

the necessary

knowing it, or else he will not even believe it in which case he will be equally ignorant, whether he actually infers the mere fact through middle terms or the reaconclusion without

—

soned fact and from immediate premisses. Of accidents that are not essential according to our definition of essential there is no demonstrative knowledge; for since an accident, in [20] the sense in which I here speak of it, may also not inhere, it is impossible to prove its inherence as a necessary conclusion. A difficulty, however, might be raised as to why in dialectic, if the conclusion is not a necessary connexion, such and such determinate premisses should be proposed in order to deal with such and such determinate problems. Would not the result be the same if one asked any questions

whatever and then merely stated one's conclu[25] sion? The solution is that determinate questions have to be put, not because the replies

to

them

facts affirmed

affirm facts

which

necessitate

by the conclusion, but because

these answers are propositions

which

if

the an-

swerer affirm, he must affirm the conclusion and affirm it with truth if they are true. Since it is just those attributes within every genus which are essential and possessed by their respective subjects as such that are necessary, it is clear that both the conclusions and [50] the premisses of demonstrations which

produce

scientific

knowledge are

essential.

For

accidents are not necessary: and, further, since accidents are not necessary one does not necessarily

follows that

It

have reasoned knowledge of a conclusion (this is so even if the acci-

drawn from them

dental premisses are invariable but not essen-

we cannot

from one genus

pass

is

103

through signs; for though the conclusion be actually essential, one will not know it as essential nor know its reason); but [35] to have reasoned knowledge of a conclusion is to know it through its cause. We may conclude that the middle must be consequentially connected with the minor, and the major with the middle. as in proofs

tial,

A

not.

[75] his conclusion

5-7

in demonstrating

to another.

We

for instance, prove geometrical truths

cannot,

by

metic. For there are three elements in

arith-

demon-

[40] stration: (1) what is proved, the conclusion an attribute inhering essentially in a ge-

—

75 b nus; (2) the axioms,

i.e.

axioms which are

premisses of demonstration; (3) the subjectgenus whose attributes, i.e. essential properties, are revealed by the demonstration. The axioms which are premisses of demonstration may be identical in two or more sciences: but in the case of two different genera such as arithmetic and geometry you cannot apply arithmetical demonstration to the properties [5] of magnitudes unless the magnitudes in question are numbers. in certain cases

How

1 will explain later. Arithmetical demonstration and the other

transference

is

possible

I

sciences likewise possess, each of them, their

own

genera; so that

pass

from one sphere

must be

if

the demonstration to another, the

is

to

genus

some extent the not so, transference is clearly impossible, because the extreme and the middle terms must be drawn from the same genus: otherwise, as predicated, they will not either absolutely or to

same.

[10]

If this

is

be essential and will thus be accidents. That is why it cannot be proved by geometry that op-

under one science, nor even that two cubes is a cube. Nor can the theorem of any one science be demonstrated by

posites fall

the product of

[75] means of another science, unless these theorems are related as subordinate to superior (e.g. as optical theorems to geometry or harmonic theorems to arithmetic). Geometry again cannot prove of lines any property which they do not possess qua lines, i.e. in virtue of the fundamental truths of their peculiar genus: it cannot show, for example, that the straight line

is

the most beautiful of lines or the con-

do not belong to lines in virtue of their peculiar genus, but through some property which it shares [20] with other genera. trary of the circle; for these qualities

x

Cf.

1,

9 and 13.

POSTERIOR ANALYTICS

104

76 a

propriate' to

the subject

—unless

we know,

property of possessing angles equal to two right angles as belonging to that subject in e.g. the

It is also clear that if the premisses from which the syllogism proceeds are commensurately universal, the conclusion of such dem-

—demonstration, — must be

onstration

i.e.

in the unquali-

Therefore no attribute can be demonstrated nor known by fied sense

eternal.

also

strictly scientific

ishable things.

knowledge

to inhere in per-

The proof can

only be acciden-

[25] tal, because the attribute's connexion with its perishable subject is not commensurately

universal but temporary and special. If such a demonstration is made, one premiss must be perishable and not commensurately universal (perishable because only if it is perishable will the conclusion be perishable; not commensurately universal, because the predicate will be

which from

and

inheres essentially,

it

basic

premisses

essential

priate' to that subject: so that

if

as inferred

and 'approthat middle

term also belongs essentially to the minor, the middle must belong to the same kind as the major and minor terms. The only exceptions to this rule are such cases as theorems in harmonics which are demonstrable by arithmetic. [10] Such theorems are proved by the same middle terms as arithmetical properties, but with a qualification the fact falls under a separate science (for the subject genus is sep-

—

arate), but the reasoned fact concerns the superior science, to which the attributes essentially belong. Thus, even these apparent excep-

and

tions

show

not of others); so that the conclusion can only be that a fact is true at the moment not com[jo] mensurately and universally. The same is

ic]

strable except

sciences have the requisite identity of char-

true of definitions, since a definition

acter.

predicable of

some

instances of the subject

—

is

either a

primary premiss or a conclusion of a demonstration, or else only differs from a demonstration in the order of its terms. Demonstration and science of merely frequent occurrences are, e.g. of eclipse as happening to the moon as such, clearly eternal: whereas so far as they

—

are not eternal they are not fully

commensu-

[55] rate. Other subjects too have properties attaching to them in the same way as eclipse attaches to the

It is clear

that

moon.

if

the conclusion

is

to

show an dem-

attribute inhering as such, nothing can be

onstrated except from

its

'appropriate' basic

truths. Consequently a proof even from true, indemonstrable, and immediate premisses does [40] not constitute knowledge. Such proof s are like Bryson's method of squaring the circle; for they operate by taking as their middle a common

character

—a

character, therefore,

76 a subject may share with another

which the

—and con-

sequently they apply equally to subjects differThey therefore afford knowledge of an attribute only as inhering accidentally, not as belonging to its subject as such: otherwise they would not have been applicable to another genus.

ent in kind.

Our knowledge

of

any

attribute's

that

is

no

less

attribute

from

its

is

strictly

demon-

'appropriate' basic

however, in the case of these

truths, which,

It

no

evident that the peculiar basic

indemonfrom which they might

truths of each inhering attribute are strable; for basic truths

be deduced would be basic truths of all that is, and the science to which they belonged would possess universal sovereignty. This

knows

is

so be-

whose knowledge is deduced from higher causes, for his knowledge [20] is from prior premisses when it derives from causes themselves uncaused: hence, if he knows better than others or best of all, his knowledge would be science in a higher or the cause he

better

highest degree. But, as things are, demonstrais not transferable to another genus, with such exceptions as we have mentioned of the application of geometrical demonstrations to theorems in mechanics or optics, or of arith[25] metical demonstrations to those of harmonics. It is hard to be sure whether one knows or not; for it is hard to be sure whether one's knowledge is based on the basic truths appropriate to each attribute the differentia of think we have scientific true knowledge. knowledge if we have reasoned from true and primary premisses. But that is not so: the conclusion must be homogeneous with the basic

tion

—

We

[jo] facts of the science.

connexion

with a subject is accidental unless we know that connexion through the middle term in [5] virtue of which it inheres, and as an inference from basic premisses essential and 'ap-

10

the basic truths of every genus those elements in it the existence of which cannot be proved. As regards both these primary truths I

call

BOOK

IT

L

CHAPTERS

and the attributes dependent on them the meaning of the name is assumed. The fact of their existence as regards the primary truths must be assumed; but it has to be proved of the remainder, the attributes. Thus we assume the meaning alike of unity, straight, and tri[35] angular; but while as regards unity and magnitude we assume also the fact of their existence, in the case of the remainder proof is required.

Of

the basic truths used in the demonstrative

8-11

105

Nevertheless in the nature of the case the essential elements of demonstration are three: the subject, the attributes, and the basic premisses. That which expresses necessary self-grounded

and which we must necessarily believe, is both from the hypotheses of a science and from illegitimate postulate I say 'must believe', because all syllogism, and therefore

fact,

distinct

—

a fortiori demonstration, is addressed not to the [25] spoken word, but to the discourse within the soul, and though we can always raise ob-

some are peculiar to each science, and some are common, but common only in the

jections to the

sense of analogous, being of use only in so far province of the science in question.

capable of proof but assumed by the teacher without proof is, if the pupil believes and accepts it, hypothesis, though only in a limited

40] Peculiar truths are, e.g. the definitions of

sense hypothesis

sciences

as they fall within the ]

ine

and

straight;

'take equals

Only

so

genus constituting the

common

truths are such as

from equals and equals remain'.

much

of these

common

truths

is

re-

within the genus in question: 76 b for a truth of this kind will have the same force even if not used generally but applied by the geometer only to magnitudes, or by the arithmetician only to numbers. Also peculiar to quired as

falls

a science are the subjects the existence as well as the meaning of which it assumes, and the essential attributes of

which

it

investigates, e.g.

spoken word,

we cannot always

course

—that

is,

inward disThat which is

to the

object.

relatively to the pu-

[30] pil; if the pupil has no opinion or a contrary opinion on the matter, the same assumption

an illegitimate postulate. Therein

is

the distinction between hypothesis and

mate

postulate: the latter

is

lies

illegiti-

the contrary of the

opinion, demonstrable, but assumed

pupil's

and used without demonstration. [55] The definition viz. those which are not

—

expressed as statements that anything is or is not are not hypotheses: but it is in the prem-

—

isses of a science that its

hypotheses are con-

[5] in arithmetic units, in geometry points and lines. Both the existence and the meaning of

tained. Definitions require only to be under-

the subjects are assumed by these sciences; but

contended that the pupil's hearing is also an hypothesis required by the teacher. Hypoth-

of their essential attributes only the meaning is assumed. For example arithmetic assumes the

meaning

of

odd and even, square and cube,

geometry that of incommensurable, or of deflection or verging of lines, whereas the existence of these attributes is demonstrated by [10] means of the axioms and from previous conclusions as premisses.

Astronomy

too pro-

ceeds in the same way. For indeed every demonstrative science has three elements: (1) that

genus whose essenexamines; (2) the so-called [75] axioms, which are primary premisses of its demonstration; (3) the attributes, the meaning of which it assumes. Yet some sciences may very well pass over some of these elements; e.g. we might not expressly posit the existence of the genus if its existence were obvious (for instance, the existence of hot and cold is more evident than that of number); or we might omit to assume expressly the meaning of the attributes if it were well understood. In the [20] same way the meaning of axioms, such as 'Take equals from equals and equals remain', is well known and so not expressly assumed.

which tial

it

posits, the subject

attributes

it

stood,

eses,

and

this

is

not hypothesis

on the contrary, postulate

—unless

facts

it

on the

be

be-

ing of which depends the being of the fact [40] inferred. Nor are the geometer's hypoth-

some have held, urging that one must not employ falsehood and that the geom-

eses false, as

eter line

is

uttering falsehood in stating that the

which he draws

when

it

is

is

a foot long or straight,

actually neither.

The

truth

is

that

77 a the geometer does not draw any conclusion from the being of the particular line of which he speaks, but from what his diagrams symbolize.

A

further distinction

is

that

all

hy-

potheses and illegitimate postulates are either universal or particular, whereas a definition is neither.

n [5] So demonstration does not necessarily imply the being of Forms nor a One beside a

Many, but

it

bility of truly

without

this

universal, dle

does necessarily imply the possipredicating one of many; since

and

possibility if

we cannot

save the

the universal goes, the mid-

term goes with

it,

and

so demonstration be-

POSTERIOR ANALYTICS

io6

77 h

comes impossible. We conclude, then, that there must be a single identical term unequivocally predicable of a

[w] The law

number

of individuals.

12 If a syllogistic

osition

when the conclusion also has to be expressed in that form; in which case the proof lays down as its major premiss that

clusion

it is

demonstration except

the

major

is

truly affirmed of the

falsely denied. It

ever,

if

we add

makes no

middle but

difference,

how-

to the middle, or again to the

minor term, the corresponding negative. For [75] grant a minor term of which it is true to

man

predicate

—even —

if it

be also true to predi-

not-man of it still grant simply that man animal and not not-animal, and the conclu-

cate is

sion follows: for Callias

it

will

still

—even be — animal and if it

be true to say that

also true to say that not-

not not-animal. The is predicable not only of the middle, but of something other than the middle as well, being of wider appli[20] cation; so that the conclusion is not affected even if the middle is extended to cover the original middle term and also what is not Callias

reason

is

is

that the major term

the original middle term.

The law

that every predicate can be either

truly affirmed or truly denied of every subject is posited by such demonstration as uses reductio ad impossibile, and then not always universally, but so far as it is requisite; within the

limits, that

is,

of the genus

—the genus,

I

mean

1 have already explained ), to which the [25] man of science applies his demonstrations. In virtue of the common elements of demonstration I mean the common axioms which are used as premisses of demonstration, not the subjects nor the attributes demonall the sciences strated as belonging to them have communion with one another, and in communion with them all is dialectic and any science which might attempt a universal proof of axioms such as the law of excluded middle, [jo] the law that the subtraction of equals from equals leaves equal remainders, or other axioms of the same kind. Dialectic has no definite sphere of this kind, not being confined to a single genus. Otherwise its method would not

(as

I

—

—

be interrogative; for the interrogative method is barred to the demonstrator, who cannot use the opposite facts to prove the [55] This

was shown

in

gism. 2 l 2

Cf. 75 a 42fF. and 76b 13. Prior Analytics, 1. 1.

same nexus.

my work on

the syllo-

question

is

equivalent to a prop-

embodying one of the two sides of a contradiction, and if each science has its peculiar propositions from which its peculiar con-

impossible to affirm and deny simultaneously the same predicate of the same subject is not expressly posited by any that

is

developed, then there

such a thing

is

as a distinctively scientific question,

and

it

is

the interrogative form of the premisses from which the 'appropriate' conclusion of each sci[40] ence is developed. Hence it is clear that not every question will be relevant to geometry, nor to medicine, nor to any other science: only 77 h those questions will be geometrical which form premisses for the proof of the theorems of

geometry or of any other science, such as which uses the same basic truths as ge-

optics,

Of the other sciences the like is true. these questions the geometer is bound to

ometry.

Of

give his account, using the basic truths of gein conjunction with his previous con-

ometry

[5] elusions; of the basic truths the geometer, as such, is not bound to give any account. The like

is

There is a which we may put

true of the other sciences.

limit, then, to the questions

man of science; nor is each man of science bound to answer all inquiries on each several subject, but only such as fall within the defined field of his own science. If, then, in controversy with a geometer qua geometer the disputant confines himself to geometry and to each

[10] proves anything from geometrical premhe is clearly to be applauded; if he goes

isses,

outside these he will be at fault, and obviously cannot even refute the geometer except accidentally.

One

should therefore not discuss ge-

ometry among those who are not geometers, for in such a company an unsound argument will pass unnoticed. This is correspondingly true in [75] the other sciences. Since there are 'geometrical' questions, does it follow that there are also distinctively 'un-

geometrical' questions? Further, in each special science geometry for instance what kind

—

of error

is it

that

—

may vitiate

questions,

and

yet

not exclude them from that science? Again, is the erroneous conclusion one constructed from premisses opposite to the true premisses, or is [20] it formal fallacy though drawn from geometrical premisses? Or, perhaps, the erroneous conclusion is due to the drawing of premisses from another science; e.g. in a geometrical controversy a musical question is distinctively ungeometrical, whereas the notion that parallels meet is in one sense geometrical, being ungeometrical in a different fashion: the reason

BOOK

78 h

I,

CHAPTERS

being that 'ungeometrical', like 'unrhythmical', is equivocal, meaning in the one case not ge[25] ometry at It is this

this

kind

i.e.

bad geometry? on premisses of

in the other

all,

error based

—'of the science but error,

false

—that

is

the

contrary of science. In mathematics the formal fallacy is not so common, because it is the middle term in which the ambiguity lies, since the

major is predicated of the whole of the middle [50] and the middle of the whole of the minor (the predicate of course never has the prefix and in mathematics one can, so to speak,

'all');

middle terms with an intellectual while in dialectic the ambiguity may escape detection. E.g. 'Is every circle a figure?' A diagram shows that this is so, but the minor premiss 'Are epics circles?' is shown by the diagram to be false. If a proof has an inductive minor premiss, [35] one should not bring an 'objection' against it. For since every premiss must be applicable to a number of cases (otherwise it will not be true in every instance, which, since the syllosee these

vision,

gism proceeds from universals, it must be), then assuredly the same is true of an 'objection'; since premisses and 'objections' are so far the same that anything which can be validly advanced as an 'objection' must be such that it could take the form of a premiss, either [40] demonstrative or dialectical. On the other hand, arguments formally illogical do sometimes occur through taking as middles mere

major and minor terms.

attributes of the

78 a instance of

An

Caeneus' proof that fire increases in geometrical proportion: 'Fire', he argues, 'increases rapidly, and so does geometrical proportion'. There is no syllogism so, but there

is

this

a syllogism

is

if

the most rapidly increas-

ing proportion is geometrical and the most rapidly increasing proportion is attributable to [5] fire in its motion. Sometimes, no doubt, it is impossible to reason from premisses predicating sible,

false

mere attributes: but sometimes it is posthough the possibility is overlooked. If

premisses could never give true concluwould be easy, for premisses

sions 'resolution'

and conclusion would in that case inevitably reciprocate. I might then argue thus: let A be an existing fact; let the existence of A imply such and such facts actually known to me to exist, which we may call B. I can now, since they reciprocate, infer A from B. [10] Reciprocation of premisses and concluis more frequent in mathematics, because mathematics takes definitions, but never an a second characteraccident, for its premisses

sion

—

11-13

107

mathematical

istic

distinguishing

from

dialectical disputations.

reasoning

A

science expands not by the interposition of fresh middle terms, but by the apposition of

fresh extreme terms. E.g.

A

is

predicated of B,

[75] B of C, C of D, and so indefinitely. Or the expansion may be lateral: e.g. one major,

A, may be proved of two minors, C and E. Thus let A represent number a number or number taken indeterminately; B determinate odd number; C any particular odd [20] number. We can then predicate A of C. represent determinate even numNext let ber, and E even number. Then A is predicable

D

ofE.

Knowledge

of the fact differs

from knowledge

To begin

with, they differ

of the reasoned fact.

within the same science and in two ways: (1) when the premisses of the syllogism are not [25] immediate (for then the proximate cause a necessary condiis not contained in them tion of knowledge of the reasoned fact): (2) when the premisses are immediate, but instead of the cause the better known of the two reciprocals is taken as the middle; for of two reciprocally predicable terms the one which is not the cause may quite easily be the better

—

known and

so

become the middle term of the

demonstration. Thus (2) (a) you might prove [jo] as follows that the planets are near because they do not twinkle: let C be the planets, B not twinkling, A proximity. Then B is predicable of C; for the planets do not twinkle. But A is also predicable of B, since that which does not twinkle is near we must take this truth [55] as having been reached by induction or sense-perception. Therefore A is a necessary

—

predicate of C; so that

we have demonstrated

that the planets are near. This syllogism, then,

proves not the reasoned fact but only the fact; since they are not near because they do not twinkle, but, because they are near, do not twinkle. The major and middle of the proof, however, may be reversed, and then the dem[40] onstration will be of the reasoned fact. let C be the planets, B proximity,

A

78 b Thus:

not twinkling. Then B is an attribute of C, and A not twinkling of B. Consequently A is predicable of C, and the syllogism proves the reasoned fact, since its middle term is the proximate cause. Another example is the inference

—

—

that the

moon

[5] waxing. is spherical,

is spherical from its manner of Thus: since that which so waxes and since the moon so waxes,

POSTERIOR ANALYTICS

o8 clearly the

moon

spherical.

is

Put

in this

form,

79.

matical and nautical astronomy, mathematical

the syllogism turns out to be proof of the fact, but if the middle and major be reversed it is

and acoustical harmonics.) Here

proof of the reasoned fact; since the moon is not spherical because it waxes in a certain manner, but waxes in such a manner because it is [10] spherical. (Let C be the moon, B spherical, and A waxing.) Again (b), in cases where the cause and the effect are not reciprocal and

fact, of

is the better known, the fact is demonstrated but not the reasoned fact. This also occurs (1) when the middle falls outside the

particular instances.

the effect

major and minor, for here too the strict cause is not given, and so the demonstration is of the [75] fact, not of the reasoned fact. For example, the question 'Why does not a wall breathe?' might be answered, 'Because it is not an animal'; but that answer would not give the strict cause, because if not being an animal causes the absence of respiration, then being an animal should be the cause of respiration, according to the rule that if the negation of x [20] causes the non-inherence of y, the affirmation of x causes the inherence of y; e.g. if the disproportion of the hot and cold elements is the cause of ill health, their proportion is the cause of health; and conversely, if the assertion of x causes the inherence of y, the negation of x must cause y's non-inherence. But in the case given this consequence does not result; for not every animal breathes. A syllogism with this kind of cause takes place in the second figure. Thus: let A be animal, B respiration, C [25] wall. Then all that breathes

A

is

predicable of

all

B

(for

is animal), but of no C; and consequently B is predicable of no C; that is, the wall does not breathe. Such causes are like

far-fetched explanations,

which

precisely con-

making

the cause too remote, as in [30] Anacharsis' account of why the Scythians have no flute-players; namely because they sist

in

have no vines. Thus, then, do the syllogism of the fact and the syllogism of the reasoned fact differ within one science and according to the position of the middle terms. But there is another way too in which the fact and the reasoned fact differ,

and

that

is

when

they are investigated respec-

by different sciences. This occurs in the case of problems related to one another as

ts]

tively

subordinate and

superior,

as

when

optical

problems are subordinated to geometry, mechanical problems to stereometry, harmonic problems to arithmetic, the data of observation [40] to astronomy. (Some of these sciences 79 a bear almost the same name; e.g. mathe-

the busi-

it is

know know the

ness of the empirical observers to

soned

the mathematicians to

the rea-

fact; for the latter are in possession of

the demonstrations giving the causes,

often ignorant of the fact: just as

and are

we have

often

[5] a clear insight into a universal, but through lack of observation are ignorant of some of its

These connexions have a though they are manifestations of forms. For the mathematical sciences concern forms: they do not demonstrate properties of a substratum, since, even though perceptible existence

the geometrical subjects are predicable as prop-

substratum, it is not as thus predicable that the mathematician demon-

erties of a perceptible

[10] strates properties of them.

As

optics

lated to geometry, so another science

is

is

re-

related

namely the theory of the rainbow. Here knowledge of the fact is within the province of the natural philosopher, knowledge

to optics,

of the reasoned fact within that of the optician, either

optician.

qua optician or qua mathematical

Many

sciences not standing in this

mutual relation enter into medicine and geometry: it

it

is

at

points; e.g.

the physician's

[75] business to know that circular wounds heal more slowly, the geometer's to know the

reason why.

Of

all

Thus, all

the figures the most scientific it is

is

the

first.

the vehicle of the demonstrations of

the mathematical sciences, such as arith-

metic, geometry,

and

optics,

and

practically of

[20] all sciences that investigate causes: for the syllogism of the reasoned fact is either exclusively or generally speaking

—a

and

in

most

second proof that this figure is the most scientific; for grasp of a reasoned conclusion is the primary condition of knowledge. Thirdly, the first is the only figure [25] which enables us to pursue knowledge of the essence of a thing. In the second figure no affirmative conclusion is possible, and knowledge of a thing's essence must be affirmative; while in the third figure the conclusion can be affirmative, but cannot be universal, and essence must have a universal character: e.g. man is not two-footed animal in any qualified sense, but universally. Finally, the first figure [30] has no need of the others, while it is by cases in this figure

first that the other two figures are and have their intervals closepacked until immediate premisses are reached.

means

of the

developed,

BOOK

80*

Clearly, therefore, the first figure

mary condition

is

I,

CHAPTERS

the pri-

of knowledge.

13-16

109

[25] ( 1 ) Let us first consider propositions asserting a predicate's immediate connexion with

or disconnexion

from

a subject. Here,

may befall one in may arise where one

positive error

A may (as we saw) be connected with a subject B, so its disconnexion may be atomic. I call 'atomic' connexions or disconnexions which involve no [35] intermediate term; since in that case the connexion or disconnexion will not be mediated by something other than the terms themselves. It follows that if either A or B, or both A and B, have a genus, their disconnexion cannot be primary. Thus: let C be the genus of A. Then, if C is not the genus of B for A may well have a genus which is not the genus of there will be a syllogism proving A's [40] B Just as an attribute

atomically

—

—

disconnexion from

79 b

B

all

thus:

A is C,

no B is C, no B is A. Or if it is B which has a genus D, we have all£isD, noD is A, :. no B is A, by syllogism; [5] and the proof will be similar if both A and B have a genus. That the genus of A need not be the genus of B and vice versa, is shown by :.

the existence of mutually exclusive coordinate

no term

series of predication. If

ACD

...

series

BEF

mer

series

.

.

—

in the series

predicable of any term in the

is

is

.,

and

if

G —a

term

in the for-

the genus of A, clearly

G

will

[10] not be the genus of B; since, if it were, the series would not be mutually exclusive. So if B has a genus, it will not be the genus of A. If, on the other hand, neither A nor B has a genus and A does not inhere in B, this disconnexion must be atomic. If there be a middle term, one or other of them is bound to have a

also

[75] genus, for the syllogism will be either in the first or the second figure. If it is in the first,

B

will

ing

it

either

have a genus

must be

A

or

B

—

for the premiss contain-

affirmative;

if

in the second,

indifferently, since syllogism

is

contained in a negative [20] premiss, but not if both premisses are

possible

if

either

is

negative.

stated

true,

directly beways; for it lieves a connexion or disconnexion as well as where one's belief is acquired by inference. The error, however, that consists in a direct belief is without complication; but the error which here concerns resulting from inference us takes many forms. Thus, let A be atomically disconnected from all B: then the conclu|jo] sion inferred through a middle term C, that all B is A, will be a case of error produced by syllogism. Now, two cases are possible. Either (a) both premisses, or (b) one premiss only, may be false, (a) If neither A is an attribute of any C nor C of any B, whereas the contrary was posited in both cases, both prem-

—

—

W M De false. (C may quite well be A and B that C is neither subordinate to A nor a universal attribute of B: for B, since A was said to be primarily disconnected from B cannot have a genus, and A ie]

i

sses

so related to

y

need not necessarily be a universal attribute of all things. Consequently both premisses may [40] be false.) On the other hand, (b) one of the premisses may be true, though not either 80 a indifferently but only the major A-C; since, B having no genus, the premiss C-B will always be false, while A-C may be true. This is the case if, for example, A is related atomically to both C and B; because when the same term is related atomically to more terms than one, neither of those terms will belong to the other. [5]

It is,

of course, equally the case

if

A-C

not atomic.

is

Error of attribution, then, occurs through and in this form only for we

—

these causes

found that no syllogism of universal attribu1 tion was possible in any figure but the first. On the other hand, an error of non-attribution

may

occur either in the

first

or in the second

figure. Let us therefore first explain the various

forms

it

takes in the

first

figure

and the char-

[10] acter of the premisses in each case.

may

occur when both premisses are supposing A atomically connected with both C and B, if it be then assumed that no C is A, and all B is C, both premisses are (c) It

false; e.g.

it is clear that one thing may be atomdisconnected from another, and we have

Hence ically

it is

alternative

when and how

this

is

possible.

false.

(d) 16

—defined

Ignorance

not as the negation of

knowledge but as a positive error produced by inference.

state of

mind

—

is

It is

also possible

when one

is false.

This

be either premiss indifferently. A-C may be true, C-B false A-C true because A is not an attribute of all things, C-B false be[75]

1

may

Prior Analytics,

i.

i

POSTERIOR ANALYTICS

no

cause C, which never has the attribute A, cannot be an attribute of B; for if C-B were true, the premiss A-C would no longer be true, and [20] besides if both premisses were true, the

conclusion would be true. be true and

B

contain

A-C

Or

as genera,

C and A one of them must be sub-

ordinate to the other, so that takes the

makes

form

it

clear

No C

both if

the premiss

A, it will be false. This that whether either or both is

[25] premisses are false, the conclusion will equally be false. In the second figure the premisses cannot

both be wholly

false; for if all

B

A, no mid-

is

dle term can be with truth universally affirmed

of one extreme

and universally denied of the

[50] other: but premisses in which the middle is affirmed of one extreme and denied of the if one is to Therefore if, taken in this way, they are wholly false, their contraries conversely should be wholly true. But this is impossible. On the other hand, there is nothing to prevent both premisses being par-

other are the necessary condition

get a valid inference at

all.

some A is C and some B is C, then if it is premised that all A is C and no B is C, both premisses are false, yet partially, not wholly, false. The same is true if the major is made negative instead of tially false; e.g. if actually

[55]

Or one premiss may

be wholly false, be either of them. Thus, supposing that actually an attribute of all A must also be [40] an attribute of all B, then if C is yet taken

the minor.

and

80 b

it

may

to be a universal attribute of all

versally non-attributable to B,

C-B

C-A

s

[75] propositions erroneous inference will be possible not only when both premisses are false

but also

when

only one

is

false.

C-B may

again,

false; e.g. if

81

A but uni-

will be true

(2) In the case of attributes not atomically

connected with or disconnected from their subjects, (a) (i) as long as the false conclusion is inferred through the 'appropriate' middle, only [20] the major and not both premisses can be false. By 'appropriate middle' I mean the middle term through which the contradictory i.e. the true conclusion is inferrible. Thus, let A be attributable to B through a middle term C: then, since to produce a conclusion the premiss C-B must be taken affirmatively, it is clear that [25] this premiss must always be true, for its quality is not changed. But the major A-C is false, for it is by a change in the quality of AC that the conclusion becomes its contradictory i.e. true. Similarly (ii) if the middle is taken from another series of predication; e.g. suppose to be not only contained within A as a part within its whole but also predicable of all B. Then the premiss D-B must remain un|jo] changed, but the quality of A-D must be changed; so that D-B is always true, A-D al-

—

—

—

D

ways

false.

Such error

practically identical

is

with that which is inferred through the 'appropriate' middle. On the other hand, (b) if the conclusion is not inferred through the 'appropriate' middle (i) when the middle is subordinate to A but is predicable of no B, [35] both premisses must be false, because if there is to be a conclusion both must be posited

—

Again, actually that which is an B will not be an attribute of all A either; for if it be an attribute of all A, it will also be an attribute of all B, which is contrary to supposition; but if C be nevertheless assumed to be a universal attribute of A, but [5] an attribute of no B, then the premiss C-B is true but the major is false. The case is similar if the major is made the negative premiss. For in fact what is an attribute of no A will not be an attribute of any B either; and if it be

what is actually the become false: e.g. suppose that actually all D is A but no B is D; then if these premisses are changed in quality, a conclusion will follow and both of the new

yet

assumed that C is universally non-attribuA, but a universal attribute of B, the [10] premiss C-A is true but the minor wholly false. Again, in fact it is false to assume that that which is an attribute of all B is an attribute of no A, for if it be an attribute of all 5, it must be an attribute of some A. If then C is nevertheless assumed to be an attribute of all B but of no A, C-B will be true but C-A false.

false.

table to

[5] When the erroneous inference is in the second figure, both premisses cannot be entirely false; since if B is subordinate to A, there can be no middle predicable of all of one extreme and of none of the other, as was stated before. One premiss, however, may be false, and it may be either of them. Thus, if C is [10] actually an attribute of both A and B, but

but

false.

attribute of

It

is

no

thus clear that in the case of atomic

as asserting the contrary of fact,

and

so posited both

[40] premisses will be false. When, however, (ii) the middle is not subordinate to A,

D

81 a

A-D

will be true,

D-B

false

A-D

true be-

cause A was not subordinate to D, D-B false because if it had been true, the conclusion too would have been true; but it is ex hy pot he si

1

1

Cf. 80* 29.

BOOK CHAPTERS 16-19 of A only and [5] exist in isolation —

81 b is

to be

an attribute

not of B, C-A will be true, C-B false: or again if C be assumed to be attributable to B but to no A, C-B will be true, C-A false.

We have stated when and through what 1 I 5] kinds of premisses error will result in cases where the erroneous conclusion is negative. If the conclusion is affirmative, (a) (i) it may be inferred through the 'appropriate' middle term. In this case both premisses cannot be

we

false since, as

said before,

main unchanged if there is and consequently A-C, the

1

C-B must

quality of

which

is

2

D-B must remain unchanged, while the quality of A-D must be converted, and the type of is

the same as before.

The middle may

be inappropriate. subordinate to A, A-D will be true, but D-B false; since A may quite well be predicable of several terms no one of which can be subordinated to another. If, however, (ii) is not subordinate to A, obviously A-D, since it is affirmed, will always be false, while [25] (b)

Then

(i) if

D

is

D

D-B may

be either true or false; for

A may

[jo] very well be an attribute of no D, whereas

B

is

D,

e.g.

no science

is

animal,

all

music

Equally well A may be an attribute no D, and D of no B. It emerges, then, that the middle term is not subordinate to the

science.

is

of if

major, not only both premisses but either singly may be false. [35]

Thus we have made

it

clear

it

is

re-

the case also with regard to negative error; for

error

consequently impossible to come to grasp universals except through induction. But induction is impossible for those who have not sense-perception. For it is sense-perception alone which is adequate for grasping the particulars: they cannot be objects of scientific knowledge, because neither can universals give us knowledge of them without induction, nor can we get it through induction without sense-perception. l

to be a conclusion,

[20] changed, will always be false. This is equally true if (ii) the middle is taken from another series of predication, as was stated to be

all

in

I,

assumed

how many

varieties of erroneous inference are liable to

happen and through what kinds of premisses they occur, in the case both of immediate and

It is clear, then, that these are the fundamentals and so-called hypotheses of syllogism. [75] Assume them as they have been stated, and proof is bound to follow proof that A inheres in C through B, and again that A in-

other.

—

B

through some other middle term, B inheres in C. If our reasoning aims at gaining credence and so is merely dialectical, it is obvious that we have only to see that our inference is based on premheres in

and

similarly that

[20] isses as credible as possible: so that

if

a

middle term between A and B is credible though not real, one can reason through it and complete a dialectical syllogism. If, however, one is aiming at truth, one must be guided by the real connexions of subjects and attributes. Thus: since there are attributes which are predicated of a subject essentially or naturally not, that is, in [25] and not coincidentally the sense in which we say "That white (thing)

—

is

a man',

cation as

of demonstrable truths.

9

[10] Every syllogism is effected by means of three terms. One kind of syllogism serves to prove that A inheres in C by showing that A inheres in B and B in C; the other is negative and one of its premisses asserts one term of another, while the other denies one term of an-

which

not the same

is

when we

say 'The

mode

man

is

of predi-

white': the

man

18 It is

also clear that the loss of

any one of the

senses entails the loss of a corresponding portion of knowledge,

and

that, since

we

learn

either by induction or by demonstration, this

knowledge cannot be acquired. Thus 81 b demonstration develops from universals, induction from particulars; but since it is possi[40]

with even the socalled mathematical abstractions only through induction i.e. only because each subject genus possesses, in virtue of a determinate mathematical character, certain properties which can be treated as separate even though they do not ble to familiarize the pupil

—

1

Cf. 8o b 17-26.

2

Cf. 8ob 26-32.

is white not because he is something else but because he is man, but the white is man because 'being white' coincides with 'humanity' within one substratum therefore there are terms such as are naturally subjects of predi-

—

[30] cates. Suppose, then, C such a term not attributable to anything else as to a subject, but the proximate subject of the attribute itself

B—i.e. ther E

so that

B-C

The first question or can

is

immediate; suppose fur-

related immediately to F,

it

is,

must

and

F

to B.

this series terminate,

proceed to infinity ?

The second

ques-

Suppose nothing is essentially predicated of A, but A is predicated priand of no intermediate prior [^5] marily of term, and suppose similarly related to G and tion

is

as follows:

H

H

POSTERIOR ANALYTICS

112

G to B; then can

it

much

this series also terminate, or

There

is

this

difference between the questions:

the

first is, is it

not

must

too proceed to infinity?

itself

possible to start

from that which

attributable to anything else but

is

is

the

[40] subject of attributes, and ascend to infinThe second is the problem whether one

ity?

can

from that which

start

82 a not

itself a

is

a predicate but

subject of predicates,

and de-

scend to infinity ? A third question is, if the extreme terms are fixed, can there be an infinity of middles? I mean this: suppose for example that A inheres in C and B is intermediate be-

tween them, but between B and A there are [5] other middles, and between these again fresh middles; can these proceed to infinity or can they not? This is the equivalent of inquiring, do demonstrations proceed to infinity, i.e. is everything demonstrable? Or do ultimate subject and primary attribute limit one an-

82 b

[25] termediates

—

call

them BB'B"

.

.

.

—are

then clearly you might descend from A and find one term predicated of another ad infinitum, since you have an infinity of terms between you and F; and equally, if you ascend from F, there are infinite terms between you infinite,

and A.

It follows that if these processes are impossible there cannot be an infinity of inter-

mediates between A and F. Nor is it of any [30] effect to urge that some terms of the series AB F are contiguous so as to exclude intermediates, while others cannot be taken into the argument at all: whichever terms of .

.

B

the series

.

.

.

I

.

take, the

number

of inter-

mediates in the direction either of A or of F must be finite or infinite: where the infinite

whether from the first term or is of no moment, for the suc[35] ceeding terms in any case are infinite in number.

series starts,

from

a later one,

other?

hold that the same questions arise with re[10] gard to negative conclusions and premisses: viz. if A is attributable to no B, then either this predication will be primary, or there will be an intermediate term prior to B to which A is not attributable G, let us say,

21

I

which still

attributable to all

is

be another term

attributable to all G. I

B—and

H prior

The same

to

there

may

G, which

is

questions arise,

because in these cases too either the series which A is not attributable is

say,

of prior terms to infinite or

it

terminates.

[75] One cannot ask the same questions in the case of reciprocating terms, since when subject

and predicate are convertible there

is

neither primary nor ultimate subject, seeing that

all

qua

the reciprocals

subjects stand in

one another, whether we say that the subject has an infinity of attributes or that both subjects and attributes and we raised the question in both cases are infinite in number. These questions then cannot be asked unless, indeed, the terms can reciprocate by two different modes, by accidental [20] predication in one relation and natural the

same

relation to

—

—

—

predication in the other.

20

Now,

it is

clear that

if

the predications termi*

nate in both the upward and the downward direction (by 'upward' I mean the ascent to

more

'downward' the dethe middle terms cannot be infinite in number. For suppose that A is predicated of F, and that the inthe

scent

to

universal, by

the

more

particular),

Further,

if in affirmative demonstration the terminates in both directions, clearly it will terminate too in negative demonstration. Let us assume that we cannot proceed to infin-

series

by ascending from the ultimate term (by 'ultimate term' I mean a term such as F 82 b was, not itself attributable to a subject but itself the subject of attributes), or by descending towards an ultimate from the primary term (by 'primary term' I mean a term predicate of a subject but not itself a subject). If this assumption is justified, the series will also terminate in the case of negation. For a negative conclusion can be proved in all three fig[5] ures. In the first figure it is proved thus: no B is A all C is B. In packing the interval B-C we must reach immediate propositions as is always the case with the minor premiss ity either

y

since B-C is affirmative. As regards the other premiss it is plain that if the major term is denied of a term prior to B, will have to be [10] predicable of all B, and if the major is denied of yet another term prior to D, this term must be predicable of all D. Consequently, since the ascending series is finite, the descent will also terminate and there will be a

D

D

A

which is primarily non-predicable. In the second figure the syllogism is, all A is

subject of

B, no

C

is

B,

.

.

no

C

is

A.

If

proof of this

is

[75] required, plainly it may be shown either in the first figure as above, in the second as here, or in the third. The first figure has been discussed,

and we

will proceed to display the

second, proof by which will be as follows:

all

BOOK

83 b

B B

is

D, no

C

D

is

.

.

.,

since

CHAPTERS

I,

required that

it is

should be a subject of which a predicate is is to be proved not to has a further predicate belong to C, then which is denied of C. Therefore, since the suc[20] cession of predicates affirmed of an ever affirmed. Next, since

D

D

higher universal terminates, the succession of predicates denied terminates too. third figure shows it as follows: all B A, some B is not C, :. some A is not C. This premiss, i.e. C-B, will be proved either in the same figure or in one of the two figures [25] discussed above. In the first and second

The

affirm 'the log

figure,

we

use the third

E

shall take as premisses, all

E is not

some

we

is

B,

is

jects also terminates, plainly the series of

more

universal non-predicables will terminate also.

Even supposing to

now

[50]

ond or

in the first figure,

third

nate, for the if

that the proof

is

not confined

one method, but employs them

finite

—even

now

all

is

in the sec-

so the regress will termi-

methods are

finite in

number, and

things are combined in a finite

of ways, the result

and

must be

number

may

be

made

te]

nates in both these cases

clear

by the following dialectical considera-

tions.

22 In the case of predicates constituting the essential nature of a thing, it clearly terminates, seeing that if definition is possible, or in other

form is knowable, and an cannot be traversed, predicates constituting a thing's essential nature must be 83 a finite in number. But as regards predicates generally we have the following prefatory remarks to make. (1) We can affirm without falsehood 'the white (thing) is walking', and 'that big (thing) is a log'; or again, 'the log is if

essential

infinite series

big',

and

'the

differs in the

man two

walks'. But the affirmation cases.

When

I

affirm 'the

white is a log', I mean that something which happens to be white is a log not that white is the substratum in which log inheres, for it was not qua white or qua a species of white that the white (thing) came to be a log, and the white (thing) is consequently not a log except incidentally. On the other hand, when I [5]

I

if I

said 'the musician 'the

contrary, log

is

man who

musician is white'); on the here the substratum the sub-

to be a

—

stratum which actually came to be white, and did so qua wood or qua a species of wood and qua nothing else. If

we must

lay

down

a rule, let us entitle the

[75] latter kind of statement predication, and the former not predication at all, or not strict

but accidental predication. 'White' and 'log' will thus serve as types respectively of predicate

and

We

subject.

shall

assume, then, that the predicate

is

[20] invariably predicated strictly and not accidentally of the subject, for on such predication demonstrations

depend

follows from this that is

when

for their force.

It

a single attribute

predicated of a single subject, the predicate

must

affirm of the subject either

constituting

some way

its

some element

essential nature, or that

it is

in

qualified, quantified, essentially re-

lated, active, passive, placed, or dated.

(2) Predicates which signify substance sigis identical with the predi-

nify that the subject

finite.

Thus it is plain that the regress of middles terminates in the case of negative demonstration, if it does so also in the case of affirmative demonstration. That in fact the regress termi-

words,

do not mean that which happens also to be a

white',

which would mean

white,'

happens also

C, and this premiss again will be

proved by a similar prosyllogism. But since it is assumed that the series of descending sub-

is

[10] something else, log, is white (as I should

is

figures the series terminates. If

"3

19-22

—

cate or with a species of the predicate. Predi-

[25] cates not signifying substance which are predicated of a subject not identical with themselves or

with a species of themselves are

dental or coincidental; e.g. white

is

acci-

a coinci-

dent of man, seeing that man is not identical with white or a species of white, but rather with animal, since man is identical with a spe[50] cies of animal. These predicates which do not signify substance must be predicates of some other subject, and nothing can be white which is not also other than white. The Forms we can dispense with, for they are mere sound without sense; and even if there are such things, they are not relevant to our discussion, since demonstrations are concerned with predi[35] cates sucn as we nave defined. (3 ) If A is a quality of B, B cannot be a quala quality of a quality. Therefore A ity of A and B cannot be predicated reciprocally of one another in strict predication: they can be affirmed without falsehood of one another, but not genuinely predicated of each other. For one alternative is that they should be substantially predicated of one another, i.e. B would become

—

—

83 b the genus or differentia of A the predicate now become subject. But it has been

shown

that in these substantial predications

neither the ascending predicates nor the de-

POSTERIOR ANALYTICS

II 4

scending subjects form an infinite series; e.g. neither the series, man is biped, biped is animal, &c, nor the series predicating animal of

man, man

of Callias, Callias of a further sub-

an element of its essential nature, is inFor all such substance is definable, finite. [5] and an infinite series cannot be traversed in thought: consequently neither the ascent nor ject as

the descent

infinite, since a

is

predicates were infinite

Hence they

substance whose

would not be this its

would equate a

own

species.

Nor

(the other alternative) can a quale be recipro-

nor any term belonging to an adjectival category of another such term, except by accidental predication; for all such predicates are coincidents and are cally predicated of a quale,

predicated of substances.

On

the other

in proof of the impossibility of

cending

series

subject as

an

hand

infinite as-

—every predication displays the

somehow

as characterized tival categories,

qualified or quantified or

under one of the other adjecor else is an element in its sub-

[75] stantial nature: these latter are limited in number, and the number of the widest kinds under which predications fall is also limited, for every predication

somehow

as

must exhibit

its

subject

qualified, quantified, essentially

related, acting or suffering, or in

some place

some time. assume first that predication implies a single subject and a single attribute, and secondly that predicates which are not substantial are not predicated of one another. We assume this because such predicates are all coincidents, and though some are essential coincidents, others or at I

[20] of a different type, yet we maintain that of them alike are predicated of some sub-

all

stratum and that a coincident is never a substratum since we do not class as a coincident anything which does not owe its designation to its being something other than itself, but always hold that any coincident is predicated of some substratum other than itself, and that another group of coincidents may have a different substratum. Subject to these assumptions [25] then, neither the ascending nor the descending series of predication in which a single

—

attribute finite.

is

predicated of a single subject

is

in-

For the subjects of which coincidents are

predicated are as

many

as the constitutive ele-

which are

84-

finite.

(B) primarily predicable of the first and that the series must end with a [30] term (A) not predicable of any term prior to the last subject of which it was predicated (B), and of which no term prior to it is predicable.

The argument we have given

is one of the an alternative proof follows.

so-called proofs;

Predicates so related to their subjects that there are other predicates prior to them predicable of those subjects are demonstrable; but of demonstrable propositions one cannot have something

than knowledge, nor can one without demonstration. Secondly, a consequent is only known through an better

[35]

know them if

antecedent (viz. premisses prior to it) and we neither know this antecedent nor have something better than knowledge of it, then we shall not

have

scientific

sequent. Therefore,

demonstration to ification

if

knowledge

of the con-

possible through

is

it

know anything without

and not merely

as

qual-

dependent on the

—

acceptance of certain premisses i.e. hypothetically the series of intermediate predications 84a must terminate. If it does not terminate,

—

and beyond any predicate taken as higher than another there remains another still higher, then every predicate is demonstrable. Consequently, since these demonstrable predicates are infinite in number and therefore cannot be traversed, we shall not know them by demonstration. If, therefore, we have not something better than [5] knowledge of them, we cannot through demonstration have unqualified but only hypothetical science of anything. As dialectical proofs of our contention these may carry conviction, but an analytic process will

show more

briefly that neither the ascent

nor the descent of predication can be infinite in [10] the demonstrative sciences which are the object of our investigation. Demonstration proves the inherence of essential attributes in things.

two

Now

attributes

may

be essential for

reasons: either because they are elements

in the essential nature of their subjects, or because their subjects are elements in their essential nature. An example of the latter is odd as

an attribute of number

—though

it is

number's

[75] attribute, yet number itself is an element in the definition of odd; of the former, multiplicity

in the ascending series are contained those con-

in the definition of

—both

a

attribute,

ments of each individual substance, and these seen are not infinite in number, while elements with their coincidents

is

attribute

we have stitutive

We conclude that there

given subject (D) of which some attribute (C) is primarily predicable; that there must be an

definable.

will not be predicated each as the

genus of the other; for [10] genus with one of

of

which are elements number. In neither kind of

or the indivisible,

attribution can the terms be infinite.

They

are

BOOK

84 b

I,

CHAPTERS

is related to the term number, for this would mean the inherence in odd of another attribute of odd in whose nature odd was an essential [20] element: but then number will be an ultimate subject of the whole infinite chain of attributes, and be an element in the definition of each of them. Hence, since an infinity of at-

not infinite where each

"5

22-23

from one another. But

differ

this

is

not always

we take B as

definition cannot inhere in a single thing, the

the commiddle in virtue of which A inheres in C [10] and D, clearly B would inhere in C and D through a second common middle, and this through a in turn would inhere in C and third, so that between two terms an infinity of intermediates would fall an impossibility. Thus it need not always be in virtue of a common middle term that a single attribute in-

Note, more-

heres in several subjects, since there must be

below

it

as

odd

to

is

tributes such as contain their subject in their

ascending

series is equally finite.

over, that all such attributes

the ultimate subject

number

ber and

—

in

must

so inhere in

numbe commen-

e.g. its attributes in

them

—

as to

surate with the subject and not of wider extent.

[25] Attributes which are essential elements in the nature of their subjects are equally finite: otherwise definition would be impossible.

Hence, if all the attributes predicated are essential and these cannot be infinite, the ascending series will terminate, and consequently the descending series too. If this is so,

it

follows that the intermediates

the case: for, were

so, if

it

mon

D

—

[75] immediate intervals. Yet

common

proved

to be

to

two

if

the attribute

subjects

to be

is

one of their essential attributes, the middle terms involved must be within one subject genus and be derived from the same group of immediate premisses; for we have seen that processes of proof cannot pass from one genus to another. It is

1

also clear that

when A

inheres in B, this

[20] can be demonstrated if there is a middle term. Further, the 'elements' of such a conclusion are the premisses containing the mid-

and they are

num-

between any two terms are also always limited in number. An immediately obvious con-

dle in question,

[30] sequence of this is that demonstrations necessarily involve basic truths, and that the contention of some referred, to at the outset

immediate propositions or at least such immediate propositions as are universal are the 'elements'. If, on the other hand, there is no middle term, demonstration ceases to be pos-

—

truths are demonstrable is mistaken. there are basic truths, (a) not all truths are demonstrable, and (b) an infinite regress is impossible; since if either (a) or (b) were not that

all

For

if

would mean that no interval was im[35] mediate and indivisible, but that all in-

a fact,

it

identical in

ber with the middle terms, seeing that the

—

sible:

we

Similarly

on the way

are if

—

A

to the basic truths.

does not inhere in B, this can

be demonstrated

if there is a middle term or a [25] term prior to B in which A does not inhere: otherwise there is no demonstration and

were divisible. This is true because a conclusion is demonstrated by the interposition, not the apposition, of a fresh term. If such interposition could continue to infinity there might be an infinite number of terms between any two terms; but this is impossible if both

a basic truth

84 b

monstrable basic truths asserting that

tervals

the ascending and descending series of

predication terminate; and of this fact, which shown dialectically, analytic proof

before was

has

now

been given.

as

many

clusion as there are middle terms, since

onstration rests; and as there are

an evident corollary of these conclusions

that

if

same attribute A inheres in two and D predicable either not at all, or

the

terms C [5] not of all instances, of one another, it does not always belong to them in virtue of a comIsosceles

and scalene possess

the attribute of having their angles equal to

two

right angles in virtue of a

for they possess

it

common middle;

in so far as they are both a

certain kind of figure,

and not

in so far as they

is

some

inde-

'this is

that' or that 'this inheres in that', so there are

[30] others denying that 'this is that' or that inheres in that' in fact some basic truths

—

and some

When we are

It is

it

middle terms

on which the dem-

that are the basic premisses

'this

23

middle term.

reached. There are, moreover,

propositions containing these

will affirm

mon

is

'elements' of the demonstrated con-

will

deny being.

prove a conclusion, we must take a primary essential predicate suppose it C of the subject /3, and then suppose A similarly predicable of C. If we proceed in this

—

to

—

manner, no proposition or attribute which falls beyond A is admitted in the proof: the interval is constantly condensed until subject and predi[35] cate become indivisible, i.e. one. We have our unit when the premiss becomes immediate, since the immediate premiss alone is a single * 1.

7.

POSTERIOR ANALYTICS

n6

premiss in the unqualified sense of 'single'. And as in other spheres the basic element is simple but not identical in all in a system of weight it is the mina, in music the quarterso in syllogism the unit is an tone, and so on 85° immediate premiss, and in the knowledge that demonstration gives it is an intuition. In syllogisms, then, which prove the inherence of

—

—

an

attribute,

nothing

outside the major

falls

term. In the case of negative syllogisms on the other hand, (i) in the first figure nothing falls outside the major term whose inherence is in

85 b

whereas particular demonstration proves that the subject

itself is x.

The

demonstration, then,

that a subject, as such, possesses an attribute

is

and if the particular rather than the commensurately universal form so superior. If this

is so,

[jo] demonstrates, particular demonstration

is

superior.

(2) The universal has not a separate being over against groups of singulars. Demonstration nevertheless creates the opinion that

its

question; e.g. to prove through a middle C that A does not inhere in B the premisses re-

conditioned by something like this some separate entity belonging to the real world; that, for instance, of triangle or of figure or number, over against particular trian-

[5] quired are, all B is C, no C is A. Then if it has to be proved that no C is A, a middle must

[35] gl es > figures, and numbers. But demonstration which touches the real and will not

be found between will never vary. (2) If

means all

E,

A and C;

this

procedure

D

E is not by C; no E, or not C; then the middle will never fall bewe have

yond E, and

E

is

to

show all

that

D

is

the subject of

which

D

is

to

be denied in the conclusion. [10] (3) In the third figure the middle will

never

fall

beyond the

limits of the subject

the attribute denied of

and

it.

24 Since demonstrations universal

surately

may

be either

commen-

or particular, and

affirmative or negative;

either

the question arises,

[75] which form is the better? And the same question may be put in regard to so-called 'direct' demonstration and reductio ad impossible. Let us first examine the commensurately

and the particular forms, and when up this problem proceed to 'direct' demonstration and reductio ad

universal

we have discuss

cleared

impossibile.

The

we have

greater

mislead

is

superior to that which

and

is

knowledge of

a particular in-

moves among commensu-

Now

delusory.

rately universal demonstration

is of the latter kind: if we engage in it we find ourselves reasoning after a fashion well illustrated by the argument that the proportionate is what an-

swers to the definition of some entity which is neither line, number, solid, nor plane, but a 85 b proportionate apart from all these. Since, then, such a proof is characteristically commensurate and universal, and less touches reality than does particular demonstration, and creates a false opinion, it will follow that com-

mensurate and universal lar

is

inferior to particu-

demonstration.

We may retort thus. applies sal

no more

to

( 1 ) The first argument commensurate and univer-

than to particular demonstration.

If

equal-

ly] ity to two right angles is attributable to its subject not qua isosceles but qua triangle, he

who knows that isosceles possesses that attribute knows

the subject as

qua

attribute, to a less degree

following considerations might lead some minds to prefer particular demonstration. ( 1 ) The superior demonstration is the demonstration which gives us greater knowledge (for this is the ideal of demonstration), and [20]

—

is

unrealities

of the premisses,

is

and

function

itself

possessing the

who knows To sum up the

than he

that triangle has that attribute.

whole matter: if a subject is proved to possess qua triangle an attribute which it does not in fact possess qua triangle, that is not demonstration: but if it does possess it qua triangle, the rule applies that the greater knowledge is

when we know it in itself than when we know it through something else; e.g. we know Coriscus the musician better when we [25] know that Coriscus is musical than when we know only that man is musical, and a like argument holds in all other cases. But commen-

does possess it. Since, then, triangle is the wider [10] term, and there is one identical definition of triangle i.e. the term is not equivocal and since equality to two right angles be-

surately universal demonstration, instead of proving that the subject itself actually is x, proves only that something else is x e.g. in attempting to prove that isosceles is x, it proves not that isosceles but only that triangle is x

longs to all triangles, it is isosceles qua triangle and not triangle qua isosceles which has its angles so related. It follows that he who knows a connexion universally has greater knowledge of it as it in fact is than he who knows the

dividual

—

—

his

who knows

tribute

—

qua

the subject as possessing

that in virtue of

which

it

its at-

actually

—

BOOK

86 a

I,

CHAPTERS

and the inference is that commenand universal is superior to particular

23-24

117

particular;

isosceles, there still

surate

86 a has

demonstration. If

[75] (2)

—

the

if

i.e.

equivocal ing not

there

is

a single identical definition

commensurate universal

—then the universal

less

is

un-

will possess be-

but more than some of the particu-

remains the question 'Why and its answer

isosceles this attribute?'

'Because it is a triangle, and a triangle has it because a triangle is a rectilinear figure.' If rectilinear figure possesses the property for no further reason, at this point we have full knowledge but at this point our knowledge

—

prise the imperishable, particulars that tend to

has become commensurately universal, and so we conclude that commensurately universal

perish.

demonstration

(3) Because the universal has a single meaning, we are not therefore compelled to suppose

(6)

lars,

inasmuch

as

is

it

universals

that in these examples

stance apart

than

from

we need make

it

has being as a sub-

particulars

its

which com-

—any

more

a similar supposition in

the other cases of unequivocal universal predication, viz.

where the predicate

signifies not

substance but quality, essential related-

[20]

ness, or action. If

tained, the

blame

such a supposition is enternot with the demonstra-

rests

is

superior.

The more demonstration becomes more

lar the

particu-

sinks into an indeterminate

it

manifold, while universal demonstration tends [5] to the simple and determinate. But objects so far as they are an indeterminate manifold are unintelligible, so far as they are determinate, intelligible: they are therefore intelligible rather in so far as they are universal than in so far as they are particular. From this it follows that universals are

more demonstrable: but

the

and correlative increase concomitantly, of the more demonstrable there will be fuller demonstration. Hence the commensurate and universal form, being more truly demon-

lar

[10] stration,

tion but with the hearer.

since relative

(4) Demonstration is syllogism that proves the cause, i.e. the reasoned fact, and it is rather

commensurate universal than the particuwhich is causative (as may be shown thus: that which possesses an attribute through its

[25] own essential nature is itself the cause of the inherence, and the commensurate univer-

primary; hence the commensurate universal is the cause). Consequently commensurately universal demonstration is superior as more especially proving the cause, that is the reasoned fact. (5) Our search for the reason ceases, and we think that we know, when the coming to be or existence of the fact before us is not due to the coming to be or existence of some other fact, for the last step of a search thus conducted is [30] eo ipso the end and limit of the problem. Thus: 'Why did he come?' 'To get the money wherewith to pay a debt that he might thereby do what was right.' When in this regress we can no longer find an efficient or final cause, we regard the last step of it as the end of and the coming or being or coming to be we regard ourselves as then only having full knowledge of the reason why he came. sal is

—

—

—

—

[35]

If>

then,

all

in this respect,

knowledge

we have

causes and reasons are alike

and

if

this

is

the

means

to full

in the case of final causes such as

exemplified,

it

follows that in the case

knowledge is atno longer inheres beThus, when we learn

of the other causes also full

tained

when an

attribute

cause of something

else.

that exterior angles are equal to four right angles because they are the exterior angles of

an

(7) things

is

the superior.

Demonstration is

which

two which commensu-

teaches

preferable to demonstration

teaches only one.

He who possesses

demonstration knows the particular as well, but he who possesses particular demonstration does not know the universal. So that this is an additional reason for preferring commensurately universal demonstration. And there is yet this further argument: (8) Proof becomes more and more proof of the commensurate universal as its middle term approaches nearer to the basic truth, and noth[75] ing is so near as the immediate premiss which is itself the basic truth. If, then, proof from the basic truth is more accurate than proof not so derived, demonstration which depends more closely on it is more accurate than demonstration which is less closely dependent. But commensurately universal demonstration is characterized by this closer dependence, and is therefore superior. Thus, if A had to be proved to inhere in D, and the middles were B and C, B being the higher term would ren[20] der the demonstration which it mediated rately universal

the

more

Some lectical.

universal.

of these arguments, however, are dia-

The

clearest indication of the preced-

ence of commensurately universal demonstration is as follows: if of two propositions, a prior and a posterior, we have a grasp of the prior, we have a kind of knowledge a poten-

—

POSTERIOR ANALYTICS

n8

—

For examone knows that the angles of all triangles are equal to two right angles, one grasp

tial

[25]

of the posterior as well.

pie, if

—

—

knows

that the isospotentially in a sense angles also are equal to two right angles, even if one does not know that the isosceles is a triangle; but to grasp this posterior proposiceles'

tion

is

by no means to

know

the

rate universal either potentially

commensuor actually.

Moreover, commensurately universal demonstration is through and through intelligible; [jo] particular demonstration issues in senseperception. 25

The preceding arguments

constitute our de-

fence of the superiority of commensurately universal to particular demonstration.

That affirm-

demonstration excels negative

ative

shown

may

be

as follows.

We

lowing additional

rule: as the demonstration expands, the affirmative premisses must increase in number, but there cannot be more [75] than one negative premiss in each complete proof. Thus, suppose no B is A, and all C is B. Then if both the premisses are to be again expanded, a middle must be interposed. Let us interpose between A and B, and E between B and C. Then clearly E is affirmatively reis affirmatively [20] lated to B and C, while related to B but negatively to A; for all B is D, but there must be no which is A. Thus there proves to be a single negative premiss, A-D. In the further prosyllogisms too it is the same, because in the terms of an affirmative syllogism the middle is always related affirmatively to both extremes; in a negative syllogism it [25] must be negatively related only to one of them, and so this negation comes to be a single negative premiss, the other premisses being

D

D

D

may assume the superiority ceteris (1) paribus of the demonstration which derives from fewer postulates or hypotheses in short [55] from fewer premisses; for, given that all these are equally well known, where they are fewer knowledge will be more speedily acquired, and that is a desideratum. The argu-

affirmative.

ment implied in our contention that demonstration from fewer assumptions is superior may be set out in universal form as follows. Assuming that in both cases alike the middle terms are known, and that middles which are

logism

known than such as are postesuppose two demonstrations of the inherence of A in E> the one proving it 86 b through the middles B, C and D, the other through F and G. Then A-D is known to the same degree as A-E (in the second proof), but A-D is better known than and

plains denial

—

prior are better rior,

we may

prior to

A-E

(in the

first

proof); since

A-E

proved through A-D, and the ground is more certain than the conclusion. [5] Hence demonstration by fewer premisses is ceteris paribus superior. Now both affirmative and negative demonstration operate through three terms and two premisses, but whereas the former assumes only that something is, the latter assumes both that something is and that something else is not, and thus operating through more kinds of premiss is inis

ferior. 1 [10] (2) It has been proved that no conclusion follows if both premisses are negative, but that one must be negative, the other affirma-

tive. 1

So we are compelled

Prior Analytics,

1.

7.

to lay

down

the fol-

87*

is

proved

then, that through

If,

is

a better

which

known and more

a truth certain

and if the negative proposition is proved through the affirmative and not vice versa, affirmative demonstration, being prior and bettruth,

ter

known and more certain, will be superior. The basic truth of demonstrative syl-

[30] (3)

is

the universal immediate premiss,

the universal premiss

asserts

in

and

affirmative

demonstration and in negative denies: and the affirmative proposition

known than

prior to

is

and

better

the negative (since affirmation ex-

and

is

prior to denial, just as be-

m

[35] S 1S prior to not-being). It follows that the basic premiss of affirmative demonstration is

superior to that of negative demonstration,

and the demonstration which uses superior basic premisses

is

superior.

(4) Affirmative demonstration is more of the nature of a basic form of proof, because it is a sine

qua non

of negative demonstration.

26

87* Since affirmative demonstration to negative,

it is

is

superior

clearly superior also to reduc-

ad impossibile. We must first make certain what is the difference between negative demonstration and reductio ad impossibile. Let us suppose that no B is A, and that all C is B: the conclusion necessarily follows that no C is A. tio

[5] If these premisses are assumed, therefore, is the negative demonstration that no C is

A

Reductio ad impossibile, on the other hand, proceeds as follows. Supposing we are to prove that A does not inhere in B, we have

direct.

to

assume that

it

does inhere, and further that

BOOK

87 b

B

CHAPTERS

I,

24-30

119

inheres in C, with the resulting inference

that

A

inheres in C. This

known and admitted

we have

to

and we

impossibility;

A

cannot inhere in B. [10] then infer that Thus if the inherence of B in C is not ques-

B

tioned, A's inherence in

The

is

28

suppose a

impossible.

A

single science

gle genus, viz.

parts of this total subject properties.

When

87 b

is

the

One

proofs: they differ according to

the falsity of the conclusion

is

the better

[75]

known, we use reductio ad impossible;

when

the major premiss of the syllogism

the

is

more obvious, we use direct demonstration. All the same the proposition denying A of B is, in the order of being, prior to that denying A of C; for premisses are prior to the conclusion which follows from them, and 'no C is A' is the conclusion, 'no B is A' one of its premisses. [20] For the destructive result of reductio ad impossibile is not a proper conclusion, nor are its antecedents proper premisses. On the contrary: the constituents of syllogism are premisses related to one another as whole to part or part to whole, whereas the premisses A-C and [25] A-B are not thus related to one another. Now the superior demonstration is that which proceeds from better known and prior premisses, and while both these forms depend for credence on the not-being of something, yet the source of the one is prior to that of the other. Therefore negative demonstration will have an unqualified superiority to reductio ad impossibile, and affirmative demonstration, being superior to negative, will consequently [jo] be superior also to reductio ad impossibile.

The fact

science

knowledge fact,

once of the not of the fact by at

fact, is

the

more

—

the

i.e.

their essential

from another when

science differs

their

source nor

are derived those of the one science

from those

of the other. This

is

verified

when we

reach the indemonstrable premisses of a science, for they must be within one genus with

and

conclusions:

its

this

conclusions proved by

one genus

in

—

i.e.

are

again

is

verified

means of them homogeneous.

the with-

if

fall

29 [5] the

One

can have several demonstrations of

same connexion not only by taking from the same series of predication middles which are other than the immediately cohering term

—

by taking C, D, and F severally to prove also by taking a middle from another series. Thus let A be change, alterae.g.

A-B—but

D

tion of a property,

We

relaxation.

D

B

feeling pleasure,

and

G

can then without falsehood of B and A of D, for he who

[10] predicate pleased suffers alteration of a property, and

is

that

which

we can and

changes. Again, without falsehood,

alters a property

predicate

G of B; for

A

of

G

to feel pleasure

is

to relax,

and

change. So the conclusion can be drawn through middles which are different, i.e. not in the same series yet not so that neither of these middles is predicable of the [75] other, for they must both be attributable to relax

is

to

—

some one

subject.

further point worth investigating

many ways

of proving the

is

how

same conclusion can

be obtained by varying the figure.

ex-

30

science.

science such as arithmetic,

a sin-

common

A

without the reasoned

and the prior

A

is

and of the reasoned

itself

act

which

—and

basic truths have neither a

to

27

is

the subjects constituted out

of the primary entities of the genus

same in both which of the negative propositions is the better known, the one denying A of B or the one denying A of C. order of the terms

one whose domain

is

all

which

is

not a

There

is

no knowledge by demonstration

of

qua inhering in a substratum, is more exact than and prior to a science like harmonics, which is a science of properties inhering in a substratum; and similarly a science like arithmetic, which is constituted of fewer basic elements, is more exact than and prior to geometry, which requires

chance conjunctions; for chance conjunctions exist neither by necessity nor as general con[20] nexions but comprise what comes to be as something distinct from these. Now demonstration is concerned only with one or other of these two; for all reasoning proceeds from nec-

[35] additional elements. What I mean by 'additional elements' is this: a unit is substance with position; the latter contains an ad-

ing necessary if the premisses are necessary and 2 general if the premisses are general. Con[ 5] sequently, if chance conjunctions are neither general nor necessary, they are not demon-

ditional element.

strable.

science of properties

stance without position, while a point

is

sub-

essary or general premisses, the conclusion be-

POSTERIOR ANALYTICS

120 3i

knowledge

Scientific

is

not possible through

Even if perception as a faculty is of 'the such' and not merely of a 'this somewhat', yet one must at any rate actually perceive a 'this somewhat', and at a defi[30] nite present place and time: but that which is commensurately universal and true the act of perception.

in all cases

one cannot perceive, since

it is

not

and it is not 'now'; if it were, it would the term not be commensurately universal we apply to what is always and everywhere. 'this'

—

Seeing,

that

therefore,

demonstrations

are

commensurately universal and universals imperceptible,

we

clearly cannot obtain scientific

knowledge by the act of perception: nay, obvious that even if it were possible to perceive that a triangle has its angles equal to two right angles, we should still be looking for a demonstration we should not (as some say) possess knowledge of it; for perception must be of a particular, whereas scientific knowledge involves the recognition of the [^5] is

it

—

88 b

[75] saw the pores in the glass and the light passing through, the reason of the kindling would be clear to us because we should at the same time see it in each instance and intuit that it must be so in all instances.

32 All syllogisms cannot

may

This

truths.

[20] a true inference is possible premisses, yet this occurs once only

A, for instance,

is

is

Then again, (2) falsehoods are derived from a single identical set of principles: there are falsehoods which are the not

all

and cannot coexist, and 'justice is cowand 'man is ox'; 'the

contraries of one another

'man

greater',

we

if

truly predicable of C, but B,

differ in kind.

ardice';

commensurate universal. I do not, of course, deny that by watching the frequent recur-

false

mean

false,

equal

but not the reasoned fact at is not of the

I

nevertheless,

[40] light, we should not know the cause of 88 a the eclipse: we should perceive the present since the act of perception

from

—

both A-B and B-C being if middles are taken to prove these premisses, they will be false be[25] cause every conclusion which is a falsehood has false premisses, while true conclusions have true premisses, and false and true the middle,

false;

e.g.

fact of the eclipse,

have the same basic first of all by the

shown

following dialectical considerations. (1) Some syllogisms are true and some false: for though

commensurate universal. So if we were on the moon, and saw the earth shutting out the sun's

all,

be

'justice is injustice',

is

horse',

is

and

'the

equal

is less.'

From

[30] our established principles we may argue the case as follows, confining ourselves therefore to true conclusions.

inferred

them

from the same

in fact

Not even

all

basic truths;

these are

many

have basic truths which

of

differ

onstration, for the

and are not transferable; units, for which are without position, cannot take the place of points, which have position.

elicited

The

rence of this event the

commensurate

might, after tracking

universal, possess a

dem-

commensurate universal is from the several groups of singulars. [5] The commensurate universal is precious because it makes clear the cause; so that in the case of facts like these which have a cause other than themselves universal knowledge is more precious than sense-perceptions and than intuition. (As regards primary truths there is of course a different account to be given. ) Hence it is clear that knowledge of things demon1

strable

cannot be acquired by perception, un-

[10] less the term perception is applied to the possession of scientific knowledge through

demonstration. Nevertheless certain points do arise with regard to connexions to be proved which are referred for their explanation to a failure

in

when an

sense-perception:

act of vision

there

are

cases

would terminate our

we

in-

should be knowing, but because we should have elicited the universal from seeing; if, for example, we quiry, not because in seeing

l

C£., e.g., ioo b 12.

generically instance,

transferred terms could only

fit

in as

mid-

[55] die terms or as major or minor terms, or else have some of the other terms between

them, others outside them. Nor can any of the common axioms such, serve I mean, as the law of excluded middle as premisses for the proof of all conclusions. 8S h For the kinds of being are different, and some attributes attach to quanta and some to qualia only and proof is achieved by means of the common axioms taken in conjunction with these several kinds and their attributes. Again, it is not true that the basic truths are [5] much fewer than the conclusions, for the basic truths are the premisses, and the premisses are formed by the apposition of a fresh extreme term or the interposition of a fresh middle. Moreover, the number of conclusions is indefinite, though the number of middle

— —

;

terms

is

finite;

and

lastly

some

of the basic

truths are necessary, others variable.

BOOK

89*

Looking the

at

number

in this

it

way we

of conclusions

I,

CHAPTERS

see that, since indefinite, the

is

31-33

121

monstrable knowledge, which is the grasping of 89a the immediate premiss. Since then ration-

and opinion, and what

basic truths cannot be identical or limited in

al intuition, science,

on the other hand, identity is used in another sense, and it is said, e.g. 'these and no other are the fundamental truths of geometry, these the fundamentals of calculation, these again of medicine'; would the statement

revealed by these terms, are the only things that can be 'true', it follows that it is opinion

[io] number.

If,

mean anything

except that the sciences have

To

basic truths?

call

them

identical because

they are self-identical is absurd, since everything can be identified with everything in that [75] sense of identity. Nor again can the contention that truths

all

mean

conclusions have the same basic

that

from the mass

of

all

possible

premisses any conclusion may be drawn. That would be exceedingly naive, for it is not the case in the clearly evident mathematical ences, nor

is

it

possible in analysis, since

sciit is

the immediate premisses which are the basic truths, and a fresh conclusion is only formed [20] by the addition of a

new immediate prem-

be admitted that it is these primary immediate premisses which are basic truths, each subject-genus will provide one basic truth. If, however, it is not argued that from the mass of all possible premisses any conclusion may iss:

but

if it

be proved, nor yet admitted that basic truths differ so as to be generically different for each science, it remains to consider the possibility that, while the basic truths of all knowledge are within one genus, special premisses are re[25] quired to prove special conclusions. But that this cannot be the case has been shown by our proof that the basic truths of things generically different themselves differ generically.

For fundamental truths are of two kinds, those which are premisses of demonstration and the subject-genus; and though the former are common, the latter number, for instance, and magnitude are peculiar.

—

—

33

knowledge and its object differ from opinion and the object of opinion in that scientific knowledge is commensurately universal and proceeds by necessary connexions, and that which is necessary cannot be otherwise. So though there are things which are true and real and yet can be otherwise, scientific knowledge clearly does not concern them: if it did, things which can be otherwise [35] would be incapable of being otherwise. Nor are they any concern of rational intuition by rational intuition I mean an originative source of scientific knowledge nor of inde[30] Scientific

—

—

is

concerned with that which may be and can be otherwise: opinion in fact is the grasp of a premiss which is immediate but not necessary. This view also fits the [5] observed facts, for opinion is unstable, and so is the kind of being we have described as its

that

is

true or false,

when a man thinks a truth incapable of being otherwise he always thinks

object. Besides,

that he

knows

it,

never that he opines

it.

He

thinks that he opines when he thinks that a connexion, though actually so, may quite easily

be otherwise; for he believes that such is the [10] proper object of opinion, while the necessary is the object of knowledge. In what sense, then, can the same thing be the object of both opinion and knowledge?

And

any one chooses to maintain that all knows he can also opine, why should not opinion be knowledge? For he that knows and he that opines will follow the same train of thought through the same middle terms until the immediate premisses are reached; if

that he

[75] because it is possible to opine not only the fact but also the reasoned fact, and the is the middle term; so that, since the former knows, he that opines also has knowl-

reason edge.

The

truth perhaps

is

that

if

a

man

grasp

truths that cannot be other than they are, in

way in which he grasps the definitions through which demonstrations take place, he will have not opinion but knowledge: if on the other hand he apprehends these attributes as

the

inhering in their subjects, but not in virtue of the subjects' substance and essential nature, he [20] possesses opinion and not genuine knowledge; and his opinion, if obtained through immediate premisses, will be both of the fact and of the reasoned fact; if not so obtained, of the fact alone. The object of opinion and knowledge is not quite identical; it is only in a sense identical, just as the object of true

[25] opinion

is

in a sense identical.

and

false

The

sense

which some maintain that true and false opinion can have the same object leads them in

to

embrace many strange doctrines,

particular-

what a man opines falsely he does not opine at all. There are really many senses of 'identical', and in one sense the object of true and false opinion can be the same, ly the

doctrine that

in another

it

cannot. Thus, to have a true opin-

POSTERIOR ANALYTICS

122 ion that the diagonal

is

commensurate with

would be absurd: but because the diagonal with which they are both concerned is the same, the two opinions have objects so [?o] the side

far the

same: on the other hand, as regards

their essential definable nature these objects differ. The identity of the objects of knowledge and opinion is similar. Knowledge is the apprehension of, e.g. the attribute 'animal' as incapable of being otherwise, opinion the apprehension of 'animal' as capable of being [35] otherwise e.g. the apprehension that animal is an element in the essential nature of man is knowledge; the apprehension of animal as predicable of man but not as an element in man's essential nature is opinion: man is the subject in both judgements, but the mode of in-

—

man

[5]

may

90*

not essentially animal, that assume, may be other than animal. is

is,

we

Further consideration of modes of thinking their distribution under the heads of discursive thought, intuition, science, art, practical wisdom, and metaphysical thinking, be-

and

longs rather partly to natural science, partly to moral philosophy.

34 [10]

Quick wit

is

a faculty of hitting

upon the

This also shows that one cannot opine and know the same thing simultaneously; for then one would apprehend the same thing as both capable and incapable of being otherwise an

middle term instantaneously. It would be exemplified by a man who saw that the moon has her bright side always turned towards the sun, and quickly grasped the cause of this, namely that she borrows her light from him; or observed somebody in conversation with a man of wealth and divined that he was borrowing money, or that the friendship of these people sprang from a common enmity. In all these instances he has seen the major and minor terms [75] and then grasped the causes, the middle

89 b

Knowledge and opinion of same thing can co-exist in two different

terms.

people in the sense we have explained, but not simultaneously in the same person. That would involve a man's simultaneously apprehending,

ward',

herence

differs.

—

the

e.g.

impossibility.

(1) that

man

is

essentially

cannot be other than animal

animal

—and

—

i.e.

(2) that

A

Let

B

from the sun', C the moon. B, 'lighted from the sun', is predicable of C, the moon, and A, 'having her bright side

Then

towards the source of her light', is predicable [20] of B. So A is predicable of C through B.

BOOK

II

are the

two questions we ask; but

jects of

The

kinds of question

we

ask are as

many

as

which we know. They are ( 1 ) whether the connexion of an in fact four: attribute with a thing is a fact, (2) what is the reason of the connexion, (3) whether a thing [25] exists, (4) what is the nature of the thing. Thus, when our question concerns a complex of thing and attribute and we ask whether the the kinds of things

—

— —

thus or otherwise qualified whether, sun suffers eclipse or not then we are asking as to the fact of a connexion. That our inquiry ceases with the discovery that the

thing

is

e.g. the

sun does suffer eclipse

is

an indication of

this;

we know from the start that the sun suffers eclipse, we do not inquire whether it does so or not. On the other hand, when we know the fact we ask the reason; as, for example, when we know that the sun is being eclipsed

and

[jo]

if

and that an earthquake

is

in progress,

the reason of eclipse or earthquake into

we inquire. Where a complex

is

it is

which

concerned, then, those

represent 'bright side turned sun'lighted

inquiry

we have

for

some

ob-

a different kind of

question to ask, such as whether there is or not a centaur or a God. (By 'is or is not'

mean

'is

tion'; as

On

or

is

not,

opposed to

is I

without further qualifica'is

or

is

not (e.g.) white'.)

when we have ascertained existence, we inquire as to its na-

the other hand,

the thing's

ture, asking, for instance, 'what, then,

[35] or 'what

is

is

God?'

man?'.

These, then, are the four kinds of question we ask, and it is in the answers to these questions that our knowledge consists. Now when we ask whether a connexion is a fact, or whether a thing without qualification is, we are really asking whether the connexion or the thing has a 'middle'; and when we have ascertained either that the connexion i.e. ascertained is a fact or that the thing is either the partial or the unqualified being of 90 a the thing and are proceeding to ask the reason of the connexion or the nature of the

—

—

BOOK

90b

we

thing, then

CHAPTERS 33-34— BOOK

I,

are asking

what the 'middle'

is.

(By distinguishing the fact of the connexion and the existence of the thing as respectively the partial and the unqualified being of the ask 'does the moon moon wax?', the question concerns a part of the thing's being; for what we are asking in such questions is whether a thing is this or that, i.e. has or has not this or that attribute: whereas, if we ask whether the moon or night exists, the question concerns the unqualified being of a thing.) conclude that in all our inquiries we [5] are asking either whether there is a 'middle' or what the 'middle' is: for the 'middle' here is precisely the cause, and it is the cause that we seek in all our inquiries. Thus, 'Does the moon suffer eclipse?' means 'Is there or is there not a thing,

I

mean

that

if

we

suffer eclipse?', or 'does the

We

if

CHAPTERS

II,

we were on

the

1-3

moon we

123

should not be

in-

quiring either as to the fact or the reason, but both fact and reason would be obvious simultaneously. For the act of perception would have enabled us to know the universal too; since, the present fact of an eclipse being evident, perception would then at the same time give us the present fact of the earth's screening the [50] sun's light, universal.

Thus, ture is

is

and from

this

would

arise the

we maintain, to know a thing's naknow the reason why it is; and this

as

to

equally true of things in so far as they are

opposed to being possessed of some attribute, and in so far as they are said to be possessed of some attribute such as equal to two right angles, or said without qualification to be as

greater or

less.

cause producing eclipse of the moon?', and when we have learnt that there is, our next question

'What, then,

is,

is

this cause?'; for the

—

cause through which a thing is not is this [10] or that, i.e. has this or that attribute,

—

but without qualification is and the cause through which it is not is without qualification, but is this or that as having some essential attribute or some accident are both alike the 'middle'. By that which is without qualifica-

—

—

tion

mean

I

the subject, e.g.

moon

or earth or

sun or triangle; by that which a subject

[35] ^ is clear, then, that all questions are a search for a 'middle'. Let us now state how essential nature is revealed, and in what way it can be reduced to demonstration; what defini-

tion

is,

and what things are

definable.

And

let

which these 90 b questions raise, beginning what we have to say with a point most intimately connected us

first

with

discuss certain difficulties

our

immediately

preceding

remarks,

vation of the moon's light by the interposition

namely the doubt that might be felt as to whether or not it is possible to know the same thing in the same relation, both by definition and by demonstration. It might, I mean, be urged that definition is held to concern essential nature and is in every case universal and affirmative; whereas, on the other hand, some [5] conclusions are negative and some are not

of the earth' are identical with the question

universal; e.g.

the

sense)

partial

I

mean

a

is

(in

property, e.g.

eclipse, equality or inequality, interposition or

non-interposition. is

For

in all these

examples

clear that the nature of the thing

it

and the

[75] reason of the fact are identical: the question 'What is eclipse?' and its answer 'The pri-

'What

is

the reason of eclipse?' or

moon

'Why

does

tive,

none

in

again, not even

note concordant?'

sions as these

ratio it

is

suffer eclipse?'

is

equivalent to

'Is

their

commensurate?'; and when we find that commensurate, we ask 'What, then, is

the

first

has

its

And

the third are universal.

and the reply 'Because of the failure of light through the earth's shutting it out'. Again, for 'What is a concord? A commensurate numerical ratio of a high and a low note', we may substitute 'What reason [20] makes a high and a low note concordant? Their relation according to a commensurate numerical ratio.' 'Are the high and the low the

in the second figure are nega-

all

all

affirmative conclusions in

figure are definable, e.g. 'every triangle

An

angles equal to two right angles'.

argument proving this difference between demonstration and definition is that to have scientific knowledge of the demonstrable is [10] identical with possessing a demonstration it: hence if demonstration of such conclu-

of

is

possible, there clearly cannot

also be definition of them. If there could,

might know such

definition without possessing the

their ratio?'.

its

Cases in which the 'middle' is sensible show [25] that the object of our inquiry is always the 'middle': we inquire, because we have not perceived it, whether there is or is not a 'middle' causing, e.g. an eclipse. On the other hand,

stration of

it;

one

a conclusion also in virtue of

for there

is

demon-

nothing to stop our

having the one without the other. Induction too will sufficiently convince us of [75] this difference; for never yet by defining anything essential attribute or accident did

—

—

POSTERIOR ANALYTICS

I2 4

we

get

knowledge of it. Again, if to define is knowledge of a substance, at any

to acquire

rate such attributes are not substances. It is evident, then, that not everything demonstrable can be defined. What then? Can everything definable be demonstrated, or not? There is one of our previous arguments which [20] covers this too. Of a single thing qua single there is a single scientific knowledge. Hence, since to know the demonstrable scientifically is to possess the demonstration of it, posan impossible consequence will follow: session of its definition without its demonstration will give knowledge of the demonstrable. Moreover, the basic premisses of demonstrations are definitions, and it has already been shown 1 that these will be found indemonstra[25] ble; either the basic premisses will be demonstrable and will depend on prior premisses, and the regress will be endless; or the primary truths will be indemonstrable definitions. But if the definable and the demonstrable are not wholly the same, may they yet be partially the same? Or is that impossible, because there can be no demonstration of the defin[30] able? There can be none, because definition is of the essential nature or being of something, and all demonstrations evidently posit and assume the essential nature mathematical demonstrations, for example, the nature of unity and the odd, and all the other sciences likewise. Moreover, every demonstration proves a predicate of a subject as attaching or as not attaching to it, but in definition one thing is [35] not predicated of another; we do not, e.g. predicate animal of biped nor biped of animal, nor yet figure of plane plane not being figure nor figure plane. Again, to prove essential nature is not the same as to prove the fact of a 91 a connexion. Now definition reveals essential nature, demonstration reveals that a given attribute attaches or does not attach to a given subject; but different things require different demonstrations unless the one demonstration is related to the other as part to whole. I add this because if all triangles have been proved to possess angles equal to two right angles, then this attribute has been proved to attach to

—

—

—

—

isosceles ; for isosceles

is

a part of

which

all tri-

[5] angles constitute the whole. But in the case before us the fact and the essential nature

are not so related to one another, since the one

not a part of the other. So it emerges that not all the definable is demonstrable nor all the demonstrable definis

1

Cf. 72 b 18-25 and 84* 30-* 2.

91'

and we may draw the general conclusion is no identical object of which it is possible to possess both a definition and a demable;

that there

[10] onstration. nition

It

follows obviously that defi-

and demonstration are neither

identical

nor contained either within the other: if they were, their objects would be related either as

whole and

identical or as

part.

So much, then,

for the first stage of our probnext step is to raise the question whether syllogism i.e. demonstration of the

The

lem.

—

definable nature

—

possible or, as our recent

is

argument assumed, impossible. We might argue it impossible on the lowing grounds:

fol-

(a) syllogism proves an at-

through the middle term; [75] on the other hand (b) its definable nature is both 'peculiar' to a subject and predicated of it as belonging to its essence. But in tribute of a subject

that case ( 1 ) the subject, its definition, and the middle term connecting them must be reciprocally predicable of one another; for if A is 'peculiar' to C, obviously

B

and

to

C—in

universally of

A

ing to

is

'peculiar' to

also

its

all

all

B

terms are 'pecul-

one another: and further (2)

iar' to

heres in the essence of [20]

A

fact all three

B and B

is

C as belonging to

must be predicated

of

if

A

in-

predicated

C's essence,

C

as belong-

essence.

If one does not take this relation as thus duplicated if, that is, A is predicated as being of the essence of B, but B is not of the essence of the subjects of which it is predicated A

—

will not necessarily be predicated of C as belonging to its essence. So both premisses will predicate essence, and consequently B also will be predicated of C as its essence. Since, there[25] fore, both premisses do predicate essence

—

definable

i.e.

form

— C's definable form

will

appear in the middle term before the conclusion

is

drawn.

We may

generalize by supposing that

possible to prove the essential nature of

Let

C

be man,

A

man's

essential nature

we

all

are to syllogize,

A

is

—two-

Then, must be predicated of

footed animal, or aught else if

may

it

man.

it

be.

B. But this premiss will be mediated by a

[50] fresh definition, which consequently will also be the essential nature of man. Therefore the argument assumes what it has to prove, since is,

the

B

too

is

the essential nature of

man.

It

however, the case in which there are only

—

two premisses i.e. in which the premisses and immediate which we ought

are primary

—

92

BOOK

a

because

to investigate

II,

CHAPTERS

best illustrates the

it

point under discussion. [55] Thus they who prove the essential nature

man

3-6

125

[25] not the whole of this formula be true of man, and yet not exhibit his essential nature or definable

form? Again, what guarantee

is

or anything else through recip-

there against an unessential addition, or against

rocating terms beg the question. It would be begging the question, for example, to contend

the omission of the final or of an intermediate determinant of the substantial being? The champion of division might here urge that though these lapses do occur, yet we can

of soul or

is that which causes its own life, what causes its own life is a selfmoving number; for one would have to postu-

that the soul

and

that

solve that difficulty

the attributes

if all

we

as-

late that the soul is a self-moving number in 91 b the sense of being identical with it. For if

and

A

division the requisite uninterrupted sequence

is

B of

predicable as a

A will

C,

mere consequent of

not on that account be the defin-

A

able form of C:

Even

B inasmuch

B

still it

as

merely be what

will

true to say of C.

of A,

B and

if

A

is

predicated of

identical

is

with a species an animal

—

be animal, just as

an animal

is

all

will not follow: being

since [5] is predicated of being a man true that in all instances to be human

man

was

it

it

also

is

—but not

it is is

to

true that every as identical

with

being man. We conclude, then, that unless one takes both the premisses as predicating essence, one cannot infer that

A

is

the definable

form and

es-

sume

are constituents of the definable form,

if,

of terms,

[30]

what

and omit nothing; and

we cannot

fail to fulfil

—

—

further question be (ultimately) incapable of fresh specific division. Nevertheless,

we

reply,

division does not involve inference;

if it

gives

knowledge, it gives it in another way. Nor is there any absurdity in this: induction, perhaps, is not demonstration any more than is division, yet it does make evident some truth. Yet to [^5] state a definition reached by division is

ing the conclusion, what the definable form of [10] C is; so that there has been no inference, for one has begged the question.

the alleged necessity by

Nor, as was said in

method

my

formal

logic,

1

is

of division a process of inference at

the all,

no point does the characterization of the subject follow necessarily from the premising of certain other facts: division demonic] strates as little as does induction. For in a genuine demonstration the conclusion must not be put as a question nor depend on a concession, but must follow necessarily from its premisses, even if the respondent deny it. The definer asks 'Is man animal or inanimate?' and since at

—

—

are

drawn without

pothetically,

the complete formula,

terrestrial-animal, does not follow necessarily

from the premisses: this too is an assumption, and equally an assumption whether the division comprises

many

differentiae or few. (Indeed

used by those who proceed by it, even truths that can be inferred actually fail to appear as such.) For why should as this

1

method

of division

Cf. Prior Analytics,

i.

31.

is

conclusions

which the inference is open to a ques-

as to the reason for it, so definitions reached by division invite the same question. 92 a Thus to the question 'What is the essential nature of man?' the divider replies 'Animal, mortal, footed, biped, wingless'; and when at each step he is asked 'Why?', he will say, and, as he thinks, proves by division, that all animal is mortal or immortal: but such a formula taken in its entirety is not definition; so that even if division does demonstrate its formula, definition at any rate does not turn [5] out to be a conclusion of inference.

haustive division of animal into terrestrial and [20] aquatic, he assumes that man is terrestrial. is

when

tion

Can we

man

as,

their appropriate middles,

follows from the premisses

then assumes he has not inferred that man is animal. Next, when presented with an ex-

Moreover, that

if

to be divided falls

not to state a conclusion:

suming B

if

that indeed

these conditions

whole into the division at each stage, and none of it is omitted; and that this the dividendum must without is

one does so take them, in asone will have assumed, before draw-

sence of C: but

we produce by

postulating the genus,

what and substantially is, but hyby premising (1) that its de-

nevertheless actually demonstrate

a thing essentially

finable

form

tributes of

i.e.

is

its

constituted by the 'peculiar' atessential nature; (2) that such

and such are the only attributes of its essential and that the complete synthesis of them since in this is peculiar to the thing; and thus

nature,

—

synthesis consists the being of the thing

taining our conclusion?

Or

is

—ob-

the truth that,

[10] since proof must be through the middle term, the definable form is once more assumed in this minor premiss too?

POSTERIOR ANALYTICS

126

we do

Further, just as in syllogizing

not

premise what syllogistic inference is (since the premisses from which we conclude must be related as

form within the syllogism but remain

whole and

must not

fall

part), so the definable

outside the premisses posited.

It is

only against

[75] a doubt as to its having been a syllogistic inference at all that we have to defend our ar-

gument as conforming to the definition of syllogism. It is only when some one doubts whether form conforming to the definition of definable form which we assumed. Hence syllogistic inference must be possible the conclusion proved

we have

that

to

defend

is

it

the definable

as

even without the express statement of what syllogism

is

or

what definable form

The following

[20]

is.

type of hypothetical proof

also begs the question. If evil

is

definable as

and the definition of a thing's contrary if it has one is the contrary of the thing's definition; then, if good is the contrary of evil and the indivisible of the divisible, we conclude that to be good is essentially to be indivisible. The question is begged because definable form is assumed as a premiss, and as a premiss which is to prove definable form. 'But [25] not the same definable form', you may object. That I admit, for in demonstrations also the divisible,

—

—

we premise that 'this' is predicable of 'that'; but in this premiss the term we assert of the minor is neither the major itself nor a term identical in definition, or convertible,

with the

major. Again, both proof by division and the syllogism just described are open to the question why man should be animal-biped-terrestrial and not merely animal and terrestrial, since [50] what they premise does not ensure that the predicates shall constitute a genuine unity and not merely belong to a single subject as do musical and grammatical when predicated of the

same man.

How

then by definition shall

we prove

sub-

We

cannot [55] stance or essential nature? show it as a fresh fact necessarily following

from the assumption of premisses admitted to be facts the method of demonstration: we may not proceed as by induction to establish a

—

universal on the evidence of groups of particulars

which

no exception, because inducwhat the essential nature of a but that it has or has not some

offer

tion proves not 92 b thing is

Therefore, since presumably one cannot prove essential nature by an appeal to attribute.

92 b

sense perception or by pointing with the finger, what other method remains?

To

another way: how shall we by prove essential nature? He who knows what human or any other nature is, [5] must know also that man exists; for no one knows the nature of what does not exist one can know the meaning of the phrase or name 'goat-stag' but not what the essential nature of a goat-stag is. But further, if definition can prove what is the essential nature of a thing, can it also prove that it exists? And how will it prove them both by the same process, since definition exhibits one single thing and dem[10] onstration another single thing, and what human nature is and the fact that man exists are not the same thing? Then too we hold that it is by demonstration that the being of everything must be proved unless indeed to be were its essence; and, since being is not a genus, it is not the essence of anything. Hence the being of anything as fact is matter for derai-

put

it

definition

—

—

—

—

ls]

onstration;

and

this

is

the actual proce-

dure of the sciences, for the geometer assumes the meaning of the word triangle, but that it is possessed of some attribute he proves. What is it, then, that we shall prove in defining essential nature? Triangle? In that case a man will know by definition what a thing's nature is without knowing whether it exists. But that is impossible.

Moreover it is clear, if we consider the methods of defining actually in use, that definidoes not prove that the thing defined if there does actually exist something which is equidistant from a centre, yet why should the thing named in the definition exist? Why, in other words, should this be the formula defining circle? One might equally well call it the definition of mountain copper. For definitions do not carry a further guarantee that the thing defined can exist or that it is what they claim to define: one can [25] always ask why. Since, therefore, to define is to prove either a thing's essential nature or the meaning of its name, we may conclude that definition, if it in no sense proves essential nature, is a set of tion

[20] exists: since even

words signifying precisely what a name signifies. But that were a strange consequence; for ( 1 ) both what is not substance and what does not exist at all would be definable, since even non-existents can be signified by a name: (2) [jo] all sets of words or sentences would be definitions, since any kind of sentence could be given a name; so that we should all be talking

BOOK

93 b

CHAPTERS

II,

and even the Iliad would be a definition: (3) no demonstration can prove that any particular name means any particular thing: neither, therefore, do definitions, in addition to revealing the meaning of a name, also reveal that the name has this meaning. It ap[35] P ears tnen from these considerations that neither definition and syllogism nor their objects are identical, and further that definition neither demonstrates nor proves anything, and that knowledge of essential nature is not to be in definitions,

6-8

127

[20] rant whether it exists we cannot know its essential nature. Moreover we are aware

whether a thing exists or not sometimes through apprehending an element in its character, and sometimes accidentally, as, for example, when we are aware of thunder as a noise in the clouds, of eclipse as a privation of

man

light, or of

we have

[25] exists,

tion.

ture; for

even of

We

must now

and consider which of these conclusions are sound and which are not, and what is the nature of definition, and whether essential nature is in any sense demonstrable and definable or in none.

Now

to

know

its

essential nature

is,

we

as

same as to know the cause of a thing's existence, and the proof of this depends on the [5] fact that a thing must have a cause. Moresaid,

1

the

over, this cause

either identical with the es-

is

sential nature of the thing or distinct

and

if its

cause

is

distinct

from

it,

from

it;

the essential

nature of the thing is either demonstrable or indemonstrable. Consequently, if the cause is distinct from the thing's essential nature and demonstration is possible, the cause must be

exists

often as

awareness of its essential nanot got genuine knowledge

existence,

its

is

As

we have

essential nature

start afresh

species of animal, or

knowledge that the thing we must be in a wholly negative

state as regards

93*

some

accidental

obtained either by definition or by demonstra-

8

as

of the soul as a self-moving thing.

and

to search for a thing's

when we

are

unaware

to search for nothing.

hand, whenever

On

that

we apprehend an element

the thing's character there

is

less

it

the other in

difficulty.

Thus it follows that the degree of our knowledge of a thing's essential nature is determined by the sense in which we are aware that it exists. Let us then take the following as our first instance of being aware of an element in the [jo] essential nature. Let A be eclipse, C the moon, B the earth's acting as a screen. Now to ask whether the moon is eclipsed or not is to ask whether or not B has occurred. But that is precisely the same as asking whether A has a defining condition; and if this condition actually exists,

Or

again

we assert that A also actually exists. we may ask which side of a contra-

the middle term, and, the conclusion proved being universal and affirmative, the proof is in

diction the defining condition necessitates: does it make the angles of a triangle equal or not

So the method just examined through another essential nature [10] would be one way of proving essential

equal to two right angles? When we have found the answer, if the premisses are im[55] mediate, we know fact and reason to gether; if they are not immediate, we know the fact without the reason, as in the following example: let C be the moon, A eclipse, B the

the

first figure.

of proving

it

nature, because a conclusion containing essential

nature must be inferred through a middle is an essential nature just as a 'peculiar'

which

property must be inferred through a middle which is a 'peculiar' property; so that of the two definable natures of a single thing this

one and not the other. was said before 2 that this method could not amount to demonstration of essential

method

Now

will prove it

—

nature

it is

actually a dialectical proof of

[75] so let us begin again

method

it

it

and explain by what

can be demonstrated.

When we

are

aware of a fact we seek its reason, and though sometimes the fact and the reason dawn on us simultaneously, yet we cannot apprehend the reason a moment sooner than the fact; and clearly in just the same way we cannot apprehend a thing's definable form without apprehending that it exists, since while we are igno-

moon

fails to produce shadows and though no visible body intervenes between us and her. Then if B, failure to produce shadows in spite of the ab93 b sence of an intervening body, is attributable to C, and A, eclipse, is attributable to B, it

fact that the

though she

is full

moon is eclipsed, but the reanot yet clear, and we know that eclipse exists, but we do not know what its essential nature is. But when it is clear that A is attributable to C and we proceed to ask the reason of this fact, we are inquiring what is the [5] nature of B: is it the earth's acting as a is

clear that the

son

why

is

screen, or the tion ?

But

B

is

moon's rotation or her

extinc-

the definition of the other term,

viz. in these

examples, of the major term A;

for eclipse

constituted by the earth acting as

is

POSTERIOR ANALYTICS

128 a screen. Thus, (i)

quenching of

'What

fire in cloud',

thunder?' 'Because

it

fire

is thunder?' 'The and (2) 'Why does is quenched in the

[10] cloud', are equivalent. Let C be cloud, thunder, B the quenching of fire. Then B

is

is

quenched and B assuredly the definition of the major term A.

attributable to C, cloud, since fire in

A

and A,

it;

noise,

is

is

attributable to B;

there be a further mediating cause of B, it will be one of the remaining partial definitions If

of A.

—

i.e. no dethat, while there is no syllogism monstrative syllogism of essential nature, yet it is through syllogism, viz. demonstrative syl-

—

logism, that essential nature is exhibited. So we conclude that neither can the essential nature

which has

of anything

demonstration, nor

be

can

be demonstrated; and this

it

from

a cause distinct

known without

itself

is

what we con-

[20] tended in our preliminary discussions.

1

dentally in a single subject.

That then is one way of defining definition. Another kind of definition is a formula exhibiting the cause of a thing's existence.

94 a the former

signifies

while some things have from themselves, others have

a cause distinct

evident that there are essential are immediate, that

Hence it is natures which

not.

and what some

are basic premisses;

is

of these not only that they are but also

they are must be assumed or revealed in is the actual procedure of the arithmetician, who assumes both the na[25] ture and the existence of unit. On the

the latter will clearly be a l8 contigu-

movements per

The unmovable (226 b 10) The meaning of 'together,' 'intermediate,'

'successive,

10.

BOOK Whatever

ous,' 'continuous' 4.

The

unity and diversity of move-

227b 3

6.

moved

is

VII

moved by

is

something There is a first movent which by anything else (242 s 19)

ments 5.

That which has not parts cannot move 24o b 8 Can change be infinite? (241 s 26)

22Q a 7 Contrariety of movement 229^ 22 Contrariety of movement and rest Contrariety of natural and unnatural movement or rest (23o a 18)

is

24^24 not

The movent and

the moved are together All alteration pertains to sensible

moved 243 a 3 b 245 2

qualities

BOOK 1.

Every continuum

consists of con-

23i a 20

BOOK

tinuous and divisible parts 2.

(Continued)

3.

A moment

4.

ing is moved, or rests, Whatever is moved is

is

indivisible

and noth-

in a

232 a 23 b 233 32

moment

divisible

5.

Whatever has changed as

is,

as

soon

has changed, in that to which

it

4.

similarly divided (235 s 13)

changed That in which

(directly)

it

235^6 it

has changed

is

5.

has in-

6.

divisible (235 b 32)

6.

In change there is a last but no first element (236^ 7) In whatever time a thing changes 236 b 20 (directly), it changes in any part of that time Whatever changes has changed before, and whatever has changed, before was changing (2 3 6

7.

The

b

finitude or infinity of

move-

b 23 7 23

to rest, and of rest 238 b 23 thing that is moved in any time directly is in no part of that time in a part of the space through which it moves (239 s 23) 2 39b 5 9. Refutation of the arguments against the possibility of movement

Of coming

There are things that are some253*21 times in movement, sometimes at rest b Whatever is in movement is moved 254 7 by something else The first movent is not moved 256*3 by anything outside itself The first movent is immovable (257*31) The immovable first movent is 258 b 10 eternal and one

The

first

tally

(259* 20)

movent

is

Locomotion

is

not is

moved even

8.

Only

circular

inciden-

eternal (259b 32)

the primary kind of

or change locomotion (261*28)

ment, of extension, and of the moved 8.

movement

movement No movement

32)

2 5 2b 7

Refutation of objections to the

The primum mobile 7.

250 b 10

movement

eternity of 3.

VIII

There always has been and always will be

2.

movement (234b 2i) The time, the movement, the being-in-motion, the moving body, and the sphere of movement, all

1.

234° 10

Classification of

are

248 s 10 249b 26

Comparison of movements Proportion of movements

VI

is

260* 20

continuous except

movement can be

26 b 26

continuous and infinite 9.

A

[o.

265* 13 movement is the primary kind of locomotion Confirmation of the above doctrines (265* 27) 266* 10 The first movent has no parts nor magnitude, and is at the circumference of the

Circular

world.

PHYSICS BOOK 184 a [10] When the any department, have

objects of

an inquiry, in

principles, conditions, or

through acquaintance with these that knowledge, that is to say scientific knowledge, is attained. For we do not think that we know a thing until we are acquainted with its primary conditions or first principles, and have carried our analysis as far as its simplest eleelements,

it is

ments. Plainly therefore in the science of Nat/5] ture, as in other branches of study, our first task will be to try to determine what relates to its principles.

The natural way of doing this is to start from the things which are more knowable and obvious to us and proceed towards those which are clearer and more knowable by nature; for the same things are not 'knowable relatively to us' and 'knowable' without qualification. So in the present inquiry we must follow this method and advance from what is more obscure by [20] nature, but clearer to us, towards what is more clear and more knowable by nature. Now what is to us plain and obvious at first is rather confused masses, the elements and principles of which become known to us later by analysis. Thus we must advance from generalities to particulars; for it is a whole that is [25] best known to sense-perception, and a generality is a kind of whole, comprehending

many

things within

of the 'round',

name

formula.

the

to

means vaguely

Much

its

and

all

women

(a) one,

it

must be

particular senses. all

men

either (i) motionless, assert, or (ii) in

;

Oxford

—

tioned, there

principle

is

a principle

must be the

no longer, since a some thing

principle of

or things. [5] To inquire therefore whether Being is in this sense would be like arguing against

one any

ing a merely contentious argument

Note: The bold face numbers and letters are approximate indications of the pages and columns of the standard Berlin Greek text; the bracketed numbers, of the lines in the Greek text they are here assigned as they are assigned in the

this

for a different science or for

thesis as that

'mother', but later on

Parmenides and Melissus

—

being a question one common to all so a man investigating principles cannot argue with one who denies their existence. For if Being is just one, and one in the way men-

principles of his science

e.g.

its

[75] The principles in question must be either (a) one or (b) more than one. If

one or many.

def-

name,

the

distinguishes each of them.

as

is

Now

to investigate whether Being is one and motionless is not a contribution to the sci185 a ence of Nature. For just as the geometer has nothing more to say to one who denies the

[25]

A

Similarly a child begins by calling 'father',

ment

other position maintained for the sake of argument (such as the Heraclitean thesis, or such a

a sort of whole:

inition analyses this into

motion, as the physicists hold, some declaring air to be the first principle, others water. If (b) more than one, then either (i) a finite or (ii) an infinite plurality. If (i) finite (but more than one), then either two or three or [20] four or some other number. If (ii) infinite, then either as Democritus believed one in kind, but differing in shape or form; or different in kind and even contrary. A similar inquiry is made by those who inquire into the number of existents: for they inquire whether the ultimate constituents of existing things are one or many, and if many, whether a finite or an infinite plurality. So they too are inquiring whether the principle or ele-

in the relation

like parts.

it,

184b [10] same thing happens

I

translation.

259

Being

is

one man) or

like refut-

—

a descrip-

which applies to the arguments both of Melissus and of Parmenides: their premisses [10] are false and their conclusions do not follow. Or rather the argument of Melissus is gross and palpable and offers no difficulty at all: accept one ridiculous proposition and the a simple enough proceeding. rest follows We physicists, on the other hand, must take tion

—

for granted that the things that exist by nature are, either all or

which

is

indeed

some

made

motion by induction.

of them, in

plain

Moreover, no man of science is bound to solve [75] every kind of difficulty that may be raised, but only as many as are drawn falsely from the principles of the science: it is not our business

PHYSICS

260

do not

to refute those that

just as

arise in this

way:

the duty of the geometer to refute

it is

the squaring of the circle by means of segments, but it is not his duty to refute Antiphon's proof. At the same time the holders of the theory of which we are speaking do inci-

Na-

dentally raise physical questions, though ture

is

not their subject: so

it

will perhaps be

spend a few words on them, espeas the inquiry is not without scientific

186 a

on its own whether the part and the whole are one or more than one, and how they can be one or many, and, if they are more than gument, account

yet deserving consideration

—namely,

what sense they are more than one. (Similarly with the parts of wholes which are [75] not continuous.) Further, if each of the

one, in

two

parts

is

indivisibly

one with the whole, the be indivisibly one

as well to

difficulty arises that they will

cially

with each other also. But to proceed: If (b) their One is one as indivisible, nothing will have quantity or quality, and so the one will not be infinite, as Melissus says nor, indeed, limited, as Parmenides says, for though the limit is indivisible,

interest.

'[20]

The most

pertinent question with which

to begin will be this: In

ed that

many

all

what

sense

things are one? For

senses.

is it

'is' is

Do they mean that all

assert-

used in

things

'are'

substance or quantities or qualities? And, furone man, ther, are all things one substance one horse, or one soul or quality and that one white or hot or something [25] and the same of the kind? These are all very different doctrines and all impossible to maintain. For if both substance and quantity and qual-

—

ity are, then,

—

—

whether these

exist

independently

of each other or not, Being will be If

on the other hand

it

is

many.

asserted that

all

things are quality or quantity, then, whether substance exists or not, an absurdity results, if

indeed the impossible can properly be For none of the others can exist independently: substance alone is independent: for everything is predicated of substance as subject. Now Melissus says that Being is infinite. It is then a quantity. For the infinite is in the category of quantity, whereas substance or quality or affection cannot be infinite except through a concomitant attribute, that is, if at 185 b the same time they are also quantities. For to define the infinite you must use quantity in your formula, but not substance or quality. If then Being is both substance and quantity, it is two, not one: if only substance, it is not infinite and has no magnitude; for to have that it will have to be a quantity. [5] Again, 'one' itself, no less than 'being', is used in many senses, so we must consider in what sense the word is used when it is said that [30]

called absurd.

the All

is

one.

Now we

say that (a) the continuous

or that (b) the indivisible

is

is

one

one, or (c) things

and the same,

the limited

is

not.

But if (c) all things are one in the sense of having the same definition, like 'raiment' and [20] 'dress', then it turns out that they are maintaining the Heraclitean doctrine, for it will be the same thing 'to be good' and 'to be bad', and 'to be good' and 'to be not good', and so the same thing will be 'good' and 'not good', and man and horse; in fact, their view will be, not that all things are one, but that they are nothing; and that 'to be of such-and-such a quality' is the same as 'to be of such-and-such a size'.

[25]

Even

were

the

more

recent of the ancient think-

same thing should turn out in their hands both one and many. So some, like Lycophron, were led to omit 'is',

ers

in a pother lest the

mode of expression and has been whitened' instead of 'is white', and 'walks' instead of 'is walking', for [50] fear that if they added the word 'is' they should be making the one to be many as if 'one' and 'being' were always used in one and the same sense. What 'is' may be many either in definition (for example 'to be white' is one thing, 'to be musical' another, yet the same others to change the say 'the

man

—

may

is many) or by whole and its parts. On this 186 a point, indeed, they were already getting into difficulties and admitted that the one was many as if there was any difficulty about the same thing being both one and many, provided

thing

be both, so the one

division, as the

—

these are not opposites; for 'one'

that

mean

may

either 'potentially one' or 'actually one'.

when

their essence is one and 'drink'. If (a) their One is one in the sense of con[10] tinuous, it is many, for the continuous is divisible ad infinitum. There is, indeed, a difficulty about part and

are said to be 'one',

—

as 'liquor'

whole, perhaps not relevant to the present ar-

we approach the thesis in this way seems impossible for all things to be one. Further, the arguments they use to prove their position are not difficult to expose. For both of them reason contentiously I mean both MeIf,

[5]

then, it

—

BOOK

186 b

I,

CHAPTERS

lissus

Hence

false

anything

and Parmenides. [Their premisses are and their conclusions do not follow. Or rather the argument of Melissus is gross and palpable and offers no difficulty at all: admit one ridiculous proposition and the rest follows a simple enough proceeding.] [10] The fallacy of Melissus is obvious. For he

—

supposes that the assumption 'what has come into being always has a beginning' justifies the assumption 'what has not come into being has no beginning'. Then this also is absurd, that in every case there should be a beginning of the thing not of the time and not only in the case of coming to be in the full sense but also in the

—

case of

coming

to

have a quality

—

as

if

change

[75] never took place suddenly. Again, does it follow that Being, if one, is motionless? Why should it not move, the whole of it within itself,

parts

as

of

it

do which are

unities,

this water? Again, why is qualitative change impossible? But, further, Being cannot [20] be one in form, though it may be in what it is made of. (Even some of the physicists hold it to be one in the latter way, though not in the former.) Man obviously differs from horse in form, and contraries from each other. The same kind of argument holds good against Parmenides also, besides any that may apply specially to his view: the answer to him being that 'this is not true' and 'that does not follow'. His assumption that one is used in a

e.g.

because it is used in His conclusion does not follow, take only white things, and if

single sense only

[25] several.

because

if

we

is false,

2-3

261

'substance' will not be a predicate of else.

For the subject cannot be a be-

means

several things, in such something. But ex hypothesi 'being' means only one thing. If, then, 'substance' is not attributed to anything, but other things are attributed to it, how [5] does 'substance' mean what is rather than what is not? For suppose that 'substance' is

ing, unless 'being' a

way

that each

is

also 'white'. Since the definition of the latter

white, as nothing it

which

is

follows that 'white'

is

is

even be attributed to

different (for being cannot

is

not 'substance'),

not-being

—and that

not in the sense of a particular not-being, but in the sense that it is not at all. Hence 'sub[10] stance' is not; for it is true to say that it white, which we found to mean not-being.

is

If to

avoid this we say that even 'white' means it follows that 'being' has more than

substance,

one meaning. In particular, then, Being will not have nitude,

if it is

magtwo

substance. For each of the

must be in a different sense. (2) Substance is plainly divisible into other substances, if we consider the mere nature of a [75] definition. For instance, if 'man' is a sub-

parts

and 'biped' must also be subFor if not substances, they must be attributes and if attributes, attributes either of (a) man or of (b) some other subject. But neistance, 'animal' stances.

ther

possible.

is

An

(a) [20]

—

is either that which may or not belong to the subject or that in

attribute

may

whose

definition the subject of

Thus

which it is an an exam-

meaning, none the less what is white will be many and not one. For what is white will not be one either in the sense

attribute

continuous or in the sense that it must be defined in only one way. 'Whiteness' will be different from 'what has whiteness'. Nor does this mean that there is anything that can [50] exist separately, over and above what is

attribute snubness. Further, the definition of

'white' has a single

that

it is

white. For 'whiteness' and 'that which

is

white'

differ in definition, not in the sense that they are

which can exist apart from each other. But Parmenides had not come in sight of this

things

distinction. It is

necessary for him, then, to assume not

only that 'being' has the same meaning, of whatever it is predicated, but further that it

means ( 1 ) what just is and (2) what is just one. It must be so, for (1) an attribute is predicated of some subject, so that the subject to [55] which 'being' is attributed will not be, as it is something different from 'being'. Some186 b thing, therefore, which is not will be.

is

involved.

'sitting' is

ple of a separable attribute, while 'snubness'

contains the definition of 'nose', to which the

whole

is

we

not contained in the definitions of

the contents or elements of the definitory for-

mula; that of 'man' for instance in [25] that of 'white is so,

and

if

'biped'

man' is

'biped', or

in 'white'. If then this

supposed to be an

attri-

bute of 'man', it must be either separable, so that 'man' might possibly not be 'biped', or the definition of 'man' must come into the defini-

—

which [50] tion of 'biped' the converse is the case.

is

impossible, as

on the other hand, we suppose that and 'animal' are attributes not of man but of something else, and are not each of them a substance, then 'man' too will be an attribute of something else. But we must assume that substance is not the attribute of anything, and that the subject of which both 'biped' and 'animal' and each separately are predicated is the (b)

'biped'

If,

PHYSICS

262 subject also of the

[35] Are

complex 'biped animal'.

we

then to say that the All is composed of indivisible substances? Some thinkers 187 a did, in point of fact, give way to both arguments. To the argument that all things are

being means one thing, they conceded is; to that from bisection, they yielded by positing atomic magnitudes. But obviously it is not true that if being means one thing, and cannot at the same time mean the [5] contradictory of this, there will be nothing which is not, for even if what is not cannot be without qualification, there is no reason why it should not be a particular not-being. To say that all things will be one, if there is nothing besides Being itself, is absurd. For who understands 'being itself to be anything but a particular substance? But if this is so, there is nothing to prevent there being many beings, as has been said. [10] It is, then, clearly impossible for Being to be one in this sense.

one

if

that not-being

The

physicists

modes

on the other hand have two

of explanation.

make the underlying body one one of the three or something else which is denser than fire and rarer than air [75] then generate everything else from this, and obtain multiplicity by condensation and

—

The

first set

either

rarefaction.

Now

these are contraries,

may

which

be generalized into 'excess and defect'. except Plato's 'Great and Small' that he make these his matter, the one his form, while the others treat the one which underlies

—

(Compare

as

matter and the contraries as differentiae,

i.e.

forms). [20] The second set assert that the contrarieties are contained in the one and emerge from it

by segregation, for example Anaximander and also all those who assert that 'what is' is one and many, like Empedocles and Anaxagoras; for they too produce other things from their mixture by segregation. These differ, however, from each other in that the former imagines a cycle of such changes, the latter a single series. [25] Anaxagoras again made both his 'homceomerous' substances and his contraries infinite in multitude, whereas Empedocles posits only the so-called elements.

The

theory of Anaxagoras that the princiwas probably due

ples are infinite in multitude

common

opinion of the physicists that nothing comes into being from not-being. For this is the reason why they use to his acceptance of the

187 b

[30] the phrase 'all things were together' and the coming into being of such and such a kind of thing

reduced to change of quality, while of combination and separation. Moreover, the fact that the contraries proceed from each other led them to the conclusion. is

some spoke

The

one, they reasoned,

must have already

ex-

the other; for since everything that

isted in

comes into being must arise either from what is or from what is not, and it is impossible for it to arise from what is not (on this point all the physicists agree), they thought that the [35] truth of the alternative necessarily

fol-

lowed, namely that things come into being out of existent things, i.e. out of things already present, but imperceptible to our senses because 187 b of the smallness of their bulk. So they assert that everything has been mixed in everything, because they saw everything arising out of everything. But things, as they say, appear different from one another and receive different names according to the nature of the particles which are numerically predominant among the innumerable constituents of the mixture. For nothing, they say, is purely and entirely [5] white or black or sweet, bone or flesh, but the nature of a thing is held to be that of which it contains the most.

Now

(1) the infinite

what unknowable

able, so that

size

is

finite in variety of

is

qua

infinite

infinite in

is

unknow-

multitude or

and what is inunknowable in qual-

in quantity,

kind

is

But the principles in question are inboth in multitude and in kind. Therefore it is impossible to know things which are composed of them; for it is when we know the nature and quantity of its components that we suppose we know a complex. Further (2) if the parts of a whole may be of [10]

ity.

finite

any

size in the direction either of greatness or

[75] of smallness (by 'parts' I mean components into which a whole can be divided and which are actually present in it), it is necessary that the

whole thing

itself

Clearly, therefore, since

may

it is

be of any

size.

impossible for an

animal or plant to be indefinitely big or small, its parts be such, or the whole will be the same. But flesh, bone, and the like are

neither can

[20] the parts of animals, and the fruits are the parts of plants. Hence it is obvious that neither flesh, bone, nor any such thing can be of indefinite size in the direction either of the

greater or of the

less.

to the theory all such things are already present in one another and do not come into being but are constituents

Again (3) according

BOOK

188 b

which are separated its designation from

out,

and a thing

I,

CHAPTERS

receives

its chief constituent. Furanything may come out of anything water by segregation from flesh and flesh from [25] water. Hence, since every finite body is exhausted by the repeated abstraction of a finite body, it seems obviously to follow that everything cannot subsist in everything else. For let flesh be extracted from water and again more flesh be produced from the remainder by repeating the process of separation: then, even though the quantity separated out will continually decrease, still it will not fall below a cer[30] tain magnitude. If, therefore, the process comes to an end, everything will not be in ev-

—

ther,

erything else (for there will be no flesh in the remaining water); if on the other hand it does not, and further extraction is always possible, there will be an infinite multitude of finite equal particles in a finite quantity which is [55] impossible. Another proof may be added: Since every body must diminish in size when something is taken from it, and flesh is quantitatively definite in respect both of greatness and smallness, it is clear that from the mini-

—

mum

quantity of flesh no body can be sepa188* rated out; for the flesh left would be less than the minimum of flesh. Lastly (4) in each of his infinite bodies there would be already present infinite flesh and blood and brain having a distinct existence, however, from one another, and no less real than the infinite bodies, and each infinite:

—

which [5]

is

The

contrary to reason. statement that complete separation

never will take place is correct enough, though Anaxagoras is not fully aware of what it means. For affections are indeed inseparable. If then colours and states had entered into the mixture, and if separation took place, there would be a 'white' or a 'healthy' which was nothing but white or healthy, i.e. was not the predicate of a subject. So his 'Mind' is an absurd person

aiming at the impossible, if he is supposed to [10] wish to separate them, and it is impossible to do so, both in respect of quantity and of quality of quantity, because there is no minimum magnitude, and of quality, because af-

—

fections are inseparable.

Nor

is

Anaxagoras right about the coming

homogeneous bodies. It is true there is which clay is divided into pieces of clay, but there is another in which it is not. [75] Water and air are, and are generated 'from' each other, but not in the way in which bricks come 'from' a house and again a house

3-5

263

and

'from' bricks;

is

it

better

number

smaller and finite

to

assume a

of principles,

as

Empedocles does.

making

All thinkers then agree in traries principles,

All as one

both those

who

the con-

describe the

and unmoved (for even Parmeni-

[20] des treats hot and cold as principles under the names of fire and earth) and those too

who

use the rare and the dense.

true of Democritus also, with his void, both of

which

he

exist,

The same

is

plenum and

says, the

one as

Again he speaks of differences in position, shape, and order, and these are genera of which the species are contraries, namely, of position, above and below, before and behind; of shape, angular and [25] angle-less, straight and round. being, the other as not-being.

It is plain then that they all in one way or another identify the contraries with the principles. And with good reason. For first principles must not be derived from one another nor from anything else, while everything has to be derived from them. But these conditions are fulfilled by the primary contraries, which are not derived from anything else because they are primary, nor from each other because they

are contraries.

[jo] But at as a

we must

reasoned

see

how

this

can be arrived

result, as well as in the

way

just indicated.

Our

first

presupposition must be that in nais acted on by, any oth-

ture nothing acts on, or

er thing at random, nor may anything come from anything else, unless we mean that it does so in virtue of a concomitant attribute. For [35] how could 'white' come from 'musical', unless 'musical' happened to be an attribute of the not-white or of the black? No, 'white' comes from 'not-white' and not from any 'not-white', but from black or some intermedi188 b ate colour. Similarly, 'musical' comes to be from 'not-musical', but not from any thing other than musical, but from 'unmusical' or any intermediate state there may be. Nor again do things pass into the first chance

—

thing; 'white' does not pass into 'musical' (except,

it

may be,

concomitant attrinot into any not white, but into black

in virtue of a

bute), but into 'not-white'

—and

to be of

chance thing which

a sense in

or an intermediate colour; 'musical' passes into

—

is

and not into any chance [5] 'not-musical' thing other than musical, but into 'unmusical' or any intermediate state there may be. The same holds of other things also: even

PHYSICS

264

things which are not simple but complex fol[10] low the same principle, but the opposite state has tice

not received a name, so we fail to noWhat is in tune must come from

the fact.

not in tune, and vice versa; the tuned and not into any untunedness, but into the corresponding oppo[75] site. It does not matter whether we take

what

is

passes into untunedness

—

attunement, order, or composition for our illustration; the principle is obviously the same in all, and in fact applies equally to the production of a house, a statue, or any other complex. A house comes from certain things in a certain state of separation instead of conjunction, a statue (or any other thing that has been [20] shaped) from shapelessness each of these objects being partly order and partly

—

composition. If then this

is true, everything that comes to be or passes away from, or passes into, its contrary or an intermediate state. But the intermecoldiates are derived from the contraries ours, for instance, from black and white. Ev[25] ery thing, therefore, that comes to be by a natural process is either a contrary or a prod-

—

uct of contraries.

Up

to this point

we have

practically

had

most of the other writers on the subject with I have said already for all of them identify their elements, and what they call their principles, with the contraries, giving no rea1

us, as

:

son indeed for the theory, but contrained as it were by the truth itself. They differ, however, [30] from one another in that some assume contraries which are more primary, others con-

which are less so: some those more knowable in the order of explanation, others those more familiar to sense. For some make hot and cold, or again moist and dry, the conditions of becoming; while others make odd [55] and even, or again Love and Strife; and these differ from each other in the way mentraries

tioned.

Hence

their principles are in

one sense the

same, in another different; different certainly, as indeed most people think, but the same in189 a asmuch as they are analogous; for all are taken from the same table of columns, 2 some of the pairs being wider, others narrower in extent. In this way then their theories are both

189 a

the order of explanation, the particular in the order of sense: for explanation has to do with the universal, sense with the particular.) The and the small', for example, belong to the

great

former

class,

'the

dense and the

rare' to the

latter.

[10]

It is

clear then that

our principles must be

contraries.

The are

next question is whether the principles two or three or more in number.

One

they cannot be, for there cannot be one Nor can they be innumerable, be-

contrary.

if so, Being will not be knowable: and any one genus there is only one contrariety, and substance is one genus: also a finite num[75] ber is sufficient, and a finite number, such as the principles of Empedocles, is better than an infinite multitude; for Empedocles pro-

cause,

in

fesses

to obtain

Anaxagoras

from

his principles all

that

from his innumerable principles. Lastly, some contraries are more primary than others, and some arise from others for example sweet and bitter, white and black whereas the principles must always remain principles. [20] This will suffice to show that the prin-

—

obtains

—

one nor innumerable. Granted, then, that they are a limited number, it is plausible to suppose them more than two. For it is difficult to see how either density should be of such a nature as to act in any way ciples are neither

rarity or rarity on density. The same is true any other pair of contraries; for Love does [25] not gather Strife together and make things out of it, nor does Strife make anything out of Love, but both act on a third thing different from both. Some indeed assume more than one such thing from which they construct the world of nature. Other objections to the view that it is not necessary to assume a third principle as a substratum may be added. (1) We do not find

on of

that the contraries constitute the substance of

[30] any thing. But what is a first principle ought not to be the predicate of any subject. If

explanation, others

to

it were, there would be a principle of the supposed principle: for the subject is a principle, and prior presumably to what is predicated of it. Again (2) we hold that a substance is not contrary to another substance. How then can substance be derived from what are not substances? Or how can non-substances be prior

[5] sense.

in

to substance?

the

same and

different,

worse; some, as traries

1

aj

what

9 3°»

I

have

some

better,

some

said, take as their con-

more knowable in the order what is more familiar (The universal is more knowable is

2

Metaphysics,

1.

986* 23.

of

If

then

we

accept both the former argument

BOOK

190[ £5] and

CHAPTERS

somewhat

spoken of by

investigate the characteristics of special cases.

the contraries, such as

those

who

is

We

describe the All as one nature

water or fire or what is intermediate between them. What is intermediate seems preferable; for fire, earth, air, and water are already in[5] volved with pairs of contraries. There is, therefore, much to be said for those who make the underlying substance different from these four; of the rest, the next best choice is air, as presenting sensible differences in a less degree than the others; and after air, water. All, however, agree in this, that they differentiate their

of the contraries, such as density

[10] and rarity and more and less, which may of course be generalized, as has already been said,

1

into excess

and

trine too (that the

265

as the substratum of

sume 189 b

One by means

5-7

following the natural order of inquiry if we speak first of common characteristics, and then

we must, to preserve both, as-

this one,

a third

I,

defect.

One and

Indeed excess

this doc-

and defect

would appear to be of old standing, though in different forms; for the early thinkers made the two the active

are the principles of things)

say that one thing comes to be from another thing, and one sort of thing from another sort of thing, both in the case of simple and of

complex things. I mean the following. We can say (1) the 'man becomes musical', (2) what [55] is 'not-musical becomes musical', or (3) 190* the 'not-musical man becomes a musical man Now what becomes in (1) and (2) man and 'not musical'- I call simple, and what each becomes 'musical' simple also. But when (3) we say the 'not-musical man becomes a musical man', both what becomes and what it becomes are complex. [5] As regards one of these simple 'things that become' we say not only 'this becomes so-andso', but also 'from being this, comes to be soand-so', as 'from being not-musical comes to be musical'; as regards the other we do not say this in all cases, as we do not say ( 1 ) 'from be-

—

man he came to be man became musical'.

—

and the one the passive principle, whereas [75] some of the more recent maintain the

ing a

reverse.

When a 'simple' thing something, in one case ( 1 )

To

suppose then that the elements are three in number would seem, from these and similar considerations, a plausible

before.

are

2

On

view, as

I

said

the other hand, the view that they

more than

three in

number would seem

to

be untenable. For the one substratum is sufficient to be [20] acted on; but if we have four contraries, there will be two contrarieties, and we shall have to suppose an intermediate nature for each pair separately. If, on the other hand, the contrarieties, being two, can generate from each other, the second contrariety will be super-

Moreover, it is impossible that there should be more than one primary contrariety. For substance is a single genus of being, so that the principles can differ only as prior and [25] posterior, not in genus; in a single genus there is always a single contrariety, all the other contrarieties in it being held to be refluous.

musical or exist, either

in the

187* l6.

2a 2I.

way we

are describing that, as

we

say,

must always be an underlying something, [75] namely that which becomes, and that this, though always one numerically, in form at least is not one. (By that I mean that it can be described in different ways.) For 'to be man' is not the same as 'to be unmusical'. One part survives, the other does not: what is not an there

opposite survives

(for

'man' survives), but

'not-musical' or 'unmusical' does not survive,

compound of the two, name'unmusical man'. We speak of 'becoming that from this' in-

[20] nor does the

of

1

unmusical does not continue to simply or combined with the sub-

is

These distinctions drawn, one can gather Irom surveying the various cases of becoming

then that the number of elements more than two or three; but whether two or three is, as I said, a question of

[jo] We will now give our own account, approaching the question first with reference to becoming in its widest sense: for we shall be

become

ject.

It is clear

considerable difficulty.

said to

survives through

it does not. For and is such even when he becomes musical, whereas what is not

ly

neither one nor

is it

the process, in the other (2) [10] the man remains a man

ducible to one. is

musical' but only 'the

becoming that' more in the case what does not survive the change 'becoming musical from unmusical', not 'from man' stead of 'this

—but

there are exceptions, as

—

we sometimes

[25] use the latter form of expression even of what survives; we speak of 'a statue coming to

be from bronze', not of the 'bronze becoming The change, however, from an opposite which does not survive is described indif-

a statue'.

PHYSICS

266 ferently in both ways, 'becoming that this'

or 'this

[jo]

'the

becoming

that'.

We

from

say both that

unmusical becomes musical', and

'from unmusical he becomes musical'. And so both forms are used of the complex, 'becoming a musical man from an unmusical that

man', and 'an unmusical sical man'.

man becoming

a

mu-

But there are different senses of 'coming to In some cases we do not use the expression 'come to be', but 'come to be so-and-so'. Only substances are said to 'come to be' in the be'.

than substance it is plain that there must be some subject, namely, that which becomes. For we know that when a thing comes to be of such a quantity or quality sucn a relation, time, or place, a [35] or subject is always presupposed, since substance alone is not predicated of another subject, but everything else of substance. 190 b But that substances too, and anything else that can be said 'to be' without qualification, come to be from some substratum, will appear on examination. For we find in every case something that underlies from which proin all cases other

m

ceeds that which comes to be; for instance, ani-

mals and plants from seed. [5] Generally things which come to be, come to be in different ways: (1) by change of shape, as a statue; (2) by addition, as things which grow; (3) by taking away, as the Hermes from the stone; (4) by putting together, as a house; (5) by alteration, as things

which

'turn' in respect of their material sub-

stance.

plain that these are all cases of coming from a substratum. [10] Thus, clearly, from what has been said, whatever comes to be is always complex. There something which is, on the one hand, (a) comes into existence, and again (b) something which becomes that the latter (b) in two senses, either the subject or the opposite. By It is

—

the 'opposite'

I

mean

the 'unmusical', by the

and similarly I call the absence [75] of shape or form or order the 'opposite', and the bronze or stone or gold the 'subject'. Plainly then, if there are conditions and principles which constitute natural objects and from which they primarily are or have come to be have come to be, I mean, what each is said to be in its essential nature, not what each 'subject' 'man',

—

—

concomitant attribute plainly ] ly, I say, everything comes to be from both subject and form. For 'musical man' is com-

is

—

—

in respect of a

And

incidental in the process.)

—

the positive

one the order, the acquired music, or any similar predicate. is

There

is

a sense, therefore, in

art of

which we must

declare the principles to be two, and a sense in [30] which they are three; a sense in which the say for example contraries are the principles

—

and the unmusical, the hot and the and a sense cold, the tuned and the untuned in which they are not, since it is impossible for the contraries to be acted on by each other. But this difficulty also is solved by the fact that the substratum is different from the contraries, the musical

—

not a contrary. The prinway, not more in number than the contraries, but as it were two, nor yet precisely two, since there is a difference 191 a of essential nature, but three. For 'to be [55] for

is

it

itself

ciples therefore are, in a

man'

from

different

is

be unformed' from

'to

We

have

now

'to 'to

generation, and

and

it is

be unmusical', and be bronze'.

stated the

how

number

of the prin-

which are subject

ciples of natural objects

the

number

is

to

reached:

must be a substratum and that the contraries must

clear that there

for the contraries,

to be

1

posed (in a way) of 'man' and 'musical': you can analyse it into the definitions of its elements. It is clear then that what comes to be will come to be from these elements. Now the subject is one numerically, though it is two in form. (For it is the man, the gold the 'matter' generally that is counted, for [25] it is more of the nature of a 'this', and what comes to be does not come from it in virtue of a concomitant attribute; the privation, on the other hand, and the contrary are

form

unqualified sense.

Now

191

[5] be two. (Yet in another way of putting it is not necessary, as one of the contraries

this

will serve to effect the

change by

its

successive

absence and presence.) The underlying nature entific

bronze

is an object of sciknowledge, by an analogy. For as the

wood

to the statue, the

is

to the bed,

[10] or the matter and the formless before receiving form to any thing which has form, so is the underlying nature to substance, i.e. the

'this'

or existent.

is one principle (though not one or existent in the same sense as the 'this'), and the definition was one as we agreed; then fur-

This then

ther there

is its

contrary, the privation. In

sense these are two, and in

what

what

sense more,

[75] has been stated above. Briefly, we ex1 plained first that only the contraries were principles, 1

Chapter

and

2

later that a 2

5.

Chapter

6.

substratum was

in-

BOOK

191 b dispensable,

and

that the principles

I,

CHAPTERS

were three;

1

[10]

It

7-9

267

was through

make

failure to

this dis-

our last statement has elucidated the difference between the contraries, the mutual rela-

tinction that those thinkers gave the matter up,

and the nature of the substratum. Whether the form or the sub-

farther astray as to suppose that nothing else

tion of the principles,

the essential nature of a physical obnot yet clear. But that the prinis ject [20] ciples are three, and in what sense, and the

stratum

way

in

is

which each

is

a principle,

is

and through

So much then for the question of the number and the nature of the principles.

so

much

comes to be or exists apart from Being itself, thus doing away with all becoming. We ourselves are in agreement with them in holding that nothing can be said without qualification to

clear.

went

this error that they

theless

come from what

we maintain

be from what

is

not'

—that

But never-

not.

is

may 'come

that a thing

to

in a qualified

is,

[75] sense. For a thing comes to be from the privation, which in its own nature is not-being.

proceed to show that the

diffi-

—

culty of the early thinkers, as well as our

own,

sult.

We

will

now

solved in this

is

way

they say that none of the things that are either comes to be or passes out of existence, because what comes to be must do so either from what is or from what is not, both of which are im[30] possible. For what is cannot come to be (because it is already), and from what is not

nothing could have come to be (because something must be present as a substratum). So too they exaggerated the consequence of this, and went so far as to deny even the existence of a plurality of things, maintaining that only Being itself is. Such then was their opinion, and such the reason for its adoption. explanation on the other hand is that comes to be from what is or from what is not', 'what is not or what is [_?5] does something or has something done to it or becomes some particular thing', are to be taken (in the first way of putting our explana191 b tion) in the same sense as 'a doctor does

in the

something or has something done to him', 'is or becomes something from being a doctor'. These expressions may be taken in two senses, and so too, clearly, may 'from being', and 'beis

acted on'.

A

doctor builds a

qua housebuilder, and qua doctor, but qua turns gray, not [5] darkhaired. On the other hand he doctors or fails to doctor qua doctor. But we are using qua

doctor, but

words most appropriately when we say that

Chapter

7.

and

it is

thought to be

come

way described from what is not. same way we maintain that nothing

comes not

to be

come

from being, and that being does

to be except in a qualified sense. In

way, however, it does, just as animal might come to be from animal, and an animal [20] of a certain kind from an animal of a certain kind. Thus, suppose a dog to come to be from a horse. The dog would then, it is true, come to be from animal (as well as from an animal of a certain kind) but not as animal, for that is already there. But if anything is to become an animal, not in a qualified sense, it will not be from animal: and if being, not nor from not-being either, [25] from being that

—

for

it

being'

has been explained

we mean from

Note further

that

2

that by 'from notnot-being qua not-being.

we do

not subvert the

principle that everything either

is

or

is

not.

This then is one way of solving the difficulty. Another consists in pointing out that the same things can be explained in terms of potentiality and actuality. But this has been done with greater precision elsewhere. 3

we

which condeny the existence of some of the things we mentioned are now solved. For it was this reason which also caused some of the earlier thinkers to turn so far aside from the road which leads to coming to be and passing away and change generally. If they had [jo] So, as

said, the difficulties

strain people to

come in sight of this nature, would have been dispelled.

all

their ignorance

a

doctor does something or undergoes something, or becomes something from being a doctor, if he does, undergoes, or becomes qua doctor. Clearly then also 'to come to be so-andso from not-being' means 'qua not-being'. 1

this causes surprise,

In the

Our

the phrases 'something

ing acts or

Yet

impossible that something should

alone.

The first of those who studied science were [25] misled in their search for truth and the nature of things by their inexperience, which as it were thrust them into another path. So

house, not

this not surviving as a constituent of the re-

[35] Others, indeed, have apprehended the

nature in question, but not adequately. In the first place they allow that a thing

may

come

not-

2 1.

9.

to be 8

without qualification from Metaphysics, ix, and v

(

i

o 1 7* 35~b

9).

PHYSICS

268

being, accepting on this point the statement of 192* Parmenides. Secondly, they think that if is one numerically, it must have also only a single potentiality which is

the substratum

—

a very different thing.

Now we

and privation, namely the matter, virtue of an attribute

distinguish matter

and hold that one of

these,

not-being only in which it has, while the privation in is

its

own

[5] nature is not-being; and that the matter is nearly, in a sense is, substance, while the priva-

They, on the other hand, and Small alike with notbeing, and that whether they are taken together as one or separately. Their triad is therefore of quite a different kind from ours. For they got so far as to see that there must [jo] be some underlying nature, but they make it one for even if one philosopher 1 makes a dyad of it, which he calls Great and Small, the effect is the same, for he overlooked the other nature. For the one which persists is a joint cause, with the form, of what comes to be a mother, as it were. But the negative part [75] of the contrariety may often seem, if you concentrate your attention on it as an evil

tion in

no sense

is.

identify their Great

—

—

agent, not to exist at

it,

the other such as of

ally destructive.

its

own

nature to de-

and yearn for it. But the consequence of view is that the contrary desires its own [20] extinction. Yet the form cannot desire

sire

for

it

is

contrary desire

not defective; it,

is

nor can the

for contraries are

mutu-

The

truth

is

what

that

de-

matter, as the female desires

—

and the ugly the beautiful only the ugly or the female not per se but per accidens. the male

The matter comes

[25]

one

in

to be

and

sense, while in another

which contains the

that

own

it

ceases to be

As

does not.

privation,

it

ceases to

what ceases to be contained within it. But as potentiality it does not cease to be in its own nature, but is necessarily outside the sphere of becoming and ceasing to be. For if it came to be, something must have existed as a primary substratum from which it should come and [50] which should persist in it; but this is its own special nature, so that it will be before coming to be. (For my definition of matter is just this the primary substratum of each thing, from which it comes to be without qualbe in

its

the privation

nature, for

—

is

—

ification,

And

if it

so

last,

it

and which ceases to be will

it

persists in

the result.)

will pass into that at the

have ceased

to be before ceasing

to be.

The

accurate determination of the

ciple in respect of form, it is

or

whether

it

what they

prin-

first

one or

is

are,

is

the

[35] province of the primary type of science; so these questions may stand over till then. 2

192 b But of the

we

shall

low.

natural, i.e. perishable, forms speak in the expositions which fol-

3

The

their

itself,

the form

sires

many and what

all.

For admitting with them that there is something divine, good, and desirable, we hold that there are two other principles, the one contrary to

192 b

above, then,

may

be taken as sufficient

to establish that there are principles

they are and

make

BOOK

how many

a fresh start

there are.

and what

Now

let

us

and proceed.

II

i.e.

—have

in so far as they are products of art

All the things mentioned present a feature

no innate impulse to change. But in so far as they happen to be composed of stone or of [20] earth or of a mixture of the two, they do have such an impulse, and just to that extent which seems to indicate that nature is a source or cause of being moved and of being at rest in that to which it belongs primarily, in virtue of itself and not in virtue of a concomitant

which they

attribute.

Of things that from other

exist,

some exist by nature, some

causes.

'By nature' the animals and their parts

exist,

[10] and the plants and the simple bodies (earth, fire, air, water) for we say that these

—

and the

like exist 'by nature'.

from things which are not Each of them has within itself a principle of motion and of stationari[75] ness (in respect of place, or of growth and

in

differ

constituted by nature.

by way of alteration). On the other hand, a bed and a coat and anything else of that sort, qua receiving these designations

I

say 'not in virtue of a concomitant attri-

bute', because (for instance) a

man who

doctor might cure himself. Nevertheless

is

a

it is

decrease, or

1

Plato.

2

Metaphysics, xii. 7-9. the rest of the Physics, the On the Heavens, On Generation and Corruption, etc. (especially On Generation 8 I.e.

and Corruption,

11).

193 b

BOOK

not in so far as he

is

CHAPTER 9— BOOK

I,

a patient that he pos-

[25] sesses the art of medicine:

it

merely has

happened that the same man is doctor and paand that is why these attributes are not tient always found together. So it is with all other artificial products. None of them has in itself the source of its own production. But while in some cases (for instance houses and the other products of manual labour) that principle is in something else external to the thing, in others those which may cause a change in [30]

—

—

themselves in virtue of a concomitant attribute it lies in the things themselves (but not in virtue of what they are). 'Nature' then is what has been stated.

—

which have a principle them is a substance; for

Things 'have

a nature'

II,

CHAPTER

269

1

[20] say bronze (or gold) to water, bones (or wood) to earth and so on, that (they say)

would be their nature and essence. Consequently some assert earth, others fire or air or water or some or all of these, to be the nature For whatever any one have this character whether one thing or more than one thing [25] this or these he declared to be the whole

of the things that are.

of

them supposed

of substance,

to

all else

being

its

affections, states,

or dispositions. Every such thing they held to

be eternal (for it could not pass into anything else), but other things to come into being and cease to be times without number.

This then that

it is

is

one account of

'nature',

namely

the immediate material substratum of

Each of and nature always implies a which it inheres.

things which have in themselves a principle of

[^5] The term 'according to nature' is applied to all these things and also to the attributes which belong to them in virtue of what they

defini-

of this kind. it

a subject,

is

subject in

be carwhich is not a 'nature' nor 'has ried upwards a nature' but is 'by nature' or 'according to are, for instance the

—

property of

fire to

nature'.

193a

What

nature

is,

has been stated.

ture',

would be absurd

and the meaning and 'according to naThat nature exists, it

then,

of the terms 'by nature'

to try to prove; for

many

it

is

ob-

motion or change. [jo] Another account is that 'nature' shape or form which is specified in the

is

the

tion of the thing.

For the word 'nature' is applied to what is according to nature and the natural in the same way as 'art' is applied to what is artistic or a work of art. should not say in the latter case that there is anything artistic about a thing, if it is a bed only potentially, not yet having the form of a bed; nor should we call

We

[55] ural

a

it

work

of art.

The same

compounds. What

bone has not yet

is

own

is

true of nat-

potentially flesh or

not is the mark of a man tinguish what is self-evident from what is not. (This state of mind is clearly possible. A man blind from birth might reason about colours. Presumably therefore such persons must be

and does not form specks'5 ified in the definition, which we name in defining what flesh or bone is. Thus in the second sense of 'nature' it would be the shape or form (not separable except in statement) of [5] things which have in themselves a source

talking about words without any thought to

of motion.

correspond.)

man,

vious that there are [5]

and

Some

to

prove what

things of this kind,

obvious by what is who is unable to dis-

is

identify the nature or substance of a

[10] natural object with that immediate constituent of it which taken by itself is without

arrangement,

e.g. the

wood

is

the 'nature' of

the bed, and the bronze the 'nature' of the statue.

As an

indication of this Antiphon points out you planted a bed and the rotting wood acquired the power of sending up a shoot, it would not be a bed that would come up, but wood which shows that the arrangement in [75] accordance with the rules of the art is merely an incidental attribute, whereas the real that

if

—

nature is the other, which, further, persists continuously through the process of making.

But has

if

itself

the material of each of these objects the

same

relation to

something

else,

its

exist 'by nature', until

is

it

'nature',

receives the

(The combination of the two, e.g. not 'nature' but 'by nature' or 'nat-

ural'.)

The form indeed matter; for a thing

what

it

is

when

it

is

'nature' rather than the

more properly

said to be has attained to fulfilment

is

than when it exists potentially. Again man is born from man, but not bed from bed. That is why people say that the figure is not the nature if the bed [10] of a bed, but the wood is sprouted not a bed but wood would come up. But even if the figure is art, then on the same principle the shape of man is his nature. For man is born from man. We also speak of a thing's nature as being exhibited in the process of growth by which its nature is attained. The 'nature' in this sense is not like 'doctoring', which leads not to the [75] art of doctoring but to health. Doctoring

—

PHYSICS

270

must

from the

194 b

not lead to it. But it is not in this way that nature (in the one sense) is related to nature (in the other). What grows

matical lines, but ematical.

qua growing grows from something

the matter,

start

art,

into

something. Into what then does it grow? Not into that from which it arose but into that to which it tends. The shape then is nature. 'Shape' and 'nature', it should be added, are [20] used in two senses. For the privation too is in a way form. But whether in unqualified

coming to be there is privation, i.e. a contrary what comes to be, we must consider later. 1

to

qua

physical, not

qua math-

Since 'nature' has two senses, the form and

we must investigate its objects as the essence of snubness. That is, such things are neither independent of matter nor

we would

can be defined in terms of matter only. Here [75] too indeed one might raise a difficulty. Since there are two natures, with which is the Or should he investigate the combination of the two? But if the combination of the two, then also each severally.

physicist concerned?

Does

belong then to the same or to different know each severally? If we look at the ancients, physics would [20] seem to be concerned with the matter. (It was only very slightly that Empedocles and Democritus touched on the forms and the it

sciences to

We

have distinguished, then, the different in which the term 'nature' is used. The next point to consider is how the mathematician differs from the physicist. Obviously physical bodies contain surfaces and volumes,

ways

and

and these are the

essence.)

the writers on physics obviously do discuss [jo] their shape also and whether the earth

But if on the other hand art imitates nature, and it is the part of the same discipline to know the form and the matter up to a point (e.g. the doctor has a knowledge of health and also of bile and phlegm, in which health is realized, and the builder both of the form of the house [25] and of the matter, namely that it is bricks and beams, and so forth): if this is so, it would be the part of physics also to know na-

and

ture in both

lines

points,

subject-

matter of mathematics. [25] Further, is astronomy different from physics or a department of it ? It seems absurd that the physicist should be supposed to

the nature of sun or moon, but not to

any

know know

of their essential attributes, particularly as

the world are spherical or not.

Now

the mathematician, though

he too treats of these things, nevertheless does not treat of them as the limits of a physical body; nor does he consider the attributes indicated as the attributes of such bodies. That is why he separates them; for in thought they are separable from motion, and it makes no difference, nor does any falsity result, if they are

senses.

its

Again, 'that for the sake of which', or the end, belongs to the same department of knowledge as the means. But the nature is the end or 'that for the sake of which'. For if a thing undergoes a continuous change and there is a stage

which

this stage

is last,

is

the end or

[50] 'that for the sake of which'. (That is why the poet was carried away into making an

when he

[35] separated. The holders of the theory of the same, though they are not aware

absurd statement

Forms do

for the sake of

of

every stage that is last claims to be an end, but only that which is best.) For the arts make their material (some simply 'make' it, others make it serviceable), and we use everything as if it was there for our [55] sake. (We also are in a sense an end.

it;

for they separate the objects of physics,

which are less separable than those of mathe194 a matics. This becomes plain if one tries to state in each of the two cases the definitions of the things and of their attributes. 'Odd' and 'even', 'straight' and 'curved', and likewise 'number', 'line', and 'figure', do not involve [5] motion; not so 'flesh' and 'bone' and 'man'

—

these are defined like 'snub nose', not like

'curved'.

Similar evidence

is

supplied by the

more

physical of the branches of mathematics, such as optics, harmonics, in a

way

and astronomy. These are While

the converse of geometry.

geometry investigates physical lines but not [10] qua physical, optics investigates mathe1 On Generation and Corruption, 1. 3.

That

born'.

for the sake of which' has

the distinction

osophy. 3 )

is

made

end For not

said 'he has the

which he was

in our

2

two

senses:

work On

Phil-

which govern 194 b the matter and have knowledge are two, namely the art which uses the product and the art which directs the production of it. That is

why but

arts, therefore,

the using art also

it

differs in that

as the art 8

The

which

Kock, Com. An.

* I.e. in

is

it

is

in a sense directive;

knows

the form, where-

directive as being concerned

Fr. in, p. 493. De Philosophia.

the dialogue

195

BOOK

J

II,

CHAPTERS

1-3

271

which are brought about something else as means

with production knows the matter. For the

the intermediate steps

helmsman knows and prescribes what sort helm should have, the other from what wood it should be made and by means of what operations. In the products of art, however, we make the material with a view to

through the action of towards the end, e.g. reduction of flesh, purging, drugs, or surgical instruments are means 195 a towards health. All these things are 'for

[5]

of form a

the function, whereas in the products of nature

the sake of the end, though they differ from one another in that some are activities, others

the matter

instruments.

is

there

all

along.

Again, matter is a relative term: to each form there corresponds a special matter. How far then must the physicist know the form or [10] essence? Up to a point, perhaps, as the doctor must know sinew or the smith bronze

understands the purpose of each): and the physicist is concerned only with things whose forms are separable indeed, but (i.e.

until

he

do not

exist apart

ten by

man and

of existence

from matter.

Man

by the sun as well.

is

begot-

The mode

and essence of the separable

it

is

[75] the business of the primary type of phi-

losophy to define.

Now that we have established these distinctions, we must

proceed to consider causes, their char-

and number. Knowledge is the object of our inquiry, and men do not think they know acter

a thing

till

they have grasped the 'why' of

it

[20] (which is to grasp its primary cause). So clearly we too must do this as regards both

coming

to be and passing away and every kind of physical change, in order that, know-

ing their principles, we may try to refer to these principles each of our problems. In one sense, then, (1) that out of which a thing comes to be and which persists, is called

bronze of the statue, the silver [25] of the bowl, and the genera of which the bronze and the silver are species. In another sense (2) the form or the arche'cause', e.g. the

type,

i.e.

the statement of the essence,

and

its

genera, are called 'causes' (e.g. of the octave

This then perhaps exhausts the number of in which the term 'cause' is used.

ways

As

the

word has

several senses,

that there are several causes of the

it

follows

same thing

(not merely in virtue of a concomitant attri[5] bute), e.g. both the art of the sculptor and the bronze are causes of the statue. These are causes of the statue qua statue, not in virtue of anything else that it may be only not in the same way, the one being the material cause, the other the cause whence the motion comes. Some things cause each other recipro[10] cally, e.g. hard work causes fitness and vice versa, but again not in the same way, but the one as end, the other as the origin of change. Further the same thing is the cause of contrary results. For that which by its pres-

—

ence brings about one result is sometimes blamed for bringing about the contrary by its absence. Thus we ascribe the wreck of a ship to the absence of the pilot whose presence was the cause of its safety. [75] All the causes now mentioned fall into four familiar divisions. The letters are the causes of syllables, the material of artificial products, fire, &c, of bodies, the parts of the whole, and the premisses of the conclusion, in the sense of 'that

from which'. Of

these pairs

[20] the one set are causes in the sense of substratum, e.g. the parts, the other set in the

—

the whole and the combinaand the form. But the seed and the doctor and the adviser, and generally the maker, are all sources whence the change or stationariness sense of essence tion

the relation of 2 1, and generally number), and the parts in the definition. Again (3) the primary source of the change [50] or coming to rest; e.g. the man who gave

originates, while the others are causes in the

advice

it.

:

child,

is

a cause, the father

is

cause of the

and generally what makes of what causes change of what

made and what

is is

changed.

Again (4) in the sense of end or 'that for the sake of which' a thing is done, e.g. health the cause of walking about. ('Why is he walking about?' we say. 'To be healthy', and, having said that, we think we have assigned [35] the cause.) The same is true also of all is

sense of the end or the good of the rest; for 'that for the sake of which' means what is best

[25] and the end of the things that lead up to (Whether we say the 'good itself or the 'ap-

parent good' makes no difference.) Such then is the number and nature of the kinds of cause. Now the modes of causation are many, though when brought under heads they too can be reduced in number. For 'cause' is used in many senses and even within the same kind [50] one may be prior to another (e.g. the doctor and the expert are causes of health, the

PHYSICS

272 relation 2

and number of the octave), and inclusive to what is particular.

1

:

always what

is

196

[jo]

number of

causes and the

modes

a

of causa-

tion.

Another mode of causation is the incidental and its genera, e.g. in one way 'Polyclitus', in another 'sculptor' is the cause of a statue, be[^5] cause 'being Polyclitus' and 'sculptor' are incidentally conjoined. Also the classes in which the incidental attribute is included; thus 'a man' could be said to be the cause of a

195 b statue

An

or,

generally,

'a

living creature'.

may

be more or less remote, e.g. suppose that 'a pale man' or 'a musical man' were said to be the cause of the incidental attribute too

statue.

All causes, both proper [5] be

spoken of either

and

incidental,

may

as potential or as ac-

tual; e.g. the cause of a

house being built

is

either 'house-builder' or 'house-builder building'.

Similar

distinctions

can be

made

in

the

things of which the causes are causes, e.g. of 'this statue' or of 'statue' or of 'image' generally, of 'this terial'

bronze' or of 'bronze' or of 'ma-

generally. So too with the incidental at-

[10] tributes. Again we may use a complex expression for either and say, e.g. neither 'Polyclitus'

nor 'sculptor' but 'Polyclitus, sculp-

tor'.

All these various uses, however,

come

to six

number, under each of which again the usage is twofold. Cause means either what is

But chance

also

among

causes:

and

come

and spontaneity are reckoned

many

to be as a result of

We

spontaneity.

[5] ilarly in other cases of chance possible, they maintain, to find

which

is

the cause; but real,

particular or a genus, or an incidental attri-

are by chance

either as actual or as potential. is

at

The

difference

much, that causes which are actually work and particular exist and cease to exist this

simultaneously with their effect, e.g. this healing person with this being-healed person and that housebuilding man with that being-built house; but this is not always true of potential [20] causes the house and the housebuilder do not pass away simultaneously. In investigating the cause of each thing it is always necessary to seek what is most precise (as also in other things): thus man builds because he is a builder, and a builder builds in virtue of his art of building. This last cause then is prior: and so generally. [25] Further, generic effects should be assigned to generic causes, particular effects to

—

particular causes, e.g. statue to sculptor, this statue to this sculptor;

and powers are

relative

to possible effects, actually operating causes to

things which are actually being effected.

This must

suffice

for our account of the

not chance, for

if

it

that they too did not believe that anything

chance. But there

[75] bute or a genus of that, and these either complex or each by itself; and all six

always something

it is

would seem strange indeed, and the question might be raised, why on earth none of the wise men of old in speaking of the causes of generation and decay took ac[10] count of chance; whence it would seem chance were

in

as a

things are said both to be

chance and must inquire therefore in what manner chance and spontaneity are present among the causes enumerated, and [35] whether they are the same or different, and generally what chance and spontaneity are. Some people even question whether they are 196a real or not. They say that nothing happens by chance, but that everything which we ascribe to chance or spontaneity has some definite cause, e.g. coming 'by chance' into the market and finding there a man whom one wanted but did not expect to meet is due to one's wish to go and buy in the market. Simto

is

is

by

a further circumstance that

Many

things both come to be and and spontaneity, and although all know that each of them can be ascribed to some cause (as the old argument said which surprising.

is

[75] denied chance), nevertheless they speak of some of these things as happening by chance

and others to

have

way

not.

For

this reason also they

at least referred to the

ought

matter in some

or other.

Certainly the early physicists found no place

among the

causes which they recogmind, fire, or the like. This is strange, whether they supposed that there is no such thing as chance or whether they [20] thought there is but omitted to mention it and that too when they sometimes used it, as Empedocles does when he says that the air is not always separated into the highest region, but 'as it may chance'. At any rate he says in his cosmogony that 'it happened to run that for chance

nized

—

love, strife,

—

way

1

but it often ran otherwise.' us also that most of the parts of animals came to be by chance. [25] There are some too who ascribe this heavenly sphere and all the worlds to spon-

He

1

at that time,

tells

Fr. g 3 .

BOOK

197« taneity.

They

taneously,

i.e.

II,

CHAPTERS

say that the vortex arose sponthe motion that separated and

arranged in its present order all that exists. This statement might well cause surprise. For they are asserting that chance is not responsible for the existence or generation of animals and [jo] plants, nature or mind or something of the kind being the cause of them (for it is not any chance thing that comes from a given seed but an olive from one kind and a man from another); and yet at the same time they assert

3-5

273

applicable. (Events that are for the sake of

something include whatever may be done thought or of nature.) Things of

result of

kind, then,

when

they

come

as a this

to pass incidental-

be 'by chance'. For just as a thing something either in virtue of itself or incidentally, so may it be a cause. For instance,

ly are said to

[25]

is

the housebuilding faculty

is

in virtue of itself

the cause of a house, whereas the pale or the

that the heavenly sphere

musical is the incidental cause. That which is per se cause of the effect is determinate, but the incidental cause is indeterminable, for the pos-

visible things arose spontaneously,

sible attributes of

and the divinest of having no and [55] such cause as is assigned to animals plants. Yet if this is so, it is a fact which deserves to be dwelt upon, and something might 196 b well have been said about it. For besides the other absurdities of the statement,

it

make

it

is

the

more absurd

that people should

when they see nothing coming to be spontaneously in the heavens, but much happening by chance among the things which as they say are not

due

to chance;

whereas

we

should have

expected exactly the opposite. believe that [5] Others there are who, indeed, chance is a cause, but that it is inscrutable to human intelligence, as being a divine thing

and

mystery. inquire what chance and they are the same or whether are, spontaneity full of

Thus we must

different,

and how they

fit

into our division of

causes.

able.

To resume

of the things that come to pass by necessity and always, or for the most part. But as there is a events third class of events besides these two which all say are 'by chance' it is plain that

—

—

such a thing as chance and spontaneity; [75] for we know that things of this kind are due to chance and that things due to chance are

there

is

of this kind.

But, secondly,

some events

are for the sake

of something, others not. Again,

some

of the

accordance with deliberate intention, others not, but both are in the class of things which are for the sake of something. [20] Hence it is clear that even among the

former

class are in

things which are outside the necessary and the

normal, there are some in connexion withwhich the phrase 'for the sake of something' is

thing of this events which

are for the sake of something,

it is said to be spontaneous or by chance. (The distinction between the two must be made later 1 for the present it is sufficient if it is plain that both are in the sphere of things done for the sake of something.)

—

Example:

A man

is

engaged in collecting He would have gone

subscriptions for a feast.

such and such a place for the purpose of if he had known. He [^5] actually went there for another purpose, and it was only incidentally that he got his money by going there; and this was not due to the fact that he went there as a rule or neces197 a sarily, nor is the end effected (getting the money) a cause present in himself it belongs to the class of things that are intentional to

getting the money,

—

when

others for the most part. It is clearly of neither of these that chance is said to be the cause, nor can the 'effect of chance' be identified with any

when a among

[jo] kind comes to pass

and the [10] First then we observe that some things always come to pass in the same way, and

an individual are innumerthen;

result of intelligent deliberation. It

is

these conditions are satisfied that the

man

is said to have gone 'by chance'. If he had gone of deliberate purpose and for the sake of this if he always or normally went there when he was collecting payments he would not be said to have gone 'by chance'. [5] It is clear then that chance is an incidental

—

—

cause in the sphere of those actions for the sake which involve purpose. Intelligent reflection, then, and chance are in the

of something

same sphere,

for purpose implies intelligent

reflection. It is necessary, no doubt, that the causes of what comes to pass by chance be indefinite; and that is why chance is supposed to belong to the class of the indefinite and to be in[10] scrutable to man, and why it might be

that, in a way, nothing occurs by chance. For all these statements are correct, because they are well grounded. Things do, in a way, occur by chance, for they occur incidentally and chance is an incidental cause. But

thought

1

In chapter

6.

PHYSICS

2 74

—

not the cause without qualification of anything; for instance, a housebuilder is the cause of a house; incidentally, a fluteplayer may be so. [75] And the causes of the man's coming and getting the money (when he did not come for the sake of that) are innumerable. He may strictly

—

it

is

have wished to see somebody or been following somebody or avoiding somebody, or may have gone to see a spectacle. Thus to say that chance is a thing contrary to rule is correct. For 'rule' applies to what is always true or true for the most part, whereas chance be[20] longs to a third type of event. Hence, to conclude, since causes of this kind are indefinite, chance too is indefinite. (Yet in some cases one might raise the question whether any incidental fact might be the cause of the chance occurrence, e.g. of health the fresh air or the sun's heat

may

be the cause, but having had

one's hair

cut cannot; for

causes are

more

some

incidental

relevant to the effect than

others.)

[25] Chance or fortune the result is good, 'evil'

is

called 'good'

when

when The

is evil.

it

197 b

[5] well-doing.

Hence what

is

not capable of

moral action cannot do anything by chance. Thus an inanimate thing or a lower animal or a child cannot do anything by chance, because it is incapable of deliberate intention; nor can 'good fortune' or 'ill fortune' be ascribed to them, except metaphorically, as Protarchus, 1 for example, said that the stones of which altars are

made

are fortunate because they are

[10] held in honour, while their fellows are trodden under foot. Even these things, how-

way be affected by chance, when dealing with them does something to them by chance, but not otherwise.

ever, can in a

who

one

is

The spontaneous on

hand

is

found

[75] both in the lower animals and in

many

inanimate objects. horse

the

though

his

the other

We

say, for

example, that

came 'spontaneously', because, coming saved him, he did not come

for the sake of safety. Again, the tripod 'of itself,

because, though

on

its

fall

for the sake of that.

when

it fell it

feet so as to serve for a seat,

Hence

it

is

clear that events

long to the general

it

fell

stood

did not

which (1)

class of things that

be-

may

of considerable magni-

come to pass for the sake of something, (2) do not come to pass for the sake of what actually

Thus one who comes within an ace of some great evil or great good is said to be fortunate or unfortunate. The mind affirms the

and (3) have an external cause, may be [20] described by the phrase 'from spontaneity'. These 'spontaneous' events are said to be

terms 'good fortune' and

when

either result

is

'ill

fortune' are used

tude.

presence of the attribute, ignoring the hair's [50] breadth of difference. Further, it is with reason that good fortune is regarded as unstable; for chance is unstable, as none of the things which result from it can be invariable or

normal.

Both are then, as I have said, incidental both chance and spontaneity in the sphere of things which are capable of coming to pass not necessarily, nor normally, and with [35] reference to such of these as might come

causes

—

—

to pass for the sake of something.

differ in that 'spontaneity' is the wider term. Every result of chance is from what is spontaneous, but not everything that is from what is spontaneous is from chance.

results

from chance

are appropriate to agents that are capable of

good fortune and of moral action

'from chance' if they have the further charbeing the objects of deliberate intention and due to agents capable of that mode of action. This is indicated by the phrase 'in vain', which is used when A, which is for the sake of B, does not result in B. For instance, taking a walk is for the sake of evacuation of the bowels; if this does not follow after walk-

acteristics of

we have walked 'in vain' and walking was 'vain'. This implies that [25] what is naturally the means to an end is 'in vain', when it does not effect the end towards which it was the natural means for it would be absurd for a man to say that he had bathed in vain because the sun was not eclipsed, since the one was not done with a view ing,

we

say that

that the

—

They

197 b Chance and what

results,

generally.

Therefore necessarily chance is in the sphere of moral actions. This is indicated by the fact that good fortune is thought to be the same, or nearly the same, as happiness, and happiness to be a kind of moral action, since it is

Thus the spontaneous is even according to its derivation the case in which the thing itself happens in vain. The stone that [50] struck the man did not fall for the pur-

to the other.

pose of striking him; therefore it fell spontaneously, because it might have fallen by the action of an agent and for the purpose of striking. The difference between spontaneity 1

Probably the reference

is

to the Protarchus described

as a pupil of Gorgias in Plato, Philebus, 58.

BOOK

198 b and what

II,

CHAPTERS

by chance is greatest in things that come to be by nature; for when anything

comes

results

to be contrary to nature,

[35] that

it

came

to be

we do

not say

by chance, but by spon-

Yet strictly this too is different from the spontaneous proper; for the cause of the latter is external, that of the former internal. 198* We have now explained what chance is

taneity.

and what spontaneity is, and in what they differ from each other. Both belong to the mode of causation 'source of change', for either some natural or some intelligent agent is always the cause; but in this sort of causation the of possible causes

is

number

and chance are causes of which though they might result from

[5 J Spontaneity

ef-

in-

have in

been caused by something incidentally. Now since nothing which is incidental is prior to what is per se, it is clear that no incidental cause can be prior to a cause per se. Spontaneity and chance, fact

therefore, are posterior to intelligence

and na-

[10] ture. Hence, however true it may be that the heavens are due to spontaneity, it will still

be true that intelligence and nature will be and of many things in

prior causes of this All it

*75

structible things.

The

question 'why', then,

besides.

answered by and to the respect of com-

is

reference to the matter, to the form,

primary moving cause. For in

mostly in this last way that 'what comes to be after what? what was the primary agent or patient ? and so at each step of the series. [55] Now the principles which cause motion in a physical way are two, of which one is not physical, as it has no principle of motion in ing to be

it

is

causes are investigated

infinite.

fects

telligence or nature,

5-8

such as are not of this kind are no longer inside the province of physics, for they cause motion not by possessing motion or a source of motion in themselves, but being themselves incapable of motion. Hence there are three [jo] branches of study, one of things which are incapable of motion, the second of things in motion, but indestructible, the third of de-

—

'

198 b itself. Of this kind is whatever causes movement, not being itself moved, such as ( 1 that which is completely unchangeable, the primary reality, and (2) the essence of that which is coming to be, i.e. the form; for this is the end or 'that for the sake of which'. Hence since nature is for the sake of something, we must know this cause also. We must [5] explain the 'why' in all the senses of the ( 1 ) that from this that will nec-

term, namely, It is

clear then that there are causes,

and that

number of them is what we have The number is the same as that of the

essarily result ('from this' either

without qual-

most cases); (2) that

must

[75] the

ification or in

stated.

be so if that is to be so' (as the conclusion presupposes the premisses); (3) that this was the essence of the thing; and (4) because it is better thus (not without qualification, but with reference to the essential nature in each case).

comprehended under the question 'why'. 'why' is referred ultimately either (1), in things which do not involve motion, e.g. in mathematics, to the 'what' (to the definition of 'straight line' or 'commensurable', &c), or (2) to what initiated a motion, e.g. 'why did they go to war? because there had been a raid'; [20] or (3) we are inquiring 'for the sake of what?' 'that they may rule'; or (4), in the case of things that come into being, we are looking for the matter. The causes, therefore, things

The

—

—

are these

Now,

and

so

many

in

number.

the causes being four,

it

is

the busi-

know

about them all, and if he refers his problems back to all of them, he will assign the 'why' in the way roper to his science the matter, the form, the f25] mover, 'that for the sake of which'. The

ness of the physicist to

—

last

three often coincide; for the 'what'

and

'that for the sake of which' are one, while the primary source of motion is the same in species as these (for

man

generates man), and so

which cause movement by being themselves moved; and too,

in general, are all things

'this

8

We

[jo] must explain then (1) that Nature belongs to the class of causes which act for the sake of something; (2) about the necessary and its place in physical problems, for all writers ascribe things to this cause, arguing that since the hot and the cold, &c, are of such and such a kind, therefore certain things necessarily are and come to be and if they mention any other [75] cause (one his 'friendship and strife', another his 'mind'), it is only to touch on it, and then good-bye to it. difficulty presents itself: why should not nature work, not for the sake of something, nor because it is better so, but just as the sky rains, not in order to make the corn grow, but

—

A

What is drawn up must cool, and what has been cooled must become water

of necessity ?

[20]

and descend, the

result of this being that the

PHYSICS

276 corn grows. Similarly

if a man's crop is spoiled on the threshing-floor, the rain did not fall for the sake of this in order that the crop might

—

—

be spoiled but that result just followed. Why then should it not be the same with the parts in nature, e.g. that our teeth should come up

—

the front teeth sharp, fitted for of necessity [25] tearing, the molars broad and useful for

grinding

down

the food

arise for this end, but

—

since they did not

was merely

it

a coinci-

dent result; and so with all other parts in which we suppose that there is purpose? Wherever then all the parts came about just what they would have been if they had come [jo] to be for an end, such things survived, being organized spontaneously in a fitting way; whereas those which grew otherwise perished and continue to perish, as Empedocles 1 says his 'man-faced ox-progeny' did.

Such are the arguments (and others of the kind) which may cause difficulty on this point. Yet it is impossible that this should be the true view. For teeth and all other natural [55] things either invariably or normally come about in a given way; but of not one of the results of chance or spontaneity is this true. We do not ascribe to chance or mere coinci199 a dence the frequency of rain in winter, but frequent rain in summer we do; nor heat in the dog-days, but only if we have it in winter. If then, it is agreed that things are either the result of coincidence or for an end, and these cannot be the result of coincidence or [5] spontaneity, it follows that they must be for an end; and that such things are all due to

nature even the champions of the theory which is before us would agree. Therefore action for an end is present in things which come to be

and are by nature. Further, where a

has a completion,

series

all

the preceding steps are for the sake of that. surely as in intelligent action, so in na-

Now

[10] ture; action,

action

if is

and

as in nature, so

nothing

interferes.

for the sake of

it is

Now

in each

intelligent

an end; therefore the

Thus if a house, made by nature, it would have been made in the same way as it is now by art; and if things made by nature were made also by art, they would come to be in the same way as by nature. Each step then nature of things also is e.g. had been a thing

so.

[75] in the series is for the sake of the next; art partly completes what nature

and generally

cannot bring to a her. 1

If,

finish,

and

partly imitates

therefore, artificial products are for the

Ft.6i.2.

199 b

sake of an end,

The

products.

so clearly also are natural

relation

the

of

later

to

the

terms of the series is the same in both. [20] This is most obvious in the animals other than man: they make things neither by art nor after inquiry or deliberation. Wherefore people discuss whether it is by intelligence or by some other faculty that these creatures work, spiders, ants, and the like. By gradual advance earlier

in this direction

we come

to see clearly that in

[25] plants too that is produced which is conducive to the end leaves, e.g. grow to pro-

—

vide shade for the fruit. If then

it is both by nature and for an end that the swallow makes

nest

its

and the spider

its

web, and plants grow and send their

leaves for the sake of the fruit

down

(not up) for the sake of nourishplain that this kind of cause is [jo] operative in things which come to be and

roots

ment,

it

is

And

since 'nature' means two and the form, of which the latter is the end, and since all the rest is for the sake of the end, the form must be the

are by nature.

things, the matter

cause in the sense of 'that for the sake of which'. Now mistakes come to pass even in the operations of art: the

grammarian makes

a

mistake in writing and the doctor pours out [55] the wrong dose. Hence clearly mistakes 199 b are possible in the operations of nature also. If then in art there are cases in which

what is rightly produced serves a purpose, and if where mistakes occur there was a purpose in what was attempted, only it was not attained, so must it be also in natural products, and [5] monstrosities will be failures in the purThus in the original combina-

posive effort.

tions the 'ox-progeny' if they failed to reach a determinate end must have arisen through the corruption of some principle corresponding to is now the seed. Further, seed must have come into being first, and not straightway the animals: the

what

words 'whole-natured meant seed. Again, in plants too [10]

means

ganization

to end,

is

less.

first

we

.' 2 .

.

must have

find the relation of

though the degree of

Were

or-

there then in plants

'manheaded ox-progeny', or not? An absurd suggestion; yet there must have been, if there were also 'olive-headed vine-progeny', like the

such things among animals. Moreover, among the seeds anything must have come to be at random. But the person who asserts this entirely does away with 'na2

Empedocles, Fr. 62.

4.

BOOK

200b and what

ture'

exists

II,

'by nature'.

CHAPTERS

For

[75] those things are natural which, by a continuous movement originated from an internal

some completion: the same not reached from every prin-

principle, arrive at

completion is ciple; nor any chance completion, but always the tendency in each is towards the same end, if there is no impediment. The end and the means towards it may come [20] about by chance. We say, for instance, that a stranger has come by chance, paid the ransom, and gone away, when he does so as if he had come for that purpose, though it was not for that that he came. This is incidental, for chance is an incidental cause, as I remarked before. 1 But when an event takes flace always or for the most part, it is not 25] incidental or by chance. In natural products the sequence is invariable, if there is no impediment. It is absurd to suppose that purpose is not present because we do not observe the agent deliberating. Art does not deliberate. If the ship-building art were in the wood, produce the same results by nature. fore,

purpose

is

present in

art,

it

would

it

If,

is

there-

present

[jo] also in nature. The best illustration is doctoring himself: nature is like

a doctor that.

It is plain then that nature is a cause, a cause that operates for a purpose.

As regards what

is

'of necessity',

we must

ask

[35] whether the necessity is 'hypothetical', or 'simple' as well. The current view places what is

of necessity in the process of production, just

200* as if one were to suppose that the wall of a house necessarily comes to be because what is heavy is naturally carried downwards and what is light to the top, wherefore the stones and foundations take the lowest place, with earth above because it is lighter, and wood at [5] the top of all as being the lightest. Whereas, though the wall does not come to be without these,

it is

material cause:

not due to these, except as its it comes to be for the sake of

and guarding certain things. Similarly in all other things which involve production for an end; the product cannot come to be without things which have a necessary nature, but it is not due to these (except as its ma[10] terial); it comes to be for an end. For instance, why is a saw such as it is? To effect so-and-so and for the sake of so-and-so. This sheltering

1

io6 b 23-7.

8-9

277

end, however, cannot be realized unless the saw is made of iron. It is, therefore, necessary it to be of iron, if we are to have a saw and perform the operation of sawing. What is necessary then, is necessary on a hypothesis; it

for

is

not a result necessarily determined by anteis in the matter, while 'that

cedents. Necessity

for the sake of which'

in the definition.

is

[75] Necessity in mathematics is in a way similar to necessity in things which come to be

through the operation straight line

is

what

it

is

it

But not conversely; though

gles are not equal to

straight line

is

two

a

necessary that

the angles of a triangle should equal angles.

Since

nature.

of is,

two if

right

the an-

right angles, then the

not what

it

is

either.

But in

come to be for an end, the reverse is true. If the end is to exist or does exist, [20] that also which precedes it will exist or things which

does exist; otherwise just as there, if the conclusion is not true, the premiss will not be true, so here the end or 'that for the sake of which' will not exist. For this too is itself a starting-point, but of the reasoning, not of the action; while in mathematics the startingpoint is the starting-point of the reasoning only, as there is no action. If then there is to be [25] a house, such-and-such things must be made or be there already or exist, or generally the matter relative to the end, bricks and stones if it is a house. But the end is not due to these except as the matter, nor will it come to exist because of them. Yet if they do not exist at all, neither will the house, or the saw the former in the absence of stones, the latter in the absence of iron just as in the other case the premisses will not be true, if the angles of the triangle are not equal to two right

—

—

angles.

[jo]

The

what we

necessary in nature, then,

is

plainly

by the name of matter, and the changes in it. Both causes must be stated by the physicist, but especially the end; for that is

call

and and the

the cause of the matter, not vice versa;

the end

is

beginning [55]

'that for the sake of which', starts

from the

definition

or es-

sence; as in artificial products, since a

200b house is of such-and-such a kind, certain things must necessarily come to be or be there already, or since health

must necessarily come

is

this,

these things

to be or be there already.

Similarly if man is this, then these; if these, then those. Perhaps the necessary is present also in the definition.

For

if

one defines the

[5] operation of sawing as being a certain kind of dividing, then this cannot come about un-

PHYSICS

278

saw has

the

less

and

teeth of a certain kind;

these cannot be unless

it is

of iron.

For

in the

201*

definition too there are it

BOOK

were,

some

parts that are, as

matter.

its

III

Now each

of these belongs to

all its

subjects

two ways: namely (1) substance

in either of

Nature

has been defined as a 'principle of moand change', and it is the subject of our inquiry. We must therefore see that we understand the meaning of 'motion'; for if it were unknown, the meaning of 'nature' too would

the one

tion

(2) in quality, white and black; (3) in quantity, complete and incomplete; (4) in respect of locomotion, upwards and downwards as

many

be unknown.

types of motion or change as there are

mean-

[75] When we have determined the nature of motion, our next task will be to attack in the same way the terms which are involved in it. Now motion is supposed to belong to the class of things which are continuous; and the infinite presents itself first in the continuous that is how it comes about that 'infinite' is often used in definitions of the continuous

ings of the

('what

is

infinitely divisible

is

continuous').

[20] Besides these, place, void, and time are thought to be necessary conditions of motion. Clearly, then, for these reasons

and

also be-

cause the attributes mentioned are common to, and coextensive with, all the objects of our science,

and

we must

first

take each of

them

in

hand

positive form, the other privation;

is

[5]

and heavy. Hence there are

or light

We

word

now

have

'is'.

before us the distinctions in

the various classes of being between fully real

[10] Def.

The

is

it

what

—namely, of what

alterable

is

what can be increased and its what can be decreased (there is no common name), increase and decrease: of what can come to be and can pass away, coming to be and passing away: of what can be carried along, locomotion.

[75]

Examples

motion.

When

will elucidate this definition of

the buildable, in so far as

ing, leaping, ripening, ageing.

To begin then, We may start by

as

we

said,

with motion.

and

also in fulfilment

what

an-

'relative'

is

used with

move and what can be moved. For 'what can cause movement' is relative to 'what can be moved', and vice versa. Again, there is no such thing as motion over and above the things. It is always with respect to substance or to quantity or to quality or to

what changes changes. But

it is imanything com[35] mon to these which is neither 'this' nor 201 a quantum nor quale nor any of the other

possible, as

we

The same

thing,

if it is

built,

of a certain kind, can

hot and actually cold. will act and be acted on by one another in many ways: each of them will be capable at the same time of causing alteration and of being altered. Hence, too, what effects motion as a physical agent can be moved:

'this',

[50] reference to (1) excess and defect, (2) agent and patient and generally what can

place that

roll-

being

it is

exists as potential

—one being a

being.

word

this

building. Similarly, learning, doctoring,

fully real,

[20] be both potential and fully real, not indeed at the same time or not in the same re-

other 'so much', a third 'such', and similarly in each of the other modes of the predication of

Further, the

is

it is

and

is

what what

distinguishing (1) exists in a state of fulfilment only, (2) exists as potential, (3)

mo-

altera-

opposite

butes.

[25]

qua

ble, alteration: of

just that,

it.

is

exists poten-

exists potentially, is

For the investigation of special attributes comes after that of the common attridiscuss

what

potential.

fulfilment of

so far as

tially, in

tion

and what

assert, to find

predicates. Hence neither will motion and change have reference to something over and above the things mentioned, for there is nothing over and above them.

but

spect,

e.g. potentially

Hence at once such things

when

a thing of this kind causes motion,

it is

moved. This, indeed, has led some people to suppose that every mover is moved. But this question depends on another set of arguments, and the truth will be made [25]

itself also

clear later.

1

It is

motion, though

possible for a thing to cause it is itself

incapable of being

moved. the fulfilment of what is potential when already fully real and operates not as itself

It is it is

but as movable, that is motion. What I mean by 'as' is this: Bronze is potentially a statue. [50] But it is not the fulfilment of bronze as bronze which is motion. For 'to be bronze' and 'to be a certain potentiality* are not the same. 1 viii. 5.

BOOK

202*

II,

CHAPTER 9— BOOK

they were identical without qualification,

If

in definition, the fulfilment of

i.e.

bronze as bronze

would have been motion. But they are not the same, as has been said. (This is obvious in con[35] traries. 'To be capable of health' and 'to be capable of illness' are not the same, for if 201 b they were there would be no difference between being ill and being well. Yet the subis

—

humour

—

—

both of health and of sickness whether it is one and the same.) or blood We can distinguish, then, between the two just as, to give another example, 'colour' and

ject

'visible' are different

filment of

what

is

—and

clearly

it is

the ful-

potential as potential that

is

So this, precisely, is motion. Further it is evident that motion is an attribute of a thing just when it is fully real in this way, and neither before nor after. For each thing of this kind is capable of being at one time actual, at another not. Take for instance [5] motion.

the buildable as buildable. The actuality of the [10] buildable as buildable is the process of

building. For the actuality of the buildable must be either this or the house. But when there

is

a house, the buildable

buildable.

On

the other hand,

which is being built. The being built must be the kind quired. But building is a kind the same account will apply to able

is

it is

no longer the build-

process then of of actuality reof motion,

III,

CHAPTERS

yet a thing that

motion

is

This It is

and

also

from the

otherwise.

could not easily put motion and change genus this is plain if we consider where some people put it; they identify motion [20] with 'difference' or 'inequality' or 'not being'; but such things are not necessarily moved, whether they are 'different' or 'unequal' or

One

—

Nor

change either to or from from their opposites. The reason why they put motion into these is thought to be some[ 2 5] genera is that it thing indefinite, and the principles in the sec'non-existent'

;

is

these rather than to or

ond column are indefinite because they are privative: none of them is either 'this' or 'such' or comes under any of the other modes of predication. The reason in turn why motion is thought to be indefinite

cannot be an actuality a thing that is merely capable of having a [ jo] certain size is not undergoing change, nor is

that

it

classed simply as a potentiality or as

—

but

is

why

it is

hard

what motion is. with privation or with

to grasp it

none of There remains then the [55] suggested mode of definition, namely that 202 a it is a sort of actuality, or actuality of the potentiality or with sheer actuality, yet

these seems possible.

kind described, hard

to grasp,

but not incapa-

ble of existing.

The mover too is moved, as has been said every mover, that is, which is capable of mo-

—

and whose immobility is rest when a is subject to motion its immobility is rest. [5] For to act on the movable as such is just to move it. But this it does by contact, so that at the same time it is also acted on. Hence we can define motion as the fulfilment of the movable qua movable, the cause of the attribute being contact with what can move, so that the mover is also acted on. The mover or agent will always be the vehicle of a form, either a 'this' or tion,

thing

[10] a 'such', which, when it acts, will be the source and cause of the change, e.g. the full-

formed man begets man.

man from what

is

poten-

tially

ble

in another

and

and

The soundness of this definition is evident both when we consider the accounts of motion it

to be a sort of actuality,

necessary to class

solution of the difficulty that

about the motion

defining

actually of a certain size,

is

thought

incomplete, the reason for this view being that the potential whose actuality it is is incomplete.

The

that the others have given,

279

the other kinds

[75] also.

difficulty of

1-3

—

is

plain. It

—whether

is

it is

is

raised

in the

mova-

the fulfilment of this poten-

and by the action

of that which has the power of causing motion; and the actuality of that which has the power of causing motion is [75] not other than the actuality of the movable, for it must be the fulfilment of both. A thing is capable of causing motion because it can do this, it is a mover because it actually does it. But it is on the movable that it is capable of acting. Hence there is a single actuality of both alike, just as one to two and two to one are the same interval, and the steep ascent and tiality,

—

[20] the steep descent are one for these are one and the same, although they can be described in different ways. So it is with the mover

and the moved.

This view has a dialectical difficulty. Perhaps it is necessary that the actuality of the agent and that of the patient should not be the same. The one is 'agency' and the other 'patiency'; and the outcome and completion of the one is an 'action', that of the other a 'passion'. [25] Since then they are both motions, we may ask: in

what are

they,

if

they are different?

PHYSICS

280

Either (a) both are in what is acted on and moved, or (b) the agency is in the agent and the patiency in the patient. (If we ought to call the latter also 'agency', the word would be used in two senses.) Now, in alternative (b), the motion will be in the mover, for the same statement will hold of 'mover' and 'moved'. Hence either every

mover

moved, or, though having moved. If on the other hand (a) both are in what is moved and acted on both the agency and the patiency (e.g. both teaching and learning, though they are two, in the learner), then, first, [jo]

motion,

it

will be

will not be

—

203

from each other, that the two are one and the same. To generalize, teaching is not the same as learnare at a distance vectors

AB

ing, or

agency as patiency, in the

and

BA

X

and the 'actualization of Y through the action of X' differ in definition. What then Motion is, has been stated both generally and particularly. It is not difficult to see

how

each of

[25] teration

qua

is

its

types will be defined

alterable (or,

more

what can be acted

—generally and again

ticular case, building, healing, &c.

ject

How

will there

alterations of quality in one subtowards one definite quality? The thing is

al-

scientifically, the ful-

filment of what can act and

each, and, a second absurdity, a thing will have

same time.

—

the fulfillment of the alterable

on, as such)

at the

full sense,

[20] though they belong to the same subject, the motion; for the 'actualization of in Y'

the actuality of each will not be present in

two motions [35] De two

1

in

each par-

A

similar

definition will apply to each of the other kinds

of motion.

impossible: the actualization will be one.

202 b But (some one

will say)

it is

contrary to

reason to suppose that there should be one identical actualization of two things which are different in kind. Yet there will be, if teaching

and learning are the same, and agency and patiency. To teach will be the same as to learn, and to act the same as to be acted on the

—

teacher will necessarily be learning everything that he teaches, and the agent will be acted on. [5]

One may

reply:

not absurd that the actualization of one thing should be in another. Teaching is the activity of a person who can teach, yet the ( 1 ) It is

—

operation is performed on some patient it is not cut adrift from a subject, but is of A on B. (2) There is nothing to prevent two things having one and the same actualization, provided the actualizations are not described in the same way, but are related as what can act to

what

is

acting.

[10] (3)

Nor

is

it

necessary that the teacher

should learn, even if to act and to be acted on are one and the same, provided they are not the

same

in definition (as 'raiment'

and 'dress'),

but are the same merely in the sense in which the road from Thebes to Athens and the road from Athens to Thebes are the same, as has been explained above. 1 For it is not things which are in a way the same that have all their [75] attributes the same, but only such as have the same definition. But indeed it by no means follows from the fact that teaching is the same

same as to teach, any more than it follows from the fact that there is one distance between two things which as learning, that to learn

»Cf. E i8-20.

is

the

[jo]

The

spatial

science of nature is concerned with magnitudes and motion and time, and

each of these at least is necessarily infinite or even if some things dealt with by the science are not, e.g. a quality or a point it is not necessary perhaps that such things should be put under either head. Hence it is incumbent on the person who specializes in physics [^5] to discuss the infinite and to inquire whether there is such a thing or not, and, if finite,

—

there

is,

what

it is.

The

appropriateness to the science of this problem is clearly indicated. All who have

203 a touched on this kind of science in a way worth considering have formulated views about the infinite, and indeed, to a man, make it

a principle of things.

(1) Some, as the Pythagoreans and Plato, [5] make the infinite a principle in the sense of a self-subsistent substance, and not as a mere

some other thing. Only the Pythagoreans place the infinite among the objects of sense (they do not regard number as separable from these), and assert that what is outside the heaven is infinite. Plato, on the other hand, holds that there is no body outside (the Forms are not outside, because they are nowhere), yet that the infinite is present not only in the objects of sense but in the Forms also. attribute of

[10] Further, the Pythagoreans identify the inwith the even. For this, they say, when

finite

it is cut off and shut in by the odd, provides things with the element of infinity. An indica-

tion of this

the

is

gnomons

what happens with numbers. If are placed round the one, and

without the one, in the one construction the

204

BOOK

s

III,

CHAPTERS

always different, in the [75] other it is always the same. But Plato has two infinites, the Great and the Small. The physicists, on the other hand, all of them, always regard the infinite as an attribute figure that results

of a substance

is

which

is

different

from

it

and

3-4

281

to be the principle of other things,

causes, such as

Mind

or Friendship. Further

they identify it with the Divine, for it is 'deathless and imperishable' as Anaximander says,

with the majority of the physicists.

them. Those who make them limited in number never make them infinite in amount. But those who make the elements infinite in num[20] ber, as Anaxagoras and Democritus do, say that the infinite is continuous by contact

comes mainly from

compounded

infinite.

of the

homogeneous parts accord-

mixture in the same way as the All, on the ground of the observed fact that anything comes out of anything. For it is probably for this reason that he maintains that once upon a [25] time all things were together. (This flesh and this bone were together, and so of any thing: therefore all things:

and

at the

same

time too.) For there is a beginning of separation, not only for each thing, but for all. Each thing that comes to be comes from a similar body, and there is a coming to be of all things,

same time. Hence [50] there must also be an origin of coming to be. One such source there is which he calls Mind, and Mind begins its work of thinking from some starting-point. So necessarily all things must have been together at a certain time, and must have begun to be moved at a though

not,

it is

true, at the

certain time.

Democritus, for his part, asserts the connamely that no element arises from another element. Nevertheless for him the comtrary,

203 b mon body is a source of all things, differing from part to part in size and in shape. It is clear then from these considerations that the inquiry concerns the physicist.

Nor

is

without reason that they all make it a principle or source. We cannot say that the infinite it

(1)

From

the nature of time

for

is infi-

it

—

(2) From the division of magnitudes for the mathematicians also use the notion of the (3) If coming to be and passing away do not give out, it is only because that from which things

come

to be

is

infinite.

[20] (4) Because the limited always finds its limit in something, so that there must be no if everything is always limited by something different from itself. (5) Most of all, a reason which is peculiarly appropriate and presents the difficulty that is felt by everybody not only number but also mathematical magnitudes and what is outside the heaven are supposed to be infinite because they never give out in our thought.

limit,

—

[25]

The

last fact (that

what

outside

is

infinite,

and that there

worlds.

Why

is

an

is infi-

body

nite) leads people to suppose that

infinite

also

is

number

of

should there be body in one part Grant only

of the void rather than in another?

that mass is anywhere and it follows that it must be everywhere. Also, if void and place are infinite, there must be infinite body too, for in the case of eternal things what may be must be. [50] But the problem of the infinite is difficult: many contradictions result whether we supto exist or not to exist. If

pose

it

have

still

to ask

how

it

exists; as a

as the essential attribute of

some

neither way, yet none the less

thing which

is

are infinitely

many?

infinite or

it

exists,

entity?

is

er there

is

a sensible

we

substance or

Or

in

there some-

some things which

204 a The problem, however, which

finite.

im

—

nite.

Everything is either a source or derived from a source. But there cannot be a source of the infinite or limitless, for that would be a limit of it. Further, as it is a beginning, it is both

completion, and also a termination of all passzo] ing away. That is why, as we say, there is no principle of this, but it is this which is held

infinite

five considerations:

belongs to the physicist

uncreatable and indestructible. For there must be a point at which what has come to be reaches

of the

Belief in the existence

[75]

has no effect, and the only effectiveness which we can ascribe to it is that of a principle. [5]

to en-

compass all and to steer all, as those assert who do not recognize, alongside the infinite, other

belongs to the class of the so-called elements water or air or what is intermediate between

ing to the one, of the seed-mass of the atomic shapes according to the other. Further, Anaxagoras held that any part is a

and

specially

whethmagnitude which is inis

to investigate

We

must begin by distinguishing the various senses in which the term 'infinite' is used. ( 1 ) What is incapable of being gone through, because it is not in its nature to be gone through (the sense

in

which the voice

is

'invisi-

ble').

(2) What admits of being gone through, the process however having no termination, or

PHYSICS

282

what

(3)

scarcely

admits

of

gone

being

[5] through.

What

(4)

naturally admits of being gone

through, but is not actually gone through or does not actually reach an end. Further, everything that is infinite may be so in respect of addition or division or both.

204 b

be present in mathematical objects and things which are intelligible and do not have exten-

204 b

sion, as well as among sensible objects. inquiry (as physicists) is limited to its spe-

Our

cial subject-matter,

the objects of sense,

and we

have to ask whether there is or is not among them a body which is infinite in the direction of increase.

Now

it

impossible that the infinite should

is

be a thing which

from

is

itself infinite,

sensible objects. If the infinite

separable is

neither

We may begin with a dialectical argument and show as follows that there is no such thing. [5] If 'bounded by a surface' is the definition of body there cannot be an infinite body either Nor can number taken number or that

[10] a magnitude nor an aggregate, but is itself a substance and not an attribute, it will be

intelligible or sensible.

indivisible; for the divisible must be either a magnitude or an aggregate. But if indivisible,

which has number is numerable. If then the numerable can be numbered, it would also be possible to go through the infinite. [10] If, on the other hand, we investigate the question more in accordance with principles

then not

infinite,

except in the sense (1) in

which the voice is 'invisible'. But this is not the sense in which it is used by those who say that the infinite exsts, nor that in which we are investigating it, namely as (2), 'that which cannot be gone through'. But if the infinite exists [75] as an attribute, it would not be, qua infinite, an element in substances, any more than the invisible would be an element of speech, though the voice is invisible. Further,

how

can the

thing, unless both

which

way ?

it is

If

infinite

[20]

an

infinite

be

itself

any

number and magnitude,

of

essential attribute, exist in that

they are not substances, a fortiori the is

It is

appropriate to physics, the same result.

we

are led as follows to

The infinite body must be either (1) compound, or (2) simple; yet neither alternative is

possible.

if

(1) Compound the infinite body will not be, the elements are finite in number. For they

must be more than one, and the contraries must always balance, and no one of them can be infinite. [

If

one of the bodies

g ree short of the other

J 5]

falls in

amount while

pose

fire is finite in

plain, too, that the infinite cannot be

and

a given quantity of fire exceeds in

predicated of a subject. Hence it will be either [25] indivisible or divisible into infinites. But

same thing cannot be many

just as part of air

is air,

infinites.

(Yet

so a part of the infinite

would be infinite, if it is supposed to be a substance and principle.) Therefore the infinite must be without parts and indivisible. But this cannot be true of what is infinite in full completion: for it must be a definite quantity. Suppose then that infinity belongs to substance as an attribute. But, if so, it cannot, as [50] we have said, be described as a principle, but rather that of which it is an attribute the air or the even number. Thus the view of those who speak after the manner of the Pythagoreans is absurd. With the same breath they treat the infinite as substance, and divide it into parts. This discussion, however, involves the more [55] general question whether the infinite can

—

the it

same amount of

is

any

air in

numerically definite

—the

body.

On

ratio

the other hand,

it is

all

power

provided

directions

impossible

what has and the infinite

that each should be infinite. 'Body'

[20] extension in

—sup-

air is infinite

infinite body and annihilate the

will obviously prevail over finite

any de-

in potency

not.

an actual thing and a substance and principle. For any part of it that is taken will be infinite, if it has parts: for 'to be infinite' and 'the infinite' are the same, if it is a substance and not

the

in abstraction be infinite, for

is

what is boundlessly extended, so that the inbody would be extended in all directions ad infinitum. Nor (2) can the infinite body be one and simple, whether it is, as some hold, a thing over and above the elements (from which they genis

finite

erate the elements) or

is

not thus qualified.

We

must consider the former alternative; for there are some people who make this the infinite, and not air or water, in order that (a)

[25] the other elements may not be annihilated by the element which is infinite. They have contrariety with each other air is cold, water moist, fire hot; if one were infinite, the others by now would have ceased to be. As it is, they

—

say, the infinite

is

different

from them and

is

their source. It is

impossible, however, that there should

BOOK

205 b

III,

CHAPTERS

[30] be such a body; not because it is infinite that point a general proof can be given which applies equally to all, air, water, or any-

—on

—

thing else but simply because there is, as a matter of fact, no such sensible body, alongside the so-called elements. Everything can be resolved into the elements of which it is composed. Hence the body in question would have been present in our world here, alongside air and fire and earth and water: but nothing of the kind

is

[35] (&)

N° r

fire

283

[25] what is contrary to it. (This indeed is the reason why none of the physicists made fire or earth the one infinite body, but either water or air or what is intermediate between them, because the abode of each of the two was plainly

determinate, while the others have an ambigu-

ous place between up and down.)

But (ii) if the parts are infinite in number and simple, their proper places too will be infinite in number, and the same will be true of [jo] the elements themselves. If that

observed.

can

4-5

or any other of the ele-

ments be infinite. For generally, and apart from 205 a the question of how any of them could be infinite, the All, even if it were limited, cannot either be or become one of them, as Heraclitus says that at some time all things become fire. (The same argument applies also to the [5] one which the physicists suppose to exist alongside the elements: for everything changes from contrary to contrary, e.g. from hot to

sible,

and the places are

must be

finite,

finite; for the place

is

impos-

the whole too

and the body can-

each other. Neither is the whole place larger than what can be filled by the body (and then the body would no longer be [55] infinite), nor is the body larger than the place; for either there would be an empty space or a body whose nature it is to be nowhere. 205 b Anaxagoras gives an absurd account of not but

why

fit

the infinite

is

at rest.

He

says that the in-

an infinite sensible body. The following arguments give a general demonstration that it is not possible. [10] It is the nature of every kind of sensible body to be somewhere, and there is a place appropriate to each, the same for the part and for the whole, e.g. for the whole earth and for a single clod, and for fire and for a spark. Suppose (a) that the infinite sensible body is homogeneous. Then each part will be either immovable or always being carried along. Yet neither is possible. For why downwards rather than upwards or in any other direction? I mean, e.g. if you take a clod, where will it be [75] moved or where will it be at rest? For ex hypothesi the place of the body akin to it is infinite. Will it occupy the whole place, then?

being fixed. This because it is in itself, since nothing else conon the assumption that wherever anytains it [5] thing is, it is there by its own nature. But this is not true: a thing could be somewhere by compulsion, and not where it is its nature to be. Even if it is true as true can be that the whole is not moved (for what is fixed by itself and is in itself must be immovable), yet we must explain why it is not its nature to be moved. It is not enough just to make this statement and then decamp. Anything else might [10] be in a state of rest, but there is no reason why it should not be its nature to be moved. The earth is not carried along, and would not be carried along if it were infinite, provided it is held together by the centre. But it would not be because there was no other region in which it could be carried along that it would remain at the centre, but because this is its nature. Yet

And how ? What

in this case also

finite itself is the

cold).

The preceding cases serves to

consideration of the various it is or is not

show us whether

possible that there should be

rest

and

be ?

It

it

of

its

then will be the nature of

movement, or where

will either be at

will not be

—then

where But

—then

home everywhere it will be moved

moved; or it

will not

come

its

will they

every-

to rest.

if (b) the All has dissimilar parts, the proper places of the parts will be dissimilar [20] also, and the body of the All will have no

unity except that of contact. Then, further, the parts will be either finite or infinite in variety

of kind, (i) Finite they cannot be, for

All

is

if

the

some of them would have while the others were not, e.g.

to be infinite,

to be infinite,

or water will be infinite. But, as we have seen before, such an element would destroy

fire

cause of

its

—

we may

say that

it

fixes itself.

then in the case of the earth, supposed to be [75] infinite, it is at rest, not because it is infinite, but because it has weight and what is heavy rests at the centre and the earth is at the centre, similarly the infinite also would rest in itself, not because it is infinite and fixes itself, but owing to some other cause. If

Another

emerges at the same time. body ought to remain at rest. Just as the infinite remains at rest in itself because it fixes itself, so too any part of it [20] you may take will remain in itself. The appropriate places of the whole and of the part are alike, e.g. of the whole earth and

Any

difficulty

part of the infinite

PHYSICS

284 of a clod the appropriate place

gion; of

fire as a

is

the lower re-

whole and of a spark, the up-

per region. If, therefore, to be in itself is the place of the infinite, that also will be appropriate to the part.

Therefore

it

will

remain in

it-

self.

In general, the view that there is an infinite [25] body is plainly incompatible with the doctrine that there

necessarily a proper place for

is

every sensible body has either weight or lightness, and if a body has a natural locomotion towards the centre if it is

each kind of body,

if

heavy, and upwards if it is light. This would to be true of the infinite also. But neither character can belong to it: it cannot be either as a whole, nor can it be half the one and half [50] the other. For how should you divide it?

need

how can the infinite have the one part up and the other down, or an extremity and a

or

centre ?

general,

an

if it is

is

in place,

impossible that there should be

infinite place,

206 a

and

if

every body

is

in place,

there cannot be an infinite body.

Surely what

and what

is

is

in a special place

in place

is

is

in place,

in a special place. Just,

—

that then, as the infinite cannot be quantity it has a particular quantity,

would imply that e.g. two or three

—

cubits; quantity just

means

so a thing's being in place means [5] these that it is somewhere, and that is either up or

down or in some other of the six differences of position: but each of these is a limit. It is plain from these arguments that there is

no body which

is

But on the other hand to suppose that the indoes not exist in any way leads obviously

many impossible consequences:

[10] a beginning

we have

as

(There

is

no

seen, magnitude is not acBut by division it is infinite.

difficulty in refuting the

indivisible lines.)

The

theory of

alternative then remains

that the infinite has a potential existence.

But the phrase 'potential existence' is ambiguous. When we speak of the potential existence of a statue we mean that there will be an [20] actual statue.

There

nite.

word

many

not so with the infian actual infinite. The

It is

will not be

and we say that the which we say 'it is day' or 'it is the games', because one thing after another is always coming into existence. For of these things too the distinction between potential and actual existence holds. We say that there are Olympic games, both in the sense that they may occur and that they are actually ochas

'is'

infinite

'is'

senses,

in the sense in

curring.

The

—

ways

infinite

exhibits itself in different

man, and For generally the infinite has this mode of existence: one thing is always being taken after another, and each in time, in the generations of

in the division of magnitudes.

is taken is always finite, but always Again, 'being' has more than one [30] sense, so that we must not regard the infinite as a 'this', such as a man or a horse, but must suppose it to exist in the sense in which we speak of the day or the games as existing things whose being has not come to them like that of a substance, but consists in a process of coming to be or passing away; definite if you like at each stage, yet always different.

thing that different.

206 b But when this takes place in spatial magnitudes, what is taken perists, while in the succession of time and of men it takes place by the passing away of these in such a way that the source of supply never gives out.

In a way the infinite by addition is the same thing as the infinite by division. In a finite magnitude, the infinite by addition comes

actually infinite.

finite

to

Now,

tually infinite.

[25]

and the kinds or differences of place are up-down, before-behind, right-left; and these distinctions hold not only in relation to us and by arbitrary [35] agreement, but also in the whole itself. But in the infinite body they cannot exist. In Further, every sensible body

206 b

there will be

and an end of time, a mag-

about in a way inverse to that of the other. For [5] in proportion as we see division going on, in the same proportion we see addition being

made

to

what

is

already

marked

off.

For

if

we

nitude will not be divisible into magnitudes, number will not be infinite. If, then, in view of the above considerations, neither alternative seems possible, an arbiter must be called in;

take a determinate part of a finite magnitude and add another part determined by the same ratio (not taking in the same amount of the original whole), and so on, we shall not trav-

and

[10] erse the given magnitude. But if we increase the ratio of the part, so as always to take in the same amount, we shall traverse the mag-

is a sense in which the infinite and another in which it does not. We must keep in mind that the word 'is' means either what potentially is or what fully is.

clearly there

exists

[75] Further, a thing tion or by division.

is

infinite either

by addi-

magnitude is exhausted by means of any determinate quantity however

nitude, for every finite small.

BOOK

207 b

The

III,

CHAPTERS

no other way, and by reduction. It exists fully in the sense in which we say 'it is day' or 'it is the games'; and poinfinite, then, exists in

but in this

way

it

does

exist, potentially

[75] tentially as matter exists, not independently as what is finite does. By addition then, also, there is potentially an infinite, namely, what we have described as being in a sense the same as the infinite in respect of division. For it will always be possible to take something ab extra. Yet the sum of the parts taken will not exceed every determinate magnitude, just as in the direction of division every determinate magnitude is surpassed in smallness and there will be a smaller part. [20] But in respect of addition there cannot be an infinite which even potentially exceeds every assignable magnitude, unless it has the at-

tribute of being actually infinite, as the physi-

hold to be true of the body which is outside the world, whose essential nature is air or something of the kind. But if there cannot be

cists

way

in this

a sensible

body which

is

infinite in

[25] the full sense, evidently there can no more be a body which is potentially infinite in respect of addition, except as the inverse of the infinite

by division, as

we have said. made the

this reason that Plato also

It is

for

infinites

supposed to be possible to exceed all limits and to proceed ad infinitum in the direction both of increase and of reduction. Yet though he makes the infinites two, he does not use them. For in the

two

in

number, because

it

is

[50] numbers the infinite in the direction of reduction is not present, as the monad is the smallest; nor is the infinite in the direction of increase, for the parts number only up to the

out to be the contrary of what it is said to be. It is not what has nothing 207 a outside it that is infinite, but what always has something outside it. This is indicated by infinite turns

the fact that rings also that have

described as 'endless', because sible to take a part

part.

The

ilarity,

which

is

it is

description depends

but

it is

not true in the

on a

certain sim-

full sense of the

is

taken should never be the same. In is not satisfied:

only the adjacent part from which the is

Our

—

[10] ing is wanting, as a whole man or a whole box. What is true of each particular is

—

whole as such the whole is that of which nothing is outside. On the other hand that from which something is absent and outside, however small that may be, is not 'all'. 'Whole' and 'complete' are either quite identical or closely akin. Nothing is complete (reXetov) which has no end (reXos ) and the end is a limit. [75] Hence Parmenides must be thought to true of the

;

have spoken better than Melissus. The latter says that the whole is infinite, but the former describes it as limited, 'equally balanced from 1 the middle'. For to connect the infinite with not like joining two this they get the dignity they ascribe to the infinite its contain[20] ing all things and holding the all in itthe

all

and the whole

pieces of string; for

self

—from

whole. ness

It is

its

is

it is

from

—

having a certain similarity

to the

in fact the matter of the complete-

which belongs to size, and what whole, though not in the full

tially a

is

poten-

sense. It

divisible both in the direction of reduction

is

and of the inverse addition.

It is

a

limited; not, however, in virtue of ture, but in virtue of

what

is

whole and its

own

other than

na-

it.

It

does not contain, but, in so far as it is infinite, [25] is contained. Consequently, also, it is unknowable, qua infinite; for the matter has no form. (Hence it is plain that the infinite stands in the relation of part rather

than of whole.

For the matter is part of the whole, as the bronze is of the bronze statue.) If it contains in

new

different.

definition then

is

and the small ought to it is absurd and imposunknowable and indeterminate should contain and determine.

ligible things the great

[50] contain them. But sible to suppose that the

always pos-

outside a given

the circle, the latter condition part

ready ta\en. On the other hand, what has nothing outside it is complete and whole. For thus we define the whole that from which noth-

no bezel are

it is

[5] word. This condition alone is not sufficient: it is necessary also that the next part

which

285

the case of sensible things, in the case of intel-

decad.

The

5-7

as follows:

A quantity is infinite if it is such that we can always ta\e a part outside what has been al-

reasonable that there should not be held an infinite in respect of addition such as to surpass every magnitude, but that there It is

to be

should be thought to be such an infinite in the For the matter and the [35] infinite are contained inside what contains them, while it is the form which con207 b tains. It is natural too to suppose that in direction of division.

number there is a limit in the direction of the minimum, and that in the other direction every assigned number is surpassed. In magnitude, 1

Fr. 8. 44.

PHYSICS

286

on the contrary, every assigned magnitude

is

surpassed in the direction of smallness, while [5] in the other direction there is no infinite magnitude. The reason is that what is one is indivisible

one man, not

hand

may be, e.g. a man is many. Number on the other

whatever

it

and a certain quantity of them. Hence number must stop at the indivisible: for 'two' and 'three' are merely derivative terms, and so with each of the other [10] numbers. But in the direction of largeness

is

it

a plurality of 'ones'

is

number:

from the process of bisection, and its infinnot a permanent actuality but consists a process of coming to be, like time and the

ity is

number of time. [75] With magnitudes is

but there

continuous is

no

is

holds.

divided ad infinitum,

infinite in the direction of in-

For the size which it can potentially be, can also actually be. Hence since no sensible magnitude is infinite, it is impossible to exceed every assigned magnitude; for if it were possi[20] ble there would be something bigger than crease.

the heavens.

not the same in magnitude in the sense of a single nature, but its secondary sense depends on infinite

is

and movement and time, its

infinite instead,

while

its

existence will be in the sphere of real magnitudes.

[55] In the fourfold plain that the infinite

scheme of is

causes,

it

is

a cause in the sense of

matter, and that its essence is privation, the 208 a subject as such being what is continuous and sensible. All the other thinkers, too, evi-

—

dently treat the infinite as matter that is why it is inconsistent in them to make it what contains, and not what is contained.

primary sense,

i.e.

movement

is

called infi-

magnitude covered by the movement (or alteration or growth), and time because of the movement. (I use these terms [25] for the moment. Later I shall explain what each of them means, and also why every magnitude is divisible into magnitudes.) nite in virtue of the

Our account

remains to dispose of the arguments to support the view that the infinite exists not only potentially but as a separate thing. Some have no cogency; others can be met by fresh objections that are valid. (1) In order that coming to be should not fail, it is not necessary that there should be a [5]

It

which are supposed

sensible

the contrary

it

The

have such an

always possible to think of a larger number of times a magnitude

ble

What

to

for the

can be bisected is infinite. Hence this infinite is potential, never actual: the number of parts that can be taken always surpasses any assigned number. But this number is not separa-

in

208*

them

does not rob the mathemati-

passing

body which is actually infinite. The of one thing may be the coming

away

[10] to be of another, the All being limited. (2) There is a difference between touching

and being limited. The former is relative to something and is the touching of something (for everything that touches touches some-

and further is an attribute of some one which are limited. On the other hand, what is limited is not limited in relation thing),

of the things

Again, contact is not necessarily between any two things taken at ran-

to anything.

possible

dom. [75] (3)

is.

existence of the infinite in the direction of in-

finite,

crease, in the sense of the untraversable. In point of fact they do not need the infinite and [50] do not use it. They postulate only that the

part that

be produced as far as they wish. It is possible to have divided in the same ratio as the largest quantity another magnitude of any size you like. Hence, for the purposes of proof, it will make no difference to

on mere thinking

is absurd, not in the thing might think that one is

The thought is an accident. Time indeed and movement

[20] (a)

may

rely

but in the thought. One of us is bigger than he is and magnify him ad infinitum. But it does not follow that he is bigger than the size we are, just because some one thinks he is, but only because he is the size he

cians of their science, by disproving the actual

finite straight line

To

for then the excess or defect

and

are in-

also thinking, in the sense that each is

taken passes in succession out of

existence.

(b) Magnitude is not infinite either in the of reduction or of magnification in thought. This concludes my account of the way in which the infinite exists, and of the way in which it does not exist, and of what it is.

way

BOOK

209 a

III,

CHAPTERS 7-8— BOOK

BOOK

IV,

CHAPTER

287

1

IV

have no

real place, they nevertheless, in respect

of their position relatively to us, have a right

The

must have

physicist

a

knowledge

Place, too, as well as of the infinite

whether there

manner

of

its

[30] because

is

such a thing or not,

existence

all

of

—namely, and the —both

and what

it

is

suppose that things which ex-

ist are somewhere (the non-existent is nowhere where is the goat-stag or the sphinx? ), and because 'motion' in its most general and primary sense is change of place, which we call

—

'locomotion'.

The

question,

difficulties.

An

what

is

place? presents many all the relevant

examination of

seems to lead to divergent conclusions. Moreover, we have inherited nothing from previous thinkers, whether in the way of

and

water has gone out as from a vessel, air is present. When therefore another body occupies [ 5] this same place, the place is thought to be dif-

account of it when he made chaos first, At least he says: First of all things came chaos to being, then broad-breasted earth ^

[jo]

implying that things need to have space first, because he thought, with most people, that everything its

can

else

others,

exist,

is

mar-

a

while

it

can exist without the for place does not

first;

pass out of existence

when

the things in

are annihilated.

True, but even if we suppose its existence question of its nature presents dif-

settled, the

they passed was something different from both. Further, the typical locomotions of the elementary natural bodies namely, fire, earth, and the like show not only that place is some-

ficulty

[10] thing, but also that it exerts a certain influence. Each is carried to its own place, if it is

must be

and take precedence of all other which nothing

must needs be

the place or space into

—

in place. If this

[35] things. For that without

it

—

somewhere and

vellous thing,

209 a

formerly contained water, so that clearly which and out of which

is

nature, the potency of place

it

air

in

rect

ferent

from all the bodies which come to be in and replace one another. What now contains

them only

and that every sensible body is in place. Hesiod too might be held to have given a cor-

[35]

vious from the fact of mutual replacement. Where water now is, there in turn, when the

ascribed to

bodies,

facts

a statement of difficulties or of a solution. 208 b The existence of place is held to be ob-

left as attributes

consequence of their relative position, not having by nature these various characteristics. [25] Again, the theory that the void exists involves the existence of place: for one would define void as place bereft of body. These considerations then would lead us to suppose that place is something distinct from

—

whether it is some sort of 'bulk' of body or some entity other than that, for we must first determine its genus.

Now

it has three dimensions, length, [5] (1) breadth, depth, the dimensions by which all

body

also

is

bounded. But the place cannot be were there would be two bodies

not hindered, the one up, the other down. Now these are regions or kinds of place up and

body; for

the rest of the six directions. Nor do such distinctions (up and down and right and

(2) Further, if body has a place and space, clearly so too have surface and the other limits of body; for the same statement will apply

—

down and

[75] left, &c.) hold only in relation to us. To us they are not always the same but change with the direction in which we are turned: that is why the same thing may be both right and left, up and down, before and behind. But in nature each is distinct, taken apart by itself. It is not every chance direction which is 'up', but where fire and what is light are carried; [20] similarly, too, 'down' is not any chance direction but where what has weight and what is

made

of earth are carried

—the implication

being that these places do not differ merely in relative position, but also as possessing distinct

potencies. This jects

is

made

plain also by the ob-

studied by mathematics.

Though

they

in the

to

if it

same

place.

them: where the bounding planes of the

[10] water were, there in turn will be those of the air. But when we come to a point we can-

not

make

Hence

if

from the

a distinction between

it

and

the place of a point

is

not different

point,

its

place.

no more will that of any of the and place will not be somefrom each of them. the world then are we to sup-

others be different,

thing different

(3) What in pose place to be ? If it has the sort of nature described, it cannot be an element or composed [75] of elements, whether these be corporeal or incorporeal: for while it has size, it has not 1 Theogony, n6f.

PHYSICS

2 88

body. But the elements of sensible bodies are bodies, while nothing that has size results from a combination of intelligible elements. (4) Also we may ask: of what in things is space the cause? None of the four modes of causation can be ascribed to it. It is neither [20] cause in the sense of the matter of existents (for nothing is composed of it), nor as the form and definition of things, nor as end, nor

does

it

move

existents.

(5) Further, too, if it is itself an existent, where will it be? Zeno's difficulty demands an explanation: for if everything that exists has a [25] place, place too will have a place, on ad infinitum.

(6) Again, just as every body too, every place has a body in

is it.

and

so

their place

is

and space are

pant'

identical. (It

is different from what he says in [75] his so-called 'unwritten teaching'. Nevertheless, he did identify place and space.) I men-

tion Plato because, while

all hold place to be something, he alone tried to say what it is. In view of these facts we should naturally

expect to find difficulty in determining what is, if indeed it is one of these two things, [20] matter or form. They demand a very

place

close scrutiny, especially as

it

it

any

at

is

—

not easy to

rate not difficult to see that

The form and from the thing,

the matter are not separate

neither less

is

recognize them apart.

What

nor greater than they are. By asking these questions, then, we must not only raise the whole problem about place [30] as to what it is, but even whether there is such a thing.

'partici-

true, in-

'participant'

But then

is

deed, that the account he gives there of the

place cannot be either of them.

we say about growing things? It follows from these premisses that their place must if

matter and space are the same; for the

in place, so,

shall

grow with them,

210 a

whereas the place can be separated. As we pointed out, 2 where air was, water in turn comes to be, the one replacing the other; and [25] similarly with other bodies. Hence the place of a thing is neither a part nor a state of it, but is separable from it. For place is supposed to be something like a vessel the vessel being a transportable place. But the vessel is no part of the thing.

—

it is separable from the not the form: qua containing, it different from the matter. Also it is held that what is anywhere is both

[jo] In so far then as

We

may icating B

distinguish generally between pred-

A because it (A) is itself, and besomething else; and particularly between place which is common and in which cause

of

primarily by each. I mean, for instance, that you are now in the heavens because you are in the air and it is in the heavens; and you are in the air because you are on the earth; and simile] larly on the earth because you are in this place which contains no more than you. 209 b Now if place is what primarily contains each body, it would be a limit, so that the place would be the form or shape of each body by which the magnitude or the matter of the magnitude is defined: for this is the limit of each

body.

we

look at the question in this is its form. But, if we regard the place as the extension of the magni[5]

way

If,

then,

the place of a thing

tude,

is

it is

bodies are, and the special place occupied

all

thing,

it is

the matter. For this

the magnitude:

it is

what

is

is

different

from

contained and de-

itself

it

is

something and that there

thing outside

ought to

gress,

[55]

numbers

ticipates' is

it.

is

(Plato of course, tell

us

why

—whether

a different

if

we may

di-

form and the

the

are not in place,

place

is

if

what

'what parparticipates

the Great and the Small or the matter, as he

210a

called

it

in writing in the

Timaeus.) 3

how

could a body be carried to its was the matter or the form? It is impossible that what has no reference to motion or the distinction of up and down can be place. So place must be looked for among things which have these characteristics. [5] If the place is in the thing (it must be if it is either shape or matter) place will have a place: for both the form and the indeterminate undergo change and motion along with the thing, and are not always in the same place, but are where the thing is. Hence the place will Further,

own place,

if

place

fined by the form, as by a bounding plane. Matter or the indeterminate is of this nature;

have a place.

when

[10] the place has been destroyed, for the resulting body is not in the same place. What

the boundary

and

attributes of a sphere

[10] are taken away, nothing but the matter

is

l

5*

when water

is

sort of destruction then

left.

This

Further,

is

why

Plato in the

Timaeus

1

This concludes

says that 2

2o8 b

2.

52.

my

is

produced from

air,

that?

statement of the rea-

BOOK

210 b sons

why

space

IV,

CHAPTERS

must be something, and again

of the difficulties that

may

be raised about

its

essential nature.

it

1-4

289

resides in the visible surface.

We

cannot go

[5] further and say that it is in surface in virtue of something other than itself. (Yet it is not in itself: though these are in a way the differ in essence, each having a special nature and capacity, 'surface' and

same thing,) they

The next step we must many senses one thing

take is

to see in

is

said to be

how an-

'in'

'white'.

Thus

other. (1)

[75]

As

the finger

is 'in'

the

hand and gen-

erally the part 'in' the whole.

is

(2) As the whole is 'in' the parts: for there no whole over and above the parts. (3) As man is 'in' animal and generally spe-

genus.

cies 'in'

(4)

As

the genus

is 'in'

the species and gen-

erally the part of the specific

form

the

'in'

if

we look

at the

matter inductively

we

any of the senses that have been distinguished; and it can be seen by argument that it is impossible. [10] For each of two things will have to be both, e.g. the jar will have to be both vessel and wine, and the wine both wine and jar, if

do not find anything

it is

to be 'in' itself in

possible for a thing to be in itself; so that,

however true

it

might be

were in each wine in virtue

that they

definition of the specific form.

other, the jar will receive the

[20] (5) As health is 'in' the hot and the cold and generally the form 'in' the matter. (6) As the affairs of Greece centre 'in' the king, and generally events centre 'in' their

[75] not of its being wine but of the wine's being wine, and the wine will be in the jar in virtue not of its being a jar but of the jar's being a jar. Now that they are different in re-

primary motive agent.

spect of their essence

(7) its

As

the existence of a thing centres

good and generally

for the sake of which'

'in' its it

end,

i.e.

'in'

in 'that

exists.

(8) In the strictest sense of all, as a thing is 'in' a vessel, and generally 'in' place. [25] One might raise the question whether a

thing can be in itself, or whether nothing can be in itself everything being either wowhere

—

or in something else.

ambiguous; we may mean or qua something else. When there are parts of a whole the one that in which a thing is, the other the thing which is in it the whole will be described as being in itself. For a thing is described in

The

question

the thing

qua

is

itself

—

—

terms of its parts, as well as in terms of the thing as a whole, e.g. a man is said to be white because tr^e visible surface of him is white, or to be scientific because his thinking faculty [30] has been trained. The jar then will not be in itself and the wine will not be in itself.

But the

jar of

wine

will: for the contents

the container are both parts of the

and

same whole.

In this sense then, but not primarily, a thing

can be in

itself,

namely, as 'white' is in body is in body), and science

is

evident; for 'that in

which something is' and 'that which would be differently defined.

—

primarily.

Zeno's problem

—that

if

because

it is

in body,

or as the hot

body

is 'in'

as

in

is

in

body because

an

affection.

So we

escape the infinite regress. is no (what contains in the different from what is con-

Another thing what is

part of strict

sense

is

is

plain: since the vessel

in

it

tained), place could not be either the matter

or the form of the thing contained, but

—

must

[30] be different for the latter, both the matter and the shape, are parts of what is con-

This then

and

something

—

of the difficulties involved.

man

is

[25] deed in that as 'in' place, but as health is 'in' the hot as a positive determination of it

tained.

parts, a thing will be in itself, as 'white'

Place

—

must be in something is not difficult to solve. There is nothing to prevent the first place from being 'in' something else not init

in the mind. 210b It is from these,

which are 'parts' (in the sense at least of being 'in' the man), that the man is called white, &c. But the jar and the wine in separation are not parts of a whole, though together they are. So when there are

it'

Nor is it possible for a thing to be in itself even incidentally: for two things would be at [20] the same time in the same thing. The if a thing whose nature jar would be in itself it is to receive can be in itself; and that which it receives, namely (if wine) wine, will be in it. Obviously then a thing cannot be in itself

(for the visible surface is

in

is

What

may

then after

serve as a critical statement

all

may

is

place?

The answer

to

be elucidated as follows. Let us take for granted about it the various characteristics which are supposed correctly to this question

PHYSICS

290 belong to ( i )

essentially.

it

Place

is

We assume

what contains

that of

then

which

it is

the place.

21 l a (2) Place is no part of the thing. (3) The immediate place of a thing is neither less nor greater than the thing. (4) Place can be left behind by the thing

and

is

separable. In addition:

[5] carried to its appropriate place and rests there, and this makes the place either up or

these

we must try to make

foundations,

[10] the cause of the trouble and of the diffiabout it. Such is the most satisfactory

culties

kind of exposition. First then we must understand that place would not have been thought of, if there had not been a special kind of motion, namely

that with respect to place.

It is chiefly

for this

reason that we suppose the heaven also to be in place, because it is in constant movement. Of this kind of change there are two species locomotion on the one hand and, on the other, [75] increase and diminution. For these too involve variation of place: what was then in this place has

now

in turn

changed

to

what

is

larger or smaller.

when we

say a thing

is

'moved', the

predicate either (1) belongs to it actually, in virtue of its own nature, or (2) in virtue of something conjoined with it. In the latter case

be either (a) something which by its own [20] nature is capable of being moved, e.g. the parts of the body or the nail in the ship, or (b) something which is not in itself capable of being moved, but is always moved through its conjunction with something else, as 'whiteness' or 'science'. These have changed their place only because the subjects to which they belong

it

may

do

so.

We

say that a thing

is

in the world, in the

[25] sense of in place, because it is in the air, and the air is in the world; and when we say

we do not mean it is in every but that it is in the air because of the outer surface of the air which surrounds it is

in the air,

part of the

it;

for

if all

a thing

not in the sense of in place, but as a part in a whole. But when the thing is separate and in it is

air,

the air were

its

place, the place of

would not be equal

to the thing

immediately

'in'

of the surrounding body,

neither a part of

than

its

what

is

the inner surface

and in

it

this surface

is

nor yet greater

extension, but equal to

it;

for the ex-

which touch are coincident. one body is in continuity with an-

tremities of things

Further, laid

complete the theory. We ought to our investigation such as will render an account of place, and will not only solve the difficulties connected with it, but will also show that the attributes supposed to belong to it do really belong to it, and further will make clear

Again,

which it is supposed to be, and which the primary place in which a thing is actually is. When what surrounds, then, is not separate [30] from the thing, but is in continuity with it, the thing is said to be in what surrounds it,

contact,

(5) All place admits of the distinction of up and down, and each of the bodies is naturally

down. Having

211 b

if

[35] other, it is not moved in that but with that. On the other hand it is moved in that if it is

separate.

what contains 21 l b

It

makes no

difference whether

moved or not. Again, when it is not separate is

it is described as a part in a whole, as the pupil in the eye or the hand in the body: when it is sep-

water in the cask or the wine in hand is moved with the body and the water in the cask. [5] It will now be plain from these consideraarate, as the

the jar. For the

what place is. There are just four things which place must be one the shape, or the matter, or some sort of extension between the bounding surfaces of the containing body, or this boundary itself if it contains no extension over and above the bulk of the body which comes to be in it. Three of these it obviously cannot be: tions

—

of

[10] (1) The shape is supposed to be place because it surrounds, for the extremities of what contains and of what is contained are coincident. Both the shape and the place, it is true, are boundaries. But not of the same

thing: the the place

contains

form

is

is

the boundary of the thing,

the boundary of the body

which

it.

(2) The extension between the extremities is thought to be something, because what is contained and separate may often be changed [75] while the container remains the same (as water may be poured from a vessel) the assumption being that the extension is something over and above the body displaced. But there is no such extension. One of the bodies which change places and are naturally capable of being in contact with the container falls in whichever it may chance to be. If there were an extension which were such [20] as to exist independently and be permanent, there would be an infinity of places in the same thing. For when the water and the air change places, all the portions of the two

—

BOOK

212 b

IV,

CHAPTERS

together will play the same part in the whole which was previously played by all the water in the vessel; at the same time the place too will be undergoing change; so that there will be another place which is the place of the [25] place, and many places will be coincident. There is not a different place of the part, in which it is moved, when the whole vessel

changes

place:

its

it is

always the same: for

it

(proximate) place where they are that the air and the water (or the parts of the water) succeed each other, not in that place in is

in the

4-5

291

what contains plays the part of a

river,

vessel

rather than that of place. Place on the other

hand

rather

is

what

is

motionless:

rather the whole river that a

whole

it is

is

so

it

is

place, because as

motionless.

Hence we conclude that the innermost motionless boundary of what contains is place. [20]

This explains

why

the middle of the heaven

and the surface which

faces us of the rotating system are held to be 'up' and 'down' in the

strict

and

always

fullest sense for all

men:

for the

one

while the inner side of the rotating body remains always coincident with is

at rest,

which they come to be, which is part of the which is the place of the whole world. [3°] (3) The matter, too, might seem to be place, at least if we consider it in what is at rest and is thus separate but in continuity. For just as in change of quality there is something which was formerly black and is now white, or formerly soft and now hard this is just

contains in the direction of the outermost part of the universe, and the outermost part itself,

why we

are up.

place

—

because

say that the matter exists

presents a similar

it

[55] thought to say so because

exist

—only

—so

place,

phenomenon,

in the

one case

we

what was air is now water, in where air formerly was there

now

is

before,

1

is

contains

water. But the matter, as

we

said

neither separable from the thing nor

it,

what what

is is

down, the boundary which contains in the direction of the middle of the universe, and the middle itself, are down, and that which carried

For

is

the other because

212*

[25] itself. Hence since the light is naturally carried up, and the heavy

is thought to be a were a vessel, i.e. a

this reason, too, place

kind of surface, and as

it

container of the thing. [50] Further, place is coincident with the thing, for boundaries are coincident with the

bounded.

whereas place has both character-

istics. if place is none of the three form nor the matter nor an extension which is always there, different from, and over and above, the extension of the thing place necessarily is the [5] which is displaced one of the four which is left, namely, the boundary of the containing body at which it is in contact with the contained body. (By the contained body is meant what can be moved

Well, then,

neither the

—

by

way

of locomotion.)

is thought to be something important and hard to grasp, both because the matter and the shape present themselves along with it, and because the displacement of the body

Place

that

is

moved

takes place in a stationary con-

[10] tainer, for

it

seems possible that there is other than the

should be an interval which bodies which are moved.

The

air, too,

which

is

to be incorporeal, contributes something to the belief: it is not only the boundaries of the vessel which seem to be place, but also what is between them, regarded as empty. Just, in fact, as the vessel is transportable [75] place, so place is a non-portable vessel. So when what is within a thing which is moved, is moved and changes its place, as a boat on a

thought

1

209 b 22-32.

If then a body has another body outside it and containing it, it is in place, and if not, not. That is why, even if there were to be water which had not a container, the parts of it, on the one hand, will be moved (for one part is contained in another), while, on the other hand, the whole will be moved in one sense, [55] but not in another. For as a whole it does not simultaneously change its place, though it 21 b will be moved in a circle: for this place is the place of its parts. (Some things are moved, not up and down, but in a circle; others up and down, such things namely as admit of condensation and rarefaction.) As was explained, 2 some things are potentially in place,

others actually. So,

when you

have a homogeneous substance which

is

con-

[5] tinuous, the parts are potentially in place: when the parts are separated, but in contact, like a heap, they are actually in place.

Again, (1) some things are per se namely every body which is movable

in place,

either by

of locomotion or by way of increase is per somewhere, but the heaven, as has been 3 said, is not anywhere as a whole, nor in any [10] place, if at least, as we must suppose, no

way se

7-b5-

%

3*

PHYSICS

292

body contains it. On the line on which it is moved, its parts have place: for each is contiguous to the next. But (2) other things are in place indirectly, through something conjoined with them, as the soul and the heaven. in place, for all

its

The

latter

parts are: for

in a way, on the orb

is,

one part contains another. That is why the upper part is moved in a circle, while the All [75] is not anywhere. For what is somewhere is itself something, and there must be alongside it some other thing wherein it is and which contains it. But alongside the All or the Whole there is nothing outside the All, and for this reason all things are in the heaven; for the heaven, we may say, is the All. Yet their not the same as the heaven. It is part the innermost part of it, which is in

place of

is

it,

[20] contact with the movable body; and for this reason the earth is in water, and this in

and the aether in heaven, but we cannot go on and say that the heaven is in anything else. It is clear, too, from these considerations that all the problems which were raised about place will be solved when it is explained in this way: (1) There is no necessity that the place should grow with the body in it, the

air,

and the

air in the aether,

[25]

Nor that a point should have a place, (3) Nor that two bodies should be in the

same

place,

(2)

These [5]

distinctions will be

fully later.

was necessary

1

On

the

to refer to

drawn more

care-

present occasion

them: what has

it

now

been stated obscurely will then be made more clear. If the matter and the fulfilment are the same thing (for water is both, the one potentially, the other completely), water will be related to air in a way as part to whole. That is why these have contact: it is organic union when both become actually one. [10] This concludes my account of place both of its existence and of its nature.

The

investigation of similar questions about

must be held whether exists or what it

the void, also,

to belong to the

physicist

it

—namely

and how place.

it

The views taken of it

is

exists

or not,

—

just as

about

involve arguments

both for and against, in much the same sort [75] of way. For those who hold that the void exists regard it as a sort of place or vessel which is supposed to be 'full' when it holds the bulk which it is capable of containing, 'void' when it is deprived of that as if 'void' and 'full' and 'place' denoted the same thing,

—

though the essence of the three is different. [20] We must begin the inquiry by putting

down

the account given by those

who

say that

then the account of those who say does not exist, and third the current

exists,

it

that

Nor

213 b

it

is between the boundaries of any body which may chance to be there, not an interval in body. Further, (5) place is also somewhere, not in

view on these questions. Those who try to show that the void does not exist do not disprove what people really mean by it, but only their erroneous way of speaking; this is true of Anaxagoras and of those

the sense of being in a place, but as the limit

who

(4)

that place should be a corporeal in-

what

terval: for

the place

is

is

place, but only

Also (6)

it

way. They merely give an ingenious demonstration that air is something by

reasonable that each kind of

and showing the resistance of the air, and by cutting it off in clepsydras. But people really mean that there is an empty interval in which there is no sensible body. They hold that everything which is is [jo] body and say that what has nothing in it at all is void (so what is full of air is void).

is is

movable body. is

[jo] body should be carried to its own place. For a body which is next in the series and in contact (not by compulsion) is akin, and bodies which are united do not affect each other, while those which are in contact interact on each other. Nor (7) is it without reason that each should remain naturally in its proper place. For this part has the

same

relation to

its

place, as a

I35] separable part to its whole, as when one 21 3 a moves a part of water or air: so, too, air is related to water, for the one is like matter, the other form water is the matter of air, air as it were the actuality of water, for water is potentially air, while air is potentially water, though in another way.

—

refute the existence of the void in this

in

in the limited; for not everything that

[25]

—

straining wine-skins

It is

not then the existence of air that needs

to be proved, but the non-existence of

an

inter-

val, different

from the

bodies, either separable

or actual

interval

which divides the whole

body

—an

so as to break

its

continuity, as

Democ-

ritus and Leucippus hold, and many 21 3 b physicists or even perhaps as

—

other

some-

thing which is outside the whole body, which remains continuous. 1

On

Generation and Corruption,

1.

3.

BOOK

214 a

IV,

CHAPTERS

These people, then, have not reached even the threshold of the problem, but rather those who say that the void exists.

They

( 1 )

argue, for one thing, that change

(i.e. locomotion and increase) would not be. For it is maintained that motion would seem not to exist, if there were no void, since what is full cannot contain anything more. If it could, and there were two bodies in the same place, it would also be true that any

place

in

[5]

number

of bodies could be together; for

it

is

impossible to draw a line of division beyond which the statement would become untrue. If this were possible, it would follow also that

thus also

body would contain the

the smallest

[10]

greatest; for

'many

a

little

makes

many equal bodies can be can many unequal bodies. if

a mickle':

together, so

from these considimmovable; for if it

Melissus, indeed, infers erations that the All

is

were moved there must, he void

is

not

among

This argument, then, they

says, be void,

but

the things that exist. is

one way in which

show that there is a void. 2 They reason from the ( )

skins into which the wine has been decanted, which implies that the compressed body contracts into the voids present in

Again (3)

increase, too,

[20] place always by

means

is

thought to take

of void, for nutri-

in place, void

is

place in

weight or lightness. Hence, by a syllogism, what has nothing heavy or light in it, is void. This result, then, as I have said, is reached [5] by syllogism. It would be absurd to suppose that the point is void; for the void must be place which has in it an interval in tangible body. But at all events we observe then that in one way the void is described as what is not full of body perceptible to touch; and what has heaviness and lightness is perceptible to touch. So we would raise the question: what would they is say of an interval that has colour or sound [10] it void or not? Clearly they would reply that if it could receive what is tangible it was

—

and

void,

if

not, not.

way

which there some say that the void is the matter of the body (they identify the place, too, with this), and in this In another

no

'this'

void

is

that in

or corporeal substance. So

they speak incorrectly; for the matter [75] separable

from the

is

not

things, but they are

inquiring about the void as about something separable.

we have determined

Since

it.

293 is

which there is no body, so that where there is no body, there must be void. 214 a Every body, again, they suppose to be tangible; and of this nature is whatever has

is

fact that some 1 I 5] things are observed to contract and be compressed, as people say that a cask will hold the wine which formerly filled it, along with the

5-7

while every body

the nature of

and void must, if it exists, be place deprived of body, and we have stated both in what sense place exists and in what sense it does not, it is plain that on this showing void

place,

body, and it is impossible for two bodies to be together. A proof of this they find also in what happens to ashes, which absorb as

does not

much water as the empty vessel. The Pythagoreans, too, (4) held

[20] for the void is meant to be, not body but rather an interval in body. This is why the

ment

is

that void

and that it enters the heaven itself, which as it were inhales it, from the infinite air. Further it is the void which distinguishes the na[25] tures of things, as if it were like what separates and distinguishes the terms of a series. This holds primarily in the numbers, for

exists

the void distinguishes their nature.

These, then, and so many, are the main grounds on which people have argued for and against the existence of the void.

[jo]

As

true,

we must

which view is determine the meaning of the

a step towards settling

name.

The

void

is

thought to be place with noth-

ing in it. The reason for this is that people take what exists to be body, and hold that

unseparated or separated;

thought to be something,

viz.

because

and for the same reasons. For the fact of motion in respect of place comes to the aid place

is,

both of those who maintain that place is something over and above the bodies that come to occupy it, and of those who maintain that the void is something. They state that the void is the condition of movement in the

which movement takes place; would be the kind of thing that

sense of that in

[25]

and

this

some say place is. But there is no necessity for there being a void if there is movement. It is not in the least needed for

void

is

exist, either

a

as a condition of

reason

which,

movement

in general,

incidentally,

escaped

Melissus; viz. that the full can suffer qualitative change.

But not even movement in respect of place

PHYSICS

294 involves a void; for bodies

make room [jo]

for

may

simultaneously

one another, though there

no

is

and apart from the movement. And this is plain

separate

interval

bodies that are in

even in the rotaion of continuous things, as in that of liquids.

And

things can also be compressed not into

a void but because they squeeze out

contained in them ter

compressed the

is

214 b

air

within

what

is

when wa-

(as, for instance, it is

squeezed

out); and things can increase in size not

215'

body

placed as a whole in a place conceived

is

of as separate

and permanent;

what rather turns out

to be the case,

any and every part of the body

is

bodies may be increased otherwise than by the addition of body, or there may be two bodies in the same place (in which case they are claiming to solve a quite general difficulty, but are not proving the existence of void), or the

whole body must be void, every part and

is

if it is

increased by

The same argument

increased in

means

of void.

applies to the ashes.

one

if

[30] studies the matter, is the opposite, that not a single thing can be moved if there is a void; for as with those who for a like reason

admits no difference. 215 a The second reason

increased, or

it,

it

only by the entrance of something but also by qualitative change; e.g. if water were to be transformed into air. In general, both the argument about increase of size and that about water poured on to the [5] ashes get in their own way. For either not is

for a part of

be placed apart, will not be in a place but in the whole. Further, if separate place does not exist, neither will void. If people say that the void must exist, as being necessary if there is to be movement, unless

say the earth is at rest, so, too, in the void things must be at rest; for there is no place to which things can move more or less than to another; since the void in so far as it is void

this: all

is

movement

either compulsory or according to nature,

and if there is compulsory movement there must also be natural (for compulsory movement is contrary to nature, and movement contrary to nature is posterior to that according to nature, so that if each of the natural bodies has not a natural movement, none of the [5] other movements can exist); but how can there be natural movement if there is no dif-

[10] It is evident, then, that it is easy to refute the arguments by which they prove the ex-

ference throughout the void or the infinite?

istence of the void.

or

For

in so far as

down

void,

up

is

no void

some maintain.

ex-

each of the simple bodies has a natural locomotion, isting separately, as

upward and

e.g. fire

earth

If

downward and

[75] towards the middle of the universe, it is clear that it cannot be the void that is the condition of locomotion.

be the condition of? dition of

What,

It is

movement

then, will the void

thought to be the con-

in respect of place,

and

it

not the condition of this. Again, if void is a sort of place deprived of body, when there is a void where will a body placed in it move to ? It certainly cannot move into the whole of the void. The same argu[20] ment applies as against those who think is

that place

things

is

something separate, into which

are carried;

placed in

it

move, or

viz.

rest?

how will what is Much the same ar-

gument will apply to the void as to the 'up' and 'down' in place, as is natural enough since those

void

make

And

in

who it

maintain the existence of the

a place.

what way

will things be present

[25] either in place or in the void? expected result does not take place

For the

when

a

infinite, there will

and

be no up

in so far as

it

is

a

no whit from down; for as no difference in what is nothing,

differs

[jo] there

Let us explain again that there

it is

or middle,

is

none

in the void (for the void seems to be a non-existent and a privation of being), but natural locomotion seems to be differenti-

there

is

ated, so that the things that exist by nature

must be

differentiated. Either, then, nothing

has a natural locomotion, or

else there is

no

void.

Further, in point of fact things that are

thrown move though that which gave them their impulse

is

not touching them, either by

[75] reason of mutual replacement, as some maintain, or because the air that has been

pushed pushes them with a movement quicker than the natural locomotion of the projectile

wherewith it moves to its proper place. But in a void none of these things can take place, nor can anything be moved save as that which is carried is moved. Further, no one could say why a thing once [20] set in motion should stop anywhere; for why should it stop here rather than here? So that a thing will either be at rest or must be moved ad infinitum, unless something more powerful get in

its

way.

Further, things are

now

thought to move

216

BOOK

s

IV,

CHAPTERS

but in a void this quality is present equally everywhere, so that things should move in all directions. Further, the truth of what we assert is plain [25] from the following considerations. We see the same weight or body moving faster than another for two reasons, either because there is a difference in what it moves through, into the void because

it

yields;

7-8

29:

Z which

stance

exceeds air in thickness in the

which the time E bears to the time Z be as much thinner than exceeds H, A, if it moves through Z,

[50] ratio

H. For

A

E

as

the body

if

will traverse

216 a

it

time inverse to the speed of

in a

other things being equal, the moving body differs from the other owing to excess of weight

movement, i.e. in a time equal to H. If, then, there is no body in Z, A will traverse Z still more quickly. But we supposed that its traverse of Z when Z was void occupied the time H. So that it will traverse Z in an equal time whether Z be full or void. But this is im-

or of lightness.

possible. It

as

between water,

Now cause

it

medium

the

and

earth, or because,

causes a difference be-

impedes the moving thing, most of

moving

if it is

air,

all

in the opposite direction, but in

[50] a secondary degree even if it is at rest; especially a medium that is not easily di-

and

vided, i.e. a medium that is somewhat dense. 215 b A, then, will move through B in time I\ and through A, which is thinner, in time E (if the length of B is equal to A), in proportion to the density of the hindering body. For let B be water and A air; then by so much as [5] air is thinner and more incorporeal than water, A will move through A faster than through B. Let the speed have the same ratio to the speed, then, that air has to water.

Then

twice as thin, the body will traverse B in twice the time that it does A, and the time T will be twice the time E. And always, by so if air is

medium is more incorporeal and more easily divided, the faster will be the movement. Now there is no ratio in which the void is exceeded by body, as there is no ratio of to a number. For if 4 exceeds 3 by 1, and 2 by more than 1, and 1 by still more than it exceeds 2, [75] still there is no ratio by which it exceeds o; for that which exceeds must be divisible into the excess + that which is exceeded, so that 4 will be what it exceeds o by + 0. For this

much

[10]

and

as the

less resistant

reason, too, a line does not exceed a point

unless

it is

composed

to

of points! Similarly the

movement through

the other, but

if

a

thing moves through the thickest medium such and such a distance in such and such a time, it moves through the void with a speed beyond any ratio. For let Z be void, equal in magnitude to B and to A. Then if is to traverse

A

and move through

it

in a certain time,

H,

a

[25] time less than E, however, the void will bear this ratio to the full. But in a time equal to

H,

A will

traverse the part

of A.

will surely also traverse in that time

And

which

it

any sub-

is

it

plain, then, that

will

if

there

move through any

is

a time

part of the

void, this impossible result will follow:

it

will

be found to traverse a certain distance, whether this be full or void, in an equal time; for there will be some body which is in the [5]

same

ratio to the other

body

as the

time

is

to

the time.

To sum sult

the matter up, the cause of this reobvious, viz. that between any two

is

movements

there

is

a ratio (for they occupy

[10] time, and there is a ratio between any two times, so long as both are finite), but is no ratio of void to full. These are the consequences that result from a difference in the media; the following depend upon an excess of one moving body over another. We see that bodies which have a greater impulse either of weight or of light-

there

ly] ness, if they are alike move faster over an equal

in other respects,

and in the magnitudes bear to each other. Therefore they will also move through the void with this ratio of speed. But that is impossible; for why should one move faster? (In moving through plena it must be so; for ratio

which

space,

their

the greater divides

them

by

faster

its

force.

For a moving thing cleaves the medium either by its shape, or by the impulse which the body [20] that ity.

But

It is

carried along or

is

Therefore

sesses.)

[20] void can bear no ratio to the full, and therefore neither can movement through the

one

in

the

this

is

is

is

projected pos-

will possess equal veloc-

impossible.

evident from

that, if there is

all

what has been

said, then,

a void, a result follows

the very opposite of the reason for

those

who

believe in a void set

movement

think that

if

exist, the

void cannot

itself;

[25]

but this is

is

it

up.

which which

They

in respect of place

is

to

separated all by the same as to say that place exist,

a separate cavity;

and

this has already

been stated to be impossible. But even if we consider it on its own merits the so-called vacuum will be found to be really vacuous. For as, if one puts a cube in water, an amount of water equal to the cube will be

PHYSICS

296

but the effect is imperceptible to sense. And indeed always, in the [30] case of any body that can be displaced, it must, if it is not compressed, be displaced in the direction in which it is its nature to be displaced always either down, if its locomodisplaced; so too in air;

—

tion

is

downwards as

in the case of earth, or up,

or in both directions

if it is fire,

—whatever be

the nature of the inserted body.

void this

is

impossible; for

it is

Now

in the

not body; the

void must have penetrated the cube to a dis[^5] tance equal to that which this portion of void formerly occupied in the void, just as if 216 b the water or air had not been displaced by the wooden cube, but had penetrated right

through it. But the cube also has a magnitude equal to that occupied by the void; a magnitude which, if it is also hot or cold, or heavy or light, is [5] none the less different in essence from all its attributes, even if it is not separable from them; I mean the volume of the wooden cube. So that even if it were separated from everything else and were neither heavy nor light, it will occupy an equal amount of void, and fill

same place, as the part of place or of the void equal to itself. How then will the body of [10] the cube differ from the void or place that is equal to it? And if there can be two such the

why

things,

cannot there be any number coin-

ciding? This, then, is one absurd and impossible implication of the theory. It is also evident that

same volume even if it an attribute possessed by all other bodies also. Therefore if this differs in no respect from its place, why need we assume a place for bodies over and above the the cube will have this is

displaced,

which

is

volume of each, if their volume be conceived [75] of as free from attributes? It contributes nothing to the situation interval

attached to

it

if

there

as well.

is

an equal

[Further,

it

by the study of moving things what sort of thing void is. But in fact it is found nowhere in the world. For air is somenor, thing, though it does not seem to be so for that matter, would water, if fishes were

ought to be

clear

—

made

of iron; for the discrimination of the

tangible

is

by touch.]

[20] It is clear, then, from these considerations that there is no separate void.

217*

can things contract and be comif this were not to take place, [25] either there would be no movement at

say, neither

pressed. But

would bulge, as Xuthus and water must always change into equal amounts (e.g. if air has been made out of a cupful of water, at the same time out of an equal amount of air a cupful of water must have been made), or void must necessarily exist; for compression and expansion cannot or the universe

all,

said, or air

take place otherwise.

Now, if they mean by the rare that which many voids existing separately, it is plain

[jo]

has

that if void cannot exist separate any more than a place can exist with an extension all to itself, neither can the rare exist in this sense. But if they mean that there is void, not separately existent, but still present in the rare, this is less impossible, yet, first, the void turns out not to be a condition of all movement, but [_?5] only of movement upwards (for the rare 21 7 a is light, which is the reason why they say fire is rare) second, the void turns out to be a condition of movement not as that in which it takes place, but in that the void carries things up as skins by being carried up themselves carry up what is continuous with them. Yet how can void have a local movement or a place? For thus that into which void moves is till then void of a void. [5] Again, how will they explain, in the case ;

movement downwards? the rarer and more void a thing is the quicker it will move upwards, if it were completely void it would move with a of

what

And

it is

is

heavy,

its

plain that

maximum

if

speed! But perhaps even this

possible, that

it

should

move

at all; the

is

im-

same

reason which showed that in the void all things are incapable of moving shows that the void

cannot move, viz. the fact that the speeds are incomparable. [10] Since we deny that a void exists, but for the rest the problem has been truly stated, that either there will be

no movement,

if

there

is

not to be condensation and rarefaction, or the universe will bulge, or a transformation of water into air will always be balanced by an equal transformation of air into water (for it is clear that the air produced from water is bulkier [75] than the water): it is necessary therefore, if compression does not exist, either that the next portion will be pushed outwards and

make There are some who think that the existence of rarity and density shows that there is a void. If rarity and density do not exist, they

where

the outermost part bulge, or that someelse there must be an equal amount of

water produced out of air, so that the entire bulk of the whole may be equal, or that noth-

BOOK

218 a

IV,

CHAPTERS

ing moves. For when anything is displaced this will always happen, unless it comes round in a circle; but locomotion is not always circular,

but sometimes in a straight line. [20] These then are the reasons for which they might say that there is a void; our statement is

based on the assumption that there is a single matter for contraries, hot and cold and the other natural contrarieties, and that what exists

produced from a potential existent, and that matter is not separable from the Cottle ] traries but its being is different, and that a single matter may serve for colour and heat and cold. The same matter also serves for both a large and a small body. This is evident; for when air is produced from water, the same matter has become something different, not by acquiring an addition to it, but has become actually what it was potentially, and, again, water is produced from air in the same way, the [50] change being sometimes from smallness to greatness, and sometimes from greatness to smallness. Similarly, therefore, if air which is large in extent comes to have a smaller volume, or becomes greater from being smaller, it is the matter which is potentially both that comes actually

is

each of the two. as the same matter becomes hot from being cold, and cold from being hot, because it was potentially both, so too from hot it can 21 7 b become more hot, though nothing in the matter has become hot that was not hot when the thing was less hot; just as, if the arc or curve of a greater circle becomes that of a smaller, whether it remains the same or becomes a different curve, convexity has not come [5] to exist in anything that was not convex but straight (for differences of degree do not depend on an intermission of the quality); nor can we get any portion of a flame, in which both heat and whiteness are not present. So too, then, is the earlier heat related to the later. to be

For

So that the greatness and smallness, also, of the volume are extended, not by the matter's acquiring anything new, but because the sensible

matter

is

potentially matter for both states; so

[10] that the same thing is dense and rare, the two qualities have one matter.

The dense

is

heavy, and the rare

is

and

light.

[Again, as the arc of a circle when contracted into a smaller space does not acquire a new part which is convex, but what was there has been contracted; and as any part of fire that [75] one takes will be hot; so, too, it is all a question of contraction and expansion of the

8-10

297

same matter.] There are two types in each case, both in the dense and in the rare; for both the heavy and the hard are thought to be dense, and contrariwise both the light and the soft are rare; and weight and hardness fail to coincide in the case of lead and iron. [20] From what has been said it is evident, then, that void does not exist either separate (either absolutely separate or as a separate ele-

ment

one

in the rare) or potentially, unless

willing to call the condition of

movement

is

void,

whatever it may be. At that rate the matter of the heavy and the light, qua matter of them, would be the void; for the dense and the rare are productive of locomotion in virtue of this [25J contrariety, and in virtue of their hardness and softness productive of passivity and impassivity,

i.e.

not of locomotion but rather of

qualitative change.

So much, then, for the discussion of the void, and of the sense in which it exists and the sense in which it does not exist. 10

Next

subjects menTime. The best plan will be to begin by working out the difficulties connected for discussion after the

[jo] tioned

with First,

it,

is

making use

does

it

of the current arguments.

belong to the

class of things that

do not

exist or to that of things that

Then then:

secondly, the

make one

what

following suspect that

is

its

nature?

considerations it

exist?

To

start,

would

either does not exist

and in an obscure way. One part of it has been and is not, while the other 218 a is going to be and is not yet. Yet time both infinite time and any time you like to take is made up of these. One would naturally suppose that what is made up of things which do not exist could have no share in reality. at all or barely,

—

Further,

if

a divisible thing

when

is

to exist,

it is

some of its [5] parts must exist. But of time some parts have been, while others have to be, and no part of it is, though it is divisible. For what is necessary that,

it

exists, all

or

'now' is not a part: a part is a measure of the whole, which must be made up of parts. Time, on the other hand, is not held to be made up of 'nows'.

Again, the 'now' which seems to bound the and the future does it always remain one [10] and the same or is it always other and other? It is hard to say. (1) If it is always different and different, and if none of the parts in time which are other and other are simultaneous (unless the past

—

PHYSICS

298

one contains and the other is contained, as the shorter time is by the longer), and if the 'now' which is not, but formerly was, must have [75] ceased-to-be at some time, the 'nows' too cannot be simultaneous with one another, but the prior 'now' must always have ceased-to-be. But the prior 'now' cannot have ceased-to-be in itself (since it then existed); yet it cannot have ceased-to-be in another 'now'. For we may lay it down that one 'now' cannot be next to another, any more than point to point. If then it did not cease-to-be in the next 'now' [20] but in another, it would exist simultaneously with the innumerable 'nows' between the

—which

two

is

is

it

a

it is

which moves or But time is present equally everywhere and with all things. Again, (b) change is always faster or slower, [75] whereas time is not: for 'fast' and 'slow' are defined by time 'fast' is what moves much changes

may chance

itself

to be.

—

in a short time, 'slow'

what moves

in a

little

long time; but time is not defined by time, by being either a certain amount or a certain kind of

it.

Clearly then

it is

(We

not movement.

need

[20] not distinguish at present between 'movement' and 'change'.) 11

possible for the

'now' to remain always the same. No determinate divisible thing has a single termination, in

or where the thing

impossible.

Yes, but (2) neither

whether

219*

continuously extended in one or the 'now' is

more than one dimension: but termination, and it is possible

to cut off a

[25] determinate time. Further, if coincidence in time (i.e. being neither prior nor posterior)

But neither does time exist without change; for when the state of our own minds does not change at all, or we have not noticed its changing, we do not realize that time has elapsed, any more than those who are fabled to [25] sleep among the heroes in Sardinia do when they are awakened; for they connect the earlier 'now' with the later and make them

one and the same "now" ', both what is before and what is after

one, cutting out the interval because of their

same 'now', things which happened ten thousand years ago would be simultaneous with what has happened to-day, and nothing would be before or after anything else,

were not different but one and the same, there would not have been time, so too when

means then,

to be 'in

if

are in this

failure to notice

it.

So, just as,

the 'now'

if

[jo] This

its difference escapes our notice the interval does not seem to be time. If, then, the non-realiza[ jo] tion of the existence of time happens to us

culties

when we do

may serve as a statement of the diffiabout the attributes of time. As to what time is or what is its nature, the traditional accounts give us as little light as the preliminary problems which we have worked through. Some

assert that

it is

218 b the whole, others

(1) the

that

it is

movement

of

(2) the sphere

itself. ( 1 ) Yet part, too, of the revolution is a time, but it certainly is not a revolution: for what is taken is part of a revolution, not a revolution. Besides, if there were more heavens than one, the movement of any of them equally would be time, so that there would be many times at the

same time. [5] (2) Those who said that time is the sphere of the whole thought so, no doubt, on the ground that all things are in time and all things are in the sphere of the whole.

view

is

too naive for

it

to be

The

worth while

consider the impossibilities implied in

to

it.

But as time is most usually supposed to be (3) motion and a kind of change, we must consider this view. [10]

Now

each thing

(a) the change or is

movement

of

only in the thing which changes

not distinguish any change, but

the soul seems to stay in one indivisible state,

and when we perceive and distinguish we say time has elapsed, evidently time

not inde-

is

pendent of movement and change.

219 a

dent, then, that time

is

neither

It

is

evi-

movement

nor independent of movement. We must take this as our starting-point and since we wish to know what try to discover time is what exactly it has to do with movement. Now we perceive movement and time together: for even when it is dark and we are not [5] being affected through the body, if any movement takes place in the mind we at once suppose that some time also has elapsed; and not only that but also, when some time is thought to have passed, some movement also along with it seems to have taken place. Hence time is either movement or something that belongs to movement. Since then it is not movement, it must be the other. [10] But what is moved is moved from something to something, and all magnitude is continuous. Therefore the movement goes with the magnitude. Because the magnitude is con-

—

—

BOOK

220*

movement

tinuous, the ous,

and

the time that has passed

is

CHAPTERS

IV,

must be continu-

movement, then the time;

the

if

too

for

always thought to be

movement. The distinction of 'before' and 'after' holds primarily, then, in place; and there in virtue in proportion to the

[75] of relative position. Since then 'before'

hold in magnitude, they must hold also in movement, these corresponding to those. But also in time the distinction of 'before' and 'after' must hold, for time and movement always correspond with each other. The

and

'after'

'before'

and

'after' in

motion

is

identical in sub-

[20] stratum with motion yet differs from

it

and is not identical with motion. But we apprehend time only when we have marked motion, marking it by 'before' and 'after'; and it is only when we have perceived 'before' and 'after' in motion that we say that [25] time has elapsed. Now we mark them by judging that A and B are different, and that some third thing is intermediate to them. in definition,

When we

think of the extremes as different

from the middle and the mind pronounces that the 'nows' are two, one before and one after, it is

then that

we

say that there

is

time,

and this that we say is time. For what bounded by the 'now' is thought to be time we may assume this.

is

[30] When, therefore, we perceive the 'now' as one, and neither as before and after in a motion

nor as an identity but in relation to a 'before' and an 'after', no time is thought to have elapsed, because there has been no motion either. On the other hand, when we do per219 b ceive a 'before' and an 'after', then we say numthat there is time. For time is just this ber of motion in respect of 'before' and 'after'. Hence time is not movement, but only movement in so far as it admits of enumeration. A proof of this: we discriminate the more or the less by number, but more or less movement by time. Time then is a kind of number. (Num[5] ber, we must note, is used in two senses both of what is counted or the countable and also of that with which we count. Time obviously is what is counted, not that with which we count: there are different kinds of thing.) Just as motion is a perpetual succession, so [10] also is time. But every simultaneous time is self-identical; for the 'now' as a subject is an identity, but it accepts different attributes. The 'now' measures time, in so far as time involves

—

the 'before

and

The 'now' other

it

is

after'.

one sense is the same, in annot the same. In so far as it is in in

10-11

299

(which is just what being now was supposed to mean), but [75] substratum is an identity: for motion, was said, goes with magnitude, and time, succession,

it is

different

1

its its

as as

we

maintain, with motion. Similarly, then, there corresponds to the point the body which

and by which we are aware of and of the 'before and after' involved in it. This is an identical substratum (whether a point or a stone or something else

is

carried along,

the motion

of the kind), but

it

has different attributes

—

[20] as the sophists assume that Coriscus' being in the Lyceum is a different thing from Coriscus' being in the market-place.

body which far as

there.

is

carried along

is

And

the

different, in so

it is at one time here and at another But the 'now' corresponds to the body

that is carried along, as time corresponds to the motion. For it is by means of the body that is carried along that we become aware of the 'be[25] fore and after' in the motion, and if we regard these as countable we get the 'now'. Hence in these also the 'now' as substratum remains

the same (for it is what is before and movement), but what is predicated

after in

of

it

is

and after' is numerable that we get the 'now'. This is what is most knowable: for, similarly, motion is known because of that which is moved, locomotion because of that which is carried. [30] For what is carried is a real thing, the movement is not. Thus what is called 'now' in one sense is always the same; in another it is not the same: for this is true also of what is different; for

it is

in so far as the 'before

carried.

Clearly, too, if there were no time, there 220 a would be no 'now', and vice versa. Just as the moving body and its locomotion involve each other mutually, so too do the number of the moving body and the number of its locomotion. For the number of the locomotion is time, while the 'now' corresponds to the moving body, and is like the unit of number. Time, then, also is both made continuous by [5] the 'now' and divided at it. For here too

there

is

a correspondence with the locomotion

and the moving body. For the motion or locomotion is made one by the thing which is moved, because it is one not because it is one in its own nature (for there might be pauses in

—

—

movement of such a thing) but because it one in definition: for this determines the movement as 'before' and 'after'. Here, too, [10] there is a correspondence with the point; for the point also both connects and terminates the is

PHYSICS

300

—

the length it is the beginning of one and the end of another. But when you take it in this way, using the one point as two, a pause is necessary, if the same point is to be the beginning and the end. The 'now' on the other hand, since the body carried is moving, is always different.

Hence time

not

is

number

in the sense in

which there cause

it

is 'number' of the same point bebeginning and end, but rather as

is

[75] the extremities of a line form a number, as the parts of the line do so, both for

and not

the reason given (for we can use the middle point as two, so that on that analogy time might stand still), and further because obviously the 'now' is no part of time nor the section

any part of the movement, any more than

the points are parts of the line

—

for

it

is

[20] lines that are parts of one line. In so far then as the 'now' is a boundary,

two it is

(e.g. ten)

is

number

the

of these horses,

and

belongs also elsewhere. It

is

then, that time

clear,

movement

[25]

and is continuous what is continuous.

after',

of

is

'number of and an attribute

in respect of the before

since

it is

The smallest number, in the strict sense of the word 'number', is two. But of number as concrete, sometimes there is a minimum, somee.g. of a 'line',

of multiplicity

two

is

the smallest in respect

(or,

if

you

like,

one),

[30] but in respect of size there is no minimum; for every line is divided ad infinitum.

Hence the

it is

so

minimum

extent there

is

with time. In respect of number is one (or two); in point of

no minimum. that time

is not described as but as many or few and as long or short. For as continuous it is long or short and as a number many or few, but it is not fast or slow any more than any number with which we number is fast or slow. [5] Further, there is the same time everywhere at once, but not the same time before and after, for while the present change is one, the change which has happened and that which will happen are different. Time is not number with which we count, but the number of things which are counted, and this according as it occurs before or after is always different, [10] for the 'nows' are different. And the num-

It is clear, too,

220b

fast or slow,

—

—

movement can

be one and the same again and

again, so too can time, e.g. a year or a spring or

an autumn. [75] Not only do we measure the movement by the time, but also the time by the movement, because they define each other. The time marks the movement, since it is its num-

and the movement the time. We describe much or little, measuring it by the movement, just as we know the number by what is numbered, e.g. the number of the [20] horses by one horse as the unit. For we ber,

the time as

know how many

horses there are by the use of

number; and again by using the one horse

the

as unit

we know

the

number

of the horses

it-

with the time and the movement; for we measure the movement by the time and vice versa. It is natural that this should happen; [25] for the movement goes with the distance and the time with the movement, because they are quanta and continuous and divisible. The movement has these attributes because the distance is of this nature, and the time has them because of the movement. And we measure both the distance by the movement and the movement by the distance; for we say that the road is long, if the journey is long, and that [30] this is long, if the road is long the time,

So

it is

—

12

times not:

s

ber of a hundred horses and a hundred men is the same, but the things numbered are different the horses from the men. Further, as a

self.

not time, but an attribute of it; in so far as it numbers, it is number; for boundaries belong only to that which they bound, but number

221

too, if the

movement, and the movement,

if

the time.

221 a Time is a measure of motion and of being moved, and it measures the motion by determining a motion which will measure exactly the whole motion, as the cubit does the length by determining an amount which will measure out the whole. Further 'to be in time' means, for movement, that both it and its essence are measured by time (for simultaneously it measly] ures both the movement and its essence, and this is what being in time means for it, that its essence should be measured). Clearly then 'to be in time' has the same

meaning

for other things also, namely, that

measured by time. 'To one of two things: (1) to exist [70] when time exists, (2) as we say of some things that they are 'in number'. The latter

their being should be

be in time'

means

—

is

either

what

is

a part or

mode

of

num-

something which belongs to number or that things have a number. Now, since time is number, the 'now' and ber

in general,

—

[75] the 'before' and the like are in time, just and 'odd' and 'even' are in number,

as 'unit'

BOOK

222'

CHAPTERS

IV,

one set belongs to number, the other to time. But things are in time as they are in number. If this is so, they are contained by time as things in place are contained by place. Plainly, too, to be in time does not mean to [20] co-exist with time, any more than to be in motion or in place means to co-exist with motion or place. For if 'to be in something' is to mean this, then all things will be in anything, and the heaven will be in a grain; for when the grain is, then also is the heaven. But this is a merely incidental conjunction, whereas the in the sense that the

i.e.

which

necessarily involved: that

other

is

is

in

[25]

time necessarily involves that there

is

when

and that which is in motion that there is motion when it is. Since what is 'in time' is so in the same sense as what is in number is so, a time greater than everything in time can be found. So it is time

it is,

necessary that all the things in time should be contained by time, just like other things also which are 'in anything', e.g. the things 'in flace'

jo]

by place,

A

thing, then, will be affected by time,

we

just as

are accustomed to say that time

wastes things away, and that

all

things

old through time, and that there

is

grow

oblivion

to the lapse of time, but we do not 221 b say the same of getting to know or of becoming young or fair. For time is by its

owing

nature the cause rather of decay, since it is the number of change, and change removes

what

is.

Hence,

plainly, things

which are always

are

not, as such, in time, for they are not contained

by time, nor is their being measured by time. [5] A proof of this is that none of them is affected by time, which indicates that they are not in time. Since time is the measure of motion, it will be the measure of rest too indirectly. For all rest is in time. For it does not follow that what is in time is moved, though what is in motion [10] is necessarily moved. For time is not motion, but 'number of motion': and what is at rest, also, can be in the number of motion. Not everything that is not in motion can be said to be 'at rest' but only that which can be moved, though it actually is not moved, as was said above. 1

—

—

'To be in number' means that there is a [75] number of the thing, and that its being is measured by the number in which it is. Hence if a thing is 'in time' it will be measured by 1

202*

4.

11-13

301

what is moved the one qua moved, the it will measure their mo-

time. But time will measure

and what

is

at rest,

other qua at rest; for

and rest respectively. Hence what is moved will not be measurable

tion

by the time simply in so far as it has quantity, [20] but in so far as its motion has quantity.

Thus none moved nor time'

is 'to

of the things

which are neither

at rest are in time: for 'to be in

be measured by time', while time

the measure of motion and rest.

is

Plainly, then, neither will everything that does not exist be in time, i.e. those non-existent things that cannot exist, as the diagonal cannot be commensurate with the side. [25] Generally, if time is directly the measure of motion and indirectly of other things, it is clear that a thing whose existence is measured by it will have its existence in rest or motion. Those things therefore which are subject to perishing and becoming generally, tho.se

—

which

at

one time

exist, at

another do not

[50] are necessarily in time: for there is a greater time which will extend both beyond

and beyond the time which measures their existence. Of things which do not exist but are contained by time some were, 222 a e.g. Homer once was, some will be, e.g. a future event; this depends on the direction in which time contains them; if on both, they have both modes of existence. As to such things as it does not contain in any way, they neither were nor are nor will be. These are those nonexistents whose opposites always are, as the [5] incommensurability of the diagonal always and this will not be in time. Nor will the is commensurability, therefore; hence this eternally is not, because it is contrary to what their existence

—

A

thing whose contrary is not and not be, and it is of such things that there is coming to be and passing eternally

is.

eternal can be

away. !3

The 'now'

[10] said

and

2

is the link of time, as has been connects past and future time), a limit of time (for it is the beginning

(for

it is

it

and the end of the other). But this it is with the point, which is divides potentially, and in so far as it

of the one is

not obvious as

fixed. It

[75] is dividing the 'now' is always different, but in so far as it connects it is always the same, as it is with mathematical lines. For the intellect it is not always one and the same point, since it is other and other when one divides 2

220*

5.

PHYSICS

302 the line; but in so far as

same in every respect. So the 'now' also is

it

is

one,

it

is

the

223

'Lately',

if

'Long ago' in

one way a potential

dividing of time, in another the termination of both parts, and their unity. And the dividing and the uniting are the same thing and in the same reference, but in essence they are not the

the time

[75] 'Suddenly' refers to what has departed its former condition in a time impercepti-

from

ble because of

its

the wisest of

which is not 'sometime', every time will be determined. Will time then fail ? Surely not, if motion al[30] ways exists. Is time then always different or does the same time recur? Clearly time is,

same way as motion is. For if one and same motion sometimes recurs, it will be one and the same time, and if not, not. 222 b Since the 'now' is an end and a beginning of time, not of the same time however, but the end of that which is past and the beginning of that which is to come, it follows that, as the circle has its convexity and its concavity, in a sense, in the same thing, so time is always at a beginning and at an end. And for in the

Paron

called

also forget;

it

the nature

their

former

things

things, but the

Pythagorean

the most stupid, because in

and

clear then that

all

for

all

it is

from

come into being which reason some called it

condition. In time

and pass away;

'at some time' there will be a flood; for it must be determined with reference to the 'now'. There will thus be a determinate time from this 'now' to that, and there was such in reference to the past event. But if there be no time

smallness; but

of all change to alter things

[20] So one kind of 'now' is described in this way: another is when the time is near this

[25] relation to the first of the two types of 'now', e.g. 'at some time' Troy was taken, and

near the existing now.

refers to the distant past.

same.

kind of 'now'. 'He will come now' because he will come to-day; 'he has come now' because he came to-day. But the things in the Iliad have not happened 'now', nor is the flood 'now' not that the time from now to them is not continuous, but because they are not near. 'At some time' means a time determined in

is

s

was the truer view. must be in itself, as we

his

it

it

we

It

is

said

1

the condition of destruction [20] before, rather than of coming into being (for change,

makes things depart from

in itself,

mer

their for-

condition), and only incidentally of com-

ing into being, and of being. A sufficient evidence of this is that nothing comes into being without itself moving somehow and acting, but a thing can be destroyed even if it does not move at all. And this is what, as a rule, we [25] chiefly mean by a thing's being destroyed by time. Still, time does not work even this change; even this sort of change takes place incidentally in time.

We

have

stated, then, that time exists and and in how many senses we speak of the 'now', and what 'at some time', 'lately', 'presently' or 'just', 'long ago', and 'suddenly' mean.

what

it

is,

the

this reason

it

seems to be always different; for

[5] the 'now' is not the beginning and the end of the same thing; if it were, it would be at the

same time and sites.

And

in the

same

time will not

respect

two oppo-

fail; for it is

always

at

moves is in time; for the distinction of and slower exists in reference to all change, since it is found in every instance. In the phrase 'moving faster' I refer to that which 223 a changes before another into the condition in question, when it moves over the same interval and with a regular movement; e.g. in the that

faster

case of locomotion,

'Presently' or 'just' refers to the part of fu-

[10] ture time which is near the indivisible present 'now' ('When do you walk?' 'Present-

because the time in which he is going to do near), and to the part of past time which is not far from the 'now' ('When do you walk?' 'I have just been walking'). But to say that Troy has just been taken we do not say that, because it is too far from the 'now'. 'Lately', too, refers to the part of past time which is near the present 'now'. 'When did you go?' ly',

is

—

if

both things

move along

the circumference of a circle, or both along a straight line;

But what

a beginning.

so

14 [50] These distinctions having been drawn, it is evident that every change and everything

is

and

similarly in

before

is

all

in time; for

other cases.

we

say 'be-

and 'after' with reference to the distance from the 'now', and the 'now' is the boundary of the past and the future; so that since 'nows' are in time, the before and the after will be in time too; for in that in which the 'now' is, the distance from the 'now' will also be. But 'before' is used contrariwise with refer[10] ence to past and to future time; for in the past we call 'before' what is farther from the 'now', and 'after' what is nearer, but in the [5] fore'

224

BOOK

s

future ther

we

the nearer 'before'

call

'after'.

So that since the

IV,

and the

'before'

is

CHAPTERS 13-14 farNow there is

in time,

[75] and every movement involves a 'before', evidently every change and every movement is in time. It is also worth considering how time can be related to the soul; and why time is thought to be in everything, both in earth and in sea and in heaven. Is it because it is an attribute, or state, or movement (since it is the number of movement) and all these things are mov-

able (for they are

[20]

movement

potentiality

and

Whether exist or not,

if

all

in place),

and time and

are together, both in respect of

is

Now

in respect of actuality?

soul did not exist time a question that

may

would

fairly

be

asked; for if there cannot be some one to count there cannot be anything that can be counted, so that evidently there cannot be number; for number is either what has been, or what can [25] be, counted. But if nothing but soul, or in soul reason, is qualified to count, there would not be time unless there were soul, but only

which time is an attribute, i.e. if movement can exist without soul, and the before and after are attributes of movement, and time is these qua numerable. One might also raise the question what sort [30] of movement time is the number of. Must we not say 'of any kind'? For things both come into being in time and pass away, and grow, and are altered in time, and are moved locally; thus it is of each movement qua movement that of

that time

the

is

number

the number.

And

of continuous

so

it

is

303

such a thing as locomotion, and in locomotion there is included circular movement, and everything is measured by some one thing homogeneous with it, units by a unit, horses by a horse, and similarly times 1 [75] by some definite time, and, as we said, time is measured by motion as well as motion by time (this being so because by a motion definite in time the quantity both of the motion and of the time is measured): if, then, what is first is the measure of everything homogeneous with it, regular circular motion is above all else the measure, because the num-

simply

movement, not of

any particular kind of it. 223 b But other things as well may have been moved now, and there would be a number of each of the two movements. Is there another time, then, and will there be two equal times at once? Surely not. For a time that is both equal and simultaneous is one and the same time, and even those that are not simultaneous are one in kind; for if there were dogs, and [5] horses, and seven of each, it would be the same number. So, too, movements that have simultaneous limits have the same time, yet the one may in fact be fast and the other not, and one may be locomotion and the other alteration; still the time of the two changes is the same if their number also is equal and simul[10] taneous; and for this reason, while the movements are different and separate, the time

[20] ber of this is the best known. neither alteration nor increase nor coming into

being can be regular, but locomotion can be. This also is why time is thought to be the movement of the sphere, viz. because the other movements are measured by this, and time by this movement. This also explains the common saying that [25] there

human is

natural

affairs

a circle in

all

form

a circle,

and that

other things that have a

movement and coming

into being

and

passing away. This is because all other things are discriminated by time, and end and begin as

though conforming to a cycle; for even time thought to be a circle. And this opin-

itself is

[50]

ion again

is

held because time

is

the

measure of this kind of locomotion and is itself measured by such. So that to say that the things that come into being form a circle is to say that there is a circle of time; and this is to say that it is measured by the circular movement; for apart from the meas224 a ure nothing else to be measured is observed; the whole is just a plurality of measures. It is

said rightly, too, that the

number

of the

same number if the two numbers are equal, but not the same decad or the same ten; just as the equilateral [5] and the scalene are not the same triangle, yet they are the same figure, because they are both triangles. For things are called the same so-and-so if they do not differ by a differentia sheep and of the dogs

of that thing, but not differs

from

the

is

if

they do; e.g. triangle

triangle by a differentia of

tri-

angle, therefore they are different triangles;

but they do not differ by a differentia of figure, but are in one and the same division of it. For a figure of the one kind

is

a circle

and

a figure

is

[70] of another kind of triangle, and a triangle of one kind is equilateral and a triangle of

of equal

another kind scalene. They are the same figure,

everywhere the same, because the number and simultaneous movements is everywhere one and the same.

1

220b 28.

PHYSICS

3 o4

and

then,

that, triangle,

but not the same

tri-

number of two groups same number (for their number does

angle. Therefore the also

is

the

not differ by a differentia of number), but it not the same decad; for the things of which

is

224b

asserted differ; one

group are dogs, and the

other horses. [75]

We have now

discussed time

—both time

is

itself

and the matters appropriate

to the con-

it

sideration of

it.

BOOK V Everything which changes does three senses.

It

as for instance

so in

one of

may change (1) accidentally, when we say that something

musical walks, that which walks being something in which aptitude for music is an accident. Again (2) a thing is said without qualification to change because something belonging to it changes, i.e. in statements which refer [25] to part of the thing in question: thus the body is restored to health because the eye or the chest, that is to say a part of the whole body, is restored to health. And above all there is (3) the case of a thing which is in motion neither accidentally nor in respect of something else belonging to it, but in virtue of being itself directly in motion. Here we have a thing which is essentially movable: and that which is so is a different thing according to the particular variety of motion: for instance it may be a thing capable of alteration: and within the sphere of alteration it is again a different thing according [50] as it is capable of being restored to health or capable of being heated. And there are the same distinctions in the case of the mover: (1) one thing causes motion accidentally, (2) another partially (because something belonging to it causes motion), (3) another of itself directly, as, for instance, the

hand

strikes.

tors: (a)

We have,

physician heals, the

then, the following fac-

on the one hand that which directly and (b) on the other hand that

causes motion,

which

is

in motion: further,

we have

(c) that

nor experienced by the form or the place or the quantity. So we are left with a mover, a moved, and a goal of motion. I do not include the starting-point of motion: for it is the goal rather than the starting-point of motion that gives its name to a particular process of change. Thus 'perishing' is change to not-being, though it is also true that that which perishes changes from being: and 'becoming' is change to being,

though

it is

also

change from not-being.

Now

a definition of motion has been giv[10] en above, 1 from which it will be seen that every goal of motion, whether it be a form, an affection, or a place,

stance,

may be raised. Affections, it may be motions, and whiteness is an affection: thus there may be change to a motion. To this [75] we may reply that it is not whiteness but whitening that is a motion. Here also the same distinctions are to be observed: a goal of motion may be so accidentally, or partially and with reference to something other than itself,

said, are

and with no reference to anything which is becoming white changes accidentally to an object of or directly else:

for instance, a thing

thought, the colour being only accidentally the [20] object of thought; it changes to colour, because white is a part of colour, or to Europe, because Athens is a part of Europe; but it changes essentially to white colour. It is now clear in what sense a thing is in motion essentially,

accidentally, or in respect of

other than

itself,

'itself directly' is

224 b from which and

clear that the

which it proceeds: for every motion proceeds from something and to something, that which is directly in motion being distinct from that to which it is in motion and that from which it is in motion:

we may

take the three things 'wood', 'hot', and 'cold', of which the first is that which is in motion, the second is that to which the motion proceeds, and the third is for instance,

from which it proceeds. This being so, it is clear that the motion is in the wood, not in [5] its form: for the motion is neither caused

that

as, for in-

heat. Here, however, a

difficulty

[55] in which motion takes place, namely time, and (distinct from these three) (d) that (e) that to

immovable,

is

knowledge and

[25] that

mover and which

is

in

what

something

sense the phrase

used in the case both of the of the

motion

is

moved: and

Now

also

it is

not in the form but in

in motion, that

able in activity'.

may

and

is

to say 'the

mov-

accidental change

leave out of account: for

it is

to be

we

found

any time, and in any respect. Change which is not accidental on the other hand is not to be found in everything, but only in everything, at

in contraries, in things intermediate

between

[30] contraries, and in contradictories, as be proved by induction. An intermediate

may may

be a starting-point of change, since for the 1

20I a 10.

BOOK

225 b

purposes of the change

two

either of

IV,

serves as contrary to

it

contraries: for the intermediate

in a sense the extremes.

is

CHAPTER 14— BOOK

Hence we speak

of

for

CHAPTERS

V,

1-2

although that which

305 or

'not-white'

is

'not-good'

may

nevertheless be in motion ac-

cidentally

(for

example that which is 'notwhich is

the intermediate as in a sense a contrary rela-

white' might be a man), yet that

tively to the extremes and of either extreme as a contrary relatively to the intermediate: for instance, the central note is low relatively to the highest and high relatively to the lowest,

without qualification 'not-so-and-so' cannot in [25] any sense be in motion: therefore it is impossible for that which is not to be in motion. This being so, it follows that 'becoming' cannot be a motion: for it is that which 'is not' that 'becomes'. For however true it may

and grey

light relatively to black

is

and dark

relatively to white.

And

change is from somesomething as the word itself (lj,eTa(3o\r)) indicates, implying something 'after' (fxeTa ) something else, that is to say something earlier and something later that which changes must change in one of four ways: from subject to subject, from subject to non[5] subject, from non-subject to subject, or from non-subject to non-subject, where by 'subject' I mean what is affirmatively expressed. So it follows necessarily from what has been said above that there are only three kinds of change, that from subject to subject, that from subject to non-subject, and that from non[35]

since every

225 a thing

to

—

—

1

[10] subject to subject: for the fourth conceivable kind, that from non-subject to non-

not change, as in that case there is no opposition either of contraries or of consubject,

is

tradictories.

Now

change from non-subject

to

subject,

the relation being that of contradiction, is 'coming to be' 'unqualified coming to be'

—

when

the change takes place in an unqualified

way, 'particular coming to be' when the change is change in a particular character: for instance, a change from not-white to white is a coming to be of the particular thing, white, while [75] change from unqualified not-being to being is coming to be in an unqualified way, in respect of which we say that a thing 'comes to be' without qualification, not that it 'comes to be'

some

particular thing.

ject to non-subject

when

perishing'

not-being,

change

is

Change from

'perishing'

the change

'particular

is

sub—'unqualified

from being

perishing'

when

coming

same

as that

made

in the case

'is

not' in respect of the affirma-

similarly

it is

224b 28, 29.

'is

not'

And not'

[30] There are these difficulties, then, in the of the assumption that that which 'is not'

can be in motion: and

it

may

be further ob-

which is which 'is not' is not would be somewhere.

jected that, whereas everything

in

motion

in

is

in space, that

space: for then

it

is not a motion: for a contrary either another mo-

So, too, 'perishing'

motion has

for

tion or rest,

whereas 'perishing'

its

is

the contrary

of 'becoming'. Since, then, every motion is a kind of change, and there are only the three kinds of 2 [35] change mentioned above, and since of these three those which take the form of 'be-

225 b coming' and 'perishing', that is to say those which imply a relation of contradiction, are not motions:

it

necessarily follows that only

motion. And an inbe allowed to

change from subject

to subject

every such subject

either a contrary or

is

is

termediate (for a privation may rank as a contrary) and can be affirmatively expressed, as naked, toothless, or black. If, then, [5] the categories are severally distinguished as Being, Quality, Place, Time, Relation, Quantity,

and Activity or

Passivity,

it

necessarily

follows that there are three kinds of motion qualitative, quantitative,

and

local.

[10] In respect of Substance there is no mobecause Substance has no contrary among

tion,

of Relation: for

Nor is there motion in respect it may happen that when one

correlative changes, the other, although this

does not

itself

change,

is

Nor

only potentially 'is', that is to say the opposite of that which actually 'is' in an unqualified sense: 1

'is

way

which

it

neverthe-

impossible for that which

so that in these cases the

not' in the sense that

it is

which

to be at rest.

tion or negation of a predicate, nor of that 'is

that

that in an unqualified sense 'becomes'.

things that are.

to be.

Now

which

it is

to

the expression 'not-being' is used in [20] several senses: and there can be motion neither of that

accidentally 'becomes',

it

less correct to say that

the

to the opposite negation, the distinc-

tion being the

of

is

be that

is

Patient

no longer motion is

there motion in respect of

—

in fact there can never be

mover and moved, because 2

1.7.

applicable, accidental.

Agent and motion of

there cannot be

PHYSICS

3°6

[75] motion of motion or becoming of becoming or in general change of change. For in the first place there are two senses in which motion of motion is conceivable. (1) The motion of which there is motion might be conceived as subject; e.g. a man is in motion because he changes from fair to dark. Can it be that in this sense motion grows hot or cold, or [20] changes place, or increases or decreases? Impossible: for change is not a subject. Or (2) can there be motion of motion in the sense that some other subject changes from a change to another mode of being, as e.g. a man changes

from

falling

ill

to getting well?

Even

this

is

possible only in an accidental sense. For, what-

ever the subject

movement another. (And

may

be,

change the same is

from one form to [25] holds good of becoming and perishing, except that in these processes we have a change

kind of opposite, while the change to a different kind.) So, if there is to be motion of motion, that which is changing from health to sickness must simultaneously be changing from this very change to another. It is clear, then, that by the time that it has become sick, it must also have changed to whatever may be the other change concerned (for that it should be at rest, though logically possible, is excluded by the theory). Moreover this other can never be any casual change, but must be a change from [50] something definite to some other definite thing. So in this case it must be the opposite to

a particular

other, motion,

is

a

change, viz. convalescence. It is only accidentally that there can be change of change, e.g. there

is

a change

from remembering

to for-

getting only because the subject of this change

changes

at

one time

to

knowledge,

at

another

motion, it ing contrary

lar

coming to becoming quently, that

if

there

is

to be

change

and becoming of becoming, we shall have an infinite regress. Thus if one of a series [35] of changes is to be a change of change, 226 a the preceding change must also be so: e.g. if simple becoming was ever in process of becoming, then that which was becoming simple becoming was also in process of becoming, so that we should not yet have arrived at what was in process of simple becoming but only at what was already in process of becoming in process of becoming. And this again was someof change

time in process of becoming, so that even then we should not have arrived at what was in process of simple becoming. And since in an infinite series there is no first term, here there will be no first stage and therefore no follow-

is

also capable of the correspond-

motion or the corresponding rest, and a thing that is capable of also capable of perishing: conse-

is

if

there be

which

is

becoming of becoming, becoming is in

process of

in

process of perishing at the very

moment when

has reached the stage of becoming: since it cannot be in process of perishing when it is just beginning to become or after it has ceased it

to

become: for that which

ishing

must be

is

in process of per-

in existence.

[10] Fourthly, there must be a substrate underlying all processes of becoming and chang-

What

can this be in the present case? It body or the soul that undergoes alteration: what is it that correspondingly becomes motion or becoming? And again what is the goal of their motion? It must be the motion or becoming of something from something to something else. But in what sense [75] can this be so? For the becoming of learning cannot be learning: so neither can the becoming of becoming be becoming, nor can the becoming of any process be that process. Finally, since there are three kinds of motion, the substratum and the goal of motion must be one or other of these, e.g. locomotion will have to be altered or to be locally moved. To sum up, then, since everything that is moved is moved in one of three ways, either ing.

either the

is

accidentally, or partially, or essentially,

change

[20] can change only accidentally, as e.g. when a man who is being restored to health runs or learns:

and accidental change we have long

ago 1 decided

to ignorance.

In the second place,

226"

[5] ing stage either. On this hypothesis, then, nothing can become or be moved or change. Thirdly, if a thing is capable of any particu-

to leave out of account.

motion can belong neither to Being nor to Relation nor to Agent and Patient, it remains that there can be motion only in respect of Quality, Quantity, and Place: for [25] with each of these we have a pair of contraries. Motion in respect of Quality let us call Since, then,

alteration, a general designation that

is

used to

include both contraries: and by Quality I do not here mean a property of substance (in that sense that tion

is

which

constitutes a specific distinc-

a quality) but a passive quality in vir-

is said to be acted on or being acted on. Motion in [30] respect of Quantity has no name that includes both contraries, but it is called increase or decrease according as one or the other is

tue of

which

a thing

to be incapable of

1

224b 26.

ij

BOOK

227"

V,

CHAPTERS

motion in the direction of complete magnitude is increase, motion in the contrary direction is decrease. Motion in respect of Place has no name either general or particular: but we may designate it by the general name of locomotion, though strictly the term 'locomotion' is applicable to things that change their place only when they have not [35] tne power to come to a stand, and to things that do not move themselves locally. 226 b Change within the same kind from a lesser to a greater or from a greater to a lesser degree is alteration: for it is motion either from a contrary or to a contrary, whether in an unqualified or in a qualified sense: for change to a lesser degree of a quality will be called change to the contrary of that quality, [5] and change to a greater degree of a quality will be regarded as change from the contrary of that quality to the quality itself. It makes no difference whether the change be qualified or unqualified, except that in the former case the contraries will have to be contrary to one another only in a qualified sense: and a thing's designated: that

is

to say

possessing a quality in a greater or in a lesser degree means the presence or absence in it of

2-3

307

Things are said to be together in place when they are in one place (in the strictest sense of the word 'place') and to be apart when they are in different places.

Things are

said to be in contact

when

their

extremities are together.

That which a changing thing, if it changes [25] continuously in a natural manner, naturally reaches before it reaches that to which it

changes

last, is

between. Thus 'between' im-

plies the presence of at least three things: for

change it is the contrary that is and a thing is moved continuously if it leaves no gap or only the smallest possible gap not in the time (for a gap in in the material in a process of 'last':

—

the time does not prevent things having a 'be-

tween', while, on the other hand, there is nothing to prevent the highest note sounding [30] immediately after the lowest) but in the material in which the motion takes place. This is manifestly true not only in local changes but in every other kind as well. (Now every 227 a [7] change implies a pair of opposites,

and opposites may be

either contraries or con-

tradictories; since then contradiction

admits of

clear, then, that there are

no mean term, it is obvious that 'between' must imply a pair of contraries.) That is locally con226 b [32] trary which is most distant in a

of motion.

straight line: for the shortest line

more

or less of the opposite quality. It is now only these three kinds

The term 'immovable' we

apply in the first place to that which is absolutely incapable of being moved (just as we correspondingly apply the term invisible to sound); in the sec[10]

ond

place to that

which

culty after a long time or

—

is

moved with

diffi-

whose movement is what we describe as

slow at the start in fact, hard to move; and in the third place to that which is naturally designed for and capable of motion, but is not in motion when, where, and as it naturally would be so. This last is the only kind of immovable thing of which I use the term 'being at

rest':

for rest

is

con-

[75] trary to motion, so that rest will be negation of motion in that which is capable of

admitting motion. The foregoing remarks are sufficient to explain the essential nature of motion and rest, the number of kinds of change, and the different varieties of motion.

Let us

now

gether'

and

[20] ous',

proceed to define the terms

succession',

and

to

'to-

'apart', 'in contact', 'between', 'in

show

of these terms

is

and 'continuwhat circumstances each

limited,

and that which

is

is

definitely

definitely limited

constitutes a measure.

A [_?5]

thing

is

'in succession'

when

it

the beginning in position or in

is

after

form or

in some other respect in which it is definitely 227 a so regarded, and when further there is nothing of the same kind as itself between it and that to which it is in succession, e.g. a line or lines

if it is

a line, a unit or units

if it is

nothing to prevent something of a different kind being between). For that which is in succession is in succession to a particular thing, and is something posterior: for one is not 'in succession' to [5] two, nor is the first day of the month to be second: in each case the latter is 'in succession' a unit, a house

if it is

a house (there

is

to the former.

A

thing that

is

in succession

and touches

is

[10] 'contiguous'. The 'continuous' is a subdivision of the contiguous: things are called

continuous when the touching limits of each become one and the same and are, as the word implies, contained in each other: continuity is impossible if these extremities are two. This

makes

plain that continuity be-

'contiguous',

definition

in

longs to things that naturally in virtue of their [75] mutual contact form a unity. And in

naturally applicable.

it

PHYSICS

3 o8

whatever way that which holds them together is one, so too will the whole be one, e.g. by a rivet or glue or contact or organic union. obvious that of these terms 'in succesin order of analysis: for that which touches is necessarily in succession, but not It is

sion'

is first

in succession touches: and so property of things prior in [20] definition, e.g. numbers, while contact is not. And if there is continuity there is necessarily contact, but if there is contact, that alone

everything that succession

is

is

a

does not imply continuity: for the extremities may be 'together' without necessarily being one: but they cannot be one without being necessarily together. So natural junction is

of things

coming to be: for the extremities must come into contact if they are to be

last in

necessarily

[25] naturally joined: but things that are in contact are not all naturally joined, while there is no contact clearly there is no natural

junction either. Hence,

if

as

some say

'point'

have an independent existence of their own, it is impossible for the two to be identical: for points can touch while units can [30] only be in succession. Moreover, there can always be something between points (for all lines are intermediate between points), whereas it is not necessary that there should possibly be anything between units: for there can be nothing between the numbers one and

and

'unit'

two.

We have now defined what is meant by 'to227 b gether' and 'apart', 'contact', 'between' and 'in succession', 'contiguous' and 'continuous': and we have shown in what circumstances each of these terms

There are many senses to be 'one': for

we

in

is

applicable.

which motion

use the term 'one' in

said

is

many

senses.

Motion [5]

is

one generically according

different categories to

which

assigned: thus any locomotion cally

any other

with

alteration

is

it

to the

may

be

one generilocomotion, whereas is

different generically

from

loco-

motion.

Motion is one specifically when besides being one generically it also takes place in a species incapable of subdivision: e.g. colour has spedifferences: therefore blackening and whitening differ specifically; but at all events every whitening will be specifically the same with every other whitening and every blackening with every other blackening. But white[10] ness is not further subdivided by specific cific

228*

any whitening

differences: hence

is

specifically

one with any other whitening. Where it happens that the genus is at the same time a species, it is clear that the motion will then in a sense be one specifically though not in an unqualified sense: learning is an example of this, knowledge being on the one hand a species of apprehension and on the other hand a genus including the various knowledges. A difficulty, however, may be raised as to whether a mo[75] tion is specifically one when the same thing changes from the same to the same, e.g. when one point changes again and again from a particular place to a particular place:

motion

is

if

this

motion will motion, and rolling

specifically one, circular

be the same as rectilinear the same as walking. But

is

not this difficulty

removed by the principle already laid down that if that in which the motion takes place is specifically different (as in the present instance

the circular path

is

specifically different

from

[20] the straight) the motion itself is also different? have explained, then, what is

We

meant by saying

that

motion

is

one generically

or one specifically. is one in an unqualified sense when one essentially or numerically: and the

Motion it

is

following distinctions will

make

clear

what

kind of motion is. There are three classes of things in connexion with which we speak of motion, the 'that which', the 'that in which', and the 'that during which'. I mean that there [25] must be something that is in motion, e.g. a man or gold, and it must be in motion in something, e.g. a place or an affection, and during something, for all motion takes place during a time. Of these three it is the thing in which the motion takes place that makes it one generically or specifically, it is the thing moved that makes the motion one in subject, and it is the time that makes it consecutive: but it is the three together that make it one without qualification: to effect this, that in [50] which the motion takes place (the species) must be one and incapable of subdivision, that during which it takes place (the time) must be one and unintermittent, and that which is in motion must be one not in an accidental sense (i.e. it must be one as the white that blackens is one or Coriscus who walks is one, not in the accidental sense in 228 a which Coriscus and white may be one), nor merely in virtue of community of nature (for there might be a case of two men being restored to health at the same time in the same way, e.g. from inflammation of the eye, yet this

—

BOOK

228 b this

motion

cifically

V,

CHAPTERS

not really one, but only spe-

is

one).

Suppose, however, that Socrates undergoes an alteration specifically the same but at one time and again at another: in this case if it is possible for that which ceased to be again to come into being and remain numerically the [5] same, then this motion too will be one: otherwise it will be the same but not one. And

akin to this difficulty there is another; viz. is health one? and generally are the states and

one

affections in bodies severally

them Thus

in essence al-

clear) the things that contain are obviously in motion and in flux?

though (as

is

if a person's health at daybreak and at [10] the present moment is one and the same, why should not this health be numerically one

with that which he recovers after an interval ?

The same argument applies in each case. There is, however, we may answer, this difference: that

if

the states are

two then

it

follows simply

from this fact that the activities must also in point of number be two (for only that which is numerically one can give rise to an activity [75] that is numerically one), but if the state is one, this is not in itself enough to make us regard the activity also as one: for when a man ceases walking, the walking no longer is, but it will again be if he begins to walk again. But, be this as it may, if in the above instance the health is one and the same, then it must be

which

possible for that

come

to be

and

is

one and the same to

to cease to be

many

times.

3-4

309

ends of the two things are one. Hence motions [jo] may be consecutive or successive in virtue of the time being continuous, but there can be continuity only in virtue of the motions themselves being continuous, that is when the end of each is one with the end of the other. Mo228 b tion, therefore, that is in an unqualified sense continuous and one must be specifically the same, of one thing, and in one time. Unity is required in respect of time in order that there may be no interval of immobility, for

where there is intermission of motion there must be rest, and a motion that includes intervals of rest will be not one but many, so that [5] a motion that is interrupted by stationariness is not one or continuous, and it is so interrupted if there is an interval of time. And though of a motion that is not specifically one (even

if

the time

unintermittent) the time

is

and motion that is one [10] must be specifically one, though motion that is specifically one is not necessarily one in an unqualified sense. We have now explained what we mean when we call a motion one is

one, the motion

specifically different,

is

so cannot really be one, for

without qualification. Further, a motion

is

also said to be

nerically, specifically, or essentially

one ge-

when

it is

complete, just as in other cases completeness

and wholeness are

characteristics of

one: and sometimes a motion even plete

is

if

what

is

incom-

said to be one, provided only that

it is

continuous.

ent inquiry.

[75] And besides the cases already mentioned there is another in which a motion is said to be

tion that

[20] Since every motion is continuous, a mois one in an unqualified sense must

motion that

motion is divisible) be continuous, and a continuous motion must be one. There will not be continuity between any motion and any other indiscriminately any more than there is between any two things chosen at random in any other sphere: there can be continuity only when the extremities of the two things are one. Now some things have no extremities at all: and the extremities of others differ spe[25] cifically although we give them the same

that

However, these

difficulties lie

outside our pres-

(since every

name

of 'end':

how

should

e.g.

the 'end' of a

and the 'end' of walking touch or come to be one ? Motions that are not the same either specifically or generically may, it is true, be consecutive (e.g. a man may run and then at once fall ill of a fever), and again, in the line

torch-race we have consecutive but not continuous locomotion: for according to our definition there can be continuity only when the

one, viz.

title

when

it

is

regular: for in a sense a

is not regarded as one, belonging rather to that which is reg-

is

irregular

ular, as a straight line

is

regular, the irregular

being as such divisible. But the difference would seem to be one of degree. In every kind of motion we may have regularity or irregu[20] larity: thus there may be regular alteration, and locomotion in a regular path, e.g. in a circle or on a straight line, and it is the same with regard to increase and decrease. The difference that makes a motion irregular is sometimes to be found in its path: thus a motion cannot be regular if its path is an irregular magnitude, e.g. a broken line, a spiral, or any other magnitude that is not such that any part of it taken at random fits on to any other that [25] may be chosen. Sometimes it is found neither in the place nor in the time nor in the goal but in the manner of the motion: for in some cases the motion is differentiated by

PHYSICS

310 quickness and slowness: thus

if

its

velocity

is

229 b

tion to a contrary or to an intermediate (of

however, we shall speak later), 1 but changing to a contrary rather than changing from a contrary would seem to be the

uniform a motion is regular, if not it is irregular. So quickness and slowness are not species of motion nor do they constitute specific dif-

this,

ferences of motion, because this distinction occurs in connexion with all the distinct species [jo] of motion. The same is true of heaviness

cause of the contrariety of motions, the latter being the loss, the former the gain, of con-

and lightness when they refer to the same thing: e.g. they do not specifically distinguish earth from itself or fire from itself. Irregular 229 a motion, therefore, while in virtue of being continuous gree, as

is

it

is

one,

is

so in a lesser de-

the case with locomotion in a broken

and a lesser degree of something always means an admixture of its contrary. And since

line:

is one can be both regular motions that are consecutive [5] but not specifically the same cannot be one and continuous: for how should a motion composed of alteration and locomotion be regular? If a motion is to be regular its parts ought to fit one another.

every motion that

and

irregular,

[25] trariness. Moreover, each several motion takes its name rather from the goal than from the starting-point of change, e.g. motion to

health

we

call

ease sickening.

convalescence, motion to dis-

Thus we

are left with motions

and motions respecfrom the opposite contraries. Now it would seem that motions to contraries are at the same time motions from contraries (though their essence may not be the same; 'to health' is distinct, I mean, from 'from disease', and 'from health' from 'to disrespectively to contraries,

contraries

to

tively

ease').

[30] Since then change differs from motion (motion being change from a particular subject to a particular subject),

it

follows that con-

trary motions are motions respectively

We have further to determine what motions are contrary to each other, and to determine sim-

with rest. And we have first to decide whether contrary motions are motions

ilarly

how

it is

from and to the same thing, e.g. [10] a motion from health and a motion to health (where the opposition, it would seem, is of the same kind as that between coming to be and ceasing to be); or motions respectively from contraries, e.g. a motion from health and a motion from disease; or motions respectively to contraries, e.g. a motion to health and a motion to disease; or motions respectively from a contrary and to the opposite contrary, e.g. a motion from health and a motion to disease; or motions respectively from a contrary to the opposite contrary and from the latter to the former, e.g. a motion from health to disease and a motion from disease to health: for motions [75] must be contrary to one another in one or more of these ways, as there is no other way in which they can be opposed. Now motions respectively from a contrary and to the opposite contrary, e.g. a motion from health and a motion to disease, are not contrary motions: for they are one and the respectively

same. (Yet their essence

is

not the same, just

changing from health is different from changing to disease.) Nor are motions re[20] spectively from a contrary and from the

as

opposite contrary contrary motions, for a tion from a contrary is at the same time a

momo-

from

a

contrary to the opposite contrary and from the 229 b latter to the former, e.g. a motion from health to disease and a motion from disease to health. Moreover, the consideration of particular

examples will also show what kinds of

processes are generally recognized as contrary:

thus falling ill is regarded as contrary to recov[5] ering one's health, these processes having contrary goals, and being taught as contrary to being led into error by another, it being possible to

one's ilarly

acquire error, like knowledge, either by

own agency or by that of another. Simwe have upward locomotion and down-

ward locomotion, which

are contrary length-

and locomotion which are contrary breadthwise, and forward locomotion and backward locomotion, which too are contraries. On the other wise, locomotion to the right

to the left,

[10]

hand, a process simply to a contrary, that denoted by the expression 'becom-

e.g.

ing white', where no starting-point is specified, is a change but not a motion. And in all cases of a thing that has no contrary we

have as contraries change from and change to the

same

thing.

Thus coming

to be

is

contrary

and losing to gaining. But these are changes and not motions. And wher[75] ever a pair of contraries admit of an intermediate, motions to that intermediate must be held to be in a sense motions to one or other of to ceasing to be,

the contraries: for the intermediate serves as a contrary for the purposes of the motion, in 1

1.

28 sqq.

BOOK

230b

V,

CHAPTERS

whichever direction the change may be, e.g. grey in a motion from grey to white takes the place of black as starting-point, in a motion from white to grey it takes the place of black as goal, and in a motion from black to grey it takes the place of white as goal: for the middle [20] is opposed in a sense to either of the ex1 tremes, as has been said above. Thus we see that two motions are contrary to each other only when one is a motion from a contrary to the opposite contrary and the other is a motion

from the

latter to the

former.

4-6

3"

[10] there be a particular subject, absence of change in its being will be contrary to absence its not-being. And here a difficulty be raised: if not-being is not a particular something, what is it, it may be asked, that is contrary to absence of change in a thing's being? and is this absence of change a state of rest? If it is, then either it is not true that every state of rest is contrary to a motion or else

of change in

may

coming

to be

and ceasing

to be are motion.

[75] It is clear then that, since we exclude these from among motions, we must not say that this absence of change

we must But since a motion appears to have contrary it not only another motion but also a state of rest, we must determine how this is so. A motion has for its contrary in the strict sense of the term another motion, but it also has for an opposite a state of rest (for rest is the priva[25] tion of motion and the privation of anything may be called its contrary), and motion of one kind has for its opposite rest of that kind, e.g. local motion has local rest. This statement, however, needs further qualification: there remains the question, is the opposite of remaining at a particular place motion from or motion to that place? It is surely clear that since there are two subjects between which [jo] motion takes place, motion from one of these (A) to its contrary (B) has for its opposite remaining in A, while the reverse motion has for its opposite remaining in B. At the same time these two are also contrary to each other: to

for

would be absurd to suppose that there and not opposite states of

it

are contrary motions

230*

of rest in contraries are optake an example, a state of rest in ( 1 ) contrary to a state of rest in dis-

rest. States

posed.

To

health

is

and (2) the motion to which it is conis that from health to disease. For (2) it would be absurd that its contrary motion should be that from disease to health, since motion to that in which a thing is at rest is [5] rather a coming to rest, the coming to rest being found to come into being simultaneously with the motion; and one of these two motions it must be. And (1) rest in whiteness is of ease,

trary

and

call

say that it

it is

is

a state of rest:

similar to a state of rest

absence of change.

And

change from it and the thing's coming to be is change to it. Again, a further difficulty may be raised. How is it, it may be asked, that whereas in local change both remaining and moving may [20] be natural or unnatural, in the other changes this is not so? e.g. alteration is not now

and now unnatural, for convalescence no more natural or unnatural than falling ill, whitening no more natural or unnatural than blackening; so, too, with increase and decrease: natural is

these are not contrary to each other in the sense

[25] that either of them is natural while the other is unnatural, nor is one increase contrary to

another in this sense; and the same account be given of becoming and perishing: it is

may

not true that becoming

is natural and perishing unnatural (for growing old is natural), nor do we observe one becoming to be natural

and another unnatural. We answer that if [50] what happens under violence is unnatural, then violent perishing is unnatural and as such contrary to natural perishing. Are there then also some becomings that are violent and not the result of natural necessity, and are therefore contrary to natural becomings, and 230 b violent increases and decreases, e.g. the rapid growth to maturity of profligates and the rapid ripening of seeds even when not packed close in the earth?

And how

is it

[5] urally according as they

throw

from being and change

the critical days or not. But,

it

such things there is no remaining though there is absence of change. Should

tion. So, too, of

some

with

we may

tions? Surely just the same:

no mo-

will have

its

course not contrary to rest in health. Of all things that have no contraries there are opposite changes (viz. change from the thing and change to the thing, e.g. change to being), but

it

contrary either nothing or absence of change in the thing's not-being, or the ceasing to be of the thing: for such ceasing to be is for

altera-

say that

alterations are violent while others are

natural, e.g. patients alter naturally or unnat-

may

off fevers

on

be objected, then we shall have perishings contrary to one another, not to becoming. Certainly: and why should not this in a sense be so? Thus it is so if

PHYSICS

3 12

one perishing is pleasant and another painful: and so one perishing will be contrary to another not in an unqualified sense, but in so far as one has this quality and the other that. [10] Now motions and states of rest universalthe manner described upward motion and rest above are

ly exhibit contrariety in 1

above, e.g.

downward motion and

respectively contrary to

below, these being instances of local conand upward locomotion belongs nat-

rest

trariety;

urally to fire

and downward

to earth,

i.e.

the

locomotions of the two are contrary to each other.

And

down

unnaturally: and

moves up naturally and its natural motion is contrary to its unnatural mo-

again, fire

[75] certainly Similarly

with remaining: remaining above is contrary to motion from above downwards, and to earth this remaining comes unnaturally, this motion naturally. So the unnatural remaining of a thing is contrary to its natural motion, just as we find a similar contion.

[20] trariety in the motion of the same thing: one of its motions, the upward or the downward, will be natural, the other unnatural. Here, however, the question arises, has every state of rest that is not permanent a becoming,

and

is

this

If so, there

at

is

becoming a coming to a standstill ? must be a becoming of that which unnaturally, e.g. of earth at rest

rest

23 1«

it still appears to have that which is [30] being discarded, so that if a state of rest is itself contrary to the motion from the state

thing,

of rest to its contrary, the contraries rest and motion will be simultaneously predicable of the same thing. May we not say, however, that in so far as the thing

is still

stationary

it is

in a

state of rest in a qualified sense? For, in fact,

whenever

a thing

is

in

motion, part of

the starting-point while part

is

it is

at

at the goal to

23 a which it is changing: and consequently a motion finds its true contrary rather in another motion than in a state of rest. With regard to motion and rest, then, we have now explained in what sense each of them is one and under what conditions they exhibit contrariety.

[With regard

to coming to a standstill the be raised whether there is an opposite state of rest to unnatural as well as to natural motions. It would be absurd if this

[5]

question

may

were not the case: for a thing may remain still merely under violence: thus we shall have a thing being in a non-permanent state of rest without having become so. But it is clear that it must be the case: for just as there is unnatural motion, so, too, a thing may be in an un[10] natural state of rest. Further, some things have a natural and an unnatural motion,

coming

to a standstill.

has a natural upward motion and an unnatural downward motion: is it, then, this unnatural downward motion or is it the nat-

of that

which comes

ural

above: and therefore this earth during the time that it was being carried violently upward was

But whereas the velocity to a standstill seems always to increase, the velocity of that which is [25] carried violently seems always to decrease: so it will be in a state of rest without having become so. Moreover 'coming to a standstill' is generally tical

recognized to be iden-

or at least concomitant with the locomo-

proper place. There is also another difficulty involved in the view that remaining in a particular place is

tion of a thing to

its

contrary to motion from that place. For

a thing

is

moving from

when

or discarding some-

e.g. fire

downward motion of earth that is contrary upward motion? Surely it is

to the natural

it though not in motion of earth is contrary inasmuch as the motion of fire is [75] also natural, whereas the upward motion

clear that both are contrary to

the

same

of fire

sense: the natural

as

being natural

remaining. But there would seem to be a sense in

which a

state of rest

understood as defined above 2 being 'continuous' if their extrem-

'in succession' are

ities

are one, 'in contact'

together,

of their 1

and

own

In chapter

5.

if

their extremities are

nothing kind intermediate between them 'in succession' if

2 v. 3.

there

is

a

motion are op-

VI

—nothing that

—things

and

posites.]

BOOK Now if the terms 'continuous', 'in contact', and

contrary to the

is

downward motion of fire as being unnatural. The same is true of the corresponding cases of

is

continuous can be composed

[25] of indivisibles: e.g. a line cannot be composed of points, the line being continuous and the point indivisible. For the extremities of

two points can neither be one (since of an indivisible there can be no extremity as distinct from some other part) nor together (since that which has no parts can have no extremity, the

BOOK

232*

V,

CHAPTER 6— BOOK

extremity and the thing of which it is the extremity being distinct). Moreover, if that which is continuous is [_?o] composed of points, these points must be either continuous or in contact with

one anand the same reasoning applies in the

other:

231^ case

of

all indivisibles.

Now

for the rea-

son given above they cannot be continuous: and one thing can be in contact with another only if whole is in contact with whole or part with part or part with whole. But since indivisibles have no parts, they must be in contact with one another as whole with whole. And if they are in contact with one another as whole with whole, they will not be continuous: [5] for that which is continuous has distinct

and these parts

parts:

into

are different in this way,

which

i.e.

Nor, again, can a point be

it is

divisible

spatially separate.

in succession to a

point or a moment to a moment in such a way that length can be composed of points or time of

moments:

for things are in succession

if

nothing of their own kind intermediate between them, whereas that which is intermediate between points is always a line and that which is intermediate between moments is always a period of time. [10] Again, if length and time could thus be composed of indivisibles, they could be divided into indivisibles, since each is divisible into the parts of which it is composed. But, as we saw, no continuous thing is divisible into things without parts. Nor can there be anything of any other kind intermediate between the parts or between the moments: for if there could be any such thing it is clear that it must be either there

is

indivisible or divisible, it

must be

and

if

it

is

divisible,

divisible either into indivisibles or

into divisibles that are infinitely divisible, in

which

case

it is

[75] Moreover,

tinuous

is

continuous. it is

divisible

plain that everything coninto divisibles

that are

were divisible into indivisibles, we should have an indivisible in contact with an indivisible, since the extremities of things that are continuous with one another are one and are in contact. The same reasoning applies equally to magnitude, to time, and to motion: either all of these are composed of indivisibles and are divisible into indivisibles, or none. This may be [20] made clear as follows. If a magnitude is composed of indivisibles, the motion over that magnitude must be composed of corresponding indivisible motions: e.g. if the magnitude ABr is composed of the indivisibles A, B, I\ infinitely divisible: for if

it

VI,

CHAPTER

1

313

each corresponding part of the motion AEZ [25] of 12 over ABr is indivisible. Therefore, since where there is motion there must be something that is in motion, and where there is something in motion there must be motion, therefore the being-moved will also be com-

posed of indivisibles. So 12 traversed A when its motion was A, B when its motion was E,

and T similarly when its motion was Z. Now a thing that is in motion from one place to another cannot at the moment when it was in motion both be in motion and at the same time have completed its motion at the place to which it was in motion: e.g. if a man is walking to Thebes, he cannot be walking to Thebes [30] and at the same time have completed his walk to Thebes: and, as we saw, 12 traverses 232 a the partless section A in virtue of the presence of the motion A. Consequently, if 12 actually passed through A after being in process of passing through, the motion must be divisible: for at the time when 12 was passing through, it neither was at rest nor had completed its passage but was in an intermediate state: while if it is passing through and has completed its passage at the same moment, [5] then that which is walking will at the moment when it is walking have completed its walk and will be in the place to which it is walking; that is to say, it will have completed its motion at the place to which it is in motion. And if a thing is in motion over the whole ABT and its motion is the three A, E, and Z, and if it is not in motion at all over the partless section A but has completed its motion over it, then the motion will consist not of motions but of starts, and will take place by a thing's having completed a motion without being in motion: for on this assumption it has completed its passage through A without pass[10] ing through it. So it will be possible for a thing to have completed a walk without ever walking: for on this assumption it has completed a walk over a particular distance without walking over that distance. Since, then, everything must be either at rest or in motion, and 12 is therefore at rest in each of the sections A, B, and T, it follows that a thing can be continuously at rest and at the same time in motion: for, as we saw, 12 is in motion over the whole ABr and at rest in any part (and conse[75] quently in the whole) of it. Moreover, if the indivisibles composing AEZ are motions, it would be possible for a thing in spite of the presence in it of motion to be not in motion but at rest, while if they are not motions, it would

PHYSICS

3M

be possible for motion to be composed of something other than motions. And if length and motion are thus indivisible, it is neither more nor less necessary that

time also be similarly indivisible, that

is

to

composed of indivisible moments: for if [20] the whole distance is divisible and an

say be

equal

will

velocity

through

less of

it

cause

thing

a

in less time, the

to

also be divisible,

and conversely,

which

carried over the section

a thing

is

divisible, this section

And

since every

magnitudes

—

for

A

must

magnitude

if

pass

time must the time in

A

is

also be divisible.

is

divisible into

we have shown

that

it is

im-

possible for anything continuous to be composed of indivisible parts, and every magniit necessarily follows [25] tude is continuous that the quicker of two things traverses a greater magnitude in an equal time, an equal

—

and

magni-

magnitude

in less time,

tude in

time, in conformity with the defi-

less

a greater

nition sometimes given of 'the quicker'. Sup-

A

is quicker than B. Now since of pose that two things that which changes sooner is quicker, in the time ZH, in which A has [50] changed from T to A, B will not yet have arrived at A but will be short of it: so that in an equal time the quicker will pass over a greater magnitude. More than this, it will pass over a greater magnitude in less time: for in has arrived at A, B being the time in which

A

let us say, at E. Then in has occupied the whole time 23 b arriving at A, it will have arrived at in less time than this, say ZK. Now the magnitude TO that A has passed over is greater than the magnitude TE, and the time ZK is less than the whole time ZH: so that the quicker

the slower has arrived, since

ZH

A

will pass over a greater

[5]

And from

this

it

magnitude is

in less time.

also clear that the

quicker will pass over an equal magnitude in less time than the slower. For since it passes over the greater magnitude in less time than the slower, and (regarded by itself) passes over the greater in more time than AH the lesser, the time IIP in which it passes over will be more than the time IIS in which [10] it passes over AS: so that, the time IIP being less than the time IIX in which the slower passes over AS, the time H£ will also be less than the time IIX: for it is less than the time IIP, and that which is less than something else that is less than a thing is also itself less than that thing. Hence it follows that the

AM AM

233*

quicker will traverse an equal magnitude in less time than the slower. Again, since the mot/5] tion of anything must always occupy either an equal time or less or more time in comparison with that of another thing, and since, whereas a thing is slower if its motion occupies more time and of equal velocity if its motion occupies an equal time, the quicker is neither of equal velocity nor slower, it follows that the motion of the quicker can occupy neither an equal time nor more time. It can only be, then, that it occupies less time, and thus we get the necessary consequence that the quicker will pass over an equal magnitude [20] (as well as a greater) in less time than the slower.

And since every motion is in time and a momay occupy any time, and the motion of everything that is in motion may be either tion

quicker or slower, both quicker motion and slower motion may occupy any time: and this being so, it necessarily follows that time also is continuous. By continuous I mean that which is

divisible into divisibles that are infinitely

[25] divisible: and if we take this as the definition of continuous, it follows necessarily that

time

is

continuous. For since

it

has been

shown mag-

that the quicker will pass over an equal

less time than the slower, suppose quicker and B slower, and that the [50] slower has traversed the magnitude TA in the time ZH. Now it is clear that the quicker will traverse the same magnitude in less time than this: let us say in the time Z9. Again, since the quicker has passed over the whole TA in the time ZO, the slower will in the same time pass over TK, say, which is less 233 a than TA. And since B, the slower, has passed over TK in the time Z6, the quicker will pass over it in less time: so that the time ZO will again be divided. And if this is diwill also be divided vided the magnitude just as TA was: and again, if the magnitude is divided, the time will also be divided. And [5] we can carry on this process for ever, taking the slower after the quicker and the quicker after the slower alternately, and using what has been demonstrated at each stage as a new point of departure: for the quicker will divide the time and the slower will divide the length. If, then, this alternation always holds good, and at every turn involves a division, it [10] is evident that all time must be continuous. And at the same time it is clear that all magnitude is also continuous; for the divisions of which time and magnitude respec-

nitude in that

A

is

TK

BOOK

233 b

VI,

CHAPTERS

same and equal. Moreover, the current popular arguments make it plain that, if time is continuous, magnitude is continuous also, inasmuch as a thing passes over half a given magnitude in half the lively are susceptible are the

[75] time taken to cover the whole: in fact without qualification it passes over a less magnitude in less time; for the divisions of time and of magnitude will be the same. And if either is infinite, so is the other, and the one is so in the same way as the other; i.e. if time is infinite in respect of

its

extremities, length

also infinite in respect of

time

is

infinite

[20] length

and magnitude

bility:

respect

in

extremities:

its

of

is

if

divisibility,

also infinite in respect of divisi-

is

both respects,

if

time

is

also infinite in both respects.

is

infinite in

Hence Zeno's argument makes

a false as-

sumption in asserting that it is impossible for a thing to pass over or severally to come in contact with infinite things in a finite time. For there are two senses in which length and time and generally anything continuous are called

[25]

'infinite':

they are called so either in re-

spect of divisibility or in respect of their ex-

So while a thing in a finite time cannot come in contact with things quantitatively infinite, it can come in contact with things intremities.

finite in respect of divisibility: for in this sense

and

we

1-3

magnitude

3i5

Moreover, if it is the case that infinite time is not occupied in passing over every magnitude, but it is possible to pass over some magnitude, say BE, in a finite [10] time, and if this BE measures the whole of which it is a part, and if an equal magnitude is passed over in an equal time, then it follows that the time like the magnitude is finite. That infinite time will not be occupied in passing over BE is evident if the time be taken as limited in one direction: for as the part will be passed over in less time than the whole, the time occupied in traversing this part must be finite, the limit in one direction being given. The same reasoning will also show the falsity of the assumption that infinite length can be divisible.

is

[75] traversed in a finite time. It is evident, then, from what has been said that neither a line nor a surface nor in fact anything continuous can be indivisible. This conclusion follows not only from the present argument but from the consideration that the opposite assumption implies the di-

For since the disand slower may apply to [20] motions occupying any period of time and in an equal time the quicker passes over a greater length, it may happen that it will pass over a length twice, or one and a half times, as visibility of the indivisible.

tinction of quicker

find

great as that passed over by the slower: for

that the time occupied by the passage over the

their respective velocities may stand to one another in this proportion. Suppose, then, that the quicker has in the same time been carried over a length one and a half times as great as that traversed by the slower, and that the re-

the time

itself is also infinite:

so

not a finite but an infinite time, and the contact with the infinites is made by means of moments not finite but infinite in [jo] infinite

is

number.

The passage over the infinite, then, cannot occupy a finite time, and the passage over the finite cannot occupy an infinite time: if the time is infinite the magnitude must be infinite also,

and

if

the

magnitude

may

is

infinite, so also is

shown

spective magnitudes are divided, that of the quicker, the magnitude ABrA, into three indivisibles,

and

that of the slower into the

two

[25] indivisibles EZ, ZH. Then the time may also be divided into three indivisibles, for an

be the segment that it has thus passed over. (This will be either an exact measure of AB or less or greater than an exact measure: it makes no difference which it is.)

equal magnitude will be passed over in an equal time. Suppose then that it is thus divided into KA, AM, MN. Again, since in the same time the slower has been carried over EZ, ZH, the time may also be similarly divided into two. Thus the indivisible will be divisible, and that [jo] which has no parts will be passed over not in an indivisible but in a greater time. It is evident, therefore, that nothing continuous is without parts.

Then, since a magnitude equal to BE will always be passed over in an equal time, and BE [5] measures the whole magnitude, the whole

The

the time. This

be

as follows.

Let

AB

be a finite magnitude, and let us suppose that it is traversed in infinite time T, and let [_J5J a finite period TA of the time be taken. 233 b Now in this period the thing in motion will pass over a certain

tude:

let

segment of the magni-

BE

time occupied in passing over AB will be finite: for it will be divisible into periods equal in number to the segments into which the

present also

—

is necessarily indivisible the not in the sense in which the word is applied to one thing in virtue of another, but in its proper and primary sense; in

present, that

is,

PHYSICS

7l6

inherent in all time. For something that is an extremity of the past (no part of the future being on this side of it) and also of the future (no part of the past being on the other side of it): it is, as we have said, a limit of both. And if it is once shown that it is essentially of this character and one and the same, it will at once [55] which sense 234* the present

ersing

is

present, whereas

be evident also that it is indivisible. [5] Now the present that is the extremity of

both times must be one and the same: for if each extremity were different, the one could not be in succession to the other, because nothing continuous can be composed of things having no parts: and if the one is apart from the other, there will be time intermediate between them, because everything continuous is such that there is something intermediate between its limits and described by the same name as itself. But if the intermediate thing is time, it will be 2 [10] divisible: for all time has been shown to be divisible. Thus on this assumption the is

divisible.

But

if

the present

is

divisi-

be part of the past in the future and part of the future in the past: for past time will be marked off from future time at the actual point of division. Also the present will [75] be a present not in the proper sense but in ble, there will

virtue of something else: for the division yields

it

which

will not be a division proper. Further-

more, there will be a part of the present that

is

and a part that is future, and it will not always be the same part that is past or future: in fact one and the same present will not be past

simultaneous: for the time

may

be divided at many points. If, therefore, the present cannot possibly have these characteristics, it follows that it must be the same present that belongs [20] to each of the two times. But if this is so it is evident that the present is also indivisible: for if it is divisible it will be involved in the

same implications as before. It is clear, then, from what has been said that time contains something indivisible, and this is what we call a present.

We

will

now show

that nothing can be in

[25] motion in a present. For if this is possible, there can be both quicker and slower motion in the present.

N

Suppose then that

in the present

AB.

the quicker has traversed the distance

That being

so,

the slower will in the

present traverse a distance less than

AT. But the

same

AB,

say

since the slower will have occupied

whole

Thus we shall have we found it

it is

1

present

234b

present

in

traversing

Ar,

the

[50] quicker will occupy less than this in trav1 2 Chapter 222a 12. 2.

it.

impossible, therefore, for anything to be

It is

motion

in

a division of the to be indivisible.

in a present.

Nor can anything be at rest in a present: 3 as we were saying, that only can be at

for,

rest

which

is naturally designed to be in motion but not in motion when, where, or as it would naturally be so: since, therefore, nothing is is

naturally designed to be in motion in a present, that nothing can be at rest in a

clear

is

it

present either.

Moreover, inasmuch as

it is

the

same present

[35] that belongs to both the times, and it is possible for a thing to be in motion throughout

one time and to be at rest throughout the other, and that which is in motion or at rest for the whole of a time will be in motion or at rest as the case may be in any part of it

234 b

in

which

it

is

naturally designed to be in

mo-

tion or at rest: this being so, the assumption

motion or

that there can be will carry

with

rest in a present

the implication that the

it

same

thing can at the same time be at rest and in motion: for both the times have the same extremity, viz. the present. [5] Again,

we imply part

is

what

it

when we that

its

say that a thing is at rest, condition in whole and in

time of speaking uniform with was previously: but the present con-

at the

no 'previously': consequently, there can be no rest in it. It follows then that the motion of that which

tains

in

is

rest

motion and the rest must occupy time.

of that

which

is

at

[10] Further, everything that changes must be For since every change is from some-

divisible.

thing to something, and when a thing is at the goal of its change it is no longer changing, and when both it itself and all its parts are at the starting-point of (for that

which

its is

change it is not changing whole and in part in an

in

unvarying condition is not in a state of [75] change); it follows, therefore, that part of that which is changing must be at the startingpoint and part at the goal: for as a whole it cannot be in both or in neither. (Here by 'goal of change' I mean that which comes first in the process of change: e.g. in a process of change from white the goal in question will be grey, not black: for

it is

not necessary that that which

[20] is changing should be at either of the extremes.) It is evident, therefore, that 8

226 b 12 sqq.

BOOK

235 b

everything that changes must be

.

VI,

CHAPTERS

divisible.

Now motion is divisible in two senses. In the first

place

that

it

it is

time

divisible in virtue of the

occupies. In the second place

it is

divis-

according to the motions of the several which is in motion: e.g. if the whole Ar is in motion, there will be a motion of AB and a motion of Br. That being so, let ible

parts of that

AB

and EZ the be the motion of the part [25] motion of the part BI\ Then the whole AZ must be the motion of Ar: for AZ must

AE

constitute the

and of

parts.

its

AT

[75] follows that the time, the motion, the being-in-motion, the thing that is in motion,

and the sphere of the motion must all be sussame divisions (though spheres of motion are not all divisible in a like man-

ceptible of the

AE

ner: thus quantity

dentally divisible).

inasmuch

as

But the motion of a thing can never

be constituted by the motion of something else: consequently the whole motion is the mo-

whole magnitude. Again, since every motion is a motion of something, and the whole motion AZ is not the motion of either of the parts (for each of the parts AE, EZ is the motion of one of the [30] parts AB, Br ) or of anything else (for, the whole motion being the motion of a whole, the parts of the motion are the motions of the parts of that whole: and the parts of AZ are the motions of AB, Br and of nothing else: 1 for, as we saw, a motion that is one cannot be the motion of more things than one): since this is so, the whole motion will be the motion tion of the

magnitude ABI\

of the

3i7

motion is in time and all time is divisible, and in less time the motion is less, it follows that every motion must be divisible according to time. And since everything that is in motion is in motion in a certain sphere and for a certain time and has a motion belonging to it, it all

constitute the motions of each

motion of

EZ severally

3-4

essentially, quality acci-

is

For suppose that A is the time occupied by the motion B. Then if all the [20] time has been occupied by the whole motion, it will take less of the motion to occupy half the time, less again to occupy a further subdivision of the time, and so on to infinity. Again, the time will be divisible similarly to the motion: for if the whole motion occupies all the time half the motion will occupy half the time, and less of the motion again will occupy less of the time. [25] In the same way the being-in-motion will also be divisible.

For

Then

in-motion.

let

the

T

be the whole beingbeing-in-motion that

corresponds to half the motion will be less than the whole being-in-motion, that which corresponds to a quarter of the motion will be less

again,

and

so

on

to infinity.

Moreover by

Again, if there is a motion of the whole other than AZ, say 01, the motion of each of the parts may be subtracted from it: and these [55] motions will be equal to AE, EZ respec-

out successively the being-in-motion corresponding to each of the two motions Ar (say) and TE, we may argue that the whole

235 a tively: for the motion of that which is one must be one. So if the whole motion 01

whole motion (for

may

be divided into the motions of the parts, AZ: if on the other hand there is any remainder, say KI, this will be a

01

will be equal to

[5] motion of nothing: for it can be the motion neither of the whole nor of the parts (as

setting

[jo] being-in-motion will correspond to the if it were some other beingin-motion that corresponded to the whole motion, there would be more than one being-inmotion corresponding to the same motion), the argument being the same as that whereby

we showed 2

the motion of that which is one must be one) nor of anything else: for a motion that is con-

thing: for

tinuous must be the motion of things that are continuous. And the same result follows if the

tions,

01

division of

reveals a surplus

on the

the motions of the parts. Consequently, impossible, the whole motion

is

same

as

and equal

to

side of if

this

must be the

AZ.

This then is what is meant by the division of motion according to the motions of the

must be applicable

parts:

and

that

divisible into parts.

is

it

to everything

[10] Motion is also susceptible of another kind of division, that according to time. For since 1

223b

1

sqq.

if

motion of a thing is dimotions of the parts of the

that the

visible into the

we

take separately the being-in-

motion corresponding

we

motion

two mowhole being-in-

to each of the

shall see that the

continuous. reasoning will show the divisibility of the length, and in fact of everything that forms a sphere of change (though some is

The same

[55] of these are only accidentally divisible because that which changes is so): for the division of one term will involve the division of all.

So, too, in the matter of their being finite

or infinite, they will

all

alike be either the

one

235 b or the other. And we now see that in most cases the fact that all the terms are divisi2

b 234 24

sqq., especially

234b

34 sqq.

PHYSICS

3 i8

consequence of the that the thing that changes is divisible or

ble or infinite fact

infinite:

is

a direct

for the attributes 'divisible'

and

'in-

belong in the first instance to the thing [5] that changes. That divisibility does so we have already shown: that infinity does so will 2 be made clear in what follows. finite'

1

Since everything that changes changes from something to something, that which has changed must at the moment when it has first changed be in that to which it has changed. For

which changes retires from or leaves that from which it changes: and leaving, if not identical with changing, is at any rate a con-

that

[10] sequence of

And

it.

if

leaving

is

a conse-

quence of changing, having left is a consequence of having changed: for there is a like relation between the two in each case. One kind of change, then, being change in a relation of contradiction, where a thing has changed from not-being to being it has left [75] not-being. Therefore it will be in being: for everything must either be or not be. It is evident, then, that in contradictory change that which has changed must be in that to which it has changed. And if this is true in this kind of change,

it

will be true in all other kinds as

what holds good in the good likewise in the case

well: for in this matter

case of one will hold

of the rest.

Moreover,

if

we

take each kind of change

separately, the truth of our conclusion will be

equally evident, on the ground that that which

has changed must be somewhere or in some[20] thing. For, since it has left that from which

has changed and must be somewhere, it must be either in that to which it has changed or in something else. If, then, that which has changed to B is in something other than B, say T, it must again be changing from T to B: for it cannot be assumed that there is no interval be-

it

[25] ous.

tween T and B, since change is continuThus we have the result that the thing

moment when it has changed, is changing to that to which it has changed, which is impossible: that which has changed, therefore, must be in that to which it has changed. So it is evident likewise that that that has changed, at the

which has come

to be, at the

moment when

it

has come to be, will be, and that which has ceased to be will not-be: for what we have said applies universally to every kind of change, and its truth is most obvious in the case of *

Chapter

7.

236«

[30] contradictory change. It is clear, then, that that which has changed, at the moment

when

it has first changed, has changed.

is

in that to

which

it

We

will now show that the 'primary when' which that which has changed effected the completion of its change must be indivisible, where by 'primary' I mean possessing the characteristics in question of itself and not in virtue of the possession of them by something else belonging to it. For let AT be divisible, and [55] let it be divided at B. If then the completion of change has been effected in AB or again in BI\ AT cannot be the primary thing in which the completion of change has been effected. If, on the other hand, it has been changing in both AB and Br (for it must either have changed or be changing in each of 236a them), it must have been changing in the whole Ar: but our assumption was that

in

AT

only the completion of the equally impossible to suppose that one part of Ar contains the process and the other the completion of the change: for then contains

change.

It is

we

shall have something prior to what is primary. So that in which the completion of change has been effected must be indivisible.

[5]

It

is

also evident, therefore, that that in

which that which has ceased to be has ceased to be and that in which that which has come to be has come to be are indivisible. But there are two senses of the expression 'the primary when in which something has changed'. On the one hand it may mean the primary when containing the completion of the process of change the moment when it is correct to say 'it has changed': on the other hand it may mean the primary when containing the beginning of the process of change. Now the [10] primary when that has reference to the end of the change is something really existent: for a change may really be completed, and there is such a thing as an end of change, which we have in fact shown to be indivisible because it is a limit. But that which has reference to the beginning is not existent at all: for there is no such thing as a beginning of a process of change, and the time occupied by the change does not contain any primary when [75] in which the change began. For suppose that AA is such a primary when. Then it can-

—

not be indivisible: for, if it were, the moment immediately preceding the change and the moment in which the change begins would be consecutive (and moments cannot be consecutive). Again, if the changing thing is at

BOOK

237' rest in the

may

TA

whole preceding time

suppose that

AA

at rest),

it is

it is

VI,

(for

CHAPTERS

we

at rest in

A

without parts, it will simultaneously be at rest and have changed: for it is [20] at rest in A and has changed in A. Since then AA is not without parts, it must be divisible, and the changing thing must have also: so if

changed changed

AA

in

every part of

it

(for

if

it

has

two parts into which has not changed in the whole

in neither of the

divided,

is

either:

is

if,

it

on the other hand,

in process of

it is

change in both parts, it is likewise in process of change in the whole: and if, again, it has changed in one of the two parts, the whole is not the primary when in which it has changed: [25] it must therefore have changed in every part). It is evident, then, that with reference to the beginning of change there is no primary when in which change has been effected: for the divisions are infinite. So, too, of that which has changed there is no primary part that has changed. For suppose that of AE the primary part that has changed is AZ (everything that changes having been [jo] shown to be divisible): and let GI be the time in which AZ has changed. If, then, in the whole time AZ has changed, in half the time 1

there will be a part that has changed, less than

AZ: and again there and yet aninfinity. Thus of that which

and therefore prior

to

will be another part prior to this,

and

other,

so

on

to

changes there cannot be any primary part that [55] has changed. It is evident, then, from what has been said, that neither of that which changes nor of the time in which it changes is there any primary part. 236 b With regard, however, to the actual subthat is to say that in respect of ject of change which a thing changes there is a difference to be observed. For in a process of change we may distinguish three terms that which changes,

—

— —

which it changes, and the actual subchange, e.g. the man, the time, and the fair complexion. Of these the man and the time [5] are divisible: but with the fair complexion it is otherwise (though they are all divisible that in

ject of

which the

fair coman accident is For of actual subjects of change it

accidentally, for that in

plexion or any other quality divisible).

will be seen that those

is

which are

classed as es-

not accidentally, divisible have no [10] primary part. Take the case of magnitudes: let AB be a magnitude, and suppose that it has moved from B to a primary 'where' T. Then if Br is taken to be indivisible, two sentially,

1

234

b iosqq.

4-6

3*9

things without parts will have to be contiguous (which is impossible): if on the other hand it

taken to be divisible, there will be something to T to which the magnitude has changed, and something else again prior to that, and so on to infinity, because the process [75] of division may be continued without end. Thus there can be no primary 'where' to which a thing has changed. And if we take the case of quantitative change, we shall get a like result, for here too the change is in something continuous. It is evident, then, that only in qualitative motion can there be anything essenis

prior

tially indivisible.

[20] time,

Now everything that and that

in

two

changes changes in

senses: for the time in

which a thing is said to change may be the primary time, or on the other hand it may have an extended reference, as e.g. when we say that a thing changes in a particular year because it changes in a particular day. That being so, that which changes must be changing in any part of the primary time in which it changes. This is clear from our definition of 2

'primary', in

which the word

may

is

said to express

however, be made evident by the following argument. Let XP be the pri[25] mary time in which that which is in motion is in motion: and (as all time is divisible) let it be divided at K. Now in the time it either is in motion or is not in motion, and the same is likewise true of the time KP. Then if it is in motion in neither of the two parts, it will be at rest in the whole: for it is impossible that it should be in motion in a time in no [50] part of which it is in motion. If on the other hand it is in motion in only one of the two parts of the time, XP cannot be the primary time in which it is in motion: for its motion will have reference to a time other than XP. It must, then, have been in motion in any part of XP. And now that this has been proved, it is evident that everything that is in motion must have been in motion before. For if that which is in motion has traversed the distance KA in [55] the primary time XP, in half the time a thing that is in motion with equal velocity and began its motion at the same time will have traversed half the distance. But if this second thing whose velocity is equal has traversed a just this:

it

also,

XK

237 a

certain distance in a certain time, the

original

thing that

is

in

motion must have

PHYSICS

320

same distance in the same time. which is in motion must have been

traversed the

Hence

that

Again, if by taking the extreme moment of for it is the moment that defines [5] the time the time, and time is that which is intermediwe are enabled to say ate between moments that motion has taken place in the whole time XP or in fact in any period of it, motion may likewise be said to have taken place in every other such period. But half the time finds an extreme in the point of division. Therefore motion will have taken place in half the time and in fact in any part of it: for as soon as any division is made there is always a time defined by moments. If, then, all time is divisible, and [10] that which is intermediate between moments is time, everything that is changing must have completed an infinite number of changes. Again, since a thing that changes continuously and has not perished or ceased from its change must either be changing or have changed in any part of the time of its change,

—

—

and it

since

it

cannot be changing in a moment, it must have changed at every

follows that

[75] moment in the time: consequently, since the moments are infinite in number, every-

thing that infinite

is

changing must have completed an

number

of changes.

And not only must that which is changing have changed, but that which has changed must also previously have been changing, since everything that has changed from something [20] to something has changed in a period of time. For suppose that a thing has changed from A to B in a moment. Now the moment in which it has changed cannot be the same as that in which it is at A (since in that case it would be in A and B at once): for we have shown above that that which has changed, when it has changed, is not in that from which it has changed. If, on the other hand, it is a different moment, there will be a period of time intermediate between the two: for, as we 1

saw,

2

moments

are not consecutive. Since, then,

[25] it has changed in a period of time, and all time is divisible, in half the time it will have completed another change, in a quarter another, and so on to infinity: consequently when it has changed, it must have previously been changing. Moreover, the truth of what has been said is more evident in the case of magnitude, because [jo] the magnitude over which what is changing changes is continuous. For suppose that a 1

b 235 6sqq.

thing has changed from F to A. Then if TA is indivisible, two things without parts will be consecutive. But since this

motion before.

in

237 b

2

23i b 6sqq.

is

impossible, that

which is intermediate between them must be a magnitude and divisible into an infinite numsegments: consequently, before the completed, the thing changes to those segments. Everything that has changed, therefore, must previously have been changing: for [55] the same proof also holds good of change 237 b with respect to what is not continuous, changes, that is to say, between contraries and ber

of

change

is

between contradictories. In such cases we have only to take the time in which a thing has changed and again apply the same reasoning. So that which has changed must have been changing and that which is changing must have changed, and a process of change is preceded by a completion of change and a com[5] pletion by a process: and we can never take any stage and say that it is absolutely the first. The reason of this is that no two things without parts can be contiguous, and therefore in change the process of division is infinite, just as lines may be infinitely divided so that one part

is

continually increasing and the other

continually decreasing. [10] So it is evident also that that which has become must previously have been in process of becoming, and that which is in process of becoming must previously have become, everything (that is) that is divisible and continuous: though it is not always the actual thing that is in process of becoming of which this is true:

sometimes

it is

something

some part of the thing

else,

that

is

to say,

in question, e.g. the

foundation-stone of a house. So, too, in the case of that which is perishing and that which has

which becomes and that which perishes must contain an element of infiniteness as an immediate consequence of perished: for that

[75] the fact that they are continuous things: so a thing cannot be in process of becom-

and

ing without having become or have become without having been in process of becoming. So, too, in the case of perishing and having perished: perishing must be preceded by having perished, and having perished must be preceded by perishing. It is evident, then, that that which has become must previously have been

and that which is in becoming must previously have all magnitudes and all periods of

in process of becoming,

[20] process of

become: for time are infinitely divisible. Consequently no absolutely first stage of change can be represented by any particular

BOOK

238 b part of space or time

may

thing

VI,

CHAPTERS

which the .changing

occupy.

Now

since the motion of everything that is in motion occupies a period of time, and a greater magnitude is traversed in a longer time, it is impossible that a thing should undergo a finite [25] motion in an infinite time, if this is understood to mean not that the same motion or

a part of

it is

continually repeated, but that the

6-7

321

equal, are none the less limited in magnitude);

while on the other hand the finite stretch of motion AB is a certain multiple of AE: consequently the motion AB must be accomplished in a finite time. Moreover it is the same with coming to rest as with motion. And so it is impossible for one and the same thing to be infinitely in process of

becoming or of perishing.

The same reasoning

[20] finite

will prove that in a time there cannot be an infinite extent of

motion or of coming

to rest,

whether the mo-

time is occupied by the whole finite motion. In all cases where a thing is in motion with uniform velocity it is clear that

tion

the finite magnitude

in size individually

whole, of the magnitude will be traversed, because we assume that the traversing of the whole occupies all the time. Again, in another equal part of the time another part of the mag[25] nitude will be traversed: and similarly in each part of the time that we take, whether equal or unequal to the part originally taken.

the whole time

It

whole

infinite

we take

is

traversed in a finite

motion which shall be a measure of the whole, the whole motion is completed in as many equal periods of time. For

if

a part of the

[50] the time as there are parts of the motion. Consequently, since these parts are finite, both

and in number collectively, must also be finite: for it will

if we take a part which shall be a measure of the whole time, in this part a certain fraction, not the

regular or irregular. For

is

makes no

difference whether the parts are

be a multiple of the portion, equal to the time occupied in completing the aforesaid part mul-

equal or not, if only each is finite: for it is clear that while the time is exhausted by the

by the number of the parts. makes no difference even if the velocnot uniform. For let us suppose that the

will not be thus exhausted, since the process of

tiplied

But

it

subtraction of

its

parts, the infinite

magnitude

which a thing has been moved in the given and let TA be the infinite time. Now if 238 a one part of the stretch must have been

is finite both in respect of the quantity subtracted and of the number of times a subtraction is made. Consequently the infinite magnitude will not be traversed in a [50] finite time: and it makes no difference

traversed before another part (this

whether the magnitude

ity is

[55] line

AB

represents a finite stretch over

time,

in the earlier

and

is

clear, that

in the later part of the time a

different part of the stretch has been traversed: for as the time lengthens a different part of

the motion will always be completed in

it,

subtraction

is

infinite in only

direction or in both: for the

one

same reasoning

will hold good.

This having been proved,

it is

evident that

neither can a finite magnitude traverse an in-

[5] whether the thing in motion changes with uniform velocity or not: and whether the rate of motion increases or diminishes or remains stationary this is none the less so), let us then take AE a part of the whole stretch of motion AB which shall be a measure of AB. Now this part of the motion occupies a certain period of the infinite time: it cannot itself occupy an infinite time, for we are assuming that that is occupied by the whole AB. And if again I take

finite

[10] another part equal to AE, that also must occupy a finite time in consequence of the

the finite, the finite could traverse the infinite;

same assumption. And if I go on taking parts in this way, on the one hand there is no part which will be a measure of the infinite time (for the infinite cannot be composed of finite parts whether equal or unequal, because there must be some unity which will be a measure [75] of things finite in multitude or in magnitude, which, whether they are equal or un-

the thing in motion; either case involves the

magnitude in a finite time, the reason being the same as that given above: in part of [55] the time it will traverse a finite magnitude and in each several part likewise, so that in the

whole time

it

will traverse a finite

mag-

nitude.

And 238 b

since a finite

erse

an

magnitude

will not trav-

infinite in a finite time,

it is

clear

that neither will an infinite traverse a finite in

a finite time. for

it

For

makes no

if

the infinite could traverse

difference

which of the two

is

traversing of the infinite by the finite. For [5] when the infinite tion a part of it, say

magnitude

TA,

A

is

in

mo-

occupy the finite B, and then another, and then another, and so on to infinity. Thus the two results will coincide: the infinite will have completed a motion over the finite and the finite will have will

PHYSICS

3 22

traversed the infinite: for

it

would seem

to be

[w]

impossible for the motion of the infinite over the finite to occur in any way other than by the finite traversing the infinite either by

locomotion over fore, since this

it

is

or by measuring

it.

There-

impossible, the infinite can-

not traverse the finite. Nor again will the infinite traverse the infinite in a finite time. Otherwise it would also [75] traverse the finite, for the infinite includes the the

finite.

We

can further prove this in as our start-

same way by taking the time

ing-point. Since, then,

it

is

established that in a finite

time neither will the finite traverse the infinite, nor the infinite the finite, nor the infinite the [20] infinite, it is evident also that in a finite time there cannot be infinite motion: for what difference does it make whether we take the motion or the magnitude to be infinite? If either of the two is infinite, the other must be so likewise: for all locomotion is in space.

Since everything to which motion or rest is is in motion or at rest in the natural

natural

and manner, that which is coming it is coming to a stand, must [25] be in motion: for if it is not in motion it must be at rest: but that which is at rest cannot be coming to rest. From this it evidently follows that coming to a stand must occupy a period of time: for the motion of that which is in motion occupies a period of time, and that which is coming to a stand has been shown to be in motion: consequently coming to a stand must occupy a period of time. Again, since the terms 'quicker' and 'slower' [50] are used only of that which occupies a period of time, and the process of coming to a stand may be quicker or slower, the same contime, place, to a stand,

when

clusion follows.

And that which is coming to a stand must be coming

to a stand in any part of the primary time in which it is coming to a stand. For if it is coming to a stand in neither of two parts into which the time may be divided, it cannot be coming to a stand in the whole time, with the result that that which is coming to a stand will not be coming to a stand. If on the other hand it is coming to a stand in only one of the two parts of the time, the whole cannot be the pri[35] mary time in which it is coming to a stand: for it is coming to a stand in the whole time not primarily but in virtue of something distinct from itself, the argument being the

same

239a that

as

which we used above about

things in motion. 1

And just as there is no primary time in which that which is in motion is in motion, so 239 a too there is no primary time in which that which is coming to a stand is coming to a stand, there being no primary stage either of being in motion or of coming to a stand. For let AB be the primary time in which a thing is coming to a stand. Now AB cannot be without parts: for there cannot be motion in that which is without parts, because the moving thing would necessarily have been already moved for part of the time of its movement: [5] and that which is coming to a stand has been shown to be in motion. But since AB is therefore divisible, the thing is coming to a stand in every one of the parts of AB: for we have shown above 2 that it is coming to a stand in every one of the parts in which it is primarily coming to a stand. Since then, that in which primarily a thing is coming to a stand must be a period of time and not something indivisible, and since all time is infinitely divisible, there cannot be anything in which primarily it is coming to a stand. [10] Nor again can there be a primary time at which the being at rest of that which is at rest occurred: for it cannot have occurred in that which has no parts, because there cannot be motion in that which is indivisible, and that in which rest takes place is the same as that in which motion takes place: for we defined 3 a state of rest to be the state of a thing to which motion is natural but which is not in motion when (that is to say in that in which) motion would be natural to it. Again, our use of the [75] phrase 'being at rest' also implies that the previous state of a thing is still unaltered, not one point only but two at least being thus

needed

to

that in

which

determine its presence: consequently a thing is at rest cannot be without parts. Since, then it is divisible, it must be a period of time, and the thing must be at rest in every one of its parts, as may be shown by the same method as that used above in similar demonstrations. [20] So there can be no primary part of the time: and the reason is that rest and motion are always in a period of time, and a period of time has no primary part any more than a magnitude or in fact anything continuous: for everything continuous is divisible into an infinite

number

And 1

of parts.

since everything that 2 238b Chapter 6. 31 sqq.

is

in

motion 8

is

in

226 b 12 sqq.

BOOK

240*

VI,

CHAPTERS

motion in a period of time and changes from something to something, when its motion is comprised within a particular period of time that is to say when it fills the whole essentially [25] and not merely a part of the time in ques-

—

—

impossible that in that time that which is in motion should be over against some particular thing primarily. For if a thing tion

it

is

and each of

itself

parts

its

—occupies the same

space for a definite period of time, it is at rest: it is in just these circumstances that we use

7-9

The second amounts

[75] est

3 23 the so-called 'Achilles',

is

and

it

to this, that in a race the quick-

runner can never overtake the slowest, since

the pursuer

must

first

reach the point whence

the pursued started, so that the slower

must

always hold a lead. This argument is the same in principle as that which depends on bisec-

though

tion,

differs

it

from

it

in that the spaces

we successively have to deal are not divided into halves. The result of the ar-

with which [20]

gument

primarily changing, over

is that the slower is not overtaken: but proceeds along the same lines as the bisection-argument (for in both a division of the space in a certain way leads to the result that the goal is not reached, though the 'Achilles' goes further in that it affirms that even the quickest runner in legendary tradition must

against any particular thing (for the whole period of time is divisible), so that in one part

[25] fail in his pursuit of the slowest), so that the solution must be the same. And the axiom

for

the term 'being at after another

it

rest'

—when

at

one

moment

can be said with truth that a

and its parts, occupies the same [jo] space. So if this is being at rest it is impossible for that which is changing to be as a whole, thing, itself

at the

of

time

when

it is

after another

it

thing, itself

and

space. If this

is

sition

is

will be true to say that the

it

parts, occupies the

its

same

not so and the aforesaid propomoment, then

true only at a single

the thing will be over against a particular thing not for any period of time but only at a

moment

that limits the time. It

moment

is

true that at

always over against 239 b something stationary: but it is not at rest: for at a moment it is not possible for anything to be either in motion or at rest. So while [35] any

it

is

which is in motion is motion and is opposite

it

is

at a

moment

not in

some

particular thing, it cannot in a period of time be over against that which is at rest: for that would involve the conclusion that that which is in locomotion is at rest.

[5] Zeno's reasoning, however, is fallacious, when he says that if everything when it occupies an equal space

is

at rest,

and

if

that

which

false:

it is

is at rest, which from the assumption that time is composed of moments: if this assumption is

the effect that the flying arrow result follows

not granted, the conclusion will not follow.

The

true to say that that

it is

which holds

a lead is never overtaken not overtaken, it is true, while it holds a lead: but it is overtaken nevertheless if it is granted that it traverses the finite distance prescribed. These then are two of his arguments. [jo] The third is that already given above, to

that that

fourth argument

two rows

number of bodies of equal size, passing each other on a race-course as they proceed with equal velocity in opposite directions, the one row originally occupying the space (between the goal and the middle point of the course and the other that between the middle [35] point and the starting-post. This, he thinks, involves the conclusion that half a giv-

en time

is

equal to double that time. The fallacy

240 a

visibles.

A,

[10] Zeno's arguments about motion, which cause so much disquietude to those who try to

[5] B, B . size to A,

problems that they present, are four in number. The first asserts the non-existence of motion on the ground that that which is in locomotion must arrive at the half-way stage before it arrives at the goal. This we have dis-

of the course

cussed above. 1

follow:

in

solve the

that concerning the

row being composed

of an equal

locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless. This is false, for time is not composed of indivisible moments any more than any other magnitude is composed of indiis

is

of bodies, each

of the reasoning lies in the assumption

body occupies an equal time in passing with equal velocity a body that is in motion that a

false.

body of equal size that is at rest; which is For instance (so runs the argument), let

A

... be the stationary bodies of equal size,

and

a

.

.

the bodies, equal in

A

.

.,

.

number and

in

originally occupying the half

from the starting-post to the midand I\ T those originally occupying the other half from the goal to the middle of the A's, equal in number, size, and vedle of the A's,

locity to B,

B

.

.

.

First, as the B's

.

.

.

Then

.

three consequences

and the T's pass one another,

PHYSICS

324

B

T

same mo-

it is

B. Secondly,

else

[10] at this moment the first T has passed all the A's, whereas the first B has passed only half

that

the

first

ment

reaches the last

as the first

T

at the

reaches the

last

the A's, and has consequently occupied only half the time occupied by the first T, since each

241-

same with the sphere and everything whose motion is confined within the space the

it

occupies.

10

Our

Nor in reference to contradictory change shall we find anything unanswerable in the ar[20] gument that if a thing is changing from

that that which is without motion except accidentally: i.e. it can be in motion only in so far as the body or the magnitude is in motion and the [10] partless is in motion by inclusion therein, just as that which is in a boat may be in motion in consequence of the locomotion of the boat, or a part may be in motion in virtue of the motion of the whole. (It must be remembered, however, that by 'that which is without parts' I mean that which is quantitatively indivisible (and that the case of the motion of a part is not exactly parallel) for parts have motions belonging essentially and severally to [75] themselves distinct from the motion of the whole. The distinction may be seen most

not-white, say, to white, and

in neither con-

clearly in the case of a revolving sphere, in

will be neither white nor not-

which the velocities of the parts near the centre and of those on the surface are different from one another and from that of the whole; this implies that there is not one motion but many). As we have said, then, that which is without parts can be in motion in the sense in which a man sitting in a boat is in motion when the boat is travelling, but it cannot be in motion of [20] itself. For suppose that it is changing from AB to Br either from one magnitude to another, or from one form to another, or from some state to its contradictory and let A be the primary time in which it undergoes the change. Then in the time in which it is changing it must be either in AB or in Br or partly [25] in one and partly in the other: for this, as

two occupies an equal time in passing each A. Thirdly, at the same moment all the B's have passed all the T's: for the first T and of the

the

first

B

will simultaneously reach the oppo-

[75] site ends of the course, since (so says Zeno) the time occupied by the first T in passing each of the B's is equal to that occupied by it in pass-

ing each of the A's, because an equal time is occupied by both the first B and the first V in passing all the A's. This is the argument, but it presupposed the aforesaid fallacious assumption.

is

:

dition, then

it

is

white: for the fact that it is not wholly in either condition will not preclude us from calling it

We

call a thing white or white or not-white. not-white not necessarily because it is wholly either one or the other, but because most of its

parts or the

most

essential parts of

it

are so: not

[25] being in a certain condition is different from not being wholly in that condition. So, too, in the case of

being and not-being and

all

other conditions which stand in a contradictory relation: while the changing thing must of necessity be in

one of the two opposites,

it

is

never wholly in either. Again, in the case of circles and spheres and everything whose motion is confined within the space that it occupies, it is not true to say [jo] that the motion can be nothing but rest, on the ground that such things in motion, themselves and their parts, will occupy the same position for a period of time, and that therefore they will be at once at rest and in motion. For in the first place the parts do not occupy the same position for any period of time: and in the second place the whole also is al-

ways changing

240b

next point

parts cannot be in

to a different position: for

if

we

take the orbit as described from a point

A

on a circumference, it will not be the same as from B or T or any other point on the same circumference except in an

the orbit as described

accidental sense, the sense that

which

a musical

man

is

the

is

same

to say in as a

man.

[5] Thus one orbit is always changing into another, and the thing will never be at rest. And

—

—

we

saw, 1

is

true of everything that

is

changing.

Now it cannot be partly in each of the two:

for

then it would be divisible into parts. Nor again can it be in Br: for then it will have completed the change, whereas the assumption is that the change is in process. It remains, then, that in the time in which it is changing, it is in AB. That being so, it will be at rest: for, as we saw, 2 to be in the same condition for a period of time [30] is to be at rest. So it is not possible for that which has no parts to be in motion or to change in any way: for only one condition could have made it possible for it to have motion, viz. that time should be composed of moments, in which case at any moment it would have completed a 241 a motion or a change, so that it would never be in motion, but would always have been in *

234'

sqq.

2239*27.

BOOK

241 b

VI,

CHAPTERS 1

motion. But this we have already shown above to be impossible: time is not composed of moments, just as a line is not composed of points, and motion is not composed of starts: for this [5] theory simply makes motion consist of indivisibles in exactly the same way as time is made to consist of moments or a length of be shown in the following way no motion of a point or of any other indivisible. That which is in motion can never traverse a space greater than itself without first traversing a space equal to or less than itself. That being so, it is evident that the point [10] also must first traverse a space equal to or it

may

that there can be

less than itself. But since it is indivisible, there can be no space less than itself for it to traverse first: so it will have to traverse a distance equal

to

itself.

Thus

the line will be

points, for the point, as

it

composed of

continually traverses

a distance equal to itself, will be a measure of the whole line. But since this is impossible, it is likewise impossible for the indivisible to be in

motion. [75] Again, since motion is always in a period of time and never in a moment, and all time is divisible, for everything that is in motion there must be a time less than that in which it trav-

For that in which it is in motion will be a time, because all motion is in a period of time; and all time has erses a distance as great as itself.

been shown above 2 to be divisible. Therefore, if a point is in motion, there must be a time less than that in which it has itself traversed [20] any distance. But this is impossible, for in less time it must traverse less distance, and thus the indivisible will be divisible into something less than itself, just as the time is so divisible: the fact being that the only condition under which that which is without parts and indivisible could be in motion would have been the possibility of the infinitely small being in mo[25] tion in a moment: for in the two questhat of motion in a moment and that of

tions

—

motion of something principle

is

indivisible

—the

same

involved.

Our

next point is that no process of change every change, whether between contradictories or between contraries, is a change from something to something. Thus in contradictory changes the positive or the negais

infinite: for

1

is

325

the case

the limit of

may

be,

coming

is

the limit, e.g. being

to be

the limit of ceasing to be:

and not-being is and in contrary

changes the particular contraries are the limits, [50] since these are the extreme points of any such process of change, and consequently of every process of alteration: for alteration is alcontraries. Similar-

ways dependent upon some

points.

Again,

tive, as

9-10

23i b 18 sqq.

2

232 b 23 sqq.

ly contraries are the

extreme points of processes

and decrease: the limit of increase be found in the complete magnitude prop-

of increase is

to b er to the peculiar nature of the thing that

24 is

increasing, while the limit of decrease

complete

is

the

such magnitude. Locomotion, it is true, we cannot show to be finite in this way, since it is not always between contraries. But since that which cannot be cut (in the sense that it is inconceivable that it should be cut, the term 'cannot' being used in several loss of

—

since it is inconceivable that that [5] senses) in this sense cannot be cut should be in

which

and generally that that which cannot come to be should be in process of coming to be, it follows that it is inconceivable that that which cannot complete a change should be in process of changing to that to which it cannot complete a change. If, then, it is to be assumed that that which process of being cut,

is

in locomotion

is

in process of changing,

must be capable of completing the change. Consequently its motion is not infinite, and [10] it will not be in locomotion over an it

infinite distance, for

it

cannot traverse such a

distance. It is

evident, then, that a process of

change

cannot be infinite in the sense that it is not defined by limits. But it remains to be considered whether it is possible in the sense that one and the same process of change may be infinite in respect of the time which it occupies. If it is not one process, it would seem that there is nothing [/5J to prevent its being infinite in this sense; e.g. if a process of locomotion be succeeded by a process of alteration and that by a process of increase and that again by a process of coming to be: in this way there may be motion for ever so far as the time is concerned, but it will not be one motion, because all these motions do not compose one. If it is to be one process, no motion can be infinite in respect of the time that it occupies, with the single exception of rota[20] tory locomotion.

PHYSICS

326

BOOK

242 b

VII For

let us suppose that this the series to be infinite. Let

Everything

that

is

in

motion must be moved

[25] by something. For if of its motion in itself it

moved

has not the source evident that it is by something other than itself, for there it

is

must be something else that moves it. If on the other hand it has the source of its motion in itself, let AB be taken to represent that which is in motion essentially of itself and not in virtue of the fact that something belonging to it is in motion. Now in the first place to assume that [30] AB, because it is in motion as a whole and

moved by anything external to itself, is moved by itself this is just as if, supposing that KA is moving AM and is also itself in motion, we were to deny that KM is moved is

not

—

therefore

by anything on the ground that

it is

moving

not evident

and which moved. In the second place that which is in motion without being moved by anything does not necessarily cease from its 242* motion because something else is at rest, but a thing must be moved by something if the fact of something else having ceased from its motion causes it to be at rest. Thus, if this is accepted, everything that is in motion must be [5] moved by something. For AB, which has been taken to represent that which is in motion, must be divisible, since everything that is in motion is divisible. Let it be divided, then,

which

is

the part that

the part that

at T.

is

it

is

Now if TB is not in motion, then AB will it is clear that Ar if it

not be in motion: for

would be

in

is,

motion while

Br

is

at rest,

and

AB

cannot be in motion essentially [10] thus is in moand primarily. But ex hypothesi

AB

and primarily. Therefore if TB is not in motion AB will be at rest. But we have agreed that that which is at rest if something else is not in motion must be moved by

tion essentially

something. Consequently, everything that is in motion must be moved by something: for that [75] which is in motion will always be divisible, and if a part of it is not in motion the whole must be at rest. Since everything that is in motion must be moved by something, let us take the case in which a thing is in locomotion and is moved by something that is itself in motion, and that again is moved by something else that is in motion, and that by something else, and so on con[20] tinually: then the series cannot go on to infinity, but there must be some first movent.

not so and take then be moved by B, B by I\ T by A, and so on, each member of the series being moved by that which comes next to it. Then since ex hypothesi the movent is

A

while causing motion is also itself in motion, and the motion of the moved and the motion of the movent must proceed simultaneously (for the movent is causing motion and the [25] moved is being moved simultaneously) it evident that the respective motions of A, B,

is

T, and each of the other moved movents are simultaneous. Let us take the motion of each

and let E be the motion of A, Z of and G respectively the motions of T for though they are all moved severally one by another, yet we may still take the motion of each as numerically one, since every mo[50] tion is from something to something and separately

and and A

H

B,

:

not infinite in respect of its extreme points. a motion that is numerically one I mean a motion that proceeds from something numeriis

By

one and the same to something numerione and the same in a period of time numerically one and the same: for a motion may

cally cally

[35] be the same generically, specifically, or numerically it is generically the same if it belongs :

same category, e.g. substance or quality: it is specifically the same if it proceeds from something specifically the same to something specifically the same, e.g. from white to black or from good to bad, which is not of a kind specifically 242b distinct: it is numerically the same if it proceeds from something numerically one to something numerically one in the same period of time, e.g. from a particular white to a particular black, or from a particular place to a parto the

ticular place, in a particular period of time: for

and the same, would no longer be numerically one though it would still be specifically one.

if

the period of time were not one

the motion

We have dealt with this question above. Now let us further take the time in which A has 1

[4,8]

completed its motion, and let it be represented by K. Then since the motion of A is finite the time will also be finite. But since the movents and the things moved are infinite, the motion EZH0, i.e. the motion that is composed of all [75] the individual motions, must be infinite. For the motions of A, B, and the others may be equal, or the motions of the others may be greater: but assuming what is conceivable, we *v. 4 (227b 3 sqq.).

BOOK

243 b

find that whether they are equal or

VII,

some

CHAPTERS

are

another.

1-2

And

327

since there are three kinds of

mo-

whole motion is infimotion of A and that of each of the others are simultaneous, the whole motion must occupy the same time as the motion of A: but the time occupied by the motion of A is finite: consequently the motion will be infinite in a finite time, which is impossible. It might be thought that what we set out to [20] prove has thus been shown, but our argu-

and quantitative, there must also be three kinds of movent, that which causes locomotion, that which causes alteration, and that which causes increase or de-

ment so far does not prove it, because it does not yet prove that anything impossible results from the contrary supposition: for in a finite time there may be an infinite motion, though

themselves

greater, in both cases the

And

nite.

since the

not of one thing, but of many: and in the case we are considering this is so: for each thing accomplishes its own motion, and there that

is

no impossibility the

versally

moved

many

things being in

But

(as

in

tion simultaneously.

if

we

mo-

see to be uni-

which primarily is and corporeally must be either

case)

locally

that

[25] in contact with or continuous with that which moves it, the things moved and the movents

must be continuous or

in contact

another, so that together they

all

with one

form

a single

whether this unity is finite or infinite makes no difference to our present argument; for in any case since the things in motion are infinite in number the whole motion will be inunity:

finite,

tion

if,

is

as

theoretically possible, each

is

mo-

either equal to or greater than that

which follows

in the series: for

it

which

as actual that

is

we

shall take

theoretically possible.

[30] If, then, A, B, I\ A form an infinite magnitude that passes through the motion EZH in the finite time K, this involves the conclusion that an infinite motion is passed through

and whether the magnitude

in a finite time: in question

is

finite or infinite this is in either

must come movent and

case impossible. Therefore the series to

a

an end, and there must be a

moved:

first

243 a

for the fact that this impossibil-

ity results

particular case

sumed

is

first

only from the assumption of a immaterial, since the case as-

is

theoretically possible,

and the assumpought not to

tion of a theoretically possible case

give rise to any impossible result.

tion, local, qualitative,

[10]

crease.

Let us begin with locomotion, for this is the primary motion. Everything that is in locomotion is moved either by itself or by something else. In the case of things that are moved by

movent

it is

evident that the

moved and

the

are together: for they contain within

themselves their first movent, so that there is [75] nothing in between. The motion of things that are moved by something else must proceed in one of four ways: for there are four kinds of locomotion caused by something other than that which is in motion, viz. pulling, pushing, carrying, and twirling. All forms of locomotion are reducible to these. Thus pushing on is a form of pushing in which that which is causing motion away from itself follows up that which it pushes and continues to push it: pushing off occurs when the movent does not follow up the thing that it has moved: throw[20] ing when the movent causes a motion 243 b away from itself more violent than the natural locomotion of the thing moved, which

continues its course so long as it is controlled by the motion imparted to it. Again, pushing apart and pushing together are forms respectively of pushing off and pulling: pushing apart is pushing off, which may be a motion either away from the pusher or away from something [5] else, while pushing together is pulling, which may be a motion towards something else as well as towards the puller. We may similarly classify all the varieties of these last

two,

e.g.

packing and combing: the former is a form of pushing together, the latter a form of pushing apart.

The same

is

true of the other processes

and separation (they will all be be forms of pushing apart or of push-

of combination

found

to

ing together), except such as are involved in the processes of

becoming and perishing. (At

[10] the same time it is evident that there is no other kind of motion but combination and sepa-

may all be apportioned to one or other of those already mentioned.) Again, inhaling is a form of pulling, exhaling a form of ration: for they

That which

is

the

in the sense that

first it

movement

of a thing

supplies not 'that for the

sake of which' but the source of the motion is always together with that which is moved by it (by 'together' I mean that there is nothing [5] intermediate between them). This is universally true

wherever one thing

is

moved by

pushing: and the same is true of spitting and of all other motions that proceed through the body, whether secretive or assimilative, the assimilative being forms of pulling, the secretive [75] of pushing off. All other kinds of locomotion must be similarly reduced, for they all fall

PHYSICS And one

328

under one or other of our four heads. and twirling are reducible to pulling and pushing. For carrying always follows one of the other three methods, for that which is carried is in motion accidentally, because it is in or upon something that is [20] in motion, and that which carries it is in doing so being either pulled or pushed or again, of these four, carrying

244 a

twirled; thus carrying belongs to

other three kinds of motion in twirling for that

is

a

compound

which

is

all

the

common. And

of pulling

and pushing,

twirling a thing must be pull-

ing one part of the thing and pushing another part, since it impels one part away from itself and another part towards itself. If, therefore, it can be shown that that which is pushing and that which is pulling are adjacent respectively to that which is being pushed and that which [5] is being pulled, it will be evident that in all locomotion there is nothing intermediate be-

tween moved and movent. But the former fact is clear even from the definitions of pushing and pulling, for pushing is motion to something else from oneself or from something else, and pulling is motion from something else to oneself or to something else, when the motion of that which is pulling is quicker than the mo[10] tion that would separate from one another the two things that are continuous: for it is this that causes one thing to be pulled on along with the other. (It might indeed be thought that there is a form of pulling that arises in another way: that wood, e.g. pulls fire in a manner different from that described above. But it makes no difference whether that which pulls is in motion or is stationary when it is pulling: in the latter case it pulls to the place where it is, while in the former it pulls to the place where it was.) Now it is impossible to move anything [75] either from oneself to something else or from something else to oneself without being

244 b

in contact with

it: it is

evident, therefore,

locomotion there is nothing intermediate between moved and movent. Nor again is there anything intermediate between that which undergoes and that which causes alteration: this can be proved by inducthat in

all

245

s

another are sensible characteristics: for every body differs from another in possessing a

greater or lesser istics

number

of sensible character-

or in possessing the

same

teristics in a greater or lesser

alteration of that

which undergoes

also caused by the

[5]

istics,

sensible charac-

degree. But the alteration

is

above-mentioned character-

which are

affections of

some

particu-

underlying quality. Thus we say that a thing is altered by becoming hot or sweet or thick or dry or white: and we make these asserlar

tions alike of what is inanimate and of what is animate, and further, where animate things are in question, we make them both of the parts

no power of sense-perception and of [10] the senses themselves. For in a way even the senses undergo alteration, since the active sense is a motion through the body in the that have

course of which the sense tain

way.

We see,

is

affected in a cer-

then, that the animate

is

ca-

pable of every kind of alteration of which the inanimate is capable: but the inanimate is not capable of every kind of alteration of which the animate

is

capable, since

it is

not capable of

alteration in respect of the senses:

moreover

[75] the inanimate is unconscious of being af245 a fected by alteration, whereas the animate is conscious of it, though there is nothing to prevent the animate also being unconscious of it when the process of the alteration does not concern the senses. Since, then, the alteration of that which undergoes alteration is caused by sensible things, in every case of such alteration

it is

that

evident that the respective extremities of which causes and that which undergoes

[5] alteration are adjacent. Thus the air is continuous with that which causes the alteration, and the body that undergoes alteration is continuous with the air. Again, the colour is con-

tinuous with the light and the light with the sight. And the same is true of hearing and smelling: for the primary movent in respect to the

moved

is

the

air.

tasting, the flavour

is

Similarly, in the case of

adjacent to the sense of same in the case of

[70] taste. And it is just the things that are inanimate sense-perception.

Thus

and incapable of

there can be nothing

tive extremities of that

which causes and that which undergoes alteration are adjacent. For

intermediate between that which undergoes and that which causes alteration. Nor, again, can there be anything interme-

our assumption is that things that are undergoing alteration are altered in virtue of their being affected in respect of their so-called affec-

diate between that which suffers and that which causes increase: for the part of the latter that starts the increase does so by becoming at-

tion: for in every case

we

tive qualities, since that

quality

is

find that the respec-

which

altered in so far as

the characteristics in

of a certain

is

it is

and from

sensible,

which bodies

differ

tached in such a way to the former that the whole becomes one. Again, the decrease of that which suffers decrease is caused by a part of

BOOK

246 b

VII,

CHAPTERS

the thing becoming detached. So that which [75] causes increase and that which causes de-

must be continuous with that which suffers increase and that which suffers decrease respectively: and if two things are continuous crease

with one another there can be nothing intermediate between them. It is evident, therefore, that between the ex245 b tremities of the moved and the movent that are respectively to the

moved

there

first is

and

last in

reference

nothing intermediate.

2-3

329

into existence that are altered,

ing

is

and

their

becom-

not an alteration.

[jo] Again, acquired states, whether of the

body or of the soul, are not alterations. For some are excellences and others are defects, and neither excellence nor defect is an altera-

when anyproper excellence we call it ferfect, since it is then if ever that we have a 75] thing in its natural state: e.g. we have a perfect circle when we have one as good as possible), while defect is a perishing of or departion: excellence

thing acquires

is

a perfection (for

its

from this condition. So just as when speaking of a house we do not call its arrival at perfection an alteration (for it would be absurd to suppose that the coping or the tiling is an alter[20] ation or that in receiving its coping or its tiling a house is altered and not perfected), the same also holds good in the case of excellences and defects and of the persons or things that 246 b possess or acquire them: for excellences are perfections of a thing's nature and defects are departures from it: consequently they are not alterations. ture

Everything, tion

is

we

that

say,

undergoes

altered by sensible causes,

altera-

and there

is

alteration only in things that are said to be essentially affected

by sensible things. The truth

[5] of this is to be seen from the following considerations. Of all other things it would be

most natural to suppose that there is alteration in figures and shapes, and in acquired states and in the processes of acquiring and losing these: but as a matter of fact in neither of these

two

classes of things

In the

first place,

is

there alteration.

when

a particular forma-

Further,

we

say that

all

excellences

depend

[10] tion of a thing is completed, we do not call it by the name of its material: e.g. we do

upon

not call the statue 'bronze' or the pyramid 'wax' or the bed 'wood', but we use a derived expression and call them 'of bronze', 'waxen', and 'wooden' respectively. But when a thing has

regard as consisting in a blending of hot and cold elements within the body in due proportion, in relation either to one another or to the surrounding atmosphere: and in like manner we regard beauty, strength, and all the other bodily excellences and defects. Each of them exists in virtue of a particular relation and puts

been affected and altered in any way we still call it by the original name: thus we speak of the bronze or the wax being dry or fluid or hard or hot. [75] And not only so: we also speak of the particular fluid or hot substance as being bronze, giving the material the same name as that which we use to describe the affection. 246 a Since, therefore, having regard to the figure or shape of a thing we no longer call that which has become of a certain figure by the name of the material that exhibits the figure, whereas having regard to a thing's affections

we

still call it by the name of its evident that becomings of the former kind cannot be alterations.

or alterations material,

it

is

Moreover it would seem absurd even to speak in this way, to speak, that is to say, of a [5] man or house or anything else that has come into existence as having been altered. Though it may be true that every such becoming is necessarily the result of something's being altered, the result, e.g. of the material's being condensed or rarefied or heated or cooled, nevertheless it is not the things that are coming

Thus

particular relations.

and

lences such as health

a

bodily excel-

good

state of

body

we

[5]

that

which

possesses

tion with regard to

in a

it

good or bad condi-

proper affections, where

its

by 'proper' affections

I

mean

those influences

from the natural constitution of a thing tend to promote or destroy its existence. Since, that

[70] then, relatives are neither themselves alterations nor the subjects of alteration or of becom-

ing or in fact of any change whatever, it is evident that neither states nor the processes of losing and acquiring states are alterations, though it may be true that their becoming or perishing [75] is necessarily, like the becoming or perishing of a specific character or form, the result of the alteration of certain other things, e.g. hot

and cold or dry and wet elements or the elements, whatever they may be, on which the states primarily depend. For each several bodily

defect or excellence involves a relation with

those things from

which the possessor

defect or excellence

is

teration: thus excellence disposes to be unaffected

of the

naturally subject to its

al-

possessor

by these influences or to be

af-

PHYSICS

330

them that ought to be admitwhile defect disposes its possessor to be affected by them or to be unaffected by those of them that ought to be admitted. [20] And the case is similar in regard to the

248*

fected by those of

tivity of these states, unless

ted,

there

247 a

which

states of the soul, all of

(like those

of body) exist in virtue of particular relations, the excellences being perfections of nature and

from it: moreover, excellence puts its possessor in good condition, while defect puts its possessor in a bad condition, to meet his proper affections. Consequently these cannot any more than the bodily states be alter[5] ations, nor can the processes of losing and acquiring them be so, though their becoming the defects departures

is

necessarily the result of an alteration of the

and

sensitive part of the soul,

sensible objects: for all

this

is

altered by

moral excellence

is

con-

cerned with bodily pleasures and pains, which again depend either upon acting or upon reor upon anticipating. Now those depend upon action are determined by

a

is

becoming of

vision

that the activity in question

And

it

thought that

is

and touching and

is

similar to these.)

knowledge

the original acquisition of

is

not a becoming or an alteration: for the terms [10] 'knowing' and 'understanding' imply that the intellect has reached a state of rest and

come

to a standstill,

and there

no becoming

is

we have can have a becoming. Moreover, just as to say, when any one has that leads to a state of rest, since, as

said above,

1

no change

at all

passed from a state of intoxication or sleep or disease to the contrary state, that he has become [75] possessed of knowledge again is incorrect in spite of the fact that he was previously incapable of using his knowledge, so, too, when

any one originally acquires the state, it is incorrect to say that he becomes possessed of knowledge: for the possession of understanding and knowledge is produced by the soul's settling

membering

down

that

Hence, too, in learning and in forming judgements on matters relating to their sense-percep248 a tions children are inferior to adults owing to the great amount of restlessness and motion in their souls. Nature itself causes the soul

[10] sense-perception,

by something

i.e.

they are stimulated

and those that depend

sensible:

upon memory

or anticipation are likewise to be traced to sense-perception, for in these cases

pleasure

is

felt either in

remembering what one

has experienced or in anticipating what one is going to experience. Thus all pleasure of this

kind must be produced by sensible things: and since the presence in any one of moral defect or excellence involves the presence in him of [75] pleasure or pain (with which moral excellence and defect are always concerned), and these pleasures

and pains are

alterations of the

evident that the loss and acquisition of these states no less than the loss and acquisition of the states of the body must be the sensitive part,

it is

out of the restlessness

down and come

to settle

the performance of

some

natural to

it.

to a state of rest for

its functions, while performance of others other things do so: but in either case the result is brought about through the alteration of something in the body, as we see in the case of the use and activ[5] ity of the intellect arising from a man's becoming sober or being awakened. It is evident, then, from the preceding argument that alteration and being altered occur in sensible things

of

for the

and

in the sensitive part of the soul, and, ex-

cept accidentally, in nothing else.

something else. Conbecoming is accompa-

result of the alteration of

sequently, though their

nied by an alteration, they are not themselves alterations. 247 b Again, the states of the intellectual part

of the soul are not alterations, nor

becoming more true it

of the possession of

depends upon a particular

ther,

it is

evident that there

there any

is

of them. In the first place

it is

time, then

fur-

to a straight line, or, of course, the

no becoming

of

which is potentially posknowledge becomes actually possessed of it not by being set in motion at all itself [5] but by reason of the presence of something i.e. it is it

when

it

knows

meets with the particular

in a

we may have

that

these states. For that

object that

is

And

sessed of

else:

difficulty

knowledge

relation. is

much

A

may be raised as to whether commensurable with every other or not. Now if they are all commensurable and if two things to have the same velocity must accomplish an equal motion in an equal [70]

every motion

manner

the particular

through its knowledge of the universal. (Again, there is no becoming of the actual use and ac-

a circumference equal

one

may

greater or less than the other. Further,

if

be

one

thing alters and another accomplishes a locomotion in an equal time, we may have an alter[75] ation and a locomotion equal to one another: thus an affection will be equal to a length, which is impossible. But is it not only equal motion is accomplished by two things in an equal time that the velocities of

when an 1

v. 2 (225 b 15 sqq.).

BOOK

249*

VII,

CHAPTERS

the two are equal? Now an affection cannot be equal to a length. Therefore there cannot be an alteration equal to or less than a locomotion: and consequently it is not the case that every motion is commensurable with every other.

But

how

will our conclusion

and the

case of the circle

work out

straight line?

It

in the

would

be absurd to suppose that the motion of one [20] thing in a circle and of another in a straight line cannot be similar, but that the one must inevitably move more quickly or more slowly than the other, just as if the course of one were downhill and of the other uphill. Moreover it does not as a matter of fact make

any difference to the argument to say that the one motion must inevitably be quicker or slower than the other: for then the circumference can be greater or less than the straight line;

and

if

so

possible for the

it is

[25] For

if

A

in the time

passes over the distance B'

248 b

two

to be equal.

the quicker (B)

and the slower (T)

passes over the distance r", B' will be

greater than T':

for this

is

what we

1

motion implies that one thing traverses an equal

'quicker' to

mean: and

so quicker

took

3-4

are not

commensurable

up the same position and say that the term 'much' is equivocal? In fact there are some terms of which even the definitions are equivocal; e.g. if 'much' were defined as 'so much and more', 'so much' would mean something different in different cases: 'equal' is similarly equivocal; and 'one' again is perhaps in[20] evitably an equivocal term; and if 'one' is equivocal, so is 'two'. Otherwise why is it that some things are commensurable while others are not,

if

the nature of the attribute in the

is

really

carrying the attribute?

A

two motions

are

commen-

[5] surable, we are confronted with the consestated above, viz. that there may be a

quence

straight line equal to a circle. But these are not commensurable: and so the corresponding motions are not commensurable either. But may we say that things are always commensurable if the same terms are applied to

them without equivocation? e.g. a pen, a wine, and the highest note in a scale are not commensurable: we cannot say whether any one of them is sharper than any other: and why is this? they are incommensurable because it is only equivocally that the same term 'sharp' is applied to them: whereas the highest note in a scale is commensurable with the leading-note, because the term 'sharp' has the same meaning [10] as applied to both. Can it be, then, that the term 'quick' has not the same meaning as

applied to straight motion and to circular tion respectively ? If so, far less will

same meaning

it

mo-

have the

as applied to alteration

and

to

locomotion.

Or

we

in the first place deny that things commensurable if the same terms are applied to them without equivocation ? For shall

are always 1

vi.

2(232* 25 sqq.).

which

ference in that

dis-

is

primarily capable of

Thus horse and dog are commensurable that we may say which is

the whiteness

the

two

one and the same? Can it be that the incommensurability of two things in respect of any attribute is due to a dif-

cases

over a part of the circle equal to T', while V in passing over r'« will occupy the whole of less, if

or, if

take

so

the

it:

is

also

A

in respect of

not considered satisfactory, 'double' at any rate would seem to have the same meaning as applied to each (denoting in each case the proportion of two to one), yet water and air are not commensurable in re[75] spect of it. But here again may we not

this illustration

tance in less time than another: consequently in which B will pass there will be a part of

None

331

the term 'much' has the same meaning whether applied to water or to air, yet water and air

the whiter, since that face:

and

is

which primarily contains

the same in both, viz. the sur-

commensurable in But water and speech are not

similarly they are

respect of size.

commensurable in respect of clearness, since that which primarily contains the attribute is [25] different in the two cases. It would seem, however, that we must reject this solution, since clearly

we

could thus

make

all

equivocal

and say merely that that which contains each of them is different in dif249 a ferent cases: thus 'equality', 'sweetness', and 'whiteness' will severally always be the same, though that which contains them is different in different cases. Moreover, it is not any casual thing that is capable of carrying any atattributes univocal

tribute: each single attribute can be carried primarily only by one single thing. Must we then say that, if two things are to be commensurable in respect of any attribute, not only must the attribute in question be applicable to both without equivocation, but there must also be no specific differences either in the attribute itself or in that which contains the that these, I mean, must not be [5] attribute divisible in the way in which colour is divided into kinds? Thus in this respect one thing will not be commensurable with another, i.e. we cannot say that one is more coloured than the other where only colour in general and not any

—

249b

PHYSICS

33 2 particular colour

mensurable

is

meant; but they are com-

in respect of whiteness.

Similarly in the case of motion:

particular instances of whiteness or sweetness

same or different?

are the

two things

are of the same velocity if they occupy an equal time in accomplishing a certain equal amount of motion. Suppose, then, that in a certain time an alteration is undergone by one half of a body's length and a locomotion is accomplished by [10] the other half: can be say that in this case the alteration is equal to the locomotion and of the same velocity ? That would be absurd, and

the reason is that there are different species of motion. And if in consequence of this we must say that two things are of equal velocity if they accomplish locomotion over an equal distance in an equal tme, we have to admit the equality of a straight line and a circumference. What, then, is the reason of this? Is it that locomo-

Is it

enough

that

it

appears different in one subject from what it appears in another? Or must there be no same-

And further, where alteration is in how is one alteration to be of equal with another? One person may be

ness at all?

question, velocity

cured quickly and another slowly, and cures [30] may also be simultaneous: so that, recovery of health being an alteration, we have here alterations of equal velocity, since each altera249 b tion occupies an equal time. But what alteration? We cannot here speak of an 'equal' alteration: what corresponds in the category of quality to equality in the category of quantity is

'likeness'.

However,

let

us say that there

is

[75] tion

is

a genus?

equal velocity where the same change is accom[5] plished in an equal time. Are we, then, to find the commensurability in the subject of

(We may

leave the time out of account, since

the affection or in the affection itself? In the case

one and the same.) If the lines are specifically different, the locomotions also differ specifically from one another: for locomotion

been considering it is the fact one and the same that enables us to arrive at the conclusion that the one alteration is neither more nor less than the other, but that both are alike. If on the other hand the af-

that

is

a

genus or that

line

is

is

specifically differentiated

according to the over which it

specific differentiation of that

takes place. (It it

is

also similarly differentiated,

would seem, accordingly

of the locomotion

as the instrument

different: thus if feet are walking, if wings it is flying; but perhaps we should rather say that this is not so, and that in this case the differences in the locomotion are merely differences of posture in that which is in motion.) We may say, therefore, that things are of equal velocity [20] if in an equal time they traverse the same magnitude: and when I call it 'the same' I

the instrument,

mean

that

it

is

it is

contains no specific difference and

no difference in the motion that takes place over it. So we have now to consider how motion is differentiated: and this discussion serves to show that the genus is not a unity but contains a plurality latent in it and distinct from it, and that in the case of equivocal terms sometimes the different senses in which they are used are far removed from one another, while sometimes there is a certain likeness between them, and sometimes again they are therefore

nearly related either generically or analogical-

with the result that they seem not to be equivocal though they really are. [25] When, then, is there a difference of spely,

cies

?

Is

subject

an attribute is

specifically different if the

different while the attribute

is

the

same, or must the attribute itself be different as well? And how are we to define the limits of a species? What will enable us to decide that

that

we have

that health

fection

is

just

is

two cases, e.g. when form of becoming white

different in the

the alterations take the

and becoming healthy respectively, here there no sameness or equality or likeness inas-

is

much

as

the difference in the affections at

makes the alterations specifically different, and there is no unity of alteration any more than there would be unity of locomotion under like conditions. So we must find out how many species there are of alteration and of lo[10] once

comotion respectively. Now if the things that are in motion that is to say, the things to which the motions belong essentially and not

—

accidentally

—

differ specifically,

then their

re-

spective motions will also differ specifically:

if

on the other hand they differ generically or numerically, the motions also will differ generically or numerically as the case may be. But [75] there still remains the question whether, supposing that two alterations are of equal velocity, we ought to look for this equality in the sameness (or likeness) of the affections, or in the things altered, to see e.g. whether a certain quantity of each has become white. Or ought we not rather to look for it in both ? That is to say, the alterations are the same or different according as the affections are the same or different, while they are equal or unequal according as the things altered are equal or unequal.

And now we must

consider the same ques-

BOOK

250b

VII,

CHAPTERS

becoming and perishone becoming of equal velocity

[20] tion in the case of

how

ing:

is

with another? They are of equal velocity if in an equal time there are produced two things

same and specifically inseparable, two men (not merely generically inseparaas e.g. two animals). Similarly one is quick-

that are the e.g.

ble

er than the other

an equal time the prod-

in

if

two

cases. I state it thus because we have no pair of terms that will convey this 'difference' in the way in which unlikeness is conveyed. If we adopt the theory

uct

is

that

different in the

it is

number

that constitutes being,

we may

indeed speak of a 'greater number' and a 'lesser number' within the same species, but there is no common term that will include both relations, nor are there terms to express each of [25] them separately in the same way as we indicate a higher degree or preponderance of

an

affection by 'more', of a quantity by 'greater.'

Now

since wherever there is a movent, its motion always acts upon something, is always in something, and always extends to something (by 'is always in something' I mean that it occupies a time: and by 'extends to something' I

mean that it involves the traversing of a certain amount of distance: for at any moment when is causing motion, it also has caused motion, so that there must always be a certain amount of distance that has been traversed and a certain amount of time that has been occu-

a thing

A

the movent have moved [30] pied). If, then, 250a B a distance T in a time A, then in the

same time the same

force

A

move 14 B /2 A it will move will

twice the distance T, and in l /2 B the whole distance T: for thus the rules of l

proportion will be observed. Again if a given [5] force move a given weight a certain distance in a certain time and half the distance in half the time, half the motive

half the weight the

time. Let

power

same distance

E represent

move

will

same power A

in the

half the motive

and Z half the weight B: then the ratio between the motive power and the weight in the one case is similar and proportionate to the ratio in the other, so that

each force will cause the

4-5

333

and the whole of T is proportionate to that between A and E (whatever fraction of A E may [75] be): in fact it might well be that it will cause no motion at all; for it does not follow that, if a given motive power causes a certain amount of motion, half that power will cause motion either of any particular amount or in any length of time: otherwise one man might move a ship, since both the motive power of the ship-haulers and the distance that they all cause the ship to traverse are divisible into as many parts as there are men. Hence Zeno's rea[20] soning is false when he argues that there no part of the millet that does not make a

is

sound: for there

is

no reason why any such

part should not in any length of time

move

the air that the whole bushel

falling. In fact

it

does not of

fail to

moves

in

move even would move if

itself

such a quantity of the air as it this part were by itself: for no part even exists otherwise than potentially. [25] If on the other hand we have two forces each of which separately moves one of two weights a given distance in a given time, then the forces in combination will move the combined weights an equal distance in an equal time: for in this case the rules of proportion apply. Then does this hold good of alteration and of increase also? Surely it does, for in any given case we have a definite thing that causes in[30] crease and a definite thing that suffers increase, and the one causes and the other suffers a

certain

amount

amount

of

increase

of time. Similarly

in

a

we have

certain

a definite

thing that causes alteration and a definite thing

undergoes alteration, and a certain amount, or rather degree, of alteration is comthat

250 b

pleted in a certain

amount

of time: thus

twice as much alteration will be completed and conversely twice as much in twice as

much time

alteration will

occupy twice

the alteration of half of half as

much

its

as

much

time:

and

object will occupy

time and in half as

much

time

half of the object will be altered: or again, in

same amount of time it will be altered twice much. On the other hand if that which causes alteration or increase causes a certain amount of inthe

as

same distance to be traversed in the same time. [10] But if E move Z a distance T in a time A,

crease or alteration respectively in a certain

does not necessarily follow that E can move twice Z half the distance T in the same time.

low that half the force

it

A

If, then, move B a distance T in a time A, it does not follow that E, being half of A, will in the time A or in any fraction of it cause B to

traverse a part of

T

the ratio between

which

amount

does not necessarily folwill occupy twice the time in altering or increasing the object, or that in twice the time the alteration or increase will be completed by it: it may happen that there will be no alteration or increase at all, the case being the same as with the weight. [5]

of time,

it

PHYSICS

334

BOOK

25 V

VIII nature, but also for the investigation of the First Principle.

It remains to consider the following ques-

Was

becoming of motion before which it had no being, and is it perishing again so as to leave nothing in motion? Or are we to say that it never had any becoming and is not perishing, but always was and always will be? Is it in fact an immortal never-failing tion.

there ever a

property of things that are, a sort of life as were to all naturally constituted things?

it

Now

the existence of motion is asserted have anything to say about nature, because they all concern themselves with the construction of the world and study the ques[75]

by

all

who

becoming and perishing, which proccome about without the existence of motion. But those who say that there is an infinite number of worlds, some of which are in process of becoming while others are in tion of

esses could not

[20] process of perishing, assert that there

is al-

ways motion (for these processes of becoming and perishing of the worlds necessarily involve motion), whereas those who hold that there is only one world, whether everlasting or not, make corresponding assumptions in regard to motion. If then it is possible that at any time nothing should be in motion, this must come about in one of two ways: either in the manner described by Anaxagoras, who says that all [25] things were together and at rest for an infinite period of time, and that then Mind intro-

Let us take our start from what we have al1 ready laid down in our course on Physics. Motion,

we

say,

is

the fulfilment of the movable in

[10] so far as it is movable. Each kind of motion, therefore, necessarily involves the pres-

ence of the things that are capable of that motion. In fact, even apart from the definition of motion, every one would admit that in each kind of motion it is that which is capable of that motion that is in motion: thus it is that which is capable of alteration that is altered, and that which is capable of local change that [75] is in locomotion: and so there must be something capable of being burned before there can be a process of being burned, and something capable of burning before there can be a process of burning. Moreover, these things also must either have a beginning before which they had no being, or they must be eternal. Now if there was a becoming of every movable thing, it follows that before the motion in question another change or motion must have taken place in which that which was capable of being

moved

or of causing motion

had

its

becoming.

[20] To suppose, on the other hand, that these things were in being throughout all previous

time without there being any motion appears unreasonable on a moment's thought, and still more unreasonable, we shall find, on further consideration. For if we are to say that, while

duced motion and separated them; or in the manner described by Empedocles, according to whom the universe is alternately in motion and in motion, when Love is making the at rest one out of many, or Strife is making many out of one, and at rest in the intermediate periods

on the one hand things that are movand on the other hand things that are motive, there is a time when there is a first movent and a first moved, and another time when there is no such thing but only something that is at [25] rest, then this thing that is at rest must

account being as follows: hath learned to spring from Manifold,

previously have been in process of change: for there must have been some cause of its rest,

—

of time

—

his

[jo] 'Since

One

And One

disjoined makes Manifold arise,

251 a Thus they Become, nor

stable

their

is

life:

But

since their motion

must

alternate

be,

Thus have they ever Rest upon

their

round': for

we must suppose

that he

means by

[5] they alternate from the one other. must consider, then,

We

this that

motion

how

matabout of importance, not only for the study of

ter stands, for the discovery of the truth it is

to the

this

there are

able,

being the privation of motion. Therefore, first change there will be a previous change. For some things cause motion in only one way, while others can produce either of two contrary motions: thus fire causes heating [50] but not cooling, whereas it would seem that knowledge may be directed to two contrary ends while remaining one and the same. Even in the former class, however, there seems to be something similar, for a cold thing in a sense causes heating by turning away and retiring, just as one possessed of knowledge volrest

before this

BOOK

252*

makes an error when knowledge in the reverse way. But

untarily b

25

VIII,

he uses his at

any

rate all things that are capable respectively of

and being affected, or of causing moand being moved, are capable of it not un-

affecting tion

der

all

conditions, but only

when

they are in a

and approach one another: so it is on the approach of one thing to another that the one causes motion and the other is moved, and when they are present under such conditions as rendered the one motive and [5] the other movable. So if the motion was not always in process, it is clear that they must particular condition

in a condition not

have been

them capable

such as to render

moved and and one or other of them

respectively of being

of causing motion,

must have been in process of change: for in what is relative this is a necessary consequence: e.g. if

one thing

is

double another

when

before

was not so, one or other of them, if not both, must have been in process of change. It follows, it

CHAPTER

1

335

ing of motion would involve, as

we

saw, the [50] existence of a process of change previous to the first, in the same way a perishing of motion

would involve the

existence of a process of

change subsequent to the last: for when a thing ceases to be moved, it does not therefore at the same time cease to be movable e.g. the cessation of the process of being burned does not in-

—

volve the cessation of the capacity of being burned, since a thing may be capable of being burned without being in process of being burned nor, when a thing ceases to be movent, does it therefore at the same time cease to 252 a be motive. Again, the destructive agent will have to be destroyed, after what it destroys has been destroyed, and then that which has the capacity of destroying it will have to be destroyed afterwards, (so that there will be a process of change subsequent to the last,) for being destroyed also is a kind of change. If,

—

which we are

then, the view

criticizing in-

then, that there will be a process of change pre-

volves these impossible consequences,

vious to the

motion is eternal and cannot have existed at one time and not at another: in fact, such a view can hardly be described as anything else

how can there be any 'before' without the existence of time? Or how can there be any time without the existence of motion ? If, then, time is the number of motion or itself a kind of motion, it follows that, if there is always time, motion must also be eternal. But so far as time is concerned we see that all with one exception are in agreement [10] (Further,

and

'after'

in saying that

it is

uncreated: in

fact,

it is

just

Democritus to show that things cannot have had a becoming: for

[75] this that enables all

uncreated. Plato alone asserts 1 the creation of time, saying that it had a becoming together with the universe, the unitime, he says,

is

verse according to

Now ble

him having had

a becoming.

and is unthinkaapart from the moment, and the moment

[20]

since time cannot exist

is

a kind of middle-point, uniting as

it

both a beginning and an end, a beginning of future time and an end of past time, it follows that there must always be time: for the extremity of the last period of time that we take must be found in some moment, since time contains no point of contact for us except [25] the moment. Therefore, since the moment is both a beginning and an end, there must always be time on both sides of it. But if this is true of time, it is evident that it must also be true of motion, time being a kind of affection of motion.) The same reasoning will also serve to show the imperishability of motion: just as a becomdoes in

1

itself

Aristotle

is

it is

clear

that

frrst.

thinking of a passage in the Timaeus (38).

than fantastic. [5]

And much

the

same may be

said of the

and must be regarded as a principle, as would seem to be the view of Empedocles when he says that the constitution of the world is of necessity such that Love and Strife alternately predominate and cause motion, while in the inview that such

is

the ordinance of nature

that this

termediate period of time there is a state of rest. [10] Probably also those who, like Anaxagoras, assert a

single principle

(of

motion) would

hold this view. But that which is produced or directed by nature can never be anything disorderly: for nature is everywhere the cause of order. Moreover, there is no ratio in the relation of the infinite to the infinite, whereas order always means ratio. But if we say that there is first

a state of rest for an infinite time,

and

[75] then motion is started at some moment, and that the fact that it is this rather than a

moment is of no importance, and inno order, then we can no longer say that nature's work: for if anything is of a cer-

previous volves it is

tain character naturally,

and

it

either

is

so invari-

not sometimes of this and sometimes of another character (e.g. fire, which

ably

is

upwards naturally, does not sometimes do so and sometimes not) or there is a ratio in

travels

the variation.

It

[20] say with

who may

would be better, therefore, to Empedocles and any one else

have maintained such a theory as

PHYSICS

33 6 his that the universe

is

alternately at rest

and

in

motion: for in a system of this kind we have at once a certain order. But even here the holder of the theory ought not only to assert the fact: he ought to explain the cause of it: i.e. he should not make any mere assumption or lay down any gratuitous axiom, but should em[25] ploy either inductive or demonstrative reasoning. The Love and Strife postulated by Empedocles are not in themselves causes of the fact in question, nor is it of the essence of either that it should be so, the essential function of the former being to unite, of the latter to separate. If he is to go on to explain this alternate predominance, he should adduce cases where such a state of things exists, as he points to the fact that among mankind we have something that unites men, namely Love, while on the [30] other hand enemies avoid one another: thus from the observed fact that this occurs in certain cases comes the assumption that it oc-

some argument is needed to explain why the predominance of each of the two forces lasts for an equal period of time. But it is a wrong assumption to suppose universally that we have

curs also in the universe. Then, again,

an adequate

first

principle in virtue of the fact

that something always so.

is

so or always

Thus Democritus reduces

happens

the causes that

explain nature to the fact that things happened

same way as they happen now: but he does not think fit to seek for

in the past in the

[35]

253«

must be bounded by the contraries its course, and no motion can go on Secondly,

we

that

mark

to infinity.

see that a thing that neither

motion nor contains any motion within

in

is it-

can be

set in motion; e.g. inanimate things (whether the whole or some part is in question) not in motion but at rest, are at [75] some moment set in motion: whereas, if motion cannot have a becoming before which it had no being, these things ought to be either always or never in motion. Thirdly, the fact is evident above all in the case of animate beings: for it sometimes happens that there is no motion in us and we are quite still, and that nevertheless we are then at self

that are

some moment

set in

motion, that

is

to say

it

sometimes happens that we produce a begin[20] ning of motion in ourselves spontaneously without anything having set us in motion from without. We see nothing like this in the case of inanimate things, which are always set in motion by something else from without: the animal, on the other hand, we say, moves itself: therefore, if an animal is ever in a state of absolute rest, we have a motionless thing in which motion can be produced from the thing itself, and not from without. Now if this [25] can occur in an animal, why should not

same be true also of the universe as a whole? If it can occur in a small world it could also occur in a great one: and if it can occur in the

the world,

it

could also occur in the infinite;

25

b a first principle to explain this 'always':

that

so,

while his theory

be in motion or at rest. Of these objections, then, the first-mentioned

is

right in so far as

it

is

applied to certain individual cases, he is wrong in making it of universal application. Thus, a

two right

triangle always has

its

angles equal to

angles, but there

is

nevertheless an ulterior

cause of the eternity of this truth, whereas

first

and have no ulterior conclude what we have to

is, if

the infinite could as a whole possibly

—

that motion to opposites [30] the same and numerically one

statement; in fact, this

same

may be advanced against not difficult to dispose of. The chief considerations that might be thought to that

this position are

motion may exist though at one had not existed at all are the following: First, it may be said that no process of change is eternal: for the nature of all change [10] is such that it proceeds from something to something, so that every process of change indicate that

time

a correct

may

motion of that which is one and the always one and the same. (I mean that e.g. we may question whether the note given by a single string is one and the

ble for the

[5] cause. Let this say in support of

The arguments

not always is

be said to be a necessary conclusion, provided that it is possi-

principles are eternal

our contention that there never was a time when there was not motion, and never will be a time when there will not be motion.

is

—

to be not

same, or is different each time the string is struck, although the string is in the same condition and is moved in the same way.) But [35] still, however this may be, there is nothing to prevent there being a motion that is the 253 a same in virtue of being continuous and 1 eternal: we shall have something to say later

make this point clearer. As regards the second objection, no absurd-

that will

it

involved in the fact that something not motion may be set in motion, that which caused the motion from without being at one ity is

in

1

Chapter

8.

BOOK

253 b

VIII,

CHAPTERS

time present, and at another absent. Nevertheless, how this can be so remains matter for in-

how

quiry;

it

comes about,

I

mean, that the

same motive force at one time causes a thing motion, and at another does not do so:

to be in

[5] for the difficulty raised why really amounts to this

—

things are not always at

ways

in

The

rest,

by our objector is

it

some

that

and the

rest al-

motion?

third objection

may

be thought to pre-

more difficulty than the others, namely, that which alleges that motion arises in things in which it did not exist before, and adduces sent

in

proof the case of animate things: thus an

[10] animal is first at rest and afterwards walks, not having been set in motion apparent-

by anything from without. This, however, is false: for we observe that there is always some part of the animal's organism in motion, and the cause of the motion of this part is not the animal itself, but, it may be, its environment. Moreover, we say that the animal itself originates not all of its motions but its locomotion. [75] So it may well be the case or rather we may perhaps say that it must necessarily be that many motions are produced in the case the body by its environment, and some of these ly

—

—

and whole animal in motion: this is what happens when animals are asleep: though there is then no perceptive motion in them, there is some motion that causes [20] them to wake up again. But we will leave set in

motion the

again then

this

intellect or the appetite,

sets the

this point also to be elucidated at a later

1

stage

in our discussion.

Our enquiry

will resolve itself at the outset into

a consideration of the above-mentioned prob-

lem

—what can be the reason why some things

world at one time are in motion and at another are at rest again? Now one of three things must be true: either all things are al25] ways at rest, or all things are always in motion, or some things are in motion and others at rest: and in this last case again either the things that are in motion are always in motion and the things that are at rest are always at rest, or they are all constituted so as to be capable alike of motion and of rest; or there is in the

ii

yet a third possibility

that

some things

in the

—

remaining it may be world are always mo-

always in motion, while others again admit of both conditions. This last is [jo] the account of the matter that we must tionless, others

1

Chapter 6^

1-3

337

give: for herein lies the solution of all the

and the conclusion of the upon which we are engaged.

culties raised

tigation

To

diffi-

inves-

rest, and an attempt to show the theory to be reasonable, would be an instance of intellectual weakness: it would call in question a whole system, not a particular [25] detail: moreover, it would be an attack not only on the physicist but on almost all sciences and all received opinions, since motion 253 b plays a part in all of them. Further, just as in arguments about mathematics objections that involve first principles do not affect the mathematician and the other sciences are in

maintain that

all

things are at

to disregard sense-perception in

similar case

point that

—

—

so, too,

we have

objections involving the

just raised

do not

affect the

[5] physicist: for it is a fundamental assumption with him that motion is ultimately refer-

able to nature herself.

The assertion that all we may fairly regard as it

less

is

though

things are in motion

equally

false,

though

subversive of physical science:

for

our course on physics it was laid down that rest no less than motion is ultimately referable to nature herself, nevertheless motion is the characteristic fact of nature: moreover, the view is actually held by some that not [10] merely some things but all things in the world are in motion and always in motion, though we cannot apprehend the fact by in

Although the supporters of do not state clearly what kind of motion they mean, or whether they mean all kinds, it is no hard matter to reply to them: sense-perception. this theory

thus we may point out that there cannot be a continuous process either of increase or of decrease: that which comes between the two has [75] to be included. The theory resembles that about the stone being worn away by the drop of water or split by plants growing out of it: if so much has been extruded or removed by the drop, it does not follow that half the amount has previously been extruded or removed in half the time: the case of the hauled ship is exactly comparable: here we have so many drops setting so much in motion, but a part of them will not set as much in motion in any period of time.

The amount removed

is,

it

is

true, di-

[20] visible into a number of parts, but no one of these was set in motion separately: they were in motion together. It is evident, then, from the fact that the decrease is divisible

all set

that

into an infinite

number

of parts

it

does not

fol-

low that some part must always be passing away: it all passes away at a particular mo-

PHYSICS

33«

ment. Similarly, too, in the case of any alteration whatever if that which suffers alteration is

infinitely divisible

does not follow from

it

[25] this that the same is true of the alteration itself, which often occurs all at once, as in

when any one

freezing. Again,

must follow

there

a period of

restoration to health

is

has fallen ill, time in which his

in the future: the proc-

change cannot take place in an instant: the change cannot be a change to anything

ess of

yet

The

else but health.

assertion, therefore, that

continuous is an extravagant calico] ing into question of the obvious: for alteration is a change from one contrary to another. Moreover, we notice that a stone becomes neither harder nor softer. Again, in the matter of locomotion, it would be a strange thing if a stone could be falling or resting on the ground without our being able to perceive the fact. Further, it is a law of nature that earth and all other bodies should remain in [35] their proper places and be moved from them only by violence: from the fact then that some of them are in their proper places it follows that in respect of place also all things can254 a not be in motion. These and other similar arguments, then, should convince us that alteration

it is

ways

is

impossible either that in

motion or that

all

all

things are

al-

things are always

at rest.

Nor ways

be that some things are alothers always in motion, and

again can

at

rest,

it

nothing sometimes at rest and sometimes in [5] motion. This theory must be pronounced impossible on the same grounds as those previously mentioned: viz. that we see the abovementioned changes occurring in the case of the

same

things.

We

may

further point out that

the defender of this position

is

fighting against

the obvious, for on this theory there can be no such thing as increase: nor can there be any

such thing as compulsory motion,

if it

is

im-

possible that a thing can be at rest before being

[10] set in motion unnaturally. This theory, then, does away with becoming and perishing.

Moreover, motion, it would seem, is generally thought to be a sort of becoming and perishing, for that to which a thing changes comes to be, or occupancy of it comes to be, and that from which a thing changes ceases to be, or there ceases to be occupancy of it. It is clear, therefore, that there are cases of occasional motion

and occasional

254 b

ments previously advanced. We must take our from the possibilities that we

start as before

distinguished just above. Either all things are at rest, or all things are in motion, or some things are at rest and others in motion. And if

some things

are at rest and others in motion, must be that either all things are sometimes at rest and sometimes in motion, or some things are always at rest and the remainder always in motion, or some of the things are always at rest and others always in motion while others again are sometimes at rest and sometimes in motion. Now we have

[20] then

it

said before that

should be at

it is

rest:

impossible that

repeat that assertion.

We

may

all

things

we may now

nevertheless

point out that,

[25] even if it is really the case, as certain persons assert, that the existent is infinite and moit certainly does not appear to be so if follow sense-perception: many things that exist appear to be in motion. Now if there is such a thing as false opinion or opinion at all,

tionless,

we

is also motion; and similarly if there is such a thing as imagination, or if it is the case that anything seems to be different at different times: for imagination and opinion are [jo] thought to be motions of a kind. But to investigate this question at all to seek a reasoned justification of a belief with regard to

there

—

which we are too well off to require reasoned implies bad judgement of what is better and what is worse, what commends itself to belief and what does not, what is ultimate and what is not. It is likewise impossible that all things should be in motion or that some things should be always in motion and [55] the remainder always at rest. We have sufficient ground for rejecting all these theories in the single fact that we see some things that 254 b are sometimes in motion and sometimes at rest. It is evident, therefore, that it is no less impossible that some things should be always in motion and the remainder always at rest justification

—

than that all things should be at rest or that all things should be in motion continuously. It remains, then, to consider whether all things are so constituted as to be capable both of being in motion and of being at rest, or whether, [5] while some things are so constituted, some are always at rest and some are always in motion: for it is this last view that we have to show to be true.

rest.

We

have now to take the assertion that [75] all things are sometimes at rest and sometimes in

motion and

to confront

it

with the argu-

Now

of things that cause motion or suffer mosome the motion is accidental, to others

tion, to

255

BOOK

J

essential: thus

accidental to

it is

CHAPTERS

VIII,

what merely

3-4

339

would be experienced

cases that difficulty

belongs to or contains as a part a thing that causes motion or suffers motion, essential to a [10] thing that causes motion or suffers motion not merely by belonging to such a thing or

deciding whence the motion

containing

their

it

as a part.

Of things to which the motion is essential some derive their motion from themselves, others from something else: and in some cases their

motion

is

and

natural, in others violent

Thus

unnatural.

in things that derive their

[75] motion from themselves, e.g. all animals, the motion is natural (for when an animal is in motion its motion is derived from itself): and

whenever the source in the thing itself

that thing

is

of the

we

motion

of a thing

is

say that the motion of

natural. Therefore the animal as a

whole moves itself naturally: but the body ol the animal may be in motion unnaturally as well as naturally: it depends upon the kind ol motion that it may chance to be suffering and [20] the kind of element of which it is composed. And the motion of things that derive their motion from something else is in some cases natural, in other unnatural: e.g.

upward

motion of earthy things and downward motion of fire are unnatural. Moreover the parts of animals are often in motion in an unnatural way, their positions and the character of the motion being abnormal. The fact that a thing [25] that is in motion derives its motion from something is most evident in things that are in motion unnaturally, because in such cases it is clear that the motion is derived from something other than the thing itself. Next to things that are in motion unnaturally those whose motion while natural is derived from themselves

—

e.g.

animals

—make

this fact clear: for

not as to whether the motion is derived from something but as to how we ought to distinguish in the thing behere the uncertainty

is

motion

is

however,

is

pre-

last

distinguished.

Where

we

things derive their

motion from something else we distinguished [55] the cases in which the motion is unnatural: we are left with those that are to be contrasted with the others by reason of the fact 255 a that the motion is natural. It is in these

violent:

tion to their proper positions

—the —

light thing

up and the heavy thing down

their

natural; but in this latter case

it

evident, as

it is

when

the motion

is is

motion is no longer

unnatural,

[5] whence their motion is derived. It is impossible to say that their motion is derived

from themselves: this is a characteristic of life and peculiar to living things. Further, if it were, it would have been in their power to stop themselves cause to

(I

itself to

walk), and

mean walk

if e.g. a thing can can also cause itself not

that it

on power

so, since

this supposition fire

of upward locomoshould also possess the [10] power of downward locomotion. Moreover if things move themselves, it would be unreasonable to suppose that in only one kind of motion is their motion derived from themselves. Again, how can anything of continuous and naturally connected substance move itself? In so far as a thing is one and continuous not merely in virtue of contact, it is impassive: it is only in so far as a thing is divided that one part of it is by nature active and another [ 15] passive. Therefore none of the things that we are now considering move themselves (for they are of naturally connected substance), nor does anything else that is continuous: in each itself

tion,

possesses the

case the

is

it

movent must be separate from the

we see to be the case with inanimate when an animate thing moves them. It

moved, things

clear that

is

it

as

the fact that these things also always derive

motion from something: what it is would become evident if we were to distinguish the their

different kinds of cause.

The above-mentioned distinctions can made in the case of things that cause

capable of difficulty,

would properly occupy, when they are in mo-

verse of those they

naturally (e.g.

greatest

When

these things are in motion to positions the re-

tion.

The

in

derived, e.g. in

and heavy things.

the case of light

tween the movent and the moved. It would [50] seem that in animals, just as in ships and things not naturally organized, that which causes motion is separate from that which suffers motion, and that it is only in this sense that the animal as a whole causes its own mo-

sented by the remaining case of those that

is

[20]

also be

motion: some of them are capable of causing (e.g. the lever is not naturally capable of moving the weight), others

motion unnaturally

and

what is actually hot is naturally moving what is potentially hot):

similarly in the case of

all

other things of

this kind.

In the

same way,

too,

what

is

potentially of

a certain quality or of a certain quantity or in a

[25] certain place is naturally movable when it contains the corresponding principle in itself

and not accidentally (for the same thing may be both of a certain quality and of a certain

PHYSICS

340

an accidental, not an So when fire moved by something the motion is

quantity, but the one

is

essential property of the other).

or earth violent it

is

when

it is

unnatural, and natural

when

brings to actuality the proper activities that

[30] they potentially possess. But the fact that the term 'potentially' is used in more than one sense

the reason

is

why

not evident whence

it is

such motions as the upward motion of

downward motion

the

One who

is

fire

and

of earth are derived.

learning a

science

potentially

knows it in a different sense from one who while already possessing the knowledge is not actually exercising it. Wherever we have something capable of acting and something capable of being correspondingly acted on, in the event [^5] of any such pair being in contact what is 255 b potential becomes at times actual: e.g. the learner becomes from one potential something another potential something: for one who possesses knowledge of a science but is not actually exercising

knows

it

though not

potentially in a sense,

the science in the

same

knew it potentially before he learnt And when he is in this condition, if some-

some hindrance

thing does not prevent him, he actively exercises his

knowledge: otherwise he would be in knowing. In re-

the contradictory state of not

[5] gard to natural bodies also the case is simiThus what is cold is potentially hot: then

lar.

a change takes place

and

it is fire,

with heavy and

from heavy,

e.g. air

thing that

first

and

actually light,

its

is

burns, it.

So,

generated from water (for water is light: light

[10] the air

it

and hinders

unless something prevents too,

and is

is

potentially light),

and

will at once realize

proper activity as such unless something

prevents

it.

The

activity of lightness consists in

it

does not occupy an upper if what hinders it is

[20] position, whereas,

removed,

it

realizes

to rise higher.

The

its

activity

and continues what is of

process whereby

a certain quality

changes to a condition of

tive existence

similar: thus the exercise of

is

ac-

knowledge follows at once upon the possession it unless something prevents it. So, too, what

of is

of a certain quantity extends itself over a

something prevents it. The thing in a sense is and in a sense is not moved by one who moves what is obstructing and [25] preventing its motion (e.g. one who pulls certain space unless

a pillar from under a roof or one who removes a stone from a wineskin in the water is the accidental cause of motion): and in the same way the real cause of the motion of a ball rebounding from a wall is not the wall but the thrower. So it is clear that in all these cases the

away

[50] thing does not move itself, but it contains within itself the source of motion not of moving something or of causing motion, but of

—

suffering

sense as he it.

256 a

If

it.

then the motion of

all

things that are in

motion is either natural or unnatural and violent, and all things whose motion is violent and unnatural are moved by something, and something other than themselves, and again all things whose motion is natural are moved by something both those that are moved by themselves and those that are not moved by them[^5] selves (e.g. light things and heavy things, 256 a which are moved either by that which brought the thing into existence as such and made it light and heavy, or by that which released what was hindering and preventing it); then all things that are in motion must be

—

moved by something.

the light thing being in a certain situation,

namely high up: when

it is

in the contrary situ-

being prevented from rising. The case is similar also in regard to quantity and quality. But, be it noted, this is the question we are trying to answer how can we account for the motion of light things and heavy things to their proper situations? The reason for it is [75] that they have a natural tendency respectively towards a certain position: and this conation,

it is

—

stitutes the essence of lightness and heaviness, the former being determined by an upward, the latter by a downward, tendency. As we

have said, a thing may be potentially light or heavy in more senses than one. Thus not only when a thing is water is it in a sense potentially light,

but

when

it

it may be still be that through

has become air

potentially light: for

it

may

Now

this may come about in either of two ways. Either the movent is not itself responsible for the motion, which is to be referred

to

something

[5] or the

else

movent

which moves the movent, is itself

responsible for the

motion. Further, in the latter case, either the movent immediately precedes the last thing in the series, or there may be one or more intermediate links: e.g. the stick moves the stone and is moved by the hand, which again is moved by the man: in the man, however, we have reached a movent that is not so in virtue of being moved by something else. Now we say that the thing is moved both by the last and by the first movent in the series, but more

BOOK

256 b

CHAPTERS

VIII,

[10] strictly by the first, since the .first movent moves the last, whereas the last does not move the first, and the first will move the

thing without the

last,

not the stick will not

but the

last will

move it without the first: e.g. move anything unless it is itself moved by

the

then everything that is in motion must be moved by something, and the movent must either itself be moved by something else or not, [75] and in the former case there must be some first movent that is not itself moved by

man.

If

while in the case of the immediof this kind there is no need of an intermediate movent that is also moved (for it is impossible that there should be an infinite series of movents, each of which is

anything ate

else,

movent being

moved by something

else, since in an inno first term) if then everything that is in motion is moved by some[20] thing, and the first movent is moved but itself

—

finite series there is

not by anything

else, it

much

be

moved by

4-5

movent

And

way we

we

result as follows.

motion is an accidental attribute of the movements in question, so that each of them moves something while being itself in motion, but not always because

it

is itself

in motion, or

it

not accidental but an essential attribute. Let us consider the former alternative. If then it is an accidental attribute, it is not necessary that that which is in motion should be in motion: and if this is so it is clear that there may be a time when nothing that exists is in motion, since the accidental is not [10] necessary but contingent. Now if we asis

sume

the existence of a possibility, any con-

we

thereby reach will not be an it may be contrary to But the non-existence of motion is an im-

clusion that

though

impossibility, fact.

somewhere and not be infinite. Thus, if the stick moves something in virtue of being moved by the hand, the hand moves the stick: and if something else moves with the hand, the hand also is moved by something different from itself. So when motion by means of an instrument is at each stage caused by something different from the instrument, this must always be preceded by something else which imparts motion with itself. Therefore, if this last movent is in motion and there 256 b is nothing else that moves it, it must move itself. So this reasoning also shows that, when a thing is moved, if it is not moved immediately by something that moves itself, the

same

[5] If everything that is in motion is moved by something that is in motion, either this being in

possibility:

stop

consider the matter in yet a third

shall get this

This same argument may also be stated in another way as follows. Every movent moves something and moves it with something, either with itself or with something else: e.g. a man moves a thing either himself or with a stick, and a thing is knocked down either by the [25] wind itself or by a stone propelled by the wind. But it is impossible for that with which a thing is moved to move it without being moved by that which imparts motion by its own agency: on the other hand, if a thing imparts motion by its own agency, it is not necessary that there should be anything else with which it imparts motion, whereas if there is a different thing with which it imparts motion, there must be something that imparts motion not with something else but with itself, or else there will be an infinite series. If, then, anything is a movent while being itself moved,

must

to a

of this kind. if

itself.

[50] the series

34 1

some time or other

series brings us at

there

for

we have shown above

1

that

must always be motion.

Moreover, the conclusion to which we have been led is a reasonable one. For there must be three things the moved, the movent, and the [75] instrument of motion. Now the moved must be in motion, but it need not move anything else: the instrument of motion must both move something else and be itself in motion (for it changes together with the moved, with

—

which

it

and continuous,

in contact

is

clear in the

case of things that

move

as

is

other

things locally, in which case the two things

must up to a certain point be in contact): and the movent that is to say, that which causes motion in such a manner that it is not merely the instrument of motion must be unmoved.

—

—

[20] last

Now we

term in

have visual experience of the

this series,

namely that which has

the capacity of being in motion, but does not contain a motive principle, and also of that

which

is

in

motion but

not by anything

else:

is

it is

moved by

itself

and

reasonable, therefore,

not to say necessary, to suppose the existence of the third term also, that which causes motion but is itself unmoved. So, too, Anaxagoras [25] is right when he says that Mind passive and unmixed, since he makes principle of motion: for

it

is

im-

it

the

could cause motion

in this sense only by being itself

unmoved, and

have supreme control only by being unmixed. We will now take the second alternative. If the movent 1 Chapter 1.

is

not accidentally but necessarily

PHYSICS

34 2 in

— so that

motion

if it

were not

would not move anything

in

motion, it movent,

— then the

motion, must be in motion [50] in one of two ways: it is moved either as that is which is moved with the same kind of motion, or with a different kind either that in so far as

it

in

is

—

257 b

exercises that capacity, has as such a capacity for being made healthy, and that which has a capacity for building has as such a capacity for

being

built. It will

have the capacity for being

moved either immediately or through one more links (as it will if, while everything

thus or

which is heating, I mean, is itself in process of becoming hot, that which is making healthy in process of becoming healthy, and that which is

that has a capacity for causing

causing locomotion in process of locomotion, or else that which is making healthy is, let us say, in process of locomotion, and that which is

for suffering

causing locomotion in process of, say, increase. But it is evident that this is impossible. For if we adopt the first assumption we have to make it apply within each of the very lowest species 25 7 a into which motion can be divided: e.g. we must say that if some one is teaching some lesson in geometry, he

is

also in process of be-

ing taught that same lesson in geometry, and if he is throwing he is in process of being

that

such a capacity for being

motion has

as

moved by something

[20] else, the motion that

it has the capacity not that with which it affects what is next to it, but a motion of a different kind; e.g. that which has a capacity for making healthy might as such have a capacity for learn-

is

ing: the series, however, could be traced back,

we

as

we

said before, until at some time or other arrived at the same kind of motion).

the

Now

first

ond

is

alternative

fantastic:

it

is is

and the secabsurd that that which

impossible,

has a capacity for causing alteration should as [25] such necessarily have a capacity, let us say, for increase. It is not necessary, therefore,

same manner. Or if we reassumption we must say that one kind of motion is derived from another; e.g. that that which is causing locomotion is in process

that that

[5] of increase, that which is causing this increase is in process of being altered by some-

in motion will derive its motion either from something that is at rest or from itself. But if there were any need to consider which of the two, that which moves itself or that which is moved by something else, is the cause and principle of motion, every one would decide [jo] for the former: for that which is itself

thrown

in just the

ject this

thing tion

else,

is

and that which

is

causing this altera-

some

in process of suffering

different

kind of motion. But the series must stop somewhere, since the kinds of motion are limited;

and

if

we

say that the process

which

is

reversible,

and

causing alteration is in process of locomotion, we do no more than if we had said at the outset that that which is causing locomotion is in process of locomotion, and [10] that one who is teaching is in process of being taught: for it is clear that everything that that

that

is

moved

is

is

moved by

the

movent

that

is

which is moved should always be moved by something else that is itself moved

by something else: so there will be an end to the series. Consequently the first thing that is

independently a cause is always prior as a cause to that which is so only in virtue of being itself dependent upon something else that makes it

so.

We

must therefore make

a fresh start

and

consider the question; if a thing moves itself, in what sense and in what manner does it do

Now

motion must be

further back in the series as well as by that

so?

which immediately moves it: movent is that which more

infinitely divisible, for it has been shown al257 b ready 1 in our general course on Physics,

But

this

is

strictly

of course impossible: for

the consequence that one process of learning as

in fact the earlier

teaching

who

what he

necessarily

is

is

moves it

teaching

is

volved

that,

since

in

teaching, where-

implies

possessing

knowledge, and learning not possessing Still more unreasonable is the consequence [75]

it.

involves

everything that

moved is moved by something that moved by something else, everything

is

it.

inis

itself

that has

a capacity for causing motion has as such a corresponding capacity for being moved: i.e. it will have a capacity for being moved in the sense in which one might say that everything that has a capacity for making healthy, and

everything that

is

in

that everything that is essentially in motion is continuous. Now it is impossible that that which moves itself should in its entirety move itself: for then, while being specifically one and indivisible, it would as a whole both un-

dergo and cause the same locomotion or alteration: thus it would at the same time be both [5] teaching and being taught (the same thing), or both restoring to and being restored to the same health. Moreover, we have established the fact that it is the movable that is

moved; and

this

is

potentially, not actually, in

motion, but the potential x The reference is apparently

is

in process to actu-

to vi. 4 (234 b 10 sqq.).

258

BOOK

£

VIII,

an incomplete actuality of the movable. The movent on the other hand ality,

is

and motion

is

already in activity: e.g.

it is

which is hot that which pro-

that

that produces heat: in fact,

duces the form [10] sesses

move

it.

itself as

is always something that posConsequently (if a thing can a whole), the same thing in re-

same thing may be at the same time both hot and not hot. So, too, in every other case where the movent must be described spect of the

by the same name in the same sense as the moved. Therefore when a thing moves itself it is one part of it that is the movent and another part that is moved. But it is not self-moving in the sense that each of the two parts is moved by the other part: the following considerations [75]

make

this evident. In the first place,

it

each of the two parts is to move the other, there will be no first movent. If a thing is moved by a series of movents, that which is earlier in the series is more the cause of its being

which comes next, and will movent: for we found that there are two kinds of movent, that which is itself moved by something else and that which derives its motion from itself: and that which is further from the thing that is moved is nearer to the principle of motion than that [20] which is intermediate. In the second place, there is no necessity for the movent part

moved than be

more

to be

that

truly the

moved by anything but

itself:

so

it

can

only be accidentally that the other part moves it in return. I take then the possible case of its not moving it: then there will be a part that is

an unmoved movent. no necessity for the movent to be moved in return: on the contrary the necessity that there should always be motion makes it necessary that there should be

moved and

a part that

is

In the third place, there

some movent [25] by

that

itself.

is

is

either

unmoved or moved we should

In the fourth place

then have a thing undergoing the same motion it is causing that which is producing heat, therefore, being heated. But as a matter of fact that which primarily moves itself cannot contain either a single part that moves itself or a number of parts each of which moves itself. For, if the whole is moved by itself, it must be moved either by some part of itself or [50] as a whole by itself as a whole. If, then, it is moved in virtue of some part of it being moved by that part itself, it is this part that will be the primary self-movent, since, if this part is separated from the whole, the part will still move itself, but the whole will do so no longer. If on the other hand the whole is moved that

—

CHAPTER by

5

343

must be accidentally move themselves: and therefore,

as a whole,

itself

that the parts

it

their self-motion not being necessary,

258 a take the

we may moved

case of their not being

by themselves. Therefore in the whole of the thing we may distinguish that which imparts motion without itself being moved and that which is moved: for only in this way is it possible for a thing to be self-moved. Further, if

moves itself we may distinguish in it which imparts the motion and that which moved: so while we say that AB is moved by

the whole that is

itself,

[5]

And

we may

also say that

it is

moved by

which imparts motion may be either a thing that is moved by something else or a thing that is unmoved, and that which A.

is

since that

moved may

motion

be either a thing that imparts

something else or a thing that does not, that which moves itself must be composed of something that is unmoved but imparts motion and also of something that is moved but does not necessarily impart motion but may or may not do so. Thus let A be something that imparts motion but is unmoved, B something that is moved by A and moves T, T some[10] thing that is moved by B but moves nothto

ing (granted that we eventually arrive at T take it that there is only one inter-

we may

mediate term, though there

Then

ABT

the whole

may

moves

be more).

But if I imparting motion and B being moved, whereas T will not move itself or in fact be moved at all. Nor [75] again will BT move itself apart from A: for B imparts motion only through being moved by something else, not through being moved by any part of itself. So only AB moves take

away

itself.

T,

AB

will

move

That which moves

itself.

itself,

itself,

A

therefore,

must

comprise something that imparts motion but is unmoved and something that is moved but [20] does not necessarily move anything else: and each of these two things, or at any rate one of them, must be in contact with the other. If, then, that which imparts motion is a continuous substance that which is moved must of course be so it is clear that it is not through some part of the whole being of such a nature

—

—

moving itself that the whole moves itself as a whole, both being moved and imparting motion through [25] containing a part that imparts motion and a part that is moved. It does not impart motion as a whole nor is it moved as a whole: it is A alone that imparts motion and B alone that is moved. It is not true, further, that T is moved by A, which is impossible. as to be capable of

moves

itself:

it

PHYSICS

344

Here a difficulty arises: if something is taken away from A (supposing that that which imparts motion but is unmoved is a continuous substance), or from B the part that is moved, will the remainder of A continue to impart mo[30] tion or the remainder of B continue to be moved? If so, it will not be AB primarily that is moved by itself, since, when something is taken away from AB, the remainder of AB will still continue to move itself. Perhaps we 258 b may state the case thus: there is nothing to prevent each of the two parts, or at any rate one of them, that which is moved, being divisible is

though actually undivided,

divided

of the

it

so that

if it

capacity:

ity of

is

evident

which primarily imparts motion is unmoved: for, whether the series is closed at once by that which is in motion but moved by something else deriving its motion directly from the first unmoved, or whether the motion is derived from what is in motion but moves itself and stops its own motion, on both supthe result that in

things being in motion that

imparts motion

is

all

cases of

which primarily

unmoved.

[10] Since there must always be motion without intermission, there must necessarily be something, one thing or it may be a plurality, that first imparts motion, and this first movent must be unmoved. Now the question whether each of the things that are unmoved but impart motion is eternal is irrelevant to our present argument: but the following considerations will make it clear that there must necessarily be some such thing, which, while it has the capacof moving something moved and exempt from

is itself unchange, which [75] can affect it neither in an unqualified nor in an accidental sense. Let us suppose, if any one likes, that in the case of certain things it is possible for them at different times to be and not to be, without any process of becoming and perishing (in fact it would seem to be necessary, if a thing that has not parts at one time is and at another time is not, that any such thing should without undergoing any process of change at one time be and at another time [20] not be). And let us further suppose it

ity

possible that

some

else,

all

principles that are

clearly be

move themselves

certain particular things, while others

other things.

The

eternity

and continu-

the process cannot be caused either by

any one of them singly or by the sum of them, is

[5] that that

we have

something that causes at one time to be and at another not to be. For, since nothing that has not parts can be in motion, that which [25] moves itself must as a whole have magnitude, though nothing that we have said makes this necessarily true of every movent. So the fact that some things become and others perish, and that this is so continuously, cannot be caused by any one of those things that, though they are unmoved, do not always exist: nor again can it be caused by any of those which things that

residing primarily in

so there

things that are potentially divisible. From what has been said, then, it

positions

must

there

move move

and

to prevent self-motion

are and at another time are not. Even so, this cannot be true of all such principles, since

nothing

will not continue in the possession

same

259*

unmoved

but capable of imparting motion at one time

must be eterand necessary, whereas the sum of these movents is infinite and they do not all exist together. It is clear, then, that though there [jo] because this causal relation

nal

may

be countless instances of the perishing of

259 a some

principles that are unmoved but impart motion, and though many things that move themselves perish and are succeeded by others that come into being, and though one thing that is unmoved moves one thing while another moves another, nevertheless there is something that comprehends them all, and that as something apart from each one of them, and this

it is

that

is

some

the cause of the fact that

things are and others are not and of the con[5] tinuous process of change: and this causes the motion of the other movents, while they are the causes of the

motion of other things.

Motion, then, being eternal, the first movent, if there is but one, will be eternal also: if there are more than one, there will be a plurality of such eternal movents. We ought, however, to suppose that there is one rather than many, and a finite rather than an infinite number. When the consequences of either assumption are the same, we should always assume that things are finite rather than infinite in number, since [10] in things constituted by nature that which is finite and that which is better ought, if possible, to be present rather than the reverse: and here it is sufficient to assume only one movent, the first of unmoved things, which being eternal will be the principle of motion to everything else. The following argument also makes it evident that the first movent must be something that is one and eternal. We have shown that Chapter 1. 1

260

BOOK

a

VIII,

CHAPTERS

must always be motion. That being so, motion must also be continuous, because what is always is continuous, whereas what is merely in succession is not continuous. But further, if motion is continuous, it is one: and it is one only if the movent and the moved that constitute it are each of them one, since in the [75] there

event of a thing's being moved now by one thing and now by another the whole motion will not be continuous but successive. [20] Moreover a conviction that there is a first unmoved something may be reached not only from the foregoing arguments, but also by considering again the principles operative in movit is evident that among existing

ents.

Now

things there are

some

that are sometimes in

motion and sometimes served above to make it 1

at rest.

This

clear that

it is

fact has

not true

things are in motion or that all things are at rest or that some things are al[25] ways at rest and the remainder always in

either that

all

5-6

345

connected with other natural motions in animals, which they do not experience through their

own

[10]

crease,

instrumentality, e.g. increase, de-

and

respiration:

these

are

ex-

perienced by every animal while it is at rest and not in motion in respect of the motion set up by its own agency: here the motion is caused by the atmosphere and by many things that enter into the animal: thus in some cases the cause is nourishment: when it is being digested animals sleep, and when it is being distributed

through the system they awake and move first principle of this motion being thus originally derived from outside. Therefore animals are not always in continuous motion by their own agency: it is some[75] thing else that moves them, itself being in motion and changing as it comes into relation with each several thing that moves itself. (Moreover in all these self-moving things the themselves, the

we wish

to explain

movent and cause of their self-motion is moved by itself, though in an accidental sense: that is to say, the body changes its place, so that that which is in the body changes its place also and is a self-movent through its [20] exercise of leverage.) Hence we may con-

also the nature of each of the other

two kinds

fidently conclude that

motion: on

this

matter proof

is

supplied by

things that fluctuate between the two and have the capacity of being sometimes in motion and sometimes at rest. The existence of things of this

kind

is

clear to all: but

some things that are always unmoved and some things that are always in motion. In the course of our argument [jo] directed to this end we established the and show

that there are

fact that everything that is in motion is moved by something, and that the movent is either unmoved or in motion, and that, if it is in motion, it is moved either by itself or by something else and so on throughout the series: and so we proceeded to the position that the first

first

itself

selves

should cause continuous motion. So the neshould be motion continuously requires that there should be a first movent that is unmoved even accidentally, if, as we 2 [25] have said, there is to be in the world of things an unceasing and undying motion, and

cessity that there

the world

is

motion to be moved is that which moves itself, and the first principle of the whole series is 259 b the unmoved. Further it is evident from

the

first

1

Chapter

3.

remain permanently

self-conif

the

permanent, the universe must also be permanent, since it is continuous with principle

have the characteristic of moving themselves, animal kingdom and the whole class of living things. This being so, then, the view was suggested that perhaps it may be possible for motion to come to be in a thing without having been in existence at all before, because we [5] see this actually occurring in animals: they are unmoved at one time and then again they are in motion, as it seems. We must grasp the fact, therefore, that animals move themselves only with one kind of motion, and that this is not strictly originated by them. The cause of it is not derived from the animal itself: it is

to

tained and within the same limits: for first

e.g. the

a thing belongs to the

it

principle that directly causes things that are in

actual observation that there are things that

if

unmoved movents that are also themmoved accidentally, it is impossible that

class of

is

principle.

(We must

distinguish,

however, between accidental motion of a thing by itself and such motion by something else, the former being confined to perishable things, whereas the latter belongs also to certain first principles of heavenly bodies, of all those, that [jo] is to say, that experience more than one locomotion.)

And 260*

further,

if

there

this nature, a

is

always something of that is itself un-

movent

moved and eternal, then that which moved by it must be eternal. Indeed

is

first

this is

from the consideration that there would otherwise be no becoming and perishing and no change of any kind in other things, which require something that is in motion to clear also

2

Chapter

1.

260 b

PHYSICS

34 6

move them: for the motion imparted by the unmoved will always be imparted in the same way and be one and the same, since the unmoved does not itself change in relation to [5] that which is moved by it. But that which is moved by something that, though it is in motion, is moved directly by the unmoved stands in varying relations to the things that it moves, so that the motion that it causes will not be always the same: by reason of the fact

thus

itself:

ment

it

is

said that contrary

to contrary: but

growth

by things becoming like to

is

is

nourish-

effected only

There must be is this change contrary. But the fact like.

alteration, then, in that there

260 b from contrary that a thing

is

to

altered requires that there should

be something that alters

makes so

it is

it,

something

e.g. that

the potentially hot into the actually hot: plain that the movent does not maintain

as has been said, since it remains permanently simple and unvarying and in the same state, will cause motion that is one and

uniform relation to it but is at one time nearer to and at another farther from that [5] which is altered: and we cannot have this without locomotion. If, therefore, there must always be motion, there must also always be locomotion as the primary motion, and, if there is a primary as distinguished from a secondary form of locomotion, it must be the primary form. Again, all affections have their origin in condensation and rarefaction: thus [10] heavy and light, soft and hard, hot and cold, are considered to be forms of density and rarity. But condensation and rarefaction are nothing more than combination and separation, processes in accordance with which substances are said to become and perish: and in being combined and separated things must change in respect of place. And further, when a thing is increased or decreased its magnitude changes in respect of place. [75] Again, there is another point of view from which it will be clearly seen that locomo-

simple.

tion

that it occupies contrary positions or assumes contrary forms at different times it will pro[10] duce contrary motions in each several thing that it moves and will cause it to be at

another time in motion. then, has served to clear up the point about which we raised a

one time

at rest

and

at

The foregoing argument,

difficulty at the outset

1

—why

that instead

is it

things being either in motion or at

of

all

or

some things being always

rest,

motion and the

in

remainder always at rest, there are things that are sometimes in motion and sometimes not?

The

cause of this

is

now

while some things are

unmoved movent and

plain:

because,

is

it

moved by an

eternal

are therefore always in

[75] motion, other things are moved by a movent that is in motion and changing, so that they too must change. But the unmoved movent,

a

is

primary. As in the case of other things

so too in the case of

may [20] This matter will be made clearer, however, if we start afresh from another point.

We

must consider whether

not possible that there should be a continuous motion, and, if it is

possible,

which

it is

this

is

motion

the primary motion: for

is

or

it is

is,

and which

plain that

if

must always be motion, and a particular motion is primary and continuous, then it is [25] this motion that is imparted by the first movent, and so it is necessarily one and the same and continuous and primary. Now of the three kinds of motion that there are motion in respect of magnitude, motion in respect of affection, and motion in respect of place it is this last, which we call locomotion, that must be primary. This may be shown as there

— —

follows.

It is

impossible that there should be

[jo] increase without the previous occurrence of alteration: for that

though itself, is 1

in a sense

it is

which

3.

what

by what

is

A

thing

is

said

when, if it does not exist, the others will not exist, whereas it can exist without the others: and there is also priority in time and priority in perfection of exto be prior to other things

Let us begin, then, with the first sense. be motion continuously, and there may be continuously either continuous motion or successive motion, the former, however, in a higher degree than the latter: moreover it is better that it should be continuous rather than successive motion, and we always assume the presence in nature of the better, if it be possible: since, then, continuous 2 motion is possible (this will be proved later: istence.

[20]

Now there must

for the present let us take

it

for granted),

and

[25] no other motion can be continuous except locomotion, locomotion must be primary. For there

is

no

necessity for the subject of locomo-

like

tion to be the subject either of increase or of alteration, nor need it become or perish: on the

unlike

other hand there cannot be any one of these

increased,

increased by

in a sense increased

Chapter

is

motion the word 'primary'

be used in several senses.

is

al-

2

Chapter

8.

BOOK

261 b

VIII,

CHAPTERS

fr-7

347

when

a thing

processes without the existence of the continu-

in quantity

ous motion imparted by the first movent. Secondly, locomotion must be primary in time: for this is the only motion possible for [jo] eternal things. It is true indeed that, in the case of any individual thing that has a becoming, locomotion must be the last of its motions: for after its becoming it first experiences alteration and increase, and locomotion is a motion that belongs to such things only when they 261 a are perfected. But there must previously be something else that is in process of locomo-

creased.

Above

motion

in respect of place,

tion to be the cause even of the becoming of things that become, without itself being in process of becoming, as e.g. the begotten is pre-

ceded by what begot it: otherwise becoming might be thought to be the primary motion on the ground that the thing must first become. [5] But though this is so in the case of any individual thing that becomes, nevertheless before anything becomes, something else must be in motion, not itself becoming but being, and before this there must again be something else. And since becoming cannot be primary for, if it were, everything that is in motion would it is plain that no one of the mobe perishable tions next in order can be prior to locomotion. [10] By the motions next in order I mean increase and then alteration, decrease, and perishing. All these are posterior to becoming: consequently, if not even becoming is prior to locomotion, then no one of the other processes of change is so either.

—

—

Thirdly, that which is in process of becoming appears universally as something imperfect and proceeding to a first principle: and so what is posterior in the order of becoming is prior in the order of nature. Now all things that go through the process of becoming acquire locomotion last. It is this that accounts for the fact

some

strictest sense itself;

[25]

all it is

is

increased or de-

plain that this motion, is

what

in the

is

produced by that which moves

but

the self-movent that

it is

we

de-

clare to be the first principle of things that are

moved and impart motion and

the primary

source to which things that are in motion are to be referred. It is clear, then, from the foregoing arguments that locomotion is the primary motion. We have now to show which kind of locomotion is primary. The same process of reasoning will also make clear at the same time the truth of the assumption we have made both now and 1

[jo] at a previous stage that

it is

possible that

continuous and eternal. Now it is clear from the following considerations that no other than locomotion can be continuous. Every other motion and change is from an opposite to an opposite: thus for the processes of becoming and perishing the limits there should be a motion that

are the existent

is

and the non-existent,

for alter-

ation the various pairs of contrary affections,

[55] and for increase and decrease either greatness and smallness or perfection and imperfection of

magnitude: and changes

to the respec-

tive contraries are contrary changes. 261 b thing that

Now

a

undergoing any particular kind of motion, but though previously existent has not always undergone it, must previously have been at rest so far as that motion is concerned. It is clear, then, that for the changing is

thing the contraries will be states of

we have

rest.

And

a similar result in the case of changes

becoming and perishwhether regarded simply as such without qualification or as affecting something in parthat are not motions: for ing,

[5] ticular, are opposites: therefore provided it impossible for a thing to undergo opposite

is

many

at the same time, the change will not be continuous, but a period of time will inter-

prior to

vene between the opposite processes. The question whether these contradictory changes are contraries or not makes no difference, provided only it is impossible for them both to be present to the same thing at the same time: the point is of no importance to the argument. Nor [10] does it matter if the thing need not rest in

[75] that

living things, e.g. plants

and

kinds of animals, owing to lack of the requisite organ, are entirely without motion, whereas others acquire it in the course of their being perfected. Therefore, if the degree in which things possess locomotion corresponds to the degree in which they have realized their natural development, then this motion must be all

others in respect of perfection of ex-

[20] istence:

and not only

also because a thing that

is

for this reason but in

motion

loses

its

changes

the contradictory state, or

essential character less in the process of

may

tion than in

and that perishing

locomoany other kind of motion: it is the only motion that does not involve a change of being in the sense in which there is a change in quality when a thing is altered and a change

if

there

is

rest as a contrary to the process of

be true that the non-existent is

1

it is 11

253 29.

state of

change: it not at rest,

a process to the non-exist-

ent. All that matters

time:

is

no

is

the intervention of a

this that prevents the

change from

PHYSICS

34«

being continuous: so, too, in our previous instances the important thing was not the relation of contrariety but the impossibility of the two processes being present to a thing at the [75] same time. And there is no need to be disturbed by the fact that on this showing there may be more than one contrary to the same thing, that a particular motion will be contrary both to rest and to motion in the contrary direction. We have only to grasp the fact that a particular motion is in a sense the opposite both of a state of rest and of the contrary motion, in the same way as that which is of equal or standard measure is the opposite both of that which it and of that which it surpasses, and [20] that it is impossible for the opposite motions or changes to be present to a thing at the same time. Furthermore, in the case of becom-

surpasses

ing and perishing it would seem to be an utterabsurd thing if as soon as anything has become it must necessarily perish and cannot conly

tinue to exist for any time: and, if this is true of becoming and perishing, we have fair grounds [25] for inferring the same to be true of the other kinds of change, since it would be in the

natural order of things that they should be uni-

form

in this respect.

form or magnitude): and contraries are specifically not one and the same but distinct: and within the sphere of place we have the above-mentioned distinctions. Moreover we have an indication that motion from A to B is the contrary of motion from B to A in the fact that, if they occur at the same time, they arrest and stop either place or affection or essential [5]

a circle: the

sarily implies

now

rotatory or rectilinear or a

compound

of the

two: consequently, if one of the former two is not continuous, that which is composed of [jo] them both cannot be continuous either. Now it is plain that if the locomotion of a thing is rectilinear and finite it is not continuous locomotion: for the thing must turn back, and that which turns back in a straight line undergoes two contrary locomotions, since, so far as motion in respect of place is concerned, upward motion is the contrary of downward motion, forward motion of backward motion, and mo-

^^

of motion to the right, [35] ti on t0 tne these being the pairs of contraries in the sphere

262 a

of place. But

we have

and continuous motion

already

1

defined

motion of a and operating within a sphere admitting of no further specific differentiation (for we have three things to consider, first that which is in motion, single

to be

single thing in a single period of time

man

e.g. a iv.

4

.

coming to

a straight line that

it is

a stand, not only

is

or a god, secondly the 'when' of the

when

traversed, but also in

[75] the case of locomotion in a circle (which not the same thing as rotatory locomotion:

is

when

for,

may

a thing merely traverses a circle,

it

course without a break or turn back again when it has reached either proceed

on

its

same point from which

it

started).

We may

assure ourselves of the necessity of this

proceed to maintain that it is possible that there should be an infinite motion that is single and continuous, and that this motion is rotatory motion. The motion of everything that is in process of locomotion is either

Let us

And

the same is true in the case of motion from A towards B is the contrary of the motion from A towards T: for [10] even if they are continuous and there is no turning back they arrest each other, because contraries annihilate or obstruct one another. On the other hand lateral motion is not the contrary of upward motion. But what shows most clearly that rectilinear motion cannot be continuous is the fact that turning back neces-

each other.

the 8

262*

motion, that is to say, the time, and thirdly the sphere within which it operates, which may be

to a stand not only tion,

but also on theoretical grounds.

start as follows:

point,

coming

on the strength of observa-

we have

We

may

three points, starting-

middle-point, and finishing-point,

of

[20 J which the middle-point in virtue of the relations in which it stands severally to the other

two is both a starting-point and a finishing-point, and though numerically one is theoretically two.

We

have further the distinction between the and the actual. So in the straight line in question any one of the points lying between the two extremes is potentially a middle-point: but it is not actually so unless that which is in motion divides the line by coming to a stand at that point and beginning its motion again: thus [25] the middle-point becomes both a startingpotential

point and a goal, the starting-point of the latter part and the finishing-point of the first part of in the the motion. This is the case e.g. when

A

locomotion comes to a stand at B and starts again towards V: but when its motion is continuous A cannot either have come to be or have ceased to be at the point B: it can [jo] only have been there at the moment of passing, its passage not being contained within any period of time except the whole of which course of

its

the particular

moment

is

a dividing-point.

To

263

BOOK

s

CHAPTERS

VIII,

has come to be and ceased to be there will involve the consequence that A in the course of its locomotion will always be coming to a stand: for it is impossible that 262 b should simultaneously have come to be at B and ceased to be there, so that the two things

maintain that

it

A

must have happened at different points of time, and therefore there will be the intervening period of time: consequently

A

will be in a state

and similarly at all other points, since the same reasoning holds good in every [5] case. When to A, that which is in process of

of rest at B,

locomotion, B, the middle-point, serves both as

and as a starting-point for its must come to a stand at B, because two just as one might do in thought.

a finishing-point

motion,

A

makes it However, the point A is the real starting-point at which the moving body has ceased to be, and it

it is

at

T

that

it

has really

come

when

to be

its

and it comes to a stand. So this is how we must meet the difficulty that [10] then arises, which is as follows. Suppose

course

finished

is

A

prothe line E is equal to the line Z, that ceeds in continuous locomotion from the extreme point of E to T, and that, at the moment

when

A

is

at the point B,

A

is

proceeding in

uniform locomotion and with the same velocity as A from the extremity of Z to H: then, says before A the argument, A will have reached has reached T: for that which makes an earlier start and departure must make an earlier ar-

H

7-8

neously be there

we cannot argue

should come to a stand there. Therefore we must not hold that there was a moment when A came to be at B and that at the it

same moment A was in motion from the extremity of Z: for the fact of A's having come to [20] be at B will involve the fact of its also ceasing to be there, and the two events will not

A

at a sectional

Now

it

stands in these same two respective relations

263 a

to the

two motions. Therefore

which

that

turns back in traversing a rectilinear course

must ly

in so

doing come to a stand. Consequent-

there cannot be a continuous rectilinear

tion that

is

The same method should replying to those [5] Zeno's

mo-

eternal.

who

also be

adopted in

ask, in the terms of

argument, whether we admit that

before any distance can be traversed half the distance

must be

traversed, that these half-dis-

tances are infinite in

number, and that

it is

im-

num-

possible to traverse distances infinite in

—

or some on the lines of this same argument put the questions in another form, and would have us grant that in the time during which a motion is in progress it should be possible to reckon a half-motion before the whole for

ber

we

every half-distance that

which

sary that

A

one is actual, and regarded from below it is a finishing-point, while regarded from above it is a starting-point, so that

first

will not

at

potential: but this

we

it

will be neces-

is

is

ber,

it

H

[30] necessarily one that is actually, not pothe point in the middle

tentially, existent.

be and ceased to be at B: otherwise

happen

that

point of time and has not come to be or ceased to be there. For here the goal that is reached is

the result that

arrive later: for this to

it

moment. And here we cannot apply the argument used to solve the difficulty stated above:

[75] rival: the reason, then, for the late arrival is that it has not simultaneously come to of

A

349

would simultaand not be there at the same

taneously, for in that case

[10] ersed

when

get, so that

we have reckoned an is

we have

the whole distance

is

trav-

numNow when

infinite

admittedly impossible.

discussed the question of motion

we

1

put forward a solution of this difficulty turning on the fact that the period of time occupied in traversing the distance contains within itself an infinite number of units: there is no absurdity, we said, in supposing the traversing of in-

and the elepresent in the time no less

finite distances in infinite time,

ment

of infinity

is

be simultaneous, whereas the truth is that is at B at a sectional point of time and does not occupy time there. In this case, therefore, where

[75] than in the distance. But, although this so lution is adequate as a reply to the questioner

the motion of a thing

ble in a finite time to traverse or reckon

sible to use this

er

hand

in

its

is

continuous,

form of expression.

it is

On

impos-

the oth-

in the case of a thing that turns

course

we must do

so.

For suppose

back

H in

its locomotion proceeds to A and then turns back and proceeds downwards again: then the extreme point A has served as

the course of

finishing-point

and

as starting-point for

point thus serving as two: therefore [25] have

come

come

to be at

A

to a stand there:

it

it,

H

one

must

cannot have

and departed from

A

simul-

(the question asked being whether finite

number

it is

of units), nevertheless as

possi-

an an

in-

ac-

count of the fact and explanation of its true nature it is inadequate. For suppose the distance to be left out of account and the question asked to be no longer whether it is possible in a finite [20] time to traverse an infinite number of distances, and suppose that the inquiry is made to refer to the time taken by itself (for the time contains an infinite number of divisions): then Wt, 2 (233* 21 sqq.), and

vi. 9.

PHYSICS

350

no longer be adequate, and apply the truth that we enunciated in

264 a white in the whole of A, but must say that

this solution will

it is

we must

so in all of it except the last moment T. T belongs already to the later period, and if in the whole of A not-white was in process of becoming and white of perishing, at T the process is complete. And so T is the first moment at which it is true to call the thing white or notwhite respectively. Otherwise a thing may be non-existent at the moment when it has become and existent at the moment when it has perished: or else it must be possible for a thing at [25] the same time to be white and not white and in fact to be existent and non-existent. Fur-

our recent discussion, stating it in the following way. In the act of dividing the continuous distance into two halves one point is treated as two, since

we make

it

a starting-point

same

and a

finishing-point:

and

lyl duced by

the act of reckoning halves as

this

result

is

also pro-

well as by the act of dividing into halves. But if divisions are made in this way, neither the dis-

tance nor the motion will be continuous: for to be continuous must relate to continuous: and though what is continuous contains an infinite number of halves, they are not actual but potential halves. If the halves are made actual, we shall get not a continuous but an intermittent motion. In the case

motion

what

if it is

is

[50] of reckoning the halves,

it is

clear that this

result follows: for then one point must be reck263 b oned as two: it will be the finishing-point

and the starting-point of the not the one continuous whole but the two halves. Therefore to the question whether it is possible to pass through an infinite number of units either of time or of distance we must reply that in a sense it is and of the one half other,

if

we reckon

in a sense

it is

not. If the units are actual,

[5] not possible: sible.

For

if

they are potential,

in the course of a

it is

it is

pos-

continuous motion

the traveller has traversed an infinite

number

an accidental sense but not in an unqualified sense: for though it is an accidental characteristic of the distance to be an infinite number of half-distances, this is not its real and of units in

essential character. It

[10]

we hold from

is

also plain that unless

that the point of time that divides

always belongs only to the is concerned, we shall be involved in the consequence that the same thing is at the same moment existent and not existent, and that a thing is not existent at the moment when it has become. It is true that the point is common to both times, the earlier as well as the later, and that, while numerically one and the same, it is theoretically not so, being the finishing-point of the one and the starting-point of the other: but so far as the thing is concerned it belongs to the later stage of what [75] happens to it. Let us suppose a time ABr and a thing A, A being white in the time A and not-white in the time B. Then A is at the moment T white and not-white: for if we were right in saying that it is white during the whole time A, it is true to call it white at any moment of A, and not-white in B, and T is in both A [20] and B. We must not allow, therefore, that

earlier

later

later so far as the

thing

it is

ther,

if

anything that

exists after

having been

previously non-existent must become existent

and does not exist when it is becoming, time cannot be divisible into time-atoms. For suppose that A was becoming white in the time A and that at another time B, a time-atom consecutive with the last atom of A, A has already become white and so is white at that moment: [jo] then, inasmuch as in the time A it was becoming white and so was not white and at the moment B it is white, there must have been a becoming between A and B and therefore also a time in which the becoming took 264 a place. On the other hand, those who deny atoms of time (as we do) are not affected by this argument: according to them A has become and so is white at the last point of the actual time in which it was becoming white: and this point has no other point consecutive with or in succession to it, whereas time-atoms are conceived as successive. Moreover it is clear that if A was becoming white in the whole [5] time A, the time occupied by it in having become white in addition to having been in process of becoming white is no more than all that it occupied in the mere process of becoming white. These and

arguments from the fact that they have a special bearing on the point at issue. If we look at the question from the point of view of general theory, the same such-like, then, are the

for our conclusion that derive cogency

would also appear to be indicated by the following arguments. Everything whose motion is continuous must, on arriving at any [10] point in the course of its locomotion, have been previously also in process of locomotion to that point, if it is not forced out of its path by anything: e.g. on arriving at B a thing must also have been in process of locomotion to B, and that not merely when it was near to B, but result

from the moment of its starting on its course, since there can be no reason for its being so at

264 b

BOOK

any particular stage rather than

at

an

VIII,

earlier

one. So, too, in the case of the other kinds of we are to suppose that a thing motion.

Now

proceeds in locomotion from

A to V and that at

[75] the moment of its arrival at T the continuity of its motion is unbroken and will remain it has arrived back at A. Then when it undergoing locomotion from A to T it is at the same time undergoing also its locomotion to A from V: consequently it is simultaneously undergoing two contrary motions, since the two motions that follow the same straight line

so until

is

are contrary to each other. With this consequence there also follows another: we have a

thing that

in process of

is

change from a

posi-

has not yet been: so, inasmuch impossible, the thing must come to a

tion in

which

as this

is

it

[20] stand at T. Therefore the motion is not a single motion, since motion that is interrupted

by stationariness is not single. Further, the following argument will serve better to

make

this point clear universally in

respect of every kind of motion. If the

motion

undergone by that which is in motion is always one of those already enumerated, and the state of rest that it undergoes is one of those that are the opposites of the motions (for we found that there could be no other besides these), and moreover that which is undergoing but does not always undergo a particular motion (by [25] this I mean one of the various specifically 1

some particular part of the whole motion) must have been previously un-

distinct motions, not

dergoing the state of rest that is the opposite of the motion, the state of rest being privation of motion; then, inasmuch as the two motions that follow the

motions, and

same

it is

straight line are contrary

impossible for a thing to un-

dergo simultaneously two contrary motions, that which is undergoing locomotion from A [jo] to T cannot also simultaneously be undergoing locomotion from T to A: and since the latter locomotion is not simultaneous with the former but is still to be undergone, before it is undergone there must occur a state of rest at T: for this, as we found, 2 is the state of rest that is the opposite of the motion from T. The foregoing argument, then, makes it plain that the motion in question is not continuous.

264b Our next argument has

a

more

special

bearing than the foregoing on the point at issue. will suppose that there has occurred in something simultaneously a perishing of not-white and a becoming of white. Then if the

We

alteration to white 1

v. 2,

2

v.

and from white

6 (229b 28 sqq.)

is

a continu-

CHAPTER

35i

8

ous process and the white does not remain any [5] time, there must have occurred simultaneously a perishing of not-white, a becoming of white, and a becoming of not-white: for the time of the three will be the same. Again, from the continuity of the time in which the motion takes place we cannot infer continuity in the motion, but only successiveness: in fact, how could contraries, e.g. whiteness

and blackness, meet

in the

same extreme

point?

On

the other hand, in motion on a circular

we shall find singleness and continuity: for here we are met by no impossible consequence:

line

which is in motion from A will in same direction of energy be simultaneously in motion to A (since it is in motion to the point at which it will finally arrive), and yet will not be undergoing two contrary or opposite motions: for a motion to a point and a motion from that point are not always contra[10] that

virtue of the

ries or opposites: they are contraries only if they are on the same straight line (for then

[75] they are contrary to one another in respect of place, as e.g. the two motions along the

diameter of the

circle, since

the ends of this are

from one anand they are opposites only if they are along the same line. Therefore in the case we at the greatest possible distance

other),

now considering there is nothing to prevent the motion being continuous and free from all intermission: for rotatory motion is moare

tion of a thing

from

its

its place, wheremotion from its

place to

[20] as rectilinear motion place to another place.

is

Moreover the progress of rotatory motion never localized within certain

fixed

is

limits,

whereas that of rectilinear motion repeatedly is so. Now a motion that is always shifting its ground from moment to moment can be continuous: but a motion that is repeatedly localized within certain fixed limits cannot be so, since then the same thing would have to undergo simultaneously two opposite motions. So, too, there cannot be continuous motion in a [25] semicircle or in any other arc of a circle, since here also the

same ground must be travtwo contrary processes of

ersed repeatedly and

change must occur. The reason is that in these motions the starting-point and the termination do not coincide, whereas in motion over a circle they do coincide, and so this is the only perfect motion. This differentiation also provides another means of showing that the other kinds of motion cannot be continuous either: for in all of

265 b

PHYSICS

352

[jo] them we find that there is the same ground to be traversed repeatedly; thus in alteration there are the intermediate stages of the and in quantitative change there are

process,

the intervening degrees of magnitude: and in becoming and perishing the same thing is true. It makes no difference whether we take the intermediate stages of the process to be few or many, or whether we add or subtract one: for 265 a in either case we find that there is still the same ground to be traversed repeatedly. Moreover it is plain from what has been said that

those physicists

who

assert that all

sensible

things are always in motion are wrong: for their motion must be one or other of the mo[5] tions just mentioned: in fact they mostly conceive it as alteration (things are always in flux

and decay, they say), and they go so far as even of becoming and perishing as a

to speak

On

the other hand, our

argument has enabled us

to assert the fact, ap-

process of alteration.

plying universally to all motions, that no motion admits of continuity except rotatory motion: consequently neither alteration nor inneed now [10] crease admits of continuity. say no more in support of the position that there is no process of change that admits of infinity or continuity except rotatory locomotion.

We

whether locomotion or motion of any other kind, can be so, since in all of them rest must occur and with the occurrence of rest the motion has perished. Moreover the result at which we have arrived, that rotatory motion is single and continuous, and rectilinear motion is not, is a reasonable one. In rectilinear motion we have a definite starting-point, finishing-point, [jo] and middle-point, which all have their place in

finish

its

limits of

we

said before,

1

is

either rotatory or rectilinear

compound

of the two: and the two former must be prior to the last, since they are the elements of which the latter consists. Moreover rotatory locomotion is prior to rectilinear

[75] or a

locomotion, because it which may be

plete,

more simple and comshown as follows. The

is

motion canno such thing as an

straight line traversed in rectilinear

not be infinite: for there

is

infinite straight line; and even if there were, it would not be traversed by anything in motion: for the impossible does not happen and it is im-

[20] possible to traverse an infinite distance. rectilinear motion on a finite

On the other hand

turns back a composite motwo motions, while if it does not turn back it is incomplete and perishable: and in the order of nature, of definition, and of straight line

is if it

tion, in fact

time alike the complete is prior to the incomplete and the imperishable to the perishable. Again, a motion that admits of being eternal is [25] prior to one that does not. Now rotatory motion can be eternal: but no other motion, Chapter 8 (26

b 28).

that there

is

a point

when anything is at the whether at the startingthe finishing-point, it must be in a course,

its

state of rest).

On

the other

hand

in circular

motion there are no such definite points: for why should any one point on the line be a limit rather than any other? Any one point as much as any other is alike starting-point, middlepoint, and finishing-point, so that we can say of certain things both that they are always and that they never are at a starting-point and at a 265 b finishing-point (so that a revolving sphere, while at rest, for

place).

The

it

in motion,

it is

is

also in a sense

continues to occupy the same

reason of this

is

that in this case

all

these characteristics belong to the centre: that is

can now be shown plainly that rotation is the primary locomotion. Every locomotion, as

way

course (for

point or at

to say, the centre

dle-point, It

in such a

it

from which that which is in motion can be said to start and a point at which it can be said to

is

alike starting-point, mid-

and finishing-point of the space

trav-

not a [5] point on the circular line, there is no point at which that which is in process of locomotion ersed; consequently since this point

is

having traversed its locomotion it is proceeding always about a central point and not to an extreme point: therefore it remains still, and the whole is in a sense always at rest as well as continuously in motion. Our next point gives a convertible result: on the one hand, because rotation is the measure of motions it must be the primary motion (for all things are meas[10] ured by what is primary): on the other hand, because rotation is the primary motion it is the measure of all other motions. Again, rotatory motion is also the only motion that admits of being regular. In rectilinear locomotion can be in a state of

course, because in

rest as

its

f

the motion of things in leaving the startingpoint is not uniform with their motion in ap-

proaching the finishing-point, since the velocity of a thing always increases proportionately as it removes itself farther from its position of rest: on the other hand rotatory motion is the only motion whose course is naturally such that [75]

it

has no starting-point or finishing-point is determined from elsewhere.

in itself but

BOOK

266 b

VIII,

CHAPTERS

As to locomotion being the primary motion, this is a truth that is attested by all who have ever made mention of motion in their theories: they all assign their first principles of motion to things that impart motion of this kind. Thus 'separation' and 'combination' are motions in [20] respect of place, and the motion imparted by 'Love' and 'Strife' takes these forms, the latter 'separating' and the former 'combining'. Anaxagoras, too, says that 'Mind', his first movent, 'separates'. Similarly those who assert no cause of this kind but say that 'void' accounts they also hold that the mo[25] for motion tion of natural substance is motion in respect of place: for their motion that is accounted for by 'void' is locomotion, and its sphere of operation may be said to be place. Moreover they are of opinion that the primary substances are not subject to any of the other motions, though

—

compounds

the things that are

of these sub-

stances are so subject: the processes of increase

and decrease and

alteration, they say, are effects

[50] of the 'combination' and 'separation' of 'atoms'. It is the same, too, with those who make out that the becoming or perishing of a

accounted for by 'density' or 'rarity': by 'combination' and 'separation' that the place of these things in their systems is determined. Moreover to these we may add those who make Soul the cause of motion: for they say that things that undergo motion have as thing for

is

it is

which moves itself: and when animals and all living things move 266 a themselves, the motion is motion in retheir first principle 'that

it is to be noted that we motion' in the strict sense

spect of place. Finally

say that a thing

'is

in

of the term only

when

respect of place:

if

its

motion

a thing

is

is

motion

in

in process of in-

undergoing some altersame place, in motion in some particular

crease or decrease or

is

ation while remaining at rest in the

we

say that

respect:

it is

we do

not say that

it

'is

in motion'

[5] without qualification. Our present position, then,

is this: We have argued that there always was motion and always will be motion throughout all time, and we have explained what is the first principle of this eternal motion: we have explained further which is the primary motion and which is the only motion that can be eternal: and we have pronounced the first movent to be unmoved.

10

We

have now to assert that the first mov[10] ent must be without parts and without magnitude, beginning with the establishment of the

8-10

353

premisses on which this conclusion depends. One of these premisses is that nothing finite

can cause motion during an infinite time. We have three things, the movent, the moved, and thirdly that in which the motion takes place, namely the time: and these are either all infinite that is to say two of them or all finite or partly [75] or one of them finite and partly infinite. Let A be the movent, B the moved, and T the infinite time. Now let us suppose that A moves

— —

E, a part of B.

Then

the time occupied by this

motion cannot be equal to T: for the greater the amount moved, the longer the time occupied. It

follows that the time

Z

is

not infinite.

Now

add to A I shall use up A and by continuing to add to E I shall [20] use up B: but I shall not use up the time

we

see that by continuing to

by continually subtracting a corresponding amount from it, because it is infinite. Consequently the duration of the part of T which is occupied by all A in moving the whole of B, will be finite. Therefore a finite thing cannot impart to anything an infinite motion. It is clear, then, that

it is

impossible for the finite to

cause motion during an infinite time. [25] It has now to be shown that in no case is possible for an infinite force to reside in a fi-

it

magnitude. This can be shown as follows: it for granted that the greater force is always that which in less time than another does an equal amount of work when engaged in heating, for example, or in any activity sweetening or throwing; in fact, in causing any kind of motion. Then that on which the forces act must be affected to some extent by our supposed finite magnitude possessing an infinite force as well as by anything else, in fact to a greater extent than by anything else, since the [50] infinite force is greater than any other. But then there cannot be any time in which its action could take place. Suppose that A is the time occupied by the infinite power in the performance of an act of heating or pushing, and that AB is the time occupied by a finite power in the performance of the same act: then by 266 b adding to the latter another finite power nite

we

take

—

and continually increasing the magnitude of the power so added I shall at some time or other reach a point at which the finite power has completed the motive act in the time A: for by continual addition to a finite magnitude I must arrive at a magnitude that exceeds any assigned limit, and in the same way by continual subtraction I must arrive at one that falls short of any assigned limit. So we get the result that the finite force will occupy the same amount of

PHYSICS

354

performing the motive act as the infi[5] nite force. But this is impossible. Therefore nothing finite can possess an infinite force. So

time

in

also impossible for a finite force to reside

it

is

in

an

magnitude.

It is

true that a great-

er force can reside in a lesser

magnitude: but

infinite

the superiority of any such greater force can be still greater if the magnitude in which it resides

is

nitude.

greater.

Now let AB be an infinite mag-

Then Br

possesses a certain force that

occupies a certain time, let us say the time EZ, [10] in moving A. Now if I take a magnitude twice as great at Br, the time occupied by this will be half of EZ be the proportion): so we may call this time ZH. That being so, by continually taking a greater magnitude in this way I shall never arrive at the full AB, whereas I shall always be getting a lesser fraction of the time originally given. Therefore the force must [75] be infinite, since it exceeds any finite force. Moreover the time occupied by the action of any finite force must also be finite: for if a given force moves something in a certain time, a greater force will do so in a lesser time, but still a definite time, in inverse proportion. But

magnitude (assuming

a force

in

moving A

this to

must always be

ber or a magnitude

infinite

—

—

just as a

num-

exceeds all definite [20] limits. This point may also be proved in another way by taking a finite magnitude in which there resides a force the same in kind as that which resides in the infinite magnitude, is

if it

—

measure of the finite force residing in the infinite magnitude. [25] It is plain, then, from the foregoing arguments that it is impossible for an infinite force to reside in a finite magnitude or for a finite force to reside in an infinite magnitude. But so that this force will be a

before proceeding to our conclusion it will be well to discuss a difficulty that arises in con-

nexion with locomotion. If everything that is in motion with the exception of things that move themselves is moved by something else, how is it that some things, e.g. things thrown, continue to be in motion when their movent is no longer in contact with them? If we say [jo] that the movent in such cases moves something else at the same time, that the thrower e.g. also moves the air, and that this in being moved is also a movent, then it would be no more possible for this second thing than for the original thing to be in motion when the original movent is not in contact with it or moving it: all the things moved would have to be in motion simultaneously and also to have ceased simultaneously to be in motion when the orig-

267 a

267* inal

like the

movent

magnet,

move them, even

ceases to

makes

which

if,

has moved capable of being a movent. Therefore, while we must accept this explanation to the extent of saying that the original movent gives it

that

it

the power of being a movent either to air or to water or to something else of the kind, nat[5] urally adapted for imparting and undergoing motion, we must say further that this thing does not cease simultaneously to impart motion and to undergo motion: it ceases to be in

motion

at the

move

moment when

its

movent

ceases

remains a movent, and so it causes something else consecutive with it to be in motion, and of this again the same may be said. The motion begins to cease when the motive force produced in one member of the consecutive series is at each stage less than that possessed by the preceding member, and it finally ceases when one member no longer causes the next member to be a movent but [10] only causes it to be in motion. The motion of these last two of the one as movent to

it,

but

it

still

—

—

and of the other as moved must cease simultaneously, and with this the whole motion ceases. Now the things in which this motion is produced are things that admit of being sometimes in motion and sometimes at rest, and the motion is not continuous but only appears so: for it is motion of things that are either successive or in contact, there being not

[75] one movent but a number of movents consecutive with one another: and so motion of this kind takes place in air

and water. Some

'mutual replacement': but we must recognize that the difficulty raised cannot be solved otherwise than in the way we have described. So far as they are affected by 'mutual replacement', all the members of the series are moved and impart motion simultaneously, so that their motions also cease simultaneously: but our present problem concerns the appearance of continuous motion in a sin[20] gle thing, and therefore, since it cannot be moved throughout its motion by the same movent, the question is, what moves it? Resuming our main argument, we proceed from the positions that there must be continuous motion in the world of things, that this is a single motion, that a single motion must be a say that

it

is

motion of a magnitude (for that which is without magnitude cannot be in motion), and that the magnitude must be a single magnitude moved by a single movent (for otherwise there will not be continuous motion but a consecutive series of separate motions), and that if the

BOOK

267 b movent

is

a single thing,

[25] motion or

itself

it is

unmoved:

VIII,

either itself in if,

then,

it is

in

motion, it will have to be subject to the same conditions as that which it moves, that is to say it will itself be in process of change and in be267 b ing so will also have to be moved by something: so we have a series that must come to an end, and a point will be reached at which motion is imparted by something that is unmoved. Thus we have a movent that has no to change along with that which it moves but will be able to cause motion always (for the causing of motion under these conditions involves no effort): and this motion alone is regular, or at least it is so in a higher degree than any other, since the movent is never sub[5] ject to any change. So, too, in order that

need

the motion

may

character, the

continue to be of the same

moved must not be

subject to

change in respect of its relation to the movent. Moreover the movent must occupy either the centre or the circumference, since these are the first principles from which a sphere is derived.

But the things nearest the movent are those whose motion is quickest, and in this case it is the motion of the circumference that is the quickest: therefore the

movent occupies the

circumference.

There

is

a further difficulty in supposing

it

anything that is in motion to cause motion continuously and not merely in [10] the way in which it is caused by something repeatedly pushing (in which case the continuity amounts to no more than successiveto be possible for

CHAPTER

10

355

Such a movent must either itself continue to push or pull or perform both these actions, or else the action must be taken up by something else and be passed on from one movness).

ent to another (the process that we described before as occurring in the case of things thrown, since the air or the water, being divisible, is a

movent only

in virtue of the fact that

different parts of the air are

moved one

after

[75] another): and in either case the motion cannot be a single motion, but only a consecutive series of motions.

The

only continuous

which is caused by the unmoved movent: and this motion is continuous because the movent remains always invariable, so that its relation to that which it moves remains also invariable and continuous. motion, then,

Now that the

is

that

that these points are settled, first

it is

clear

unmoved movent cannot have any

magnitude. For

if it

has magnitude, this must

be either a finite or an infinite magnitude. Now 1 [20] we have already proved in our course on Physics that there cannot be an infinite magni-

and we have now proved that it is immagnitude to have an infinite force, and also that it is impossible for a thing to be moved by a finite magnitude during an infinite time. But the first movent causes a motion that is eternal and does tude:

possible for a finite

[25]

cause

it

during an

infinite time.

visible

and

nitude. 1

in. 5.

is

without parts

It

is

movent is indiand without mag-

clear, therefore, that the first

CONTENTS: ON THE HEAVENS Of the Heavenly

BOOK

Bodies

9.

BERLIN NOS.

CHAP. 1.

The

2.

That in addition

268 a

subject of inquiry

element, the

fifth

268 b

to the four ele-

ments, earth, water,

air,

and

movement

fire,

of

there

which

is

10. 11.

I

12.

1

is

a

cir-

13.

body is exempt from and decay

269b 18

That the circular movement has no contrary That no body is infinite: (i) Not the primary body, or fifth element

27ob 3i

That

this

alteration 4.

5.

6. 7.

14.

27i b

10.

11.

1.

Heaven That the Heaven

is

indestructible: (i)

Review of previous

and

'indestructible',

and of

3.

4.

That every simple body possesses 300*20 a natural movement; that this movement is

15 279 4

5.

2.

Of

bodies subject to generation:

(i)

What the

That the elements are limited 302 b 10 number; the view of Leucippus and De-

(ii)

this

That the elements cannot be

(iii)

6.

That the elements are not

(iv)

eternal, but are generated out of

their op-

Of

(v)

the

eration: the

planation by planes refuted II 8.

result

283 b 26

4.

which the spatial 284 b 6 up and down, right and left, can be attributed to the Heaven Why there is a plurality of move286 a 3 ments and of bodies within the Heaven That the Heaven is perfectly 286 b 10

5.

Why

BOOK 1.

2.

IV

meaning of the terms and Might'

Review of previous

307b 29

theories con-

308*34

Explanation of the variety of mo-

310* 14

cerning these

287b 22

tions exhibited

one direction rather than the other

8.

the

'heavy'

3.

revolves in

Of

3o6 b 3 by their shapes

Refutation of the attempt to

(vi)

differentiate the elements

spherical

7.

304b 24 one another

of their gen305*34 view of Empedocles and the ex-

the sense in

Heaven

303 b 9

manner

oppositions,

first

302* 10

elements are

reduced to one

theories 28o b 1

7.

Corroboration of

Of

in

281 s 28

Proof of the thesis

1.

6.

298*24

bodies into

mocritus refuted

ungenerated and

Definition of the terms 'ungen-

the

of

generation

Proved by the principles of 277b 26 form and matter, the three different senses of the term 'heaven' being explained. Corollary: There is no place or void or time outside the

BOOK

3.

the analysis

stated;

either upward or downward; how unnatural movement occurs. General results concerning

(ii)

(iii)

Bodies

planes refuted 2.

posites 12.

296* 24

III

Previous theories concerning generation

276** 18 That there cannot be more than one Heaven: (i) Proved from a consideration of the natural movements and places of the

crated'

at rest at the centre,

1

s 273 6 s 274 30

of the other elements

it is

spherical in shape

BOOK

impossible

(ii)

That

(ii)

Of the Sublunary

elements 9.

s1

and

In general, an infinite body

(iii) is

8.

None

(ii)

Of their order 291 30 291° n Of their spherical shape (vi) Solution of two problems 29i b 24 concerning their order and movements Of the Earth: (i) Review of pre293 15 (iv)

(v)

vious theories

cular 3.

That no 'harmony of the 290b 12 from their movement

(iii)

spheres' results

I

4.

That the movement of the first 288 a 13 Heaven is regular Of the stars: (i) That they are not 289 a 11 composed of fire (ii) That their movement is due 289b 1 to the movement of circles to which they are

Of

by the elements

the distinctive constitution

and

311* 15

properties of the four elements 5.

In

what sense the matter of which 312* 22 composed may be regarded

the elements are

one That the shape of a body cannot as

6.

attached

313* 14 account for the direction, but only for the pace, of

357

its

movement

ON THE HEAVENS BOOK

268 a The

science

which has

to

clearly concerns itself for the

do with nature most part with

bodies and magnitudes and their properties and movements, but also with the principles of this sort of substance, as

many

as they

may

be.

some [5] For of things constituted by nature are bodies and magnitudes, some possess body and magnitude, and some are principles of things which possess these. is

which

that

is

Now

divisible into parts

pable of subdivision, and a body is

every

three a

always that

is

ca-

which

A magnitude if divisible two ways a surface, and if body. Beyond these there is no other

way

one way

continuum

a

is

divisible.

a line,

if

[10] magnitude, because the three dimensions

are

all

that there, are,

ble in three directions

and that which is

divisible in

is

all.

divisi-

For, as

beginning and middle and end give the number of an 'all', and the number they give is the triad. And so, having taken these three from nature as (so to speak) laws of it, we make

number

say 'both', but not

number

to

priated.

And

'all':

which the term in this, as

three

'all'

is

the

said,

we do

determined by the three dimensions, an 'all'. But if it is divisible in three dimensions it is every way divisible, while the [25] other magnitudes are divisible in one diis

sort

Oxford

would

cease to

We

it

mula, since each possesses every dimension. But each is determined relatively to that part which is next to it by contact, for which reason each

them is in a sense many bodies. But the whole of which they are parts must necessarily be complete, and thus, in accordance with the [10] meaning of the word, have being, not in some respect only, but in every respect.

question as to the nature of the whole, it is infinite in size or limited in its tomass, is a matter for subsequent inquiry. 1 specifically distinct.

whole

Let us take

this

[75] as our starting-point. All natural bodies and magnitudes we hold to be, as such, capable

we say, is their prinmovement that is as we term it, is either

of locomotion; for nature, ciple of

movement. 2 But

in place, all locomotion,

downward movements

all

are in a straight line,

'upward' meaning motion away from the centre, and 'downward' motion towards it. All simple motion, then, must be motion either away from or towards or about the centre. This [25] seems to be in exact accord with what we said above: as body found its completion in

being con-

Note: The bold face numbers and letters are approximate indications of the pages and columns of the standard Berlin Greek text; the bracketed numbers, of the lines in the Greek text; they are here assigned as they are assigned in the

it

[20] straight and the circular line, are the only simple magnitudes. Now revolution about the centre is circular motion, while the upward and

mension or in two alone: for the divisibility and continuity of magnitudes depend upon the one

could,

complete magnitude.

straight or circular or a combination of these two, which are the only simple movements. And the reason of this is that these two, the

is, is

of the dimensions,

we

is

We will now speak of those parts of the

which they are applied, body alone among magnitudes can be complete. For it

number

if

only in virtue of a defect in it; and that which is complete cannot be de[5] fective, since it has being in every respect. Now bodies which are classed as parts of the whole are each complete according to our for-

which are

in that to

that

For

be true that body could pass beyond

tal

first

[20] but follow the lead which nature gives. Therefore, since 'every' and 'all' and 'complete' do not differ from one another in respect of form, but only, if at all, in their matter and

alone

face to body.

whether

has been appro-

we have

We

The

three in the

worship of the Gods. Further, we use the terms in practice in this way. Of two things, or men,

we

tinuous in one direction, another in two, another in all. All magnitudes, then, which are divisible are also continuous. Whether we can also say that whatever is continuous is divisible [50] does not yet, on our present grounds, appear. One thing, however, is clear. cannot 268 b pass beyond body to a further kind, as we passed from length to surface, and from sur-

of

the Pythagoreans say, the world and all that is in it is determined by the number three, since

[75] further use of the

I

1

translation.

359

See chapter

7.

2

Cf. Physics, i92 b 20.

ON THE HEAVENS

360 three dimensions, so itself in

its

movement completes

three forms.

Bodies are either simple or compounded of such; and by simple bodies I mean those which possess a principle of

nature, such as fire

movement

in their

and earth with

own

their kinds,

and whatever is akin to them. Necessarily, then, [jo] movements also will be either simple or simple in the case of in some sort compound 269* the simple bodies, compound in that of the composite and in the latter case the motion will be that of the simple body which pre-

—

—

composition. Supposing, then, that such a thing as simple movement, and

vails in the

there

is

269 b

straight upward and earthy bodies straight downward towards the centre since this is so, it follows that circular movement also must be the movement of some simple body. For the movement of composite bodies is, as we said,

—

determined by that simple body which prepon[jo] derates in the composition. These premises clearly give the conclusion that there is in nature some bodily substance other than the formations we know, prior to them all and more divine than they. But it may also be

proved as follows.

We may take

—

movement is an instance of it, and movement of a simple body is simple and simple movement is of a simple body (for if it is movement of a compound it will be in

269 b

[5] virtue of a prevailing simple element), then there must necessarily be some simple

natural to these bodies,

natural to another

that circular

is

that both

case with the

body which revolves naturally and in virtue of its own nature with a circular movement. By constraint, of course, it may be brought to move with the motion of something else different from itself, but it cannot so move naturally, since there is one sort of movement natural to each of the simple bodies. Again, if the unnatural movement is the contrary of the natural and [10] a thing can have no more than one contrary, it will follow that circular movement, being a simple motion, must be unnatural, if it is not natural, to the body moved. If then (1) the body, whose movement is circular, is fire or some other element, its natural motion must be the contrary of the circular motion. But a single thing has a single contrary; and upward and downward motion are the contraries of one [75] another. If, on the other hand, (2) the body moving with this circular motion which is unnatural to it is something different from the elements, there will be some other motion which is natural to it. But this cannot be. For if the natural motion is upward, it will be fire or air, and if downward, water or earth. Further, this circular motion is necessarily primary. For [20] the perfect is naturally prior to the imperfect, and the circle is a perfect thing. This cannot be said of any straight line: not of an infinite line; for, if it were perfect, it would have a limit and an end: nor of any finite line; for in every case there is something beyond it, since any finite line can be extended. And so, since the prior movement belongs to the body which

—

[25] is naturally prior, and circular movement prior to straight, and movement in a straight

is

line

belongs to simple bodies

—

fire

moving

it

that

all

move-

ment is either natural or unnatural, and that the movement which is unnatural to one body as, for instance, is

the

upward and downward move-

[55] ments, which are natural and unnatural to fire and earth respectively. It necessarily follows that circular movement, being unof

some

is

other. Further,

movement

the natural

if,

movement

on the one hand,

cir-

natural to something, it must surely be some simple and primary body

cular

is

ordained to move with a natural ciris ordained to fly up and earth down. If, on the other hand, the movement of the rotating bodies about the centre is unnatural, it would be remarkable and indeed quite inconceivable that this movement alone should be continuous and eternal, being

which

is

[5] cular motion, as fire

nevertheless contrary to nature.

evidence of [10]

And

moved ral to

At any rate the show that it

other cases goes to

the unnatural

is

away.

all

so,

if,

as

which quickest passes some say, the body so

this movement is just as unnatudownward movement; for any one

is fire,

it

as

can see that

from the

fire

centre.

fore,

we may

[75]

is

moves

On

in a straight line

all

away

these grounds, there-

infer with confidence that there something beyond the bodies that are about us on this earth, different and separate from them; and that the superior glory of its nature is proportionate to its distance from this world of ours.

In consequence of what has been said, in part by way of assumption and in part by way of it is clear that not every body either pos[20] sesses lightness or heaviness. As a preliminary we must explain in what sense we are us-

proof,

ing the words 'heavy' and 'light', sufficiently, at our present purpose: we can examine the terms more closely later, when we come to consider their essential nature. Let us then apply the term 'heavy' to that which naturally least, for

BOOK

270 b

1,

CHAPTERS

moves towards the centre, and 'light' to that which moves naturally away from the centre. The heaviest thing will be that which sinks to [25] the bottom of all things that move downward, and the lightest that which rises to the surface of everything that moves upward. Now, necessarily, everything which moves either up or

down

possesses lightness or heaviness or both

—but not both

relatively to the same thing: for things are heavy and light relatively to one an-

instance, is light relatively to waand water light relatively to earth. The body, then, which moves in a circle cannot

other;

air, for

ter,

[30]

possibly possess either heaviness or lightness.

For neither naturally nor unnaturally can it move either towards or away from the centre.

Movement belong to

in a straight line certainly does not

it

naturally, since one sort of

move-

we saw, appropriate to each simple body, and so we should be compelled to iden[35] tify it with one of the bodies which move in this way. Suppose, then, that the movement is unnatural. In that case, if it is the downward 270* movement which is unnatural, the upward movement will be natural; and if it is the upward which is unnatural, the downward will be natural. For we decided that of contrary ment

as

is,

movements,

if

the one

is

unnatural to anything,

it. But since the natwhole and of its part of earth, for instance, as a whole and of a small have one and the same direction, it [5] clod results, in the first place, that this body can possess no lightness or heaviness at all (for that would mean that it could move by its own nature either from or towards the centre, which, as we know, is impossible); and, secondly, that

the other will be natural to ural

movement

of the

—

it

cannot possibly

move

in the

way

of locomo-

tion by being forced violently aside in

an up-

[10] ward or downward direction. For neither naturally nor unnaturally can it move with any

other motion but part of

it,

its

own,

any which applies to

either itself or

since the reasoning

the whole applies also to the part. It is equally reasonable to assume that this body will be ungenerated and indestructible and exempt from increase and alteration, since everything that comes to be comes into being [75] from its contrary and in some substrate, and passes away likewise in a substrate by the

action of the contrary into the contrary, as explained in our opening discussions. 1

we

Now

the motions of contraries are contrary. If then

body can have no contrary, because there can be no contrary motion to the circular, nathis

iPhysics,

1.

7-9.

2-3

361

[20] ture seems justly to have exempted from contraries the body which was to be ungener-

ated and indestructible. For that generation

which

is

and decay

it is

in contraries

subsist.

Again, that

subject to increase increases

upon con-

with a kindred body, which is resolved [25] into its matter. But there is nothing out of which this body can have been generated. And if it is exempt from increase and diminution, the same reasoning leads us to suppose tact

For alteration is and qualitative states and dispositions, such as health and disease, do not come into being without changes of properties. But all natural bodies which [30] change their properties we see to be subject without exception to increase and diminution. This is the case, for instance, with the bodies of animals and their parts and with vegetable bodies, and similarly also with those of the elements. And so, if the body which moves with a circular motion cannot admit of inthat

it

is

movement

also unalterable.

in respect of quality;

[55] crease or diminution, it is reasonable to it is also unalterable.

suppose that

270 b The

reasons why the primary body is and not subject to increase or diminution, but unaging and unalterable and unmodified, will be clear from what has been said to any one who believes in our assumptions. Our theory seems to confirm experience and to be [5] confirmed by it. For all men have some conception of the nature of the gods, and all eternal

who

believe in the existence of gods at all, whether barbarian or Greek, agree in allotting

the highest place to the deity, surely because

they suppose that immortal

is linked with immortal and regard any other supposition as in[10] conceivable. If then there is, as there certainly is, anything divine, what we have just said about the primary bodily substance was well said. The mere evidence of the senses is enough to convince us of this, at least with human certainty. For in the whole range of time past, so far as our inherited records reach, no [75] change appears to have taken place either in the whole scheme of the outermost heaven or in any of its proper parts. The common name, too, which has been handed down from our distant ancestors even to our own day, seems to show that they conceived of it in the fashion which we have been expressing. The

same

ideas,

one must

believe, recur in

men's

[20] minds not once or twice but again and again. And so, implying that the primary body is

something

else

beyond

earth, fire, air,

water, they gave the highest place a

name

and of

its

ON THE HEAVENS

362

aither, derived from the fact that it 'runs always' for an eternity of time. Anaxagoras, [25] however, scandalously misuses this name,

own,

taking aither as equivalent to fire. It is also clear from what has been said why the number of what we call simple bodies cannot be greater than

it is.

The motion

of a sim-

be simple, and we assert that there are only these two simple motions, ple

body must

iself

[jo] the circular

and the

straight, the latter

being subdivided into motion away from and motion towards the centre.

That there

is

no other form of motion op-

posed as contrary to the circular may be proved in various ways. In the first place, there is an obvious tendency to oppose the straight line to [55] the circular. For concave and convex are 271 a not only regarded as opposed to one another, but they are also coupled together and treated as a unity in opposition to the straight. And so, if there is a contrary to circular motion,

motion in a straight line must be recognized as having the best claim to that name. But the two forms of rectilinear motion are opposed to one [5] another by reason of their places; for up and down is a difference and a contrary opposition in place. Secondly, it may be thought that the

same reasoning which holds good of the rec-

path applies also the circular, movement from A to B being opposed as contrary to movement from B to A. But what is meant is still rectilinear motion. For that is limited to a [10] single path, while the circular paths which pass through the same two points are infinite in number. Even if we are confined to the sin-

tilinear

and the opposition is between to D and from D to C along that semicircle, the case is no better. For the motion is the same as that along the diameter,

gle semicircle

movement from C

since

we

invariably regard the distance be-

tween two points as the length of the straight line which joins them. It is no more satisfactory to construct a circle and treat motion [75] along one semicircle as contrary to motion along the other. For example, taking a complete circle, motion from E to F on the semicircle G may be opposed to motion from F to E on the semicircle H. But even supposing these are contraries, it in no way follows that the reverse motions on the complete circumference [20] are contraries. Nor again can motion along the circle from A to B be regarded as the contrary of motion from AtoC: for the motion goes from the same point towards the same

271 b

and contrary motion was distinguished motion from a contrary to its contrary. And even if the motion round a circle is the contrary of the reverse motion, one of the two would be ineffective: for both move to the same point, because that which moves in a circle, at what[25] ever point it begins, must necessarily pass through all the contrary places alike. (By contrarieties of place I mean up and down, back and front, and right and left; and the contrary oppositions of movements are determined by point, as

One

those of places.)

of the motions, then,

would be ineffective, for if the two motions were of equal strength, there would be no movement either way, and if one of the two [50] were preponderant, the other would be inoperative. So that if both bodies were there, one of them, inasmuch as it would not be moving with its own movement, would be useless, in the sense in which a shoe is useless when it is not worn. But God and nature create nothing that has not

its

271 b This being

use.

we must go on to conwhich remain. First, is there

clear,

sider the questions

an

infinite body, as the majority of the ancient philosophers thought, or is this an impossibility? The decision of this question, either way,

not unimportant, but rather all-imporour search for the truth. It is this problem which has practically always been the source of the differences of those who have written about nature as a whole. So it has been [5]

is

tant, to

and so it must be; since the least initial deviation from the truth is multiplied later a thou[10] sandfold. Admit, for instance, the existence of a minimum magnitude, and you will find that the minimum which you have introduced, small as

it is,

causes the greatest truths

of mathematics to totter.

principle tent;

is

The

great rather in

reason

is

that a

power than

in ex-

hence that which was small

at the start

Now

the concep-

turns out a giant at the end.

tion of the infinite possesses this ciples,

and indeed

power

of prin-

in the sphere of quantity

[75] possesses it in a higher degree than any other conception; so that it is in no way absurd or unreasonable that the assumption that an infinite body exists should be of peculiar moment to our inquiry.

now

discuss,

The

infinite,

then,

we must

opening the whole matter from

the beginning.

Every body

is

necessarily to be classed either

as simple or as composite; the infinite body,

therefore, will be either simple or composite.

BOOK

272 b clear, further, that

I,

CHAPTERS

the simple

[20] But it is bodies are finite, the composite must also be finite, since that which is composed of bodies if

number and in magnitude is itfinite both self finite in respect of number and magnitude: in

quantity

its

is

in fact the

same

as that of the

bodies which compose it. What remains for us to consider, then, is whether any of the simple bodies can be infinite in magnitude, or wheth[25] er this

mary body

is

first,

impossible. Let us try the priand then go on to consider the

others.

must

3-5

363

(3) That the infinite cannot move may also be shown as follows. Let A be finite line mova.

ing past the

finite line,

B.

Of

B and B

of

A

pass clear of

A

necessity

at the

will

same mo-

[25] ment; for each overlaps the other to precisely the same extent. Now if the two were both moving, and moving in contrary directions, clear of one another more rapone were still and the other moving past it, less rapidly; provided that the speed of the latter were the same in both cases. This, however, is clear: that it is impossible to traverse an

they

would pass

idly;

if

nec-

infinite line in a finite time. Infinite time, then,

essarily be finite in every respect, for the fol-

[jo] would be required. (This we demonstrated above in the discussion of movement. ) And

The body which moves

in a circle

the body so moving is infinite, the radii drawn from the centre will be |jo] infinite. But the space between infinite radii is infinite: and by the space between the

lowing reasons. (1)

radii

I

mean

If

which no magnicontact with the two lines can

the area outside

tude which is in be conceived as falling. This, I say, will be infinite: first, because in the case of finite radii it 272 a is always finite; and secondly, because in it one can always go on to a width greater than any given width; thus the reasoning which forces us to believe in infinite number, because is no maximum, applies also to the space between the radii. Now the infinite cannot be traversed, and if the body is infinite the interval between the radii is necessarily infinite: circu[5] lar motion therefore is an impossibility. Yet our eyes tell us that the heavens revolve in a circle, and by argument also we have determined that there is something to which circu-

there

lar

movement

belongs.

from a finite time a finite time be subtracted, what remains must be finite and (2) Again,

if

have a beginning. And if the time of a journey [10] has a beginning, there must be a beginning also of the movement, and consequently also of the distance traversed. This applies universally. Take a line, ACE, infinite in one direction, E, and another line, BB, infinite in both directions. Let ACE describe a circle, ret/5] volving upon C as centre. In its movement it will cut BB continuously for a certain time. This will be a finite time, since the total time is finite in which the heavens complete their circular orbit, and consequently the time subtracted from it, during which the one line in its motion cuts the other, is also finite. Therefore there will be a point at which ACE began for the first time to cut BB. This, however, is impossible. The infinite, then, cannot revolve in [20] a circle; nor could the world, if it were infinite.

1

makes no difference whether a finite is pass272 b ing by an infinite or an infinite by a fiit

nite. For when A is passing B, then B overlaps A, and it makes no difference whether B is moved or unmoved, except that, if both move, they pass clear of one another more quickly. It is, however, quite possible that a moving line should in certain cases pass one which is stationary quicker than it passes one moving in an [5] opposite direction. One has only to imagine the movement to be slow where both move and much faster where one is stationary. To suppose one line stationary, then, makes no difficulty for our argument, since it is quite

A to pass B at a slower rate when both are moving than when only one is. If, [10] therefore, the time which the finite moving line takes to pass the other is infinite, then necessarily the time occupied by the motion of possible for

the infinite past the finite the infinite to

move

at all

is

is

also infinite.

possible; since the very smallest

ceivable

must take an

For

thus absolutely im-

movement con-

infinity of time.

More-

over the heavens certainly revolve, and they complete their circular orbit in a finite time; so [75] that they pass round the whole extent of any line within their orbit, such as the finite line

AB. The revolving body,

therefore, can-

not be infinite. (4) Again, as a line which has a limit cannot be infinite, or, if it is infinite, is so only in length, so a surface cannot be infinite in that

which it has a limit; or, indeed, if it completely determinate, in any respect what[20] ever. Whether it be a square or a circle or a sphere, it cannot be infinite, any more than a foot-rule can. There is then no such thing as an infinite sphere or square or circle, and where there is no circle there can be no circular moverespect in is

ment, and similarly where there ^Physics, vi. 7.

is

no

infinite

ON THE HEAVENS

3 64 at all there

from ing

this

itself

can be no infinite movement; and follows that, an infinite circle be-

it

an impossibility, there can be no

cir-

cular motion of an infinite body. [25] (5) Again, take a centre C, an infinite line,

to

it,

AB, another infinite line at right angles E, and a moving radius, CD. CD will

never cease contact with E, but the position cutting will always be something like CE,

CD

E

at F.

The

infinite line, therefore, refuses to

complete the circle. [3°] (6) Again, if the heaven is infinite and moves in a circle, we shall have to admit that in a finite time it has traversed the infinite. For suppose the fixed heaven infinite, and that which moves within it equal to it. It results that when the infinite body has completed its revolution, it has traversed an infinite equal to

273 a

itself in a finite

time. But that

we know

to be impossible.

(7) It can also be shown, conversely, that the time of revolution is finite, the area traversed must also be finite; but the area trav-

if

ersed

was equal

to itself; therefore,

it is

itself

finite.

[5]

We

have

now shown

moves

in a circle

has

limit.

its

is

that the

body which

not endless or infinite, but

Further, neither that which moves towards nor that which moves away from the centre

can be infinite. For the upward and downward motions are contraries and are therefore motions towards contrary places. But if one of a [10] pair of contraries is determinate, the other must be determinate also. Now the centre is determined; for, from whatever point the body

which sinks

to the

bottom

starts its

downward

cannot go farther than the centre. The centre, therefore, being determinate, the upper place must also be determinate. But if these two places are determined and finite, the [75] corresponding bodies must also be finite.

motion,

it

if up and down are determinate, the intermediate place is also necessarily determinate. For, if it is indeterminate, the movement within it will be infinite; and that we have already shown to be an impossibility. 1 The middle region then is determinate, and consequent-

Further,

any body which either is in it, or might be in determinate. But the bodies which move [20] up and down may be in it, since the one

ly

it, is

moves naturally away from the centre and the other towards 1

it.

Physics, viii. 8.

273 b

From

this alone it is clear that an infinite an impossibility; but there is a further point. If there is no such thing as infinite weight, then it follows that none of these bodies can be infinite. For the supposed infinite [25] body would have to be infinite in weight.

body

is

(The same argument

applies to lightness: for

one supposition involves infinite weight, so the infinity of the body which rises to the surface involves infinite lightness.) This is proved as follows. Assume the weight to be finite, and take an infinite body, AB, of the weight C. Subtract from the infinite body a fi[30] nite mass, BD, the weight of which shall be E. E then is less than C, since it is the weight of a lesser mass. Suppose then that the smaller as the

goes into the greater a certain

number

of times,

273 b and take BF bearing the same proportion to BD which the greater weight bears to the smaller. For you may subtract as much as you please from an infinite. If now the masses are proportionate to the weights, and the lesser weight is that of the lesser mass, the greater [5] must be that of the greater. The weights, therefore, of the finite and of the infinite body are equal. Again, if the weight of a greater body is greater than that of a less, the weight of GB will be greater than that of FB; and thus the weight of the finite body is greater than that of the infinite. And, further, the weight of unequal masses will be the same, since the infinite and the finite cannot be equal. It does [10] not matter whether the weights are commensurable or not. If (a) they are incommensurable the same reasoning holds. For instance, suppose E multiplied by three is rather more than C: the weight of three masses of the full size of BD will be greater than C. We thus ar[75] rive at the same impossibility as before. Again (b) we may assume weights which are commensurate; for it makes no difference whether we begin with the weight or with the mass. For example, assume the weight E to be commensurate with C, and take from the infinite mass a part BD of weight E. Then let a [20] mass BF be taken having the same proportion to BD which the two weights have to one another. (For the mass being infinite you may subtract from it as much as you please.) These assumed bodies will be commensurate in mass and in weight alike. Nor again does it make any difference to our demonstration whether the total mass has its weight equally or unequally distributed. For it must always be [25] possible to take from the infinite mass a body of equal weight to BD by diminishing or

BOOK

274 b

I,

CHAPTERS

increasing the size of the section to the necessary extent.

From what we have

said, then,

it is

clear that

the weight of the infinite body cannot be finite. have therefore It must then be infinite.

We

only to show this to be impossible in order to prove an infinite body impossible. But the im[30] possibility of infinite weight can be shown in the following way. A given weight moves a given distance in a given time; a weight which as great

is

and more moves the same distance being in inverse pro-

in a less time, the times

274 a portion one weight

is

to the weights.

twice another,

it

For instance,

It

necessarily follows

from

And though you may

movement can be

con-

[10] tinually diminished, yet there is no miniif there were, would it help us. For

mum. Nor,

finite body could have been found greater than the given finite in the same proportion which is supposed to hold between the infinite and the given finite; so that an infinite and a finite weight must have traversed an equal distance in equal time. But that is impossible. Again, whatever the time, so long as it is finite, [75] in which the infinite performs the motion, a finite weight must necessarily move a certain

some

finite distance in that

same time. Infinite weight and the same reasoning

therefore impossible,

is

applies also to infinite lightness. Bodies then of infinite

weight and of

infinite lightness are

equally impossible. is

no

we have shown

1

Physics, in. 4-8.

infinite it,

must necessarily be either fiand if infinite, either of similar

[30] Every body nite or infinite,

or of dissimilar parts.

If its

parts are dissimilar,

is

evident,

our original presuppositions

if

274 b remain unchallenged. For the primary movements being finite in number, the kinds of simple body are necessarily also finite, since

the

movement of a simple body is simple, and movements are finite, and every nat-

the simple

body must always have

its

Now if the infinite body

is

ural

[5] of a finite

must

parts

that

pose

number

it.

composed

of kinds, then each of

to say, the water, fire,

is

proper motion. to be

its

necessarily be infinite in quantity,

But

this

is

&c, which com-

we

impossible, because, as

have already shown, infinite weight and lightness do not exist. Moreover it would be necessary also that their places should be infinite in [10] extent, so that the movements too of all these bodies would be infinite. But this is not possible,

if

we

are to hold to the truth of our

and to the view that which moves downward, nor, by the same reasoning, that which moves upward, can prolong its movement to infinity. For it is true in regard to quality, quantity, and place alike that any process of change is impossible [75] which can have no end. I mean that if it original presuppositions

neither that

is

impossible for a thing to have

come

white, or a cubit long, or in Egypt,

impossible for

it

be any of these.

body may be shown, by a detailed considera[20] tion of the various cases. But it may also be shown universally, not only by such reasoning as we advanced in our discussion of princi1 ples (though in that passage we have already determined universally the sense in which the existence of an infinite is to be asserted or denied), but also suitably to our present purpose in the following way. That will lead us to a fur[25] ther question. Even if the total mass is not

That there

as

us treat of the infinite uni-

let

finite

this that infi-

a time inversely proportionate to its greatness, cannot move at all. The time should be less in proportion as the weight is greater. But there is no proportion between the infinite and the finite: proportion can only hold between a less say that the time of the

however,

First,

versally.

finite

if there is such a thing, being, on [5] the one hand, as great and more than as great as the finite, will move accordingly, but being, on the other hand, compelled to move in

a greater finite time.

infinite, it yet be great enough to admit a plurality of universes. The question might possibly be raised whether there is any obstacle to our believing that there are other universes composed on the pattern of our own, more than one, though stopping short of infinity.

finite

nite weight,

and

365

may

they must represent either a finite or an infinite number of kinds. That the kinds cannot be in-

will take half as

long over a given movement. Further, a weight traverses any finite distance in a time.

if

5-7

to be

moving

to be in process of

It is

to be

it is

also

coming

to

thus impossible for a thing

to a place at

which

in

its

motion

can never by any possibility arrive. Again, suppose the body to exist in dispersion, it may be maintained none the less that the total of all it

these scattered particles, say, of

fire, is infinite.

[20] But body we saw to be that which has extension every way. can there be several

How

dissimilar elements, each infinite?

have to be It is

finite

For,

infinitely

Each would

extended every way.

no more conceivable, again, that the

in-

should exist as a whole of similar parts. in the first place, there is no other

ON THE HEAVENS

$66

movement beyond

those mentioned: one of them. And if [25] so, wc shall have to admit either infinite weight or infinite lightness. Nor, secondly, could the body whose movement is circular be (straight)

we must

therefore give

infinite, since

move

it is

it

would be

as

[30] Moreover, in general, it is impossible that the infinite should move at all. If it did, it would move either naturally or by constraint:

and

if by constraint, it possesses also a natural motion, that is to say, there is another place,

which

infinite like itself, to is

it

move. But

will

impossible.

That

in general

is

it

impossible for the

infi-

upon by the finite or to act upon it may be shown as follows. 275 a (1. The infinite cannot be acted upon by nite to be acted

the finite) Let A be an infinite, B a finite, C the time of a given movement produced by one in the other. Suppose, then, that

A

was heated,

or impelled, or modified in any way, or caused to

undergo any

B

in the

suming

sort of

time C. Let

movement whatever, by

D be less than B; and, as-

that a lesser agent

moves

a lesser pa-

an equal time, call the quantity is to B, so is thus modified by D, E. Then, as E to some finite quantum. We assume that the alteration of equal by equal takes equal time, and the alteration of less by less or of greater by greater takes the same time, if the quantity of the patient is such as to keep the proportion [10] which obtains between the agents, greater and less. If so, no movement can be caused in the infinite by any finite agent in any time whatever. For a less agent will produce that movement in a less patient in an equal time, [5] tient in

D

and the proportionate equivalent of that pano proportion holds between finite and infinite. (2. The infinite cannot act upon the finite.) Nor, again, can the infinite produce a move[75] ment in the finite in any time whatever. Let A be an infinite, B a finite, C the time of action. In the time C, D will produce that mo-

tient will be a finite quantity, since

tion in a patient less than B, say F. Then take E, bearing the same proportion to as the

D

BF bears to F. E will produce the moin BF in the time C. Thus the finite and

can

infinite

effect this

movement.

nothing can For such time

infinite time, in that

move another

or be moved by it. has no limit, while the action and reaction have.

impossible for the infinite to

in a circle. This, indeed,

good as saying that the heavens are infinite, which we have shown to be impossible.

that

which the And, as to

275 b

There

(3.

no interaction between

is

infi-

Nor can infinite be acted upon in any way by infinite. Let A and B be infinites,

nites) [25]

CD being the time of the action of A upon B. Now the whole B was modified in a certain and the part of this infinite, E, cannot be same time, since we assume that a less quantity makes the movement in a less time. Let E then, when acted upon by A, [30] complete the movement in the time D. Then, as D is to CD, so is E to some finite part of B. This part will necessarily be moved by A in the time CD. For we suppose that the same agent produces a given effect on a greater and 275 b a smaller mass in longer and shorter times, the times and masses varying proportionately. There is thus no finite time in which infinites can move one another. Is their time then infinite? No, for infinite time has no end, but the movement communicated has. [5] If therefore every perceptible body possesses the power of acting or of being acted upon, or both of these, it is impossible that an infinite body should be perceptible. All bodies, however, that occupy place are perceptible. There is therefore no infinite body beyond the time,

so modified in the

heaven.

Nor again

extent beyond

it.

is

there anything of limited

And

so

beyond the heaven you suppose it an

For

if

[10] object of intelligence,

it

there

is

no body

at

all.

will be in a place

—since place what 'within' and 'beyond' denote —and therefore an object of perception. is

But nothing that

is not in a place is perceptible. question may also be examined in the light of more general considerations as follows. The infinite, considered as a whole of similar parts, cannot, on the one hand, move in a cir-

The

cle.

For there

is

no centre of the

infinite,

and

[75] that which moves in a circle moves about the centre. Nor again can the infinite move in a straight line.

For there would have

other place infinite like its

natural

movement

great, for the goal of

its

to be anbe the goal of and another, equally unnatural movement. itself to

movement

whole

Moreover, whether

tion

natural or constrained, in either case the force [20] which causes its motion will have to be in-

[20] the infinite effect the

equal times. But this

sumption

is

is

same

alteration in

impossible; for the as-

that the greater effects

it

in a short-

same with any time that can be taken, so that there will no time in

er time. It will be the

finite.

For

its

rectilinear

infinite force

is

force of

an

is

infinite

body, and of an infinite body the force is infinite. So the motive body also will be infinite. (The proof of this is given in our discussion of

BOOK

276 b 1

movement, where

it

shown

1,

CHAPTERS

no finite power, and no infinite then that which moves

is

that

thing possesses infinite thing finite power.) If naturally can also move unnaturally, there will

[25] be two infinites, one which causes, and another which exhibits the latter motion. Again, what is it that moves the infinite? If it moves itself, it

sibly be

must be animate. But how can it posconceived as an infinite animal? And

7-8

367

by constraint. place in

A

which

thing moves naturally to a

without constraint, and

rests

it

rests naturally in a

rests

it

by constraint, and

ther, its

if

which

rests

contrary

is

natural.

then,

If,

the centre here,

its

power.

rests

[30] If the whole

is

else that

not continuous, but

exists,

Democritus and Leucippus think, in the form of parts separated by void, there must

as

necessarily be one

movement

of all the multi-

tude. They are distinguished, we are told, from 276 a one another by their figures; but their na-

ture

is

one, like

many

pieces of gold separated

from one another. But each piece must, as we assert, have the same motion. For a single clod moves to the same place as the whole mass of earth, and a spark to the same place as the whole mass of fire. So that if it be weight that all possess, no body is, strictly speaking, light: and if [5] lightness be universal, none is heavy. Moreover, whatever possesses weight or lightness will have its place either at one of the extremes or in the middle region. But this is impossible while the world is conceived as infi-

And,

which has no centre or extreme limit, no up or down, gives the bod[10] ies no place for their motion; and without that movement is impossible. A thing must move either naturally or unnaturally, and the two movements are determined by the proper and alien places. Again, a place in which a thing rests or to which it moves unnaturally, [75] must be the natural place for some other nite.

generally, that

body, as experience shows. Necessarily, therefore, not everything possesses weight or lightness, but some things do and some do not. From these arguments then it is clear that the body of the universe is not infinite. 8

We

must now proceed to explain why there cannot be more than one heaven the further question mentioned above. For it may be thought that we have not proved universally [20] of bodies that none whatever can exist outside our universe, and that our argument applied only to those of indeterminate extent.

Now 1

—

all

things rest and

Physics, viii. 10.

move

naturally

and

by constraint in

it

moves from

something

moves

moves by constraint. Fura given movement is due to constraint,

a place to

straint that earth

is

it

[25] without constraint. On the other hand, a thing moves by constraint to a place in which

moves it, there will be two infinites, that which moves and that which is moved, differing in their form and there

if

which

place to

it

is

movement from

there will be natural,

and

if

by con-

a certain place to

here to

earth from there

here without constraint, its movement hith-

[30] er will be natural. And the natural movement in each case is one. Further, these worlds,

being similar in nature to ours, must all be composed of the same bodies as it. Moreover each of the bodies, fire, I mean, and earth and 276 b their intermediates, must have the same power as in our world. For if these names are used equivocally, if the identity of name does not rest upon an identity of form in these elements and ours, then the whole to which they belong can only be called a world by equivoca[5] tion. Clearly, then, one of the bodies will

move

naturally

away from

the centre

and an-

other towards the centre, since fire must be identical with fire, earth with earth, and so on,

fragments of each are identical in this world. That this must be the case is evident

as the

from the principles laid down in our discusmovements, 2 for these are limited number, and the distinction of the elements in [10] depends upon the distinction of the movements. Therefore, since the movements are the same, the elements must also be the same everywhere. The particles of earth, then, in another world move naturally also to our centre and its fire to our circumference. This, [75] however, is impossible, since, if it were sion of the

true, earth

must, in

wards, and

fire to

its

the earth of our world

away from

own

world,

the centre; in the

the centre

move

up-

same way

must move naturally it moves towards

when

the centre of another universe. This follows from the supposed juxtaposition of the worlds. For either we must refuse to admit the iden[20] tical nature of the simple bodies in the various universes, or, admitting this, we must

make

the centre

and the extremity one

gested. This being so,

it

as sug-

follows that there

cannot be more worlds than one. To postulate a difference of nature in the simple bodies according as they are more or less distant from their proper places is unrea2

Above, Chapters

2-4.

ON THE HEAVENS

368

277 b

sonable.

For what difference can it make whether we say that a thing is this distance [25] away or that? One would have to sup-

but to opposite points; and since the opposition in place is between above and below, these will be the limits of their movement. (Even in

pose a difference proportionate to the distance and increasing with it, but the form is in fact the same. Moreover, the bodies must have some

circular

movement,

since the fact that they

quite evident. Are

we

move

is

to say then that all their

movements, even those which are mutually to constraint? No, for a body which has no natural movement at all

contrary, are due

cannot be moved by constraint. If then the [30] bodies have a natural movement, the movement of the particular instances of each form must necessarily have for goal a place numerically one, i.e. a particular centre or a particular extremity. If it be suggested that the goal in each case is one in form but numer277* ically more than one, on the analogy of particulars which are many though each undifferentiated in form, we reply that the variety of goal cannot be limited to this portion or that but must extend to all alike. For all are equally undifferentiated in form, but any one [5] is different numerically from any other.

movement

there

is

a sort of opposition

between the ends of the diameter, though the movement as a whole has no contrary: so that [25] here too the movement has in a sense an opposed and finite goal.) There must therefore be some end to locomotion: it cannot continue to infinity.

This conclusion that local movement is not continued to infinity is corroborated by the fact that earth moves more quickly the nearer it is

to the centre,

and

fire

[30] the upper place. But

the nearer if

it

is

to

movement were

infinite speed would be infinite also; and if speed then weight and lightness. For as superior speed in downward movement implies superior weight, so infinite increase of weight

necessitates infinite increase of speed.

277 b Further, it is not the action of another body that makes one of these bodies move up and the other down; nor is it constraint, like the 'extrusion' of some writers. For in that

differs

mass of fire or earth the slower would be the upward or downward movement; but the fact is the reverse: the greater the mass of fire or earth the quicker [5] always is its movement towards its own place. Again, the speed of the movement would not increase towards the end if it were due to constraint or extrusion; for a constrained movement always diminishes in speed as the source

must

of constraint becomes

What

I

mean

is

this:

if

the portions in this

to one another another world, then the portion which is taken hence will not behave differently either from the portions in another world or from those in the same world, but similarly to them, since in form no portion

world behave similarly both

and

to those in

from another. The result is that we abandon our present assumptions [10] or assert that the centre and the extremity are each numerically one. But this being so, the heaven, by the same evidence and the same necessary inferences, must be one only and no either

more.

A

consideration of the other kinds of move-

ment

also makes it plain that there is some point to which earth and fire move naturally. For in general that which is moved changes

[75] from something into something, the starting-point and the goal being different in

form, and always

For inchange from disease to health, to increase is to change from smallness to greatness. Locomotion must be similar: for it also has its goal and startingpoint and therefore the starting-point and it is

a finite change.

stance, to recover health

is

to

—

movement must differ movement of coming to

the goal of the natural

—

form just as the [20] health does not take any direction which chance or the wishes of the mover may select. in

Thus,

too, fire

and earth move not

to infinity

case the larger the

more distant, and a body moves without constraint to the place whence it was moved by constraint.

A

consideration of these points, then, gives

adequate assurance of the truth of our contentions. The same could also be shown with the [10] aid of the discussions which fall under

from the nature of movement, which must be eternal both here and in the other worlds. It is plain, too, from the following considerations that the universe must be one. The bodily elements are three, and thereFirst Philosophy, as well as

the circular

in]

fore the places of the elements will be

three also; the place, sinks to the bottom,

first, of the body which namely the region about

the centre; the place, secondly, of the revolving

body, namely the outermost place, and thirdly, the intermediate place, belonging to the intermediate body. Here in this third place will be the body

which

rises to the surface; since, if

not here, it will be elsewhere, and it cannot be elsewhere: for we have two bodies, one weight-

BOOK

278 b

L

CHAPTERS

one endowed with weight, and below is [20] the place of the body endowed with weight, since the region about the centre has been given to the heavy body. And its position cannot be unnatural to it, for it would have to be natural to something else, and there is nothing else. It must then occupy the intermediate place. What distinctions there are within the intermediate itself we will explain less,

later on.

We

now

said enough to make plain and number of the bodily elements, the place of each, and further, in gen-

have

the character

[25] eral, places are.

how many

in

number

the various

in matter

is

We

We

This may, of course, sometimes

ticular thing.

might be, for instance, that only could be found; yet none the less the difference will remain between the being of

one

it

circle

circle

and of

this particular circle, the

one be-

ing form, the other form in matter, i.e. a par[10] ticular thing. Now since the universe is perceptible it must be regarded as a particular; for everything that is perceptible subsists, as we

know,

But if it is a particular, there between the being of 'this universe' and of 'universe' unqualified. There is a difference, then, between 'this universe' and simple 'universe'; the second is form and [75] shape, the first form in combination with matter; and any shape or form has, or may have, more than one particular instance. in matter.

will be a distinction

On

the supposition of

Forms such

as

some

a fact of observation that the

form are several or number. Hence there either

[20] in

may

be,

more heavens than

one.

infinite are, or

On

these

might be inferred either that there are or that there might be several heavens. We must, however, return and ask how much of this argument is correct and how grounds, then,

much

it

not.

Now

it is

quite right to say that the formula

from the matter must be diffrom that of the shape in the mat-

of the shape apart

and we may allow

not,

show not only that the heaven is one, but also that more than one heaven is impossible, and, further, that, as exempt from decay may and generation, the heaven is eternal. begin by raising a difficulty. From one point of [jo] view it might seem impossible that the heaven should be one and unique, since in all formations and products whether of nature or of art we can distinguish the shape in itself and the shape in combination with matter. For 278 a instance the form of the sphere is one thing and the gold or bronze sphere another; the shape of the circle again is one thing, the bronze or wooden circle another. For when we state the essential nature of the sphere or circle we do not include in the formula gold or [5] bronze, because they do not belong to the essence, but if we are speaking of the copper or gold sphere we do include them. still make the distinction even if we cannot conceive or apprehend any other example beside the par-

it is

particulars of like

[25] ferent

We must

369

must be the case, and equally on the view that no such entity has a separate existence. For in every case in which the essence assert, this

ter,

be the case:

8-9

this to be true.

We

are

however, therefore compelled to assert a

Such a plurality is in fact world contains the entirety of matter, as in fact it does. But perhaps our contention can be made clearer in this way. Suppose 'aquilinity' to be curvature in the nose [jo] or flesh, and flesh to be the matter of aquilinity. Suppose further, that all flesh came together into a single whole of flesh endowed with this aquiline quality. Then neither would there be, nor could there arise, any other thing that was aquiline. Similarly, suppose flesh and bones to be the matter of man, and suppose a [ J5] man to be created of all flesh and all bones plurality of worlds.

impossible

if

this

The possibility of anbe removed. Whatever case 278 b you took it would be the same. The general rule is this: a thing whose essence resides in indissoluble union.

other

man would

substratum of matter can never come into being in the absence of all matter. Now the universe is certainly a particular and a material thing: if however, it is composed not of a part [5] but of the whole of matter, then though the being of 'universe' and of 'this universe' in a

are

still

distinct, yet there is

and no

no other universe, being made, be-

possibility of others

cause

all the matter is already included in this. remains, then, only to prove that it is composed of all natural perceptible body. It

[10] First, however, we must explain what 'heaven' and in how many senses

mean by

we we

use the word, in order to make clearer the obour inquiry, (a) In one sense, then, we

ject of

call 'heaven' the substance of the extreme circumference of the whole, or that natural body whose place is at the extreme circumference.

We

recognize habitually a special right to the [75] name 'heaven' in the extremity or upper region, which we take to be the seat of all that is

divine, (b) In another sense,

we

use this

ON THE HEAVENS

370

279 b

name for the body continuous with the extreme circumference which contains the moon,

time is the number of movement. But in the absence of natural body there is no movement,

the sun, and some of the stars; these we say are 'in the heaven', (c) In yet another sense

and outside the heaven, as we have shown, body neither exists nor can come to exist. It is

give the name to all body included within [20] the extreme circumference, since we habitually call the whole or totality 'the heaven'. The word, then, is used in three senses. Now the whole included within the extreme circumference must be composed of all physical and sensible body, because there neither is, nor can come into being, any body outside the [25] heaven. For if there is a natural body outside the extreme circumference it must be either a simple or a composite body, and its

clear then that there

must be either natural or unnatural. But it cannot be any of the simple bodies. For, first, it has been shown that that which moves [jo] in a circle cannot change its place. And, secondly, it cannot be that which moves from the centre or that which lies lowest. Naturally

the period of

we

position

1

is neither place, nor void, nor time, outside the heaven. Hence whatever is there, is of such a nature as not to occupy any place, nor does time age it; nor is there any [20] change in any of the things which lie beyond the outermost motion; they continue through their entire duration unalterable and unmodified, living the best and most selfsufficient of lives. As a matter of fact, this word

'duration' possessed a divine significance for

the ancients, for the fulfilment life

which includes

of any creature, outside of

which no natural development can

fall,

has

[25] been called its duration. On the same principle the fulfilment of the whole heaven,

which includes

the fulfilment infinity,

is

time and

all

— name based upon the always—duration immortal and

'duration'

a

they could not be there, since their proper places are elsewhere; and if these are there unnaturally, the exterior place will be natural

divine.

some other body, since a place which is unmust be natural to another: but we saw that there is no other body besides

but others feebly, enjoy. So, too, in its concerning the divine, popular philosophy often propounds the view that

to

natural to one body [35] these.

2

Then

it

not possible that any

is

279 a simple body should be outside the heaven. But, if no simple body, neither can any mixed body be there: for the presence of the simple body is involved in the presence of the mixture. Further neither can any body come into that place: for it will do so either naturally or unnaturally, and will be either sim[5] pie or composite; so that the same argument will apply, since it makes no difference whether the question 'could

then

A

come

is

to exist?'

'does

A

exist?'

or

The world

as a whole, therefore, includes appropriate matter, which is, as we saw, natural perceptible body. So that neither are there now, nor have there ever been, nor can

all its

[10] there ever be formed more heavens than one, but this heaven of ours is one and unique

and complete. It is therefore evident that there is also no place or void or time outside the heaven. For in every place body can be present; and void

which the presence of [75] body, though not actual, is possible; and said to be that in

1

it

derive the being and

[jo] other things,

some more or

Chapters 2 and 3 above. Chapter 2 above.

life

which

less articu-

lately

discussions

whatever is divine, whatever is primary and supreme, is necessarily unchangeable. This fact confirms what we have said. For there is nothing else stronger than it to move it since that

—

—

would mean more divine and it has no 279 b defect and lacks none of its proper excellences. Its unceasing movement, then, is also [35]

reasonable, since everything ceases to

when

it

comes

whose path

is

move

proper place, but the body the circle has one and the same to

its

place for starting-point

and

goal.

10

it is

ence.

2

it is

From

From our arguments

evident not only that there is not, but also that there could never come to be, any bodily mass whatever outside the circumfer-

is

fact that

Having

established these distinctions,

we may

now

proceed to the question whether the heaven is ungenerated or generated, indestructible or destructible. Let us start with a review of the theories of other thinkers; for the proofs of a theory are difficulties for the contrary theory. Besides, those who have first heard the pleas of our adversaries will be more likely to credit the [10] assertions which we are going to make. We shall be less open to the charge of procuring judgement by default. To give a satisfac[5]

tory decision as to the truth to be rather

it

is

necessary

an arbitrator than a party

to the

dispute.

That the world was generated all are agreed, some say that it is eternal,

but, generation over,

BOOK

280 b

I,

CHAPTERS

any other natural formation. Others again, with Emped[75] ocles of Acragas and Heraclitus of

others say that

it is

destructible like

Ephesus, believe that there

is

alternation in

which takes now this and continues without

the destructive process,

now

direction,

that,

Now

was generated and

yet

to assert the impossible; for

we

to assert that

eternal

is

it

cannot reasonably attribute to anything any characteristics but those which observation [20] detects in many or all instances. But in this case the facts point the other way: generated things are seen always to be destroyed. Further, a thing whose present state had no

beginning and which could not have been other than it was at any previous moment throughout its entire duration, cannot possibly be changed. For there will have to be some cause of change, and if this had been present earlier it would have made possible another condition of that to which any other condition [25] was impossible. Suppose that the world was formed out of elements which were formerly otherwise conditioned than as they are now. Then (1) if their condition was always so and could not have been otherwise, the world could never have come into being. And (2) if the world did come into being, then, clearly, their condition must have been capable of change and not eternal: after combination therefore they will be dispersed, just as in the came into combina-

past after dispersion they tion,

tradiction.

371

The

ordered,

it is

said,

1

arose out of

and the same thing cannot be same time both ordered and unordered; there must be a process and a lapse of time separating the two states. In the figure, on the [10] other hand, there is no temporal separa-

the unordered; at the

is clear then that the universe cannot be at once eternal and generated. To say that the universe alternately combines and dissolves is no more paradoxical than to make it eternal but varying in shape. It is as if one were to think that there was now

tion. It

end. is

9-11

and

this process either

has been, or could

[75] destruction and now existence when from a child a man is generated, and from a man a

when the elements not a chance system and combination, but the very same as before especially on the view of those who hold this theory, since they say that the contrary is the cause of each state. So that if the totality of [20] body, which is a continuum, is now in this order or disposition and now in that, and if the combination of the whole is a world or heaven, then it will not be the world that comes into being and is destroyed, but only its For

child.

is

it

come together

clear that

the result

is

—

dispositions.

the world

If

possible to

is believed to be one, it is imsuppose that it should be, as a generated and then destroyed,

whole, first never to reappear; since before it came into [25] being there was always present the combination prior to it, and that, we hold, could never change if it was never generated. If, on the other hand, the worlds are infinite in num-

more

[50] have been, indefinitely repeated. But if this is so, the world cannot be indestructible, and it does not matter whether the change of

this

condition has actually occurred or remains a

possible both for the ungenerated to be de-

possibility.

[30] stroyed and for the generated to persist undestroyed. (This is held in the Timaeus, where Plato says that the heaven, though it was generated, will none the less exist to

Some

who

hold that the world, though indestructible, was yet generated, try to support their case by a parallel which is illusory. They say that in their statements about its generation they are doing what geometri[35] cians do when they construct their figures, not implying that the universe really had a beginning, but for didactic reasons facilitat280* ing understanding by exhibiting the object, like the figure, as in course of formation. The two cases, as we said, are not parallel; of those

for, in the

construction of the figure,

when

the

various steps are completed the required figure forthwith results; but in these other dem-

what

is not that which was cannot be so; for antecedent and consequent, as assumed, are in con-

onstrations

results

[5] required. Indeed

it

ber the view is,

what

or

is

is

plausible.

But whether from

not, impossible will be clear

follows.

For there are some

who

think

it

So far as the heaven is concerned we have answered this view with arguments appropriate to the nature of the heaven: on the eternity.)

general question

we examine

we

shall attain clearness

when

the matter universally. 11

280b

We

must

first

distinguish the senses in

which we use the words 'ungenerated' and 'generated', 'destructible' and 'indestructible'. These have many meanings, and though it may make no difference to the argument, yet some confusion of mind must result from treating *Cp. Plato, Timaeus, 30.

ON THE HEAVENS

372 [5] as

uniform

in

its

word which has sevThe character which

use a

eral distinct applications.

is the ground of the predication will always remain obscure. The word 'ungenerated' then is used (a) in one sense whenever something now is which formerly was not, no process of becoming or change being involved. Such is the case, according to some, with contact and motion, since there is no process of coming to be in contact

used in another sense, is capable of coming [10] to be, with or without process, does not exist; such a thing is ungenerated in the sense that its generation is not a fact but a possibility. ( partake of evil; for the bad itself is [35] one of the two elements. But the other school does not treat the good and the bad even as

principles; yet in

all

things the good

is

in the

highest degree a principle. The school we first mentioned is right in saying that it is a principle, but how the good is a principle they do not

—

whether as end or as mover or as form. 1075 b Empedocles also has a paradoxical view; for he identifies the good with love, but say

is a principle both as mover (for it brings things together) and as matter (for it is part even if it happens that of the mixture).

this

Now

[5] the

same thing

is

a principle both as mat-

ter and as mover, still the being, at least, of the two is not the same. In which respect then is love It is paradoxical also that strife should be imperishable; the nature of his 'evil'

a principle?

is

just strife.

Anaxagoras makes the good a motive principle; for his 'reason' moves things. But it moves them for an end, which must be something other than it, except according to our way of stating the case; for, on our view, the [10] medical art is in a sense health. It is paradoxical also not to suppose a contrary to the

good,

i.e.

contraries

to reason.

make no

But

all

who

speak of the

use of the contraries, unless

bring their views into shape. And why some things are perishable and others imperishable,

we

no one

tells

us; for they

make

all

some make

this

existing things out of the non-

and others

make

to avoid the necessity of things one.

all

why should there always be becomand what is the cause of becoming? this no one tells us. And those who suppose two principles must suppose another, a superior principle, and so must those who believe in the Forms; for why did things come to participate, or why do they participate, in the [20] Forms? And all other thinkers are conFurther,

—

ing,

by the necessary consequence that something contrary to Wisdom, i.e. to the highest knowledge; but we are not. For there is nothing contrary to that which is primary; for all contraries have matter, and things that have matter exist only potentially; and the ignorance which is contrary to any knowledge leads to an object contrary to the object of the knowledge; but what is primary has no fronted there

is

contrary.

[25] Again,

if

besides sensible things no others

be no first principle, no order, no becoming, no heavenly bodies, but each exist, there will

principle will have a principle before

it,

the accounts of the theologians and

the nat-

ural philosophers.

But

if

the

Forms

all

or the

as in

num-

bers are to exist, they will be causes of nothing;

not that, at least not of movement. Furhow is extension, i.e. a continuum, to be produced out of unextended parts? For number will not, either as mover or as form, proor

if

ther,

[30] duce a continuum. But again there cannot be any contrary that is also essentially a pro-

ductive or

moving

possible for

it

principle; for

not to be.

Or

it

would be

at least its action

would be posterior to its potency. The world, then, would not be eternal. But it is; one of these premisses, then, must be denied. And we have said how this must be done. Further, in virtue of what the numbers, or the soul and [35] tne body, or in general the form and the thing, are one of this no one tells us anything;

—

nor can any one that the

who

say

tell,

unless he says, as

we

do,

mover makes them one. And those mathematical number is first and go

on to generate one kind of substance after an1076 a other and give different principles for each, make the substance of the universe a mere series of episodes (for one substance has no influence on another by its existence or nonexistence), and they give us many governing principles; but the world refuses to be governed badly.

'The rule of many

existing

things out of the same principles. Further, [75]

existent;

1076'

there be.' 1 1

Cf. Iliad,

11.

204.

is

not good; one ruler

let

BOOK

1076 b

XII,

CHAPTER 10— BOOK

BOOK

XIII,

CHAPTERS

1-2

607

XIII subject of our discussion will be not

they exist but

We

have stated what

is

how they

whether

exist.

the substance of sension physics 1

ble things, dealing in the treatise

2 with matter, and later with the substance existence. Now since actual has [10] which our inquiry is whether there is or is not besides the sensible substances any which is immovable and eternal, and, if there is, what it is, we must first consider what is said by others, so that, if there is anything which they say wrongly,

time that the doctrine in question is an artificial one, has been said already in our discussion of 4 difficulties we have pointed out that it is imb 1076 possible for two solids to be in the same place, and also that according to the same argu-

we may

ment

not be liable to the same objections, is any opinion common to them and us, we shall have no private grievance [75] against ourselves on that account; for one must be content to state some points better than while,

if

there

and others no worse.

one's predecessors,

Two

opinions are held on this subject;

said that the objects of

bers

and

lines

and the

mathematics

like

—

i.e.

it is

num-

—are substances, and

again that the Ideas are substances. And since (1) some recognize these as two different [20] classes the Ideas and the mathematical numbers, and (2) some recognize both as having one nature, while (3) some others say that the mathematical substances are the only substances, we must consider first the objects of mathematics, not qualifying them by any other characteristic not asking, for instance, whether they are in fact Ideas or not, or whether they are the principles and substances [25] of existing things or not, but only wheth-

—

—

er as objects of mathematics they exist or not,

and

if

this

we must

they exist,

how

they exist.

Then

separately consider the

after

Ideas

themselves in a general way, and only as far as the accepted mode of treatment demands; for most of the points have been repeatedly made even by the discussions outside our school, and, further, the greater part of our account must [30] finish by throwing light on that inquiry, 3 viz. when we examine whether the substances and the principles of existing things are numbers

and

Ideas; for after the discussion of the

Ideas this remains as a third inquiry. If

some

impossible for mathematical objects and at the same

it is

to exist in sensible things,

;

the other powers

and

characteristics also

should exist in sensible things and none of them separately. This we have said already. But, further, it is obvious that on this theory it is impossible for any body whatever to be di[5] vided; for it would have to be divided at a plane, and the plane at a line, and the line at a point, so that if the point cannot be divided, neither can the line, and if the line cannot, neither can the plane nor the solid. What difference, then, does it make whether sensible things are such indivisible entities, or, without [10] being so themselves, have indivisible entities in them? The result will be the same; if the sensible entities are divided the others will be divided too, or else not even the sensible entities can be divided. But, again, it is not possible that such entities should exist separately. For if besides the sensible solids there are to be other solids which are separate solids,

it

from them and prior is

to the sensible

plain that besides the planes also

[75] there must be other and separate planes and points and lines; for consistency requires this. But if these exist, again besides the planes and lines and points of the mathematical solid there must be others which are separate. (For incomposites are prior to compounds; and if there are, prior to the sensible bodies, bodies

[20] which are not sensible, by the same argument the planes which exist by themselves must be prior to those which are in the motion-

Therefore these will be planes and than those that exist along with the mathematical solids to which these thinkers less solids.

lines other

the objects of mathematics exist, they

exist either in sensible objects, as

That

must

say, or

assign separate existence; for the latter exist

[35] separate from sensible objects (and this also is said by some); or if they exist in neither

along with the mathematical solids, while the others are prior to the mathematical solids.) [25] Again, therefore, there will be, belonging

of these ways, either they do not exist, or they exist only in

some

1

Physics,

3

Cf. chapters 6-9.

1.

2

special sense.

Metaphysics, vn,

vm,

So that the ix.

to these planes, lines,

will

have to

be,

4Cf. in. 998*7-19.

and prior

to

them

there

by the same argument, other

METAPHYSICS

6o8

lines and points; and prior to these points in the prior lines there will have to be other points, though there will be no others prior to (i) the accumulation becomes abthese.

Now

we

surd; for

find ourselves with one set of

apart from the sensible solids; three sets of planes apart from the sensible planes those which exist apart from the sensi[jo]

solids

—

and those and those which

in the

ble planes,

mathematical

sol-

from those in the mathematical solids; four sets of lines, and five sets of points. With which of these, then, ids,

exist apart

will the mathematical sciences deal? Certainly not with the planes and lines and points in the [55] motionless solid; for science always deals with what is prior. And (2) the same account will apply also to numbers; for there will be a

from each set of from each set of realities, sense and again from those

different set of units apart

and

points,

from the

also apart

objects of

1077 b

posterior; for the incomplete spatial

magnitude

in the order of generation prior,

but in the

is

order of substance posterior, as the

lifeless is

to the living.

[20] Again, by virtue of what, and when, wil! mathematical magnitudes be one? For things in our perceptible world are one in virtue of soul, or of a part of soul, or of something else that is reasonable enough; when these are not present, the thing is a plurality, and splits up into parts. But in the case of the subjects of mathematics, which are divisible and are quantities, what is the cause of their being one and holding together? Again, the modes of generation of the objects of mathematics show that we are right. For the dimension first generated is length, [25] then comes breadth, lastly depth, and the

process

is

complete.

If,

then, that

posterior in the order of generation

which is

is

prior in

of thought; so that there will be various classes

the order of substantiality, the solid will be

of mathematical numbers.

prior to the plane

how is it possible to solve the questions which we have already enumerated in our

also

Again,

1

For the objects of from sensible things just as the objects of geometry will; but how is it possible that a heaven and its parts or anything else which has movement discussion of difficulties

1077

a

astronomy will

?

exist apart

—

and the

line.

can

shape, as the soul perhaps

Therefore well,

it

is

sights.

plain that the other senses as

and the other

objects of sense, will exist

why should one not? And if this

apart; for

set of

them do

so

and

another is so, there will also be animals existing apart, since there will be senses.

Again, there are certain mathematical theo-

way

Again, the solid is a sort of substance; for it already has in a sense completeness. But how

should exist apart? Similarly also the objects

and

in this

senses.

of optics and of harmonics will exist apart; for [5] there will be both voice and sight besides the sensible or individual voices

And

both more complete and more whole, because it can become animate. How, on the other hand, could a line or a plane be animate ? [jo] The supposition passes the power of our it is

lines

be substances? Neither as a form or

like the solid; for

is,

nor as matter,

we have no

experience of

anything that can be put together out of lines [ £5] or planes or points, while if these had been a sort of material substance, we should have observed things which could be put together out of them. 1077 b Grant, then, that they are prior in definition. Still not all things that are prior in definition are also prior in substantiality.

For

[10] rems that are universal, extending beyond these substances. Here then we shall have

when

another intermediate substance separate both

in the

from the Ideas and from the intermediates, a substance which is neither number nor points

things are prior in definition to those whose definitions are compounded out of their defi-

And

those things are prior in substantiality which

separated from other things surpass

power

them

of independent existence, but

the former entities should exist separate from

and these two properties are not coFor if attributes do not exist apart from the substances (e.g. a 'mobile' or a

sensible things.

'pale'), pale is prior to the pale

nor spatial magnitude nor time. impossible, plainly

And,

it

is

if

this is

also impossible that

nitions; [5]

extensive.

man

in defini-

[75] to the truth and to the usual views follow, one is to suppose the objects of mathematics to exist thus as separate entities. For because

but not in substantiality. For it cannot exist separately, but is always along with the concrete thing; and by the concrete thing I mean the pale man. Therefore it is plain that

they exist thus they must be prior to sensible spatial magnitudes, but in truth they must be

that

in general, conclusion contrary alike

if

tion,

neither

is

which

the result of abstraction prior nor is

produced by adding determinants it is by adding a determi-

[10] posterior; for

BOOK

1078 s

XIII,

CHAPTERS

nant to pale that we speak of the pale man. It has, then, been sufficiently pointed out that the objects of mathematics are not substances in a higher degree than bodies are, and that they are not prior to sensibles in being, but only in definition, and that they cannot exist

somewhere apart. But since it was not possible [75] for them to exist in sensibles either, it is plain that they either do not exist at all or exist in a special sense and therefore do not 'exist' without qualification. For 'exist' has

many

For

senses.

just as the universal propositions of

mathe-

matics deal not with objects which exist separately, apart from extended magnitudes and from numbers, but with magnitudes and numbers, not however qua such as to have magni[20] tude or to be divisible, clearly it is possible that there should also be both propositions

sensibles.

virtue of

2-3

609

Many properties attach to things in their own nature as possessed of each

such character; e.g. there are attributes peculiar to the animal qua female or qua male (yet there is no 'female' nor 'male' separate from animals); so that there are also attributes which belong to things merely as lengths or as planes. And in proportion as we are dealing with things which are prior in definition and sim-

knowledge has more accuracy, which abstracts from spatial magnitude is more precise than one which takes it into account; and a science is most precise if it abstracts from movement, but if it takes account of movement, it is most precise if it deals with the primary movement, for this is the simplest; and of this again uniform movement is the sim[10] pier, our

i.e.

simplicity. Therefore a science

plest form.

The same account may

and demonstrations about sensible magnitudes, not however qua sensible but qua possessed of certain definite qualities. For as there are many

and numbers; but the

propositions about things merely considered as

ceeds in

[25) in motion, apart

thing

is

and from

their

from what each such accidents, and as it is not

therefore necessary that there should be either a mobile separate

from

sensibles, or a distinct

mobile entity in the sensibles, so too in the case of mobiles there will be propositions and sci-

them however not qua mobile but only qua bodies, or again only qua [50] planes, or only qua lines, or qua divisibles, or qua indivisibles having position, or only qua indivisibles. Thus since it is true to say

ences,

which

treat

without qualification that not only things are separable but also things which are inseparable exist (for instance, that mobiles exist), it is true also to say without qualification that the objects of mathematics exist, and with the character ascribed to them by mathe-

which

maticians.

And

as

it is

true to say of the other

sciences too, without qualification, that they

deal with such

what

and such

it

pale, if the healthy thing

is

is

ence has the healthy as

its

—

not with not with the

a subject

accidental to

[35]

(e.g.

pale,

and the

sci-

subject), but with

—

which is the subject of each science with 1078 a the healthy if it treats its object qua healthy, with man if qua man: so too is it with geometry; if its subjects happen to be sensible, though it does not treat them qua

that

—

mathematical sciences will not for nor, on the [5] other hand, of other things separate from

sensible, the

that reason be sciences of sensibles

—

be given of har-

[75] monies and optics; for neither considers its objects qua sight or qua voice, but qua lines latter

are

attributes

And

mechanics too prothe same way. Therefore if we sup-

proper to the former.

pose attributes separated from their fellowand make any inquiry concerning

attributes

them

as such,

we

shall not for this reason be

any more than when one draws a line on the ground and calls it a foot long when it in error,

[20] is not; for the error premisses.

Each question

is

not included in the

will be best investigated in

—

way by setting up by an act of separation what is not separate, as the arithmetician and the geometer do. For a man qua man is one inthis

divisible thing; and the arithmetician supposed one indivisible thing, and then considered whether any attribute belongs to a man qua indivisible. But the geometer treats him neither [25] qua man nor qua indivisible, but as a solid. For evidently the properties which would have belonged to him even if perchance he had not been indivisible, can belong to him even apart from these attributes. Thus, then, geometers speak correctly; they talk about existing [30] things, and their subjects do exist; for being has two forms it exists not only in com-

—

plete reality but also materially.

Now

good and the beautiful are

since the

former always implies conduct as its subject, while the beautiful is found also in motionless things), those who assert that the mathematical sciences say nothing of the different (for the

beautiful or the

good are

in error.

For these

[35] sciences say and prove a great deal about

METAPHYSICS

6io

them; if they do not expressly mention them, but prove attributes which are their results or their definitions, it is not true to say that they tell us nothing about them. The chief forms of beauty are order and symmetry and definite-

1078 b ness, which the mathematical sciences demonstrate in a special degree. And since these (e.g. order and definiteness) are obviously causes of sciences

must

many

things, evidently these

treat this sort of causative prin-

ciple also (i.e. the beautiful) as in

some

sense

But we shall speak more plainly elsewhere about these matters. [5] a cause.

So much then for the objects of mathematics; we have said that they exist and in what sense they exist, and in what sense they are prior and in what sense not prior. Now, regarding the Ideas, we must first examine the ideal [10] theory itself, not connecting it in any way with the nature of numbers, but treating it in the form in which it was originally understood by those who first maintained the existence of the Ideas. The supporters of the ideal theory were led to it because on the question about the truth of things they accepted the Heraclitean sayings which describe all sensible [75] things as ever passing away, so that if

knowledge or thought is to have an object, there must be some other and permanent entities, apart from those which are sensible; for there could be no knowledge of things which were in a state of flux. But when Socrates was occupying himself with the excellences of character, and in connexion with them became the first to raise the problem of universal definition (for of the physicists Democritus only [20] touched on the subject to a small extent,

and defined,

and the had before this few things, whose definitions after a fashion, the hot

cold; while the Pythagoreans

treated of a

marriage

e.g. those of opportunity, justice, or

—they connected with numbers; but

it

was

nat-

ural that Socrates should be seeking the essence, for he was seeking to syllogize, and 'what a thing is' is the starting-point of syllo[25] gisms; for there was as yet none of the dialectical power which enables people even without knowledge of the essence to speculate about contraries and inquire whether the same science deals with contraries; for two things may be fairly ascribed to Socrates inductive arguments and universal definition, both of which are concerned with the starting-point but Socrates did not make [30] of science):

—

—

1079 a

the universals or the definitions exist apart: they, however, gave them separate existence,

and

was the kind

of thing they called followed for them, almost by the same argument, that there must be Ideas of all things that are spoken of universally, and it was almost as if a man wished to count certain things, and while they were few this

Ideas. Therefore

it

[55] thought he would not be able to count them, but made more of them and then counted them; for the Forms are, one may say, more numerous than the particular sensible 1079 a things, yet it was in seeking the causes of these that they proceeded from them to the Forms. For to each thing there answers an

which has the same name and

entity

exists

apart from the substances, and so also in the case of all other groups there is a one over

many, whether these be Again, of the ways

of this in

world or

eternal.

which it is proved none is convincing;

[5] that the Forms exist, for from some no inference necessarily follows,

and from some arise Forms even of things of which they think there are no Forms. For according to the arguments from the sciences there will be Forms of all things of which there are sciences, and according to the argument of the 'one over many' there will be [10] Forms even of negations, and according to the argument that thought has an object

when

the individual object has perished, there

Forms of perishable things; for we have an image of these. Again, of the most accurate arguments, some lead to Ideas of relations, of which they say there is no independent class, and others introduce the 'third man'. And in general the arguments for the Forms will be

whose existence the believers more zealous than for the exist-

destroy things for in

Forms

are

[75] ence of the Ideas; for it follows that not the dyad but number is first, and that prior to

number

is

the relative,

the absolute

—besides

and that all

this

is

prior to

the other points on

which

certain people, by following out the opinions held about the Forms, came into con-

with the principles of the theory. Again, according to the assumption

flict

on

[20] which the belief in the Ideas rests, there will be Forms not only of substances but also

many other things; for the concept is single not only in the case of substances, but also in that of non-substances, and there are sciences of other things than substance; and a thousand other such difficulties confront them. But acof

cording to the necessities of the case and the [25] opinions about the Forms, if they can be

BOOK

1080«

XIII,

CHAPTERS

shared in there must be Ideas of substances only. For they are not shared in incidentally, but each Form must be shared in as something not predicated of a subject. (By 'being shared in incidentally' I mean that if a thing shares in 'double itself, it shares also in 'eternal', but incidentally; for 'the double' happens to be [50] eternal.) Therefore the Forms will be

same names indicate suband in the ideal world (or what will be the meaning of saying that there is something apart from the particulars the one over many?). And if the Ideas and the things that share in them have the same form, there will be something common: for why should '2' be one and the same in the perish[55] able 2's, or in the 2's which are many but eternal, and not the same in the '2 itself as in the individual 2? But if they have not the same 1079 b form, they will have only the name in common, and it is as if one were to call both Callias and a piece of wood a 'man', without observing any community between substance. But the

stance in this

—

them. But

we

are to suppose that in other respects the common definitions apply to the Forms, e.g. that 'plane figure' and the other if

the circle[5] parts of the definition apply to but 'what really is' has to be added, we

itself,

must inquire whether this meaningless. For to what is

To

is

not absolutely

this to be

added?

'centre' or to 'plane' or to all the parts of

the definition? For

all

the elements in the es-

sence are Ideas, e.g. 'animal' and 'two-footed'. [10] Further, there must be some Ideal answering to 'plane' above, some nature which will

be present in

Above

all

all

the

Forms as

their genus.

one might discuss the question what

in the world the

Forms

contribute to sensible

3-6

easy to collect to

611

many and

insuperable objections

such a view. But, further,

all

other things cannot

come

[25] from the Forms in any of the usual senses of 'from'. And to say that they are patterns and

them

to use empty For what is it that works, looking to the Ideas? And any thing can both be and come into being without being copied from something else, so that, whether Socrates exists or not, a man like Soc[30] rates might come to be. And evidently this might be so even if Socrates were eternal. And there will be several patterns of the same thing, and therefore several Forms; e.g. 'animal' and 'two-footed', and also 'man-himself, will be Forms of man. Again, the Forms are

the other things share in

words and

is

poetical metaphors.

patterns not only of sensible things, but of

Forms themselves

also;

i.e.

the genus

is

the

pattern of the various forms-of-a-genus; therefore the

same thing

will be pattern

and copy.

[35] Again, it would seem impossible that sub1080a stance and that whose substance it is

should exist apart; how, therefore, could the Ideas, being the substances of things, exist apart ? 1

Phaedo the case is stated in this way that the Forms are causes both of being and of becoming. Yet though the Forms exist, still things do not come into being, unless there is something to originate movement; and many other things come into being (e.g. a house or a [5] ring) of which they say there are no Forms. Clearly therefore even the things of which they say there are Ideas can both be and come into being owing to such causes as produce the things just mentioned, and not owing to the Forms. But regarding the Ideas it is possible, both in this way and by more abstract and

—

In the

[10] accurate arguments, to collect many obwe have considered.

jections like those

things, either to those that are eternal or to

those that come into being and cease to be; for they cause neither movement nor any change [75] in them. But again they help in no wise either towards the knowledge of other things (for they are not even the substance of these,

would have been

in them), or towards they are not in the individuals which share in them; though if they were, they might be thought to be causes, as white

else they

their being,

if

causes whiteness in a white object by entering

composition. But this argument, which was used first by Anaxagoras, and later [20] into

its

by Eudoxus in his discussion of difficulties and by certain others, is very easily upset; for it is

Since

we have

discussed these points,

to consider again the results

it is

regarding

well

numnum-

which confront those who say that and first causes [75] of things. If number is an entity and its substance is nothing other than just number, as some say, it follows that either (1) there is a first in it and a second, each being different in species, and either (a) this is true of the units without exception, and any unit is inasbers

bers are separable substances

—

[20] sociable with any unit, or (h) they are all without exception successive, and any of them

METAPHYSICS

6l2 arc associablc with any, as they say

the case

is

with mathematical number; for in mathematical number no one unit is in any way different

from another. Or (c) some units must be associable and some not; e.g. suppose that 2 is first after 1, and then comes 3 and then the rest [25] of the number series, and the units in each

number

first

2 are associable with one another, and

are associable, e.g. those in the

those in the first 3 with one another, and so with the other numbers; but the units in the '2-itself are inassociable with those in the '3-

and similarly

itself;

in the case of the other

And so while mathecounted thus after 1, 2 (which consists of another 1 besides the former 1), and 3 (which consists of another 1 besides these two), and the other numbers similarly, ideal number is counted thus after 1, a distinct 2 which does not include the first 1, and [jo] successive numbers.

matical

number

—

is

—

a 3 which does not include the 2, and the rest of the number series similarly. Or (2) one kind [55] of

number must be

named, 1 one

cians speak of, last

2

must be

like the first that was which the mathematiand that which we have named

like that

a third kind.

Again, these kinds of numbers must either 1080b be separable from things, or not separable but in objects of perception (not however in the way which we first considered, 3 but

1081'

consisting of abstract units; they suppose the [20] units to have spatial magnitude. But how

was constructed so as to have magniseem unable to say. Another thinker says the first kind of number, that of the Forms, alone exists, and some the

first

1

tude, they

say mathematical

The

number

is

identical with this.

and solids is simFor some think that those which are the objects of mathematics are different from those [25] which come after the Ideas; and of those who express themselves otherwise some speak of the objects of mathematics and in a mathematical way viz. those who do not make the Ideas numbers nor say that Ideas exist; and case of lines, planes,

ilar.

—

others speak of the objects of mathematics, but not mathematically; for they say that neither is every spatial magnitude divisible into magnify] tudes, nor do any two units taken at ran-

dom make

2.

All

who

say the

is

1

an element

and principle of things suppose numbers

to

consist of abstract units, except the Pythago-

reans; but they suppose the numbers to have magnitude, as has been said before. 4 It is clear

from this statement, then, in how many ways numbers may be described, and that all the [35] wa ys have been mentioned; and all these views are impossible, but some perhaps more than others.

in the sense that objects of perception consists

of

numbers which are present

in

one kind and not another, or

them)

all

—either

of them.

[5] These are of necessity the only ways in which the numbers can exist. And of those who say that the 1 is the beginning and substance and element of all things, and that number is formed from the 1 and something else, almost

every one has described these ways; only

are inassociable.

number

no one has

in

one of

said all the units

And this has happened

reason-

[10] ably enough; for there can be no way besides those mentioned. Some say both kinds

number

exist, that which has a before and being identical with the Ideas, and mathematical number being different from the Ideas and from sensible things, and both being sep-

of

after

arable

from

and others say

sensible things;

[75] mathematical number alone exists, as the of realities, separate from sensible things.

first

And the Pythagoreans, also, believe in one kind number

—

the mathematical only they say it not separate but sensible substances are formed out of it. For they construct the whole universe out of numbers only not numbers

of

;

is

—

1

11.

5-20. 1

2

11.

23-35.

3

Cf

.

1

076* 3 8- b

1 1

First, then, let us inquire if the units are associ-

1081 a able or inassociable, and if inassociable, in which of the two ways we distinguished. For it is possible that any unity is inassociable with any, and it is possible that those in the '2itself are inassociable with those in the '3itself,

and, generally, that those in each ideal are inassociable with those in other

number

Now

(1) if all units are as[5] ideal numbers. sociable and without difference, we get mathe-

—

number only one kind of number, and the Ideas cannot be the numbers. For what sort of number will man-himself or animal-itself or any other Form be? There is one Idea of each thing, e.g. one of man-himself and matical

[10] another one of animal-itself but the simand undifferentiated numbers are infinite;

ilar

ly many, so that any particular 3 is no more man-himself than any other 3. But if the Ideas are not numbers, neither can they exist at all. For from what principles will the Ideas come? [75] It is number that comes from the 1 and

the indefinite dyad,

ments are said *

I.19.

and the

principles or ele-

to be principles

and elements of

BOOK

1082s

CHAPTERS

XIII,

number, and the Ideas cannot be ranked as either prior or posterior to the numbers. But (2) if the units are inassociable, and inassociable in the sense that any is inassociable with any other, number of this sort cannot be mathematical number; for mathematical numunits,

ber consists of undifferentiated

[20]

and the truths proved of it suit this character. Nor can it be ideal number. For 2 will not proceed immediately from 1 and the indefinite dyad, and be followed by the successive num-

—

&-7

613

becomes part 1 [20] of 3, and 3 of 4, and the same happens in the case of the succeeding numbers, but they say 4 came from the first 2 and the indefinite 2, which makes it two 2's other than the them, from the 2 and the

for 2

;

—

2-itself; if not,

and one other 2

the 2-itself will be a part of 4 will be added. And similarly 2

[25] will consist of the i-itself and another 1; if this is so, the other element cannot be an

but

indefinite 2; for

it

generates one unit, not, as

the indefinite 2 does, a definite

2.

ideal 2 are generated at the

Again, besides the 3-itself and the 2-itself how can there be other 3's and 2's? And how

as the first holder of the theory said,

do they

bers, as they say '2, 3, 4'

for the units in the

same time, whether, from unequals (coming into being when these were [25] equalized) or in some other way since,

—

if

one unit

is

to be prior to the other,

it

will be

composed of these; for when there is one thing prior and another posterior, the resultant of these will be prior to one and prior also to the 2

posterior to the other.

1 -itself, and again a next after the second and next but one after the first 1, so the units must be prior to the numbers after which they are named when we count them; e.g. there will be a third unit in 2 before 3 exists, and a fourth

others and next after the third

which

is

—

a fifth in 3 before the numbers 4 and 5 none of these thinkers has [35] exist. said the units are inassociable in this way, but

and

—Now

according to their principles it is reasonable that they should be so even in this way, though

1081 b in truth it is impossible. For it is reasonable both that the units should have pri-

and posteriority if there is a first unit or and also that the 2's should if there is a first 2; for after the first it is reasonable and

and posterior units?

absurd and fictitious, and there cannot be a first 2 and then a 3-itself. Yet there must, if the 1 and the indefinite dyad are to be is

the elements. But it

the results are impossible,

if

also impossible that these are the gen-

is

erating principles. the units, then, are differentiated, each

If

[3°] Again, since the i-itself is first, and then there is a particular 1 which is first among the

consist of prior

[jo] All this

from each, these

results

and others similar

to

[55] these follow of necessity. But (3) if those in different numbers are differentiated, but

same number are alone undifferfrom one another, even so the difficulties that follow are no less. E.g. in the 10-itself 1082* there are ten units, and the 10 is composed both of them and of two 5's. But since the 10-itself is not any chance number nor composed of any chance 5's or, for that matter, units the units in this 10 must differ. For [5] if they do not differ, neither will the 5's of which the 10 consists differ; but since these differ, the units also will differ. But if they differ, will there be no other 5's in the 10 but only those in the

entiated

—

—

ority

these two, or will there be others? If there are

first 1,

there are, what them? For there is no other 10 in the 10 but itself. But it is actually necessary on their view that the 4 should

[5] necessary that there should be a second, if a second, a third, and so with the others

and

successively.

same time,

(And

to say both things at the

and another unit is second after the ideal 1, and that a 2 is first after it, is impossible.) But they make a first unit or 1, but not also a second and a third, and a first 2, but not also a second and a third. that a unit

is first

[10] Clearly, also, it is not possible, if all the units are inassociable, that there should be a

and a 3-itself; and so with the other numbers. For whether the units are undifferentiated or different each from each, number must be counted by addition, e.g. 2 by adding [75] another 1 to the one, 3 by adding another 1 to the two, and 4 similarly. This being so, numbers cannot be generated as they generate 2-itself

not, this

is

paradoxical; and

if

[jo] sort of 10 will consist of

not consist of any chance 2's; for the indefinite 2, as they say, received the definite 2 and made

two

2's; for its

nature was to double what

it

received.

[75] Again, as to the 2 being an entity apart its two units, and the 3 an entity apart its three units, how is this possible?

from from

Either by one's sharing in the other, as 'pale

man'

is

different

from

shares in these), or

of the other, as 'man'

and

'pale'

and 'man' (for

when one is

is

different

it

a differentia

from 'animal'

'two-footed'.

[20] Again, some things are one by contact, some by intermixture, some by position; none of which can belong to the units of which the 2

METAPHYSICS

614

or the 3 consists; but as two men are not a unity apart from both, so must it be with the

And

units.

their being indivisible will

the a

first

make

[25] no difference to them; for points too are indivisible, but yet a pair of them is nothing

1083«

But

2-itself.

and

Nor

this

not possible,

is

there

if

number. the Ideas be numbers. For

is

a second

will

particular point they are right

who

in this

claim that

get, that

it

follows that there are prior and

must be different, if there are to be 1 [25] Ideas; as has been said before. For the Form is unique; but if the units are not different, the 2's and the 3's also will not be different.

posterior

2's,

and similarly with the other num-

This

For

let

apart from the two.

But

we must

consequence also

this

not for-

the 4 be simultaneous; [3°] Y et these are prior to those in the 8, and as the 2 generated them, they generated the 4's bers.

the

2's in

in the 8-itself. Therefore

if

the

first

Idea, these 2's also will be Ideas of

And

the

same account

2

is

an

some kind.

applies to the units;

[35] f° r the units in the first 2 generate the four in 4, so that all the units come to be Ideas

and an Idea

composed

will be

of Ideas.

Clearly therefore those things also of which these posite,

happen

to be the Ideas will be comone might say that animals are

e.g.

composed of animals,

there are Ideas of

if

them.

1082 b In general, to differentiate the units in any way is an absurdity and a fiction; and by a

the units

is

all Forms will be parts of one Form. And with a view to their hypothesis their statements are right, but as a whole they are wrong; for their view is very destructive, since they will [55] admit that this question itself affords some difficulty whether, when we count and say '1, 2, 3,' we count by addition or by separate portions. But we do both; and so it is absurd to reason back from this problem to so

so

—

great a difference of essence.

1083* First of is

all

number but

which

especially that

of abstract units

—so

that

if

consists

one number

neither greater nor less than another,

is

equal to it; but things that are equal and in no wise differentiated we take to be the same when we are speaking of numbers. If not, not even the 2's

in

the

10-itself

it is

will be undifferentiated,

2'

'1,

and

and number must be

unequal

thus

ceed by adding to the given number; for if we [jo] do, neither will the numbers be generated from the indefinite dyad, nor can a number be an Idea; for then one Idea will be in another,

fiction I mean a forced statement made to suit a hypothesis. For neither in quantity nor in [5] quality do we see unit differing from unit,

either equal or

must say that —why they —we do not pro-

also the reason

when we count

8 all it is

the differentia of a

if it

well to determine

number

—and of

what

a unit,

has a differentia. Units must differ either

and neither

in quantity or in quality;

of these

seems to be possible. But number qua number differs in quantity.

And

if

the units also did

number would differ from number, though equal in number of units.

differ in quantity,

[5]

Again, are the

first

units greater or smaller,

and

[10] though they are equal; for what reason will the man who alleges that they are not

do the

differentiated be able to give?

Again, if every unit another unit makes two, a unit from the 2-itself and one from the 3-itself will make a 2. Now (a) this will consist of differentiated units; and (/3) will it be

can they differ in quality. For no attribute can [10] attach to them; for even to numbers quality is said to belong after quantity. Again, quality could not come to them either from the 1 or the dyad; for the former has no quality,

prior to the 3 or posterior ? It rather seems that [75] it must be prior; for one of the units is

and the latter gives quantity; for this what makes things to be many. If the

simultaneous with the 3, and the other is simultaneous with the 2. And we, for our part, suppose that in general 1 and 1, whether the things are equal or unequal, is 2, e.g. the good and the bad, or a man and a horse; but those who hold these views say that not even two units

[75] really otherwise, they should state this quite at the beginning and determine if pos-

+

are

ones increase or diminish? All

these are irrational suppositions.

sible,

But neither

entity

regarding the differentia of the unit,

must exist, and, they mean. it

failing this,

what

is

facts are

why

differentia

Evidently then, if the Ideas are numbers, the all be associable, nor can they be [20] inassociable in either of the two ways.

units cannot

2.

[20] If the

later

number

than that of the

of the 3-itself

2, this is

greater, clearly there

equal to the

2,

is

is

surprising; also a

so that this

is

not greater

and

number

if it is

in

it

not different from

But neither

is

the

way

in

which some others

speak about numbers correct. These are those 1

1081*5-17.

BOOK

1084*

CHAPTERS

XIII,

who do

7-8

615

number has no such nature as it separable set up for it. Again, does each unit come from the

not think there are Ideas, either without qualification or as identified with certain numbers, but think the objects of mathematics

evidently

and the numbers are the first of existing things, and the 1 -itself is the starting-point of

and the

paradoxical that there should be a 1 which is first of i's, as they say, but not a 2 [25] which is first of 2's, nor a 3 of 3's; for the

[25] neither does each thing contain all the elements, nor are the units without difference;

exist

them.

It is

same reasoning

applies to

with regard to number are poses mathematical

then, the facts

all. If,

number

and one sup-

so,

alone to

exist,

the

not the starting-point (for this sort of 1 [jo] must differ from the other units; and if this is so, there must also be a 2 which is first of 2's, and similarly with the other successive numbers). But if the 1 is the starting-point, the truth about the numbers must rather be what Plato used to say, and there must be a first 2 1

is

and the numbers must not be associable w tn one another. But if on the other hand [35] one supposes this, many impossible results, as we have said, 1 follow. But either this or the other must be the case, so that if neither is,

and

3,

i

number cannot 1083 b

It

is

third version

exist separately.

evident, also, is

the worst,

from

this that the

—the view

ideal

and

those

who make

small, equalized, or one

small, another

from the great? (a)

If

great

from the the latter,

the great and in another the contrary in its nature to the great. Again, how is it with the units in the

one there

for in

small,

which

is

is

3-itself ? One of them is an odd unit. But perhaps it is for this reason that they give i-itself the middle place in odd numbers, (b) But if [jo] each of the two units consists of both the

and the small, equalized, how will the 2, which is a single thing, consist of the great and the small? Or how will it differ from the unit? great

Again, the unit is prior to the 2; for when it is destroyed the 2 is destroyed. It must, then, be the Idea of an Idea since it is prior to an Idea, [35] and

it must have come into being before what, then? Not from the indefinite dyad, for its function was to double. Again, number must be either infinite or finite; for these thinkers think of number as capable of existing separately, so that it is not it.

From

1084a

mathematical number is the same. For two mistakes must then meet in the one opinion. [5] (1) Mathematical number cannot be of this sort, but the holder of this view has to spin it out by making suppositions peculiar to himself. And (2) he must also admit all the consequences that confront those who speak of

numbers is always odd or of an even number; in one way, when 1 operates on an even number, an odd number is produced; in

number in the sense The Pythagorean

[5] another way, when 2 operates, the numbers got from 1 by doubling are produced; in

.

of 'Forms'.

version in one

way

affords

fewer difficulties than those before named, but in another way has others peculiar to itself. [10] For not thinking of number as capable of existing separately removes many of the impossible consequences; but that bodies should be composed of numbers, and that this should be mathematical number, is impossible. For it is not true to speak of indivisible spatial magnitudes; and however much there might be magnitudes of this sort, units at least have not [75] magnitude; and how can a magnitude be

composed of indivisibles? But arithmetical number, at least, consists of units, while these thinkers identify

any as

number with

real things; at

rate they apply their propositions to bodies

if

they consisted of those numbers.

If,

then,

it is

necessary,

if

number

is

a

self-

[20] subsistent real thing, that it should exist one of these ways which have been men-

in

tioned, 1

Cf.

1

2

and

if it

cannot exist in any of these,

o8ob 37-1 083*

17.

2

! 080"* 1

5-b 36.

tives

possible that neither of those alterna-

should be true. Clearly

finite; for infinite

number

is

it

cannot be

neither

in-

odd nor

even, but the generation of the generation either of an

another way, when the odd numbers operate, the other even numbers are produced. Again, if every Idea is an Idea of something, and the

numbers are

Ideas, infinite

number

itself will

be an Idea of something, either of some sensible thing or of something else. Yet this is not possible in

view of their

reasonable in

thesis

any more than

itself, at least if

it is

they arrange the

Ideas as they do. [10] But if number is finite, how far does it go? With regard to this not only the fact but the reason should be stated. But if number goes

only up to 10, as some say, firstly the Forms will soon run short; e.g. if 3 is man-himself, what number will be the horse-itself ? The series [75] of the numbers which are the several things-themselves goes up to 10. It must, then, be one of the numbers within these limits; for is these that are substances and Ideas. Yet they will run short; for the various forms of animal will outnumber them. At the same time it

it

METAPHYSICS

6i6

way

the 3 is man-himself, the other 3's are so also (for those in identical [20] numbers are similar), so that there will is

clear that

if

bi an infinite

in this

number

and

of

numbers

Idea, each of the

men;

if each 3 is an will be man-himself,

men.

not, they will at least be

if

the smaller

number

And

if

part of the greater (be-

is

ing number of such a sort that the units in the associable), then if the 4-itself is an Idea of something, e.g. of 'horse' or of 'white', man will be a part of horse, if man is [25] 2. It is paradoxical also that there should be an Idea of 10, but not of 11, nor of the succeeding numbers. Again, there both are and come to be certain things of which there are no Forms; why, then, are there not Forms of infer that the Forms are not them also? causes. Again, it is paradoxical if the numberseries up to 10 is more of a real thing and a [50] Form than 10 itself. There is no genera-

same number are

We

and there

tion of the former as one thing,

At

least

—

is

exist separately,

—

number

is

one

or 3 or 2? Inascomposite, 1 is prior,

prior

1,

but inasmuch as the universal and the form is [5] prior, the number is prior; for each of the is

part of the

number

acts as

number form.

as

its

And

matter, and

in a sense the

right angle is prior to the acute, because it is determinate and in virtue of its definition; but in a sense the acute is prior, because it is a part and the right angle is divided into acute angles. [10] As matter, then, the acute angle and the element and the unit are prior, but in respect of the form and of the substance as expressed in the definition, the right angle, and the whole consisting of the matter and the form, are prior; for the concrete thing

is

nearer to the

form and to what is expressed in the definition, though in generation it is later. How then is 1

has been said, the right angle prior to the acute,

and each

is

is

thought

and the acute

to be

to the right,

one. Accordingly they

make

1

the

But this is impossible. For the universal is one as form or substance, while the element is one as a part or as [20] matter. For each of the two is in a sense one in truth each of the two units exists potentially (at least if the number is a unity and starting-point in both ways.

—

i.e. if different numbers conof differentiated units, as they say), but

not like a heap, sist

not in complete reality; and the cause of the fell into is that they were conducting their inquiry at the same time from the standpoint of mathematics and from that of

error they

[25] universal definitions, so that (1) from the

number can

might ask which

the

in time. In the starting-point? As

former standpoint they treated unity, their

;

units

1

first

principle, as a point; for the unit

is

a point

out of the smallest parts, as some others also have done. Therefore the unit becomes the matter of numbers and at the same time prior

e.g.

as the

is

the void, proportion, the odd,

rivatives

much

and the other

of

is

and the others of this kind within the decade. For some things, e.g. movement and rest, good and bad, they assign to the originative prin[35] ciples, and the others to the numbers. This for if the is why they identify the odd with 1 odd implied 3, how would 5 be odd? Again, spatial magnitudes and all such things are explained without going beyond a definite num1084 b ber; e.g. the first, the indivisible, line, then the 2, &c; these entities also extend only up to 10. if

definition

without position. They put things together

series.

Again,

in

which way, then,

they generate the de-

complete

—

one

work on the assumpnumbers up to 10 is a

the latter. But they try to tion that the series of

1085*

they say; but both the universal, and the particular or the element, are indivisible. But [75] they are starting-points in different ways, ble,

the starting-point? Because

it is

not

divisi-

to 2;

and again

posterior, 2 being treated as a

[30] whole, a unity, and a form. But (2) because they were seeking the universal they

which can be predicated of a number, as in this sense also a part of the number. But these characteristics cannot belong at the same time to the same thing. If the i-itself must be unitary (for it differs in nothing from other i's except that it is the starting-point), and the 2 is divisible but the unit is not, the unit must be liker the i-itself [35] than the 2 is. But if the unit is liker it, it must be liker to the unit than to the 2; therefore each of the units in 2 must be prior to the 2. But they deny this; at least they generate 1085 a the 2 first. Again, if the 2-itself is a unity and the 3-itself is one also, both form a 2. From what, then, is this 2 produced? treated the unity

not contact in numbers, but sucbetween the units between which there is nothing, e.g. between those in 2 or in [5] 3, one might ask whether these succeed the i-itself or not, and whether, of the terms that Since there

is

cession, viz.

succeed it, 2 or either of the units in 2 is prior. Similar difficulties occur with regard to the the line, classes of things posterior to number, the plane, and the solid. For some construct

—

BOOK

1086 a

and

these out of the species of the 'great

XIII,

CHAPTERS

small';

[10] e.g. lines from the 'long and short', planes from the 'broad and narrow', masses from the 'deep and shallow'; which are species of the 'great

and

small'.

And

the originative principle

of such things which answers to the

1

different

thinkers describe in different ways. And in [75] these also the impossibilities, the fictions, and the contradictions of all probability are seen to be innumerable. For (i) the geometrical classes are severed from one another, unless the principles of these are implied in one an-

other in such a

way

that the 'broad

and nar-

row' is also 'long and short' (but if this is so, the plane will be line and the solid a plane; again, how will angles and figures and such [20] things be explained?). And (ii) the same happens as in regard to number; for 'long and short', &c, are attributes of magnitude, but magnitude does not consist of these, any more than the line consists of 'straight and curved', or solids of 'smooth and rough'. (All these views share a difficulty which occurs with regard to species-of-a-genus, when one posits the universals, viz. whether it is [25] animal-itself or something other than animal-itself that is in the particular animal. True, if the universal is not separable from

no

sensible things, this will present

but

if

those

the

1

who

and the numbers are

difficulty;

separable, as

express these views say,

easy to solve the difficulty,

if

it

may

one

not apply

is

the words 'not easy' to the impossible. For

when we apprehend

the unity in

2,

or in gen-

[30] eral in a number, do we apprehend a thing-itself or something else?).

Some, then, generate spatial magnitudes from matter of this sort, others from the point and the point is thought by them to be not 1 but something like 1 and from other matter

—

—

like plurality,

[35]

which

but not identical with

principles

difficulties occur.

For

none the

if

less

the matter

is

617

number out

definite dyad.

of the one

and the

in-

For the one view generates num-

ber from the universally predicated plurality,

and not from

a particular plurality;

other generates

from a particular

it

and the

plurality,

but the first; for 2 is said to be a 'first plurality'. [10] Therefore there is practically no difference, but the same difficulties will follow, is it intermixture or position or blending or generation? and so on. Above all one might press the question 'if each unit is one, what does it come from?' Certainly each is not the one-itself. It must, then, come from the oneitself

and

plurality, or a part of plurality.

sible, for it is

from a part

is

a plurality

it

will be a plurality

unit will be divisible)

is

many

of plurality involves

objections; for (a) each of the parts indivisible (or

To

imposindivisible; and to generate it

[75] say that the unit

other

must be and the

and the elements

will

[20] not be the one and plurality; for the single units do not come from plurality and the one.

Again, (/3) the holder of this view does nothing but presuppose another number; for his plurality of indivisibles

we must

is

a

number. Again,

inquire, in view of this theory also,

whether the number is infinite or finite. For there was at first, as it seems, a plurality that [25] was itself finite, from which and from the one comes the finite number of units. And there

and

another plurality that

is

is

plurality-itself

which sort of plurality, then, is the element which co-operates with the one? One might inquire similarly about the point, i.e. the element out of which they make spatial magnitudes. For surely this is not the one and only point; at any rate, then, let them say out of what each of the other [jo] points is formed. Certainly not of some infinite plurality;

distance

-f-

the point-itself.

Nor

again can

it;

about

there be indivisible parts of a distance, as the

the

same

elements out of which the units are said to be

one, line

made are indivisible parts of plurality; for number consists of indivisibles, but spatial

and plane and solid will be the same; for from the same elements will come one and the same 1085 b thing. But if the matters are more than one, and there is one for the line and a second for the plane and another for the solid, they either are implied in one another or not, so that the same results will follow even so; for either the plane will not contain a line or

be a line. Again,

construct

8-9

it

will

magnitudes do not. All these objections, then, and others of the make it evident that number and

[55] sort spatial

magnitudes cannot

exist

things. Again, the discord about

apart from numbers be-

1086a tween the various versions it is

is a sign that the incorrectness of the alleged facts them-

selves that brings confusion into the theories.

how number

can consist of the one [5] and plurality, they make no attempt to explain; but however they express themselves, the same objections arise as confront those who

For those who make the objects of mathematics alone exist apart from sensible things, seeing the difficulty about the Forms and their [5] fictitiousness, abandoned ideal number and

METAPHYSICS

6i8 posited mathematical. But those

who wished

to

same time also numbers, but did not see, if one assumed these principles, how mathematical number was to exist apart from ideal, made ideal and mathematical number the same in words, since in fact

make

Forms

the

at the

—

[10] mathematical number has been destroyed; for they state hypotheses peculiar to themselves

and not those of mathematics. supposed that the Forms

Forms

numbers and

are

And

exist

he

who first

and that the

that the objects of

mathematics exist, naturally separated the two. Therefore it turns out that all of them are right in some respect, but on the whole not right. And they themselves confirm this, for their state[75] ments do not agree but conflict. The cause that their hypotheses

is

and

their principles are

And it is hard to make a good case out of bad materials, according to Epicharmus 'as false.

1

:

soon as

'tis

said,

'tis

seen to be wrong.'

But regarding numbers the questions we have raised and the conclusions we have reached are sufficient (for while he who is already convinced might be further convinced [20] by a longer discussion, one not yet convinced would not come any nearer to conviction); regarding the first principles and the first causes and elements, the views expressed by those who discuss only sensible substance have been partly stated in our works on na2 ture, and partly do not belong to the present inquiry; but the views of those who assert that [25]

there are other substances besides the

sensible must be considered next after those we have been mentioning. Since, then, some say that the Ideas and the numbers are such substances, and that the elements of these are elements and principles of real things, we must inquire regarding these what they say and in

what sense they say it. Those who posit numbers only, and [jo] mathematical, must be considered but as regards those

who

these later;

believe in the Ideas

one might survey at the same time their way of thinking and the difficulty into which they fall. For they at the same time make the Ideas universal and again treat them as separable and as individuals. That this is not possible has 3 [35] been argued before. The reason why those versal

who

described their substances as uni-

combined these two

one thing,

is

characteristics in

that they did not

make

substances

1

Fr. 14, Diels, Vorsokratiker. 1. 4-6; On the Heavens, in. 3-4; and Corruption, 1. 1 2

Physics,

3

in. 1003* 7-17.

On

Generation

1086 b

identical with sensible things. They thought that the particulars in the sensible world were

1086 b

in a state of flux and none of them remained, but that the universal was apart from these and something different. And Socrates gave the impulse to this theory, as we said in our earlier discussion, 4 by reason of his definitions, but he did not separate universals from individuals; and in this he thought rightly, in [5] not separating them. This is plain from the results; for without the universal it is not possible to get knowledge, but the separation is the cause of the objections that arise with regard to the Ideas. His successors, however, treating it as necessary, if there are to be any

substances besides the sensible and transient substances, that they must be separable, had no others, but gave separate existence to these uni-

[10] versally predicated substances, so that it followed that universals and individuals were almost the same sort of thing. This in itself, then,

would be one

difficulty in the

view

we

have mentioned. 10

Let us

now mention

a point

which presents

certain difficulty both to those

who

a

believe in

and to those who do not, and which was stated before, at the beginning, among the problems. If we do not suppose substances to be separate, and in the way in which the Ideas

[75]

individual things are said to be separate, we shall destroy substance in the sense in which

we understand

'substance'; but

substances to be separable,

how

if

we conceive we to con-

are

and their principles ? [20] If they are individual and not universal, (a) real things will be just of the same number

ceive their elements

as the elements, and (b) the elements will not be knowable. For (a) let the syllables in speech be substances, and their elements elements of substances; then there must be only one ba and [25] one of each of the syllables, since they are not universal and the same in form but each is one in number and a 'this' and not a kind possessed of a common name (and again they suppose that the 'just what a thing is' is in each case one). And if the syllables are unique, so too are the parts of which they consist; there will not, then, be more a's than one, nor more [30] than one of any of the other elements, on the same principle on which an identical syllable cannot exist in the plural number. But if this is so, there will not be other things existing besides the elements, but only the elements. 4 i78 b 17-30.

BOOK

1087 b

CHAPTERS 9-10— BOOK

XIII,

(b) Again, the elements will not be even knowable; for they are not universal, ana knowl1

edge

is

of universals. This is clear from demonand from definitions; for we do not

strations

conclude that this triangle has

its

angles equal

[55] to two right angles, unless every triangle has its angles equal to two right angles, nor that this man is an animal, unless every man is

an animal. But if the principles are universal, either the

1087 a substances composed

of

them

are also

or non-substance will be prior to substance; for the universal is not a substance, but the element or principle is universal, and universal,

the element or principle is prior to the things of which it is the principle or element. [5] All these difficulties follow naturally, when they make the Ideas out of elements and at the

same time claim that apart from the substances which have the same form there are Ideas, a single separate entity. But if, e.g. in the case of the elements of speech, the as and the £'s may quite well be many and there need be no aitself and ^-itself besides the many, there may

CHAPTER

XIV,

be, so far as this goes,

an

619

1

infinite

number

of

[10] similar syllables. The statement that all knowledge is universal, so that the principles of

things must also be universal and not separate substances, presents indeed, of all the points we have mentioned, the greatest difficulty, but yet the statement

in a sense true, although in a

is

For knowledge, like the know', means two things, of which one is potential and one actual. The potency, being, as matter, universal and indefinite, deals with the universal and indefinite; but the actuality, being definite, deals with a definite object, being a 'this', it deals with a 'this'. But per accidens sight sees universal colour, because [75] sense

verb

not.

it is

'to

which it sees is colour; and this individual a which the grammarian investigates is an a. For if the principles must be universal, what is derived from them must also be universal, as in demonstrations; and if this is so, there will be nothing capable i.e. no substance. But of separate existence evidently in a sense knowledge is universal, [25] and in a sense it is not. this individual colour

[20]

—

BOOK XIV

—matter

for the

One, and others making plu-

matter for the One. (The former generate numbers out of the dyad of the unequal, i.e. of the great and small, and the other thinker we have referred to generates them out of plurality, while according to both it is generated by the essence of the One.) For even the philosopher who says the unequal and the One are [10] the elements, and the unequal is a dyad rality

Regarding this kind of substance, what we have said must be taken as sufficient. All philosophers

make

the

first

principles contraries:

[50] as in natural things, so also in the case of unchangeable substances. But since there can-

not be anything prior to the first principle of things, the principle cannot be the principle

all

something else. To white is a principle, not qua anything else but qua

and yet be an suggest this first

is

attribute of

like saying that the

white, but yet that

it is

predicable of a subject,

being white presupposes its [55] being something else; this is absurd, for then that subject will be prior. But all things which are generated from their contraries involve an i.e.

that

its

underlying subject; a subject, then, must be present in the case of contraries, if anywhere. 1087 b All contraries, then, are always predi-

and none can exist apart, but appearances suggest that there is nothing contrary to substance, argument confirms

cable of a subject, just as

this. all

No

contrary, then,

is

the

first

things in the full sense; the

principle of

first

principle

something different. But these thinkers make one of the con[5] traries matter, some making the unequal

is

which they take

to be the essence of plurality

composed of the great and small, treats the unequal, or the great and the small, as being one, and does not draw the distinction that they are one in definition, but not in number. But they do not describe rightly even the principles which they call elements, for some name the great and the small with the One and treat [75] these three as elements of numbers, two being matter, one the form; while others name the many and few, because the great and the small are more appropriate in their nature to magnitude than to number; and others name rather the universal character common — which exceeds and that which

to these

'that

ceeded'.

None

is

ex-

of these varieties of opinion

makes any difference to speak some of the consequences; they [20] abstract objections, which

of, in

view of

affect only the

these thinkers take care to avoid because the demonstrations they themselves offer are abstract, with this

—

METAPHYSICS

620

exception, that if the exceeding and the exceeded are the principles, and not the great and the small, consistency requires that num-

come from the elements before 2 number is more universal than 2, as exceeding and the exceeded are more uni-

ber should

does; for the

[25] versal than the great and the small. But as is, they say one of these things but do not say the other. Others oppose the different and it

the other to the One, ity to

the One. But

consist of contraries,

and others oppose if,

plural-

as they claim, things

and

to the

One

either

nothing contrary, or if there is to be anything it is plurality, and the unequal is contrary to the equal, and the different to the same, there

is

[50 J and the other to the thing itself, those who oppose the One to plurality have most claim to plausibility, but even their view is inadequate, for the One would on their view be a few; for plurality

is

opposed to fewness, and the many

to the few.

'The one' evidently means a measure. And in every case there is some underlying thing with [55] a distinct nature of its own, e.g. in the scale a quarter-tone, in spatial magnitude a finger or a foot or something of the sort, in

rhythms a beat or a syllable; and similarly in 1088 a gravity it is a definite weight; and in the same way in all cases, in qualities a quality, in quantities a quantity (and the measure is indivisible, in the former case in kind, and in the latter to the sense); which implies that the one is not in itself the substance of anything.

And

this

is

reasonable; for 'the one'

means the

[5] measure of some plurality, and 'number' means a measured plurality and a plurality of measures. (Thus it is natural that one is not a number; for the measure is not measures, but both the measure and the one are startingpoints.) The measure must always be some identical thing predicable of all the things it measures, e.g. if the things are horses, the measure is 'horse', and if they are men, 'man'. If [10] they are a man, a horse, and a god, the measure is perhaps 'living being', and the number of them will be a number of living beings. If the things are 'man' and 'pale' and 'walking', these will scarcely have a number, because all belong to a subject which is one and the same in number, yet the number of these will be a number of 'kinds' or of some such term.

Those who treat the unequal as one thing, and the dyad as an indefinite compound of great and small, say what is very far from being probable or possible. For (a) these are

1088 b

modifications and accidents, rather than subnumbers and magnitudes the many

—

strata, of

and few of number, and the great and small of magnitude like even and odd, smooth and [20] rough, straight and curved. Again, (b) apart from this mistake, the great and the small, and so on, must be relative to something; but what is relative is least of all things a kind of entity or substance, and is posterior to quality and quantity; and the relative is an accident [25] of quantity, as was said, not its matter, since something with a distinct nature of its own must serve as matter both to the relative in general and to its parts and kinds. For there

—

nothing either great or small, many or few, something else, which without having a nature of its own is many or few, great or small, or relative to something is

or, in general, relative to

A

else.

sign that the relative

is

least of all a

[30] substance and a real thing is the fact that it alone has no proper generation or destruction or movement, as in respect of quantity is increase and diminution, in respect of quality alteration, in respect of place locomo-

there

tion, in respect of substance

simple generation

and destruction. In respect of relation there is no proper change; for, without changing, a thing will be now greater and now less or [35] equal, if that with which it is compared 1088 b has changed in quantity. And (c) the matter of each thing, and therefore of substance, must be that which is potentially of the nature in question; but the relative is neither potentially nor actually substance. It is strange, then, or rather impossible, to make not-substance an element in,

and prior

to,

substance;

for all the categories are posterior to substance.

Again, (d) elements are not predicated of the things of which they are elements, but many [5] and few are predicated both apart and to-

gether of number, and long and short of the line, and both broad and narrow apply to the plane. If there is a plurality, then, of which the one term, viz. few, is always predicated, e.g. 2

(which cannot be many, for if it were many, 1 would be few), there must be also one which is [10] absolutely many, e.g. 10 is many (if there is no number which is greater than 10), or 10,000.

How then, in view of this, can number

consist of

few and many? Either both ought

to be predicated of

it,

or neither; but in fact

only the one or the other

is

predicated.

[75]

We

must inquire

generally,

whether eternal

[75] things can consist of elements.

If

they do,

BOOK

1089 b

CHAPTERS

XIV,

1-2

621

what

sort of 'one', then, are all the

they will have matter; for everything that consists of elements is composite. Since, then, even

categories),

which it had it come into being, have come into being, and since everything comes to be what it comes to be out of that which is it potentially (for it could not have come to be out of that which had not this capacity, nor could it consist of such elements), and since the potential can be this being so, how[20] either actual or not,

[10] not to be? Is it the substances that are one, or the affections and similarly the other so that the categories as well, or all together

if

a thing exists for ever, out of that of consists it would necessarily also, if

—

number

ever everlasting

or anything else that

must be capable of not existing, just as that which is any number of years old is as capable of not existing as that which is a has matter

is, it

day old;

this

if

is

capable of not existing, so

is

things that are,

non-being

if

is

to be supposed

—

much' and the other categories that indicate each some one class of being will all be one? But it is strange, or rather impossible, that the coming into play 'this'

and the

and the

'such'

'so

of a single thing should bring of that

which

much', part a

'so

it

about that part

a 'this', part a 'such', part a

is is

'here'.

[75] Secondly, of what sort of non-being and being do the things that are consist? For 'non-

being' also has

and

many

senses, since 'being' has;

man' means not being a

'not being a

cer-

which has lasted for a time so long that it has no limit. They cannot, then, be eternal, since that which is capable of not existing is not eternal, as we had occasion to show in [25] another context. If that which we are now saying is true universally that no suband if stance is eternal unless it is actuality

tain substance, 'not being straight' not being

the elements are matter that underlies substance, no eternal substance can have elements

that are, the false

that

1

—

—

it, of which it consists. There are some who describe the element which acts with the One as an indefinite dyad, and object to 'the unequal', reasonably enough,

present in

[30] because of the ensuing difficulties; but they have got rid only of those objections which inevitably arise from the treatment of the un-

equal,

which

i.e.

the relative, as an element; those from this opinion must con-

arise apart

front even these thinkers, whether it is ideal number, or mathematical, that they construct

of a certain quality, 'not being three cubits long' not being of a certain quantity.

What

being and non-being, then, by their

sort of

union pluralize the things that are? This 3 [20] thinker means by the non-being the union of which with being pluralizes the things

why

and the character of

falsity.

used to be said that we must assume something that is false, as geometers assume the line which is not a foot long to be a foot long. But this cannot be so. For neither do geometers assume anything false (for the enunciation is extraneous to the inference), nor is it [25] non-being in this sense that the things that are are generated from or resolved into. But since 'non-being' taken in its various cases has

This

as

is

also

many

it

and beand so is

senses as there are categories,

sides this the false

the potential,

it

is

is

man from

said not to be,

from

this that

generation

the fact that they framed the difficulty in an obsolete form. For they thought that all things

which is not man but [30] potentially man, and white from that which is not white but potentially white, and this whether it is some one thing that is generated or many.

would be one (viz. Being itself), if one did not join issue with and refute the saying of

sense

Parmenides: 2

things that are

proceeds,

out of those elements. [35] There 1089 a into

are

many causes which led them off

these explanations,

and

especially

that are

lines

'For never will this be proved, that things 7 that are not are.

They thought

it

necessary to prove that that

—

But,

—

first, if

'being' has

means sometimes is

many

senses (for

it

substance, sometimes that

it

of a certain quality, sometimes that

certain quantity, 1

Cf. ix, io5ob 7

2

Fr. 7 .

fif.;

and

it is

of a

at other times the other

On the Heavens, 1.

12.

question evidently of

'the

and

is,

bodies.

how

being, in the

many; for the generated are numbers and

substances',

Now

it is

is

strange to inquire

how

which is not is; for only thus of that which is and something else could the things that are be composed, if they are many. [5]

The

that

being in the sense of the 'what' is many, [35] and not how either qualities or quantities

many. For surely the indefinite dyad or and the small' is not a reason why there should be two kinds of white or many 1089 b colours or flavours or shapes; for then these also would be numbers and units. But if they had attacked these other categories, they would have seen the cause of the plurality in substances also; for the same thing or someare

'the great

3

Plato;

cf.

Sophist, 237, 240.

METAPHYSICS

622

thing analogous is the cause. This aberration is the reason also why in seeking the opposite [5] of being and the one, from which with being and the one the things that are proceed, they posited the relative term (i.e. the unequal), which is neither the contrary nor the contradictory of these, and is one kind of being as 'what' and quality also are. They should have asked this question also, how relative terms are many and not one. But as it is, they inquire how there are many units [10] besides the first 1, but do not go on to inquire how there are many unequals besides the unequal. Yet they use them and speak of

and small, many and few (from which proceed numbers), long and short (from which proceeds the line), broad and narrow (from which proceeds the plane), deep and shallow (from which proceed solids); and they speak great

more kinds

of yet

of relative term.

why

the reason, then,

there

What

is

a plurality of

is

these? necessary, then, as

It is

[75]

we

say, to pre-

suppose for each thing that which is it potentially; and the holder of these views further

what

declared 'this'

—

and

that

is

which

a substance but

viz. that

it is

is

the relative (as

'the qualitative'),

which

potentially a

is

not in if

itself being he had said

was much more necessary, as we said, if he was inquiring how beings are many, not to inquire about those in the same category how 1

it

—

many

substances or

many

qualities

how

beings as a whole are many; for some some modifications, some relations. In the categories other than substance there is yet another problem involved in the [25] existence of plurality. Since they are not

but

are substances,

separable tities

from substances,

many

are

becomes and

is

and quansubstratum

qualities

just because their

many;

yet there ought to be a

matter for each category; only

it

cannot be

separable from substances. But in the case of 'thises', it is possible to explain how the 'this' is

many

things, unless a thing

[50] as both a 'this' The difficulty arising

and the 'what' whence or how

visible. If, then, the quantitative

are different,

we

are not told

1090 a the 'what' is many; but if any one says they are the same, he has to face many inconsistencies.

One might fix one's attention also on the question, regarding the numbers, what justifies the belief that they exist. To the believer in Ideas they provide

some

sort of cause for ex-

[5] isting things, since each number is an Idea, and the Idea is to other things somehow or

other the cause of their being; for let this supposition be granted them. But as for him who

does not hold this view because he sees the inherent objections to the Ideas (so that it is not for this reason that he posits numbers), but

who

mathematical number,

posits

why must

[10] we believe his statement that such number exists, and of what use is such number to other things? Neither does he who says it ex-

maintain that it is the cause of anything (he rather says it is a thing existing by itself), nor is it observed to be the cause of anything; for the theorems of arithmeticians will all be [75] found true even of sensible things, as was ists

said before.

2

neither potentially

is

the one or being, nor the negation of the one [20] nor of being, but one among beings. And

there are

1090*

iS5] quantity, and so does the 'unit', unless it means a measure or the quantitatively indi-

is

to be treated

and a general character. from the facts about sub-

As

for those, then,

exist

and

to be

who

suppose the Ideas to

numbers, by their assumption

in virtue of the

method

of setting out each

—

term apart from its instances of the unity of each general term they try at least to explain

somehow why number must

exist.

Since their

reasons, however, are neither conclusive nor in

themselves possible, one must not, for these reasons at

least, assert

the existence of number.

[20] Again, the Pythagoreans, because they saw many attributes of numbers belonging to sensible bodies, supposed real things to be

bers

—not

num-

separable numbers, however,

but

which real things consist. But why? Because the attributes of numbers are present in a musical scale and in the heavens and in

numbers

of

[25] many other things. Those, however, who say that mathematical number alone exists

if

the

'this'

cannot according to their hypotheses say anything of this sort, but it used to be urged that these sensible things could not be the subject of the sciences. But we maintain that they are,

are not the same,

we

are not told

as

stances

many

is

rather this,

how

there are actually

substances and not one.

and the quantitative how and why the things that are are many, but how quantities are many. For all 'number' means a But further,

la

34-

we

said before.

objects of

3

And

it

is

evident that the

mathematics do not

2

Cf. xiii.

3, esp.

3

Cf. xiii.

3.

io77 b 17-22.

exist apart; for

BOOK

1091 a

XIV,

CHAPTERS

they existed apart their attributes would not the [50] have been present in bodies. Pythagoreans in this point are open to no obif

Now

but in that they construct natural bodies out of numbers, things that have lightness and weight out of things that have not weight or lightness, they seem to speak of another heaven and other bodies, not of the sensijection;

[55] ble. But those who make number separaassume that it both exists and is separable

2-3

623

things? These contribute nothing, as the objects of mathematics contribute nothing. But

any theorem true of them, unless change the objects of mathematics and invent doctrines of our own. But it is not [jo] hard to assume any random hypotheses and spin out a long string of conclusions. These thinkers, then, are wrong in this way, in wanting to unite the objects of mathematics with not even

is

we want

to

And

who

two

ble

the Ideas.

because the axioms would not be true of sensible things, while the statements of mathematics

kinds of number, that of the Forms and that which is mathematical, neither have said nor can say how mathematical number is to exist and of what it is to consist. For they place it

are true

and

and

'greet the soul';

similarly with

the spatial magnitudes of mathematics.

1090 b

It

is

evident, then, both that the rival theory

and that the diffinow, why if numbers are

will say the contrary of this,

culty in

we

1

raised just

no way present

in sensible things their at-

tributes are present in sensible things, has to be

solved by those

who

hold these views.

[5] There are some who, because the point is the limit and extreme of the line, the line of the plane, and the plane of the solid, think there must be real things of this sort. We must therefore examine this argument too, and see whether it is not remarkably weak. For (i) ex-

tremes are not substances, but rather all these [10] things are limits. For even walking, and movement in general, has a limit, so that on their theory this will be a 'this' and a substance. But that is absurd. Not but what (ii) even if they are substances, they will all be the substances of the sensible things in this world; for

is

it

Why

to these that the

argument applied.

then should they be capable of existing

apart ?

Again, if we are not too easily satisfied, we may, regarding all number and the objects of mathematics, press this difficulty, that they con[75] tribute nothing to one another, the prior to the posterior; for if number did not exist,

none the those

less spatial

who maintain

magnitudes would

exist for

the existence of the objects

and if spatial magnitudes and sensible bodies would

of mathematics only,

did not exist.

exist, soul

But the observed

facts

show

that nature

[20] is not a series of episodes, like a bad tragedy. As for the believers in the Ideas, this

them; for they construct spatial magnitudes out of matter and number, lines

difficulty misses

out of the number 2, planes doubtless out of out of 4, or they use other numbers,

3, solids

—

which makes no difference. But will these magnitudes be Ideas, or what is their manner of [25] existence, and what do they contribute to la29.

those

first

posited

[35] between ideal and sensible number. If it consists of the great and small, it will be the same as the other ideal number (he (i)

—

makes

—

magnitudes out of some other small and great). And if (ii) he names some 1091 a other element, he will be making his spatial

elements rather many. And if the principle of each of the two kinds of number is a 1, unity will be something common to these, and we must inquire how the one is these many things, while at the same time number, according to him, cannot be generated except from one and an indefinite dyad. [5] All this is absurd, and conflicts both with itself and with the probabilities, and we seem to see in it Simonides' 'long rigmarole' 2 ; for the long rigmarole comes into play, like those of slaves, when men have nothing sound to say. And the very elements the great and the small seem to cry out against the violence [10] that is done to them; for they cannot in any way generate numbers other than those got from 1 by doubling. It is strange also to attribute generation to

—

—

things that are eternal, or rather this the things that are impossible.

is

one of

There need be

no doubt whether the Pythagoreans attribute [75] generation to them or not; for they say plainly that when the one had been constructed, whether out of planes or of surface or of seed or of elements which they cannot eximmediately the nearest part of the unand limited by the limit. But since they are constructing a world and wish to speak the language of natural science, it is fair to make some examination of their physical theories, but to let them press,

limited began to be constrained

[20] off from the present inquiry; for we are investigating the principles at work in un-

changeable things, so that it is numbers of this kind whose genesis we must study. 2

Simonides Ceius, Fr. 189. Bergk.

METAPHYSICS

624

1092 s

and most

self-sufficient this

These thinkers say there is no generation of odd number, which evidently implies that there is generation of the even; and some present the even as produced first from unequals when these are the great and the small [25] equalized. The inequality, then, must bethe

—

—

long to them before they are equalized. If they had always been equalized, they would not have been unequal before; for there is nothing before that which is always. Therefore evidently

they are not giving their account of the gen-

eration of

numbers merely

to assist contempla-

tion of their nature.

A

and a reproach to any one who [jo] finds it no difficulty, are contained in the question how the elements and the principles are related to the good and the beautiful; the difficulty is this, whether any of the elements is such a thing as we mean by the good itself and the best, or this is not so, but these are later difficulty,

than the elements. The theologians with some thinkers of the presto] ent day, who answer the question in the negative, and say that both the good and the beautiful appear in the nature of things only when that nature has made some progress. (This they do to avoid a real objection which in origin

seem

to agree

confronts those

who

say, as

some

do, that the

1091 b one is a first principle. The objection arises not from their ascribing goodness to the first principle as an attribute, but from their making the one a principle and a principle in the sense of an element and generating number from the one.) The old poets agree with this inasmuch as they say that not those who [5] are first in time, e.g. Night and Heaven or Chaos or Ocean, reign and rule, but Zeus. These poets, however, are led to speak thus

—

—

only because they think of the rulers of the world as changing; for those of them who combine the two characters in that they do not use mythical language throughout, e.g. Pherecydes [10] and some others, make the original generating agent the Best, and so do the Magi, and

some of the later sages also, e.g. both Empedocles and Anaxagoras, of whom one made love an element, and the other made reason a principle.

Of

those

who maintain

of the unchangeable substances

the existence

some

very quality

—

—

self-

and self-maintenance belongs primarily in some other way than as a good. But indeed it can be for no other reason indesufficiency

than because its nagood. Therefore to say that the first [20] principle is good is probably correct; but that this principle should be the One or, if not that, at least an element, and an element of structible or self-sufficient

ture

is

numbers,

impossible. Powerful objections

is

avoid which some have given up the theory (viz. those who agree that the One is a first principle and element, but only of mathematical number). For on this view all the units arise, to

[25] become identical with species of good, and there is a great profusion of goods. Again, if the Forms are numbers, all the Forms are identical with species of good. But let a man assume Ideas of anything he pleases. If these are Ideas only of goods, the Ideas will not be substances; but if the Ideas are also Ideas of substances, all animals and plants and all indi-

viduals that share in Ideas will be good, [jo] These absurdities follow, and it also follows that the contrary element, whether it is i.e. the great and (Hence one thinker avoided attaching the good to the One, because it would necessarily follow, since generation is from contraries, that badness is the

plurality or the unequal,

small,

the bad-itself.

is

fundamental nature of plurality; while others [35] sa Y inequality follows, then, that

is

all

—the One

the nature of the bad.)

It

things partake of the bad

itself, and that numbers more undiluted form than 1092a spatial magnitudes, and that the bad is the space in which the good is realized, and that it partakes in and desires that which tends

except one

partake of

to destroy trary.

that

for contrary tends to destroy con-

it;

And

if,

which

actual fire

in a

it

is is

bad will be

as

we were

saying, the matter

is

potentially each thing, e.g. that of

that

which

is

potentially

fire,

the

just the potentially good.

[5] All these objections, then, follow, partly because they make every principle an element, partly because they make contraries principles, partly because they make the One a principle, partly because they treat the numbers as the first substances, and as capable of existing apart,

and

as

Forms.

say the

One

itself is the good itself; but they thought substance lay mainly in its unity. [75] This, then, is the problem, which of the

its

—

two ways strange

if

of speaking

is

which

is

to that

If,

then,

it is

equally impossible not to put the

would be

good among the first principles and to put it among them in this way, evidently the prin-

primary and eternal

[10] ciples are not being correctly described,

right. It

BOOK

1092 b nor are the

first

substances.

Nor

XIV,

does any one

conceive the matter correctly if he compares the principles of the universe to that of animals

and

plants,

on the ground that the more comcomes from the indefinite and inwhich is what leads this thinker to

plete always

complete

—

say that this

is

also true of the first principles of

reality, so that the

One

[75] existing thing. This in this world of animals ciples it is

not

a

itself is is

not even an

incorrect, for

and plants the

pound

the contrary destroys 1

it,

e.g. 'strife' de-

should not; for

not to that that it is contrary). Once more, it has not been determined at all in which way numbers are the causes of subwhether (1) as boundstances and of being

first.

out of place, also, to generate place simultaneously with the mathematical solids (for

and

hence they are separate in place; but mathe[20] matical objects are nowhere), and to say that they must be somewhere, but not say what kind of thing their place is.

Those who say that existing things come from elements and that the first of existing things are the numbers, should have first distinguished the senses in which one thing comes from another, and then said in which sense number comes from its first principles. By intermixture ? But ( 1 ) not everything is [25] capable of intermixture, and (2) that which is produced by it is different from its elements, and on this view the one will not remain separate or a distinct entity; but they want it to be so. By juxtaposition, like a syllable? But then (1) the elements must have position; and (2)

who

thinks of number will be able to think of the unity and the plurality apart; number then will be this a unit and plurality, or the

he

one contrary the compound is or has come to Again, why in the world do the other things that come from contraries, or that have contraries, perish (even when all of the contrary is used to produce them), while number [5] does not? Nothing is said about this. Yet whether present or not present in the combe.

prin-

from which these come are complete; for that produces a man, and the seed is

peculiar to the individual things,

625

stroys the 'mixture'

man

is

4-6

even

It is

place

CHAPTERS

—

one and the unequal. Again, coming from certain things means in one sense that these are still to be found in the product, and in another that they are not; in [30] which sense does number come from

(yet

it

—

(as points are of spatial

aries

magnitudes).

[10] This is how Eurytus decided what was the number of what (e.g. one of man and an-

other of horse), viz. by imitating the figures of living things with pebbles, as some people bring numbers into the forms of triangle and

Or (2) is it because harmony is a ratio [75] of numbers, and so is man and everything else? But how are the attributes white square.

—

—

and sweet and hot numbers? Evidently it is not the numbers that are the essence or the causes of the form; for the ratio

while the number

is

is

the essence,

the matter. E.g. the es-

is number only in this way, 'three parts of fire and two of earth'. 2 And a number, whatever number it is, is al-

sence of flesh or bone

ways

a

number

of certain things, either of

parts of fire or earth or of units; but the es-

[20] sence thing to so

is

that there

much

is

so

much

of one

of another in the mixture;

and this is no longer a number but a ratio of mixture of numbers, whether these are corporeal or of any other kind. Number, then, whether it be number in gen-

number which consists of abstract neither the cause as agent, nor the mat-

eral or the

units, ter,

is

nor the ratio and form of things. Nor, of the final cause.

[25] course,

is it

ated can

One might

also raise the question

ent in

good

Only things that are genercome from elements which are presthem. Does number come, then, from its

it

is

these elements?

elements as from seed? But nothing can be excreted from that it

come from

its

which

contrary,

is

its

indivisible.

Does

contrary not per-

But all things that come in this way from something else which does per[35] sist. Since, then, one thinker places the 1 as contrary to plurality, and another places it 1092 b as contrary to the unequal, treating the 1 as equal, number must be being treated as coming from contraries. There is, then, something else that persists, from which and from sisting?

come

also

is

what the from numbers because expressible by a number,

that things get

their composition

is

by one which is an odd number. For in either

by honey-water is no more wholesome if it is mixed in the proportion of three times three, but it would do more good if it were in no particular ratio but well diluted than if it were numerically expressible [30] but strong. Again, the ratios of mixtures are expressed by the adding of numbers, not 1

Cf. Empedocles, Fr. 17.

2

Cf. Empedocles, Fr. 96.

easily calculable or fact

METAPHYSICS

626 by mere numbers;

e.g.

it is

'three parts to two',

not 'three times two'. For in any multiplication the genus of the things multiplied must be the same; therefore the product 1x2x3 must be measurable by 1, and 4x5x6 by 4, and therefore

products into which the same factor enters must be measurable by that factor. The number of fire, then, cannot be 2x5x3x6, and at the same time that of water 2x3. 1093* If all things must share in number, it must follow that many things are the same, and the same number must belong to one thing all

[55]

to another. Is number the cause, then, and does the thing exist because of its number, or is this not certain? E.g. the motions of the sun [5] have a number, and again those of the moon, yes, and the life and prime of each

and

—

1093 b

These people are like the old-fashioned Homeric scholars, who see small resemblances but neglect great ones.

Some

say that there are

many

such cases, e.g. that the middle strings [50] are represented by nine and eight, and that the epic verse has seventeen syllables, which is equal in number to the two strings,

and that the scansion is, in the right half of 1093 b the line nine syllables, and in the left eight.

And

letters

from alpha

they say that the distance in the to omega is equal to that from the lowest note of the flute to the highest, and that the number of this note is equal to [5] that of the whole choir of heaven. It may be suspected that no one could find difficulty either in stating such analogies or in finding them in eternal things, since they can be found

some of these some cubes, and some equal, others double? There is no reason why they should not, and indeed they must move within these limits, since all things were assumed to share in number. And it was assumed that things that differed might fall under the [10] same number. Therefore if the same number had belonged to certain things, these would have been the same as one another, since they would have had the same form of number; e.g. sun and moon would have been the same. But why need these numbers be causes ? There

even in perishable things. But the lauded characteristics of numbers, and the contraries of these, and generally the mathematical relations, as some describe them,

are seven vowels, the scale consists of seven

particular kind of

animal.

Why,

numbers be

then, should not

squares,

strings, the Pleiades are seven, at seven

lose their teeth (at least

some

do,

animals

though some

[75] do not), and the champions who fought against Thebes were seven. Is it then because the number is the kind of number it is, that the champions were seven or the Pleiad consists

Surely the champions were seven because there were seven gates or for some other reason, and the Pleiad we count as seven, as we count the Bear as twelve, while other peoples count more stars in both. Nay, of seven stars?

E, ^, and Z are concords and that because there are three concords, the double consonants also are three. [20] they even say that

They

quite neglect the fact that there might be

making them

causes of nature, seem,

when we

[10] inspect them in this way, to vanish; for none of them is a cause in any of the senses that have been distinguished in reference to 1

In a sense, however, they plain that goodness belongs to numbers, and that the odd, the straight, the square, the

first

make

principles.

it

the potencies of certain numbers, are in the of the beautiful. For the seasons and a

column [75]

number go

together;

and

the other agreements that they collect

from the theorems of mathematics all have meaning. Hence they are like coincidences. For they are accidents, but the things that agree are all appropriate to one another, and one by analogy. For in each category of being an analogous term is found as the straight is this

—

[20] in length, so is the level in surface, perhaps the odd in number, and the white in colour.

Again,

it is

not the ideal numbers that are

phenomena and the like numbers differ from one an-

the causes of musical (for equal ideal

other in form; for even the units do); so that we need not assume Ideas for this reason at

a thousand such letters; for one symbol might

least.

be assigned to TP. But if they say that each of these three is equal to two of the other letters, and no other is so, and if the cause is that

These, then, are the results of the theory, and [2$] yet more might be brought together. The fact that our opponnts have much trouble with

there are three parts of the

mouth and one each applied to sigma, it is for this reason that there are only three, not because [25] the concords are three; since as a matter of fact the concords are more than three, but of double consonants there cannot be more.

the generation of

letter is in

make

numbers and can

in

no way

a system of them, seems to indicate that the objects of mathematics are not separable from sensible things, as some say, and that

they are not the l

Cf.V. 1,2.

first principles.

ON THE SOUL

CONTENTS: ON THE SOUL I

BERLIN NOS. i.

The

2.

The

dignity, usefulness,

and

402 a

diffi-

I

culty of Psychology

12. d 403 20

opinions of early thinkers

Refutation of the view which as-

4.

The

movement to the soul harmony

BOOK 1-2.

soul not

moved with

non-local

(4o8 a 34~4o8 b 29) The soul not a self-moving 409b 18) 5. 5.

The

soul

movement

3.

number (4o8 b 30-

not composed of

s1

409 31

elements (409 b 19-41 i a 7) The soul not present in all things (411* 7-23)

The unity

1.

6.

The double operation of mind The practical mind, and the differ-

8.

412*1

9.

"

10.

4.

The The

414a 27 415a 14

5.

Sense-perception

6.

The

faculties of the soul

nutritive faculty

different kinds of sensible

4i6 b 32 4i8 a 6

Sight and

object

i

Problems about the motive faculty

432 a 15

The

liv-

a 433 8

relations of the facul-

b 433 3i a 434 23

cause of the

11.

{Continued)

12.

The mutual

13.

629

43i a

and the contemplative 431° 20

ties

4i8 a 26

it

43o a 26

Comparison of mind with sense and with imagination

of its

427 s1 16

movement

of

ing things

object 7.

425b 11

429 a 10 43o a 10

mind mind

Active

ence between

Second definition of soul

3.

Thinking, perceiving, and imagining distinguished (427 s i7~427b 26) Imagination (427b 27-429** 9) Passive

7.

4i3 a

2.

424° 20

of the external

5.

II

First definition of soul

The number

4.

of the soul (41 i a 24-41 i b 30)

BOOK

424 a 16

III

senses (424 b 20-2. 426 b 7) 2. Common sense (426 b 8~427 a 16)

(407b 27- o8 a 34) 4

The

422 a 8 422 b 17

General characteristics of the ex-

405b 32 407b 27

soul not a

42i a 6

ternal senses

about the soul 3.

signs

4i9b 3

Hearing and its object 9. Smell and its object 10. Taste and its object n. Touch and its object 8.

BOOK

of soul,

and

their fitness for the conditions

life

(Continued)

435

a

n

ON THE SOUL BOOK

I

no doubt, it is necessary to determine which of the summa genera soul lies, what

First,

in

402 a Holding of any kind

we do

as

prized, one kind of its

that,

while knowledge

honoured and

a thing to be

is

may, either by reason of and

it

greater exactness or of a higher dignity

greater wonderfulness in its objects, be more honourable and precious than another, on both accounts we should naturally be led to place in

the front rank the study of the soul. The knowledge of the soul admittedly contributes [5] greatly to the advance of truth in general,

and, above

all,

to

our understanding of Nature,

in

some

for the soul

is

animal

Our aim

stand,

life.

first its essential

properties; of these

sense the principle of

is

nature,

some

and under-

to grasp

and secondly

its

are taught to be af-

fections proper to the soul

itself,

while others

are considered to attach to the animal

owing

within it of soul. attain any assured knowledge about

to the presence

To

[10]

the soul

is

the world.

presents

one of the most difficult things in the form of question which here

As

itself, viz.

the question

recurs in other fields,

there

was some

it

single

'What

is

it?',

is

hesitations

we begin

still

tion

is

402 b

meth-

form the starting-points must be different, as e.g. bers and surfaces.

—

with what facts For the facts which

beset us

the inquiry ?

difficulties

in different subjects

in the case of

num-

Note: The bold face numbers and letters are approximate indications of the pages and columns of the standard Berlin Greek text; the bracketed numbers, of the lines in the Greek text; they are here assigned as they are assigned in the Oxford translation. 63'

Our answer

it

not

to this ques-

of the greatest importance.

We

must consider

also whether soul is without parts, and whether it is everywhere homogeneous or not; and if not homogeneous, whether its various forms are divisible or

is

different specifically or generically:

up

to the

who

have discussed and investigated soul seem to have confined thempresent time those [5] selves to the

human

soul.

ful not to ignore the question

We must

be care-

whether soul can

be defined in a single unambiguous formula, as is the case with animal, or whether we must not give a separate formula for each sort of it, as we do for horse, dog, man, god (in the latter

—and so too every —being treated

case the 'universal' animal

other

'common

predicate'

Further,

of inquiry ap-

some other known method,

shall

to the class of potential existents, or is

rather an actuality?

method

for derived properties the single

and

remaining kinds of predicates which we have [25] distinguished? Further, does soul belong

ther as nothing at

od of demonstration); in that case what we should have to seek for would be this unique method. But if there is no such single and general method for solving the question of essence, our task becomes still more difficult; in the case of each different subject we shall have to determine the appropriate process of investigation. If to this there be a clear answer, e.g. that the process is demonstration or division, or [20]

this-somewhat,' a substance, or is it quantum, or some other of the

might be supposed that

flicable to all objects whose essential nature 75] we are endeavouring to ascertain (as

there

it is; is it 'a

a quale or a

all

ei-

or as a later product).

if what exists is not a plurality of souls, but a plurality of parts of one soul, which

ought we

to investigate first, the

whole soul or

[10] its parts? (It is also a difficult problem to decide which of these parts are in nature distinct

we

from one another.) Again, which ought

to investigate first, these parts or their func-

tions,

mind

of sensation,

or thinking, the faculty or the act

and

so

on?

If

the investigation of

the functions precedes that of the parts, the further question suggests

itself:

ought we not

before either to consider the correlative objects, [75] e.g. of sense or thought? It seems not only useful for the discovery of the causes of the

derived properties of substances to be acquainted with the essential nature of those substances (as in mathematics it is useful for the understanding of the property of the equality of the [20] interior angles of a triangle to two right angles to know the essential nature of the straight and the curved or of the line and the plane) but also conversely, for the knowledge of the essential nature of a substance is largely promoted by an acquaintance with its proper-

ON THE SOUL

632 ties: for,

when we

are able to give an account

conformable to experience of properties of a substance,

all

we

or most of the

shall be in the

most favourable position to say something worth saying about the essential nature of that [25] subject; in all demonstration a definition of the essence is required as a starting-point, so

which do not enable us to discover the derived properties, or which fail to 403 a facilitate even a conjecture about them, must obviously, one and all, be dialectical and that definitions

futile.

A

further problem presented by the affec-

tions of soul

is

this: are

complex of body and

among them determine

they

all

soul, or

affections of the is

there any one

peculiar to the soul by itself?

this

indispensable but

is

To

difficult. If

[5] we consider the majority of them, there seems to be no case in which the soul can act or be acted upon without involving the body; e.g.

anger, courage, appetite, and

sensation

Thinking seems the most probable exception; but if this too proves to be a form of

generally.

imagination or to be impossible without imagination, it too requires a body as a condition of [10] its existence. If there is any way of acting or being acted upon proper to soul, soul will be

capable of separate existence; if there is none, its separate existence is impossible. In the latter case,

it

many in

it,

will be like

what

properties arising

is straight, which has from the straightness

touching a bronze sphere at a though straightness divorced from the

e.g. that of

point,

other constituents of the straight thing cannot

touch

it

way;

in this

cannot be so divorced at

it

[75] all, since it is always found in a body. It therefore seems that all the affections of soul

—

involve a body passion, gentleness, fear, pity, courage, joy, loving, and hating; in all these there is a concurrent affection of the body. In support of this we may point to the fact that,

while sometimes on the occasion of violent and striking occurrences there is no excite-

ment

[20] feeble viz.

or fear

felt,

on others

faint

and

stimulations produce these emotions,

when

the

body

tension resembling

angry. Here

is

a

is

its

still

already in a state of

condition

when we

are

clearer case: in the ab-

sence of any external cause of terror we find ourselves experiencing the feelings of a man in terror.

From

all this it is

obvious that the

affections of soul are enmattered formulable

essences.

[25] Consequently their definitions ought to correspond, e.g. anger should be defined as a

403 b

mode of movement of such and such a body (or part or faculty of a body) by this or that cause and for this or that end. That is precisely why the study of the soul must fall with-

certain

in the science of Nature, at least so far as in

Hence

its

manifests this double character. a physicist would define an affection of

affections

it

[30] soul differently from a dialectician; the would define e.g. anger as the appetite

latter

for returning pain for pain, or

something

like

while the former would define it as a boiling of the blood or warm substance surround403 b ing the heart. The latter assigns the material conditions, the former the form or formulable essence; for what he states is the formulable essence of the fact, though for its actual existence there must be embodiment of it in a material such as is described by the other. Thus the essence of a house is assigned in such a formula as 'a shelter against destruction by [5] wind, rain, and heat'; the physicist would describe it as 'stones, bricks, and timbers'; but that,

there

is

would

third

a

possible

description

was that form

which

matewith that purpose or end. Which, then, among these is entitled to be regarded as the genuine physicist? The one who confines himself to the material, or the one who restricts himself to the formulable essence alone? Is it not rather the one who combines both in a single formula ? If this is so, how are we to characterize the other two? Must we not say that there is no type of thinker who concerns himself with those qualities or attributes of the say that

it

in that

rial

material which are in fact inseparable from the material,

and without attempting even in them? The physicist

[10] thought to separate

who

concerns himself with all the propand passive of bodies or materials thus or thus defined; attributes not considered as being of this character he leaves to others, in certain cases it may be to a specialist, e.g. a carpenter or a physician, in others (a) where they is

he

erties active

are inseparable in fact, but are separable

any particular kind of body by an [75]

straction,

to

the

from

effort of ab-

mathematician,

(b)

where they are separate both in fact and in thought from body altogether, to the First Philosopher or metaphysician. But we must return from this digression, and repeat that the affections of soul are inseparable from the material substratum of animal life, to which we have seen that such affections, e.g. passion and fear, attach, and have not the same mode of being as a line or a plane.

BOOK

404 b

I,

CHAPTERS

1-2

633

what moved These motes were referred to because they are seen always in movement, clared the motes in air, others

them, to be

[20] For our study of soul it is necessary, while formulating the problems of which in our further advance we are to find the solutions, to call into council the views of those of our predecessors who have declared any opinion on this subject, in order that we may profit by whatever is sound in their suggestions and avoid their errors.

The chiefly

is an exwhich have

starting-point of our inquiry

position of those characteristics

been held to belong to soul in

[25]

nature.

above

all

Two

characteristic

its

very

marks have

others been recognized as distinguish-

ing that which has soul in it from that which has not movement and sensation. It may be said that these two are what our predecessors

—

have fixed upon as characteristic of

soul.

what originates movement is both pre-eminently and primarily soul; believing that what is not itself moved cannot origi-

Some

say that

[30] nate

movement

in another, they arrived

view that soul belongs to the class of things in movement. This is what led Democat the

ritus to say that soul

404a

is

a sort of fire or hot sub-

stance; his 'forms' or

atoms are

infinite

number; those which are spherical he calls fire and soul, and compares them to the motes in the air which we see in shafts of light coming through windows; the mixture of seeds of all sorts he calls the elements of the whole of [5] Nature (Leucippus gives a similar account); the spherical atoms are identified with soul because atoms of that shape are most adapted to permeate everywhere, and to set all in

soul.

even in a complete calm. [20] The same tendency

who

define soul as that

seem is

is what and that while alone moves itself.

moved by soul, it This belief arises from their never seeing anything originating movement which is not first all else is

moved.

itself

[25] Similarly also Anaxagoras (and whoever agrees with him in saying that mind set the

whole in movement) declares the moving cause of things to be soul. His position must, however, be distinguished from that of Democritus. Democritus roundly identifies soul

and mind, for he identifies what appears with what is true that is why he commends Ho-

—

mer

with thought he does not employ mind as a special faculty dealing with truth, but identifor the phrase 'Hector lay

[jo] distraught'

404 b

1

;

and mind. What Anaxagoras them is more obscure; in many he tells us that the cause of beauty and soul

fies

says about

places

is mind, elsewhere that it is soul; it is found, he says, in all animals, great and small, [5] high and low, but mind (in the sense of intelligence) appears not to belong alike to all animals, and indeed not even to all human be-

order

ings.

who had special

All those, then,

what has

regard to the

moved, adopted the view that soul is to be identified with what is eminently originative of movement. All, on fact that

soul in

who

what has

it

[10] piration as the characteristic mark of life; as the environment compresses the bodies of

eral

animals, and tends to extrude those atoms

elements, each of

which impart movement to them, because they themselves are never at rest, there must be a reinforcement of these by similar atoms coming in from without in the act of respiration; for they prevent the extrusion of those which are already within by counteracting the compressing and consolidating force of the environment; and animals continue to live only [75] so long as they are able to maintain this

words

doctrine of the Pythagoreans seems to rest upon the same ideas; some of them de-

those

itself; all

view that movement

to hold the

the other hand,

The

shown by

closest to the nature of soul,

the others moving by being themselves in movement. This implies the view that soul is identical with what produces movement in animals. That is why, further, they regard res-

resistance.

is

which moves

soul in

it is

looked to the fact that

knows

or perceives

what

is,

identify soul with the principle or principles

[10] of Nature, according as they admit sevsuch principles or one only. Thus Em-

pedocles declares that

it is

them

formed out of

all his

also being soul; his

are:

'tis by Earth we see Earth, by Water Water, By Ether Ether divine, by Fire destructive

For

Fire,

[75]

By Love Love, and Hate by

In the same

way

Plato in the

cruel Hate. 2

Timaeus3

fash-

ions the soul out of his elements; for like, he holds, is known by like, and things are formed out of the principles or elements, so that soul 1

Iliad, xxiii. 698.

2

Fr. 109, Diels.

3

35 S.

ON THE SOUL

634

must be so too. Similarly 'On Philosophy' it was

also in his lectures set

forth

the

that

[20] Animal-itself is compounded of the Idea of the One together with the primary

itself

length, breadth, objects of

its

and depth, everything else, the

perception, being similarly consti-

Again he puts his view in yet other Mind is the monad, science or knowledge the dyad (because it goes undeviatingly from one point to another), opinion the numtuted.

terms:

ber of the plane, sensation the

number

of the

numbers are by him expressly identiwith the Forms themselves or principles,

solid; the

fied

and are formed out of the elements; now [25] things are apprehended either by mind or science or opinion or sensation, and these same numbers are the Forms of things.

Some

both premisses, both originative of movement and cognitive, have compounded it of both and declared the soul to be a self-moving thinkers, accepting

viz. that the soul

is

number. [30] As to the nature and number of the

opinions differ. The difference is greatest between those who regard them as corporeal and those who regard them as incor-

and from both dissent those who and draw their principles from

poreal,

make

a blend

both sources.

The number

of principles

is

also

some admit one only, others assert There is a consequent diversity in their

in dispute; several.

several accounts of soul; they assume, naturally

enough, that what native of

is

in

its

own

nature origi-

movement must be among what

is

[5] primordial. That has led some to regard it as fire, for fire is the subtlest of the elements

and nearest to incorporeality; most primary sense, fire both originates

movement

further, in the is

moved and

in all the others.

Democritus has expressed himself more ingeniously than the rest on the grounds for ascribing each of these two characters to soul; soul and mind are, he says, one and the same [10] thing, and this thing must be one of the primary and indivisible bodies, and of originating

fineness of grain

he says that of

power

its

movement must be due and the shape of

all

its

to

its

atoms;

the shapes the spherical

is

and that this is the shape of of both fire and mind.

the most mobile, the particles

Anaxagoras, as we said above, 1 seems to distinguish between soul and mind, but in practice he treats them as a single substance, except [75] that it is mind that he specially posits as the principle of all things; at any rate what he 1

4o

b 1-6.

that

is

mind

alone of

all

that

is is

simple,

unmixed, and pure. He assigns both characteristics, knowing and origination of movement, to the same principle, when he says that it was mind that set the whole in movement. Thales, too, to judge from what is recorded about him, seems to have held soul to be a mo[20] tive force, since he said that the magnet has a soul in it because it moves the iron.

Diogenes (and others) held the soul to be air because he believed air to be finest in grain and

grounds of the powers of knowing and originating movement. As the primordial principle from which all other things are derived, it is cognia

first

principle; therein lay the

soul's

tive; as finest in grain,

it

has the power to origi-

nate movement. [25] Heraclitus too says that the first principle the 'warm exhalation' of which, accord-

—

ing to him, everything else

—

composed is is most inthat what is in

is

soul; further, that this exhalation

corporeal and in ceaseless flux; first

principles

405 a

says

405 b

movement

requires that what knows it should be in movement; and that all that is has its being essentially in movement (herein agreeing with the majority).

Alcmaeon

also

seems to have held a similar

[50] view about soul; he says that

immor-

it is

because it resembles 'the immortals/ and that this immortality belongs to it in virtue of tal

movement; for all the 'things dimoon, sun, the planets, and the whole heavens, are in perpetual movement. 405 b Of more superficial writers, some, e.g. Hippo, have pronounced it to be water; they seem to have argued from the fact that the seed of all animals is fluid, for Hippo tries to refute those who say that the soul is blood, on the ground that the seed, which is the primorceaseless

its

vine,'

dial soul,

[5]

is

not blood.

Another group

hold

it

(Critias, for

example) did

to be blood; they take perception to be

the most characteristic attribute of soul,

hold that perceptiveness

is

due

and

to the nature

of blood.

Each of the elements has thus found its parexcept earth earth has found no sup-

tisan,

porter unless

—

we count

as

such those

[10] declared soul to be, or to be of, all the elements. All, then, it

who have

compounded

may

be said,

characterize the soul by three marks,

Move-

ment, Sensation, Incorporeality, and each of these is traced back to the first principles. That is why (with one exception) all those who define the soul by its power of knowing make it either an element or constructed out of the ele-

BOOK

406 b

I,

CHAPTERS

ments. The language they all use is similar; [75] like, they say, is known by like- as the soul knows everything, they construct it out of

Hence

the principles.

all

who admit

those

all

but one cause or element, make the soul also one (e.g. fire or air), while those who admit a multiplicity of principles

The

multiple.

[20] alone says that

nothing in

make

exception

mind

is is

the soul also

Anaxagoras; he

impassible and has

common with anything else. But, how or in virtue of what cause can

if

this is so,

it

know? That Anaxagoras

has not explained,

nor can any answer be inferred from his words. All who acknowledge pairs of opposites

among

their principles, construct the soul also

out of these contraries, while those who admit one contrary of each pair, [25] e.g. either hot or cold, likewise make the soul some one of these. That is why, also, they

as principles only

allow themselves to be guided by the names; those who identify soul with the hot argue that derived from {eiv (to boil), identify it with the cold say \pvxh ) is so called from the process

(to live)

£rjv

while those that soul

(

is

who

and refrigeration ( kcit&vM-is ). Such are the traditional opinions concerning soul, together with the grounds on which they are maintained.

of respiration [jo]

2-3

635

moved' and participates in such direct movement. There are four species of movement locomotion, alteration, diminution, growth; consequently if the soul is moved, it must be moved with one or several or all of these species of movement. Now if its movement is not [75] incidental, there must be a movement

—

natural to it, and, if so, as all the species enumerated involve place, place must be natural to it. But if the essence of soul be to move itself, its being moved cannot be incidental to it, as it is to what is white or three cubits long; they too can be moved, but only incidentally what

—

moved

which

and 'three cubits long' are the attributes, the body in [20] which they inhere; hence they have no is

place:

that of

is

but

if

movement,

it

'white'

the soul naturally partakes in follows that

it

must have a

place.

Further, if there be a movement natural to the soul, there must be a counter-movement unnatural to it, and conversely. The same applies to rest as well as to

movement;

for the

terminus ad quern of a thing's natural move[25] ment is the place of its natural rest, and similarly the terminus ad quern of its enforced

movement is the place of its enforced rest. But what meaning can be attached to enforced movements or rests of the soul, it is difficult even to imagine.

We

must begin our examination with move-

ment; for doubtless, not only essence of soul

406*

who

able of ity

of

that

false that the

correctly described by those

is

say that

moving)

is it

what moves (or

it is

itself,

but

it

is

is

cap-

an impossibil-

movement should -be even an

attribute

it.

We no

have already 1 pointed out that

necessity that

what

originates

there*

is

movement

be moved. There are two senses in which anything may be moved either (a) indirectly, owing to something other than itself,

should

itself

—

owing to itself. Things are moved' which are moved as being contained in something which is moved, e.g. [5] or (^) directly,

'indirectly

sailors in a ship, for they are moved in a different sense from that in which the ship is moved; the ship is 'directly moved', they are 'indi-

moved', because they are in a moving vessel. This is clear if we consider their limbs; the movement proper to the legs (and so to man) is walking, and in this case the sailors [10] are not walking. Recognizing the double sense of 'being moved', what we have to consider now is whether the soul is 'directly

rectly

1

Physics, viii. 5, especially 257*

3i-258 b

9.

Further, if the natural movement of the soul be upward, the soul must be fire; if downward, it must be earth; for upward and downward movements are the definitory characteristics of these bodies. The same reasoning applies to the intermediate movements, termini, and bodies.

[30] Further, since the soul is observed to origmovement in the body, it is reasonable to

inate

suppose that

it

transmits to the body the move-

ments by which

moved, and so, reinfer from the movements of the body back to similar move406b ments of the soul. Now the body is moved from place to place with movements of locomotion. Hence it would follow that the soul too must in accordance with the body change either its place as a whole or the relait itself

versing the order,

tive places of its parts.

possibility

body and

is

we may

This carries with it the might even quit its and with this would be

that the soul re-enter

it,

involved the possibility of a resurrection of ani[5] mals from the dead. But, it may be contended, the soul can be moved indirectly by

something

else; for an animal can be pushed out of its course. Yes, but that to whose essence belongs the power of being moved by itself,

ON THE SOUL

63 6

cannot be moved by something

else except in-

what is good by or in itself goodness to something external to it or to some end to which it is a means. [10] If the soul is moved, the most probable view is that what moves it is sensible things.

cidentally, just as

cannot owe

We itself,

its

must note also that, if the soul moves it must be the mover itself that is moved,

so that

it

follows that

if

movement

is

in every

which is in movement, in that respect in which it is said to be moved, the movement of the soul must be a departure from its essential nature, at least if

case a displacement of that

self-movement

its

is

essential to

not

it,

inci-

dental.

[75] Some go so far as to hold that the movements which the soul imparts to the body in which it is are the same in kind as those with which it itself is moved. An example of this is Democritus, who uses language like that of the comic dramatist Philippus, who accounts for the movements that Daedalus imparted to his wooden Aphrodite by saying that he poured quicksilver into it; similarly Democritus says [20] that the spherical atoms which according

owing to their own movements draw the whole body after them and so produce its movements. We must urge the question whether it is these very same atoms which produce rest also how they could do so, it is difficult and even impossible to say. And, in general, we may object that it is not in this way that the soul appears it is [25] to originate movement in animals

him

to

constitute soul,

ceaseless

—

—

through intention or process of thinking. It is

in the

same fashion

that the

Timaeus

also tries to give a physical account of

how

1

the

moves its body; the soul, it is there said, is in movement, and so owing to their mutual implication moves the body also. After compounding the soul-substance out of the elements and dividing it in accordance with the harmonic numbers, in order that it may possoul

[50] sess a connate sensibility for 'harmony' and that the whole may move in movements

well attuned, the

Demiurge bent

line into a circle; this single circle

the straight

he divided

into two circles united at two common points; 407 a one of these he subdivided into seven circles. All this implies that the movements of

the soul are identified with the local move-

ments of the heavens.

Now,

in the first place,

that the soul

is

it is

a mistake to say

a spatial magnitude. It

is

evi-

dent that Plato means the soul of the whole to 1

35ff-

407"

be like the sort of soul which is called mind [5] not like the sensitive or the desiderative soul, for the movements of neither of these are circular.

Now

the sense in

mind is one and continuous in which the process of thinking is

and thinking is identical with the thoughts which are its parts; these have a serial unity like that of number, not a unity like that of a spatial magnitude. Hence mind cannot have so,

mind is either withcontinuous in some other way

that kind of unity either;

out parts or

is

than that which characterizes a spatial magnitude. How, indeed, if it were a spatial magni[10] tude, could mind possibly think? Will it think with any one indifferently of its parts? In this case, the 'part' must be understood either in the sense of a spatial magnitude or in the sense of a point (if a point can be called a part of a spatial magnitude). If

we

accept the

being infinite in number, obviously the mind can never exhaustively traverse them; if the former, the mind must think the same thing over and over again, indeed an infinite number of times (whereas [75] it is manifestly possible to think a thing once only). If contact of any part whatsoever of itself with the object is all that is required, latter alternative, the points

why need mind move magnitude

sess

in a circle, or indeed pos-

at all?

On

contact with the whole

the other hand,

circle

is

if

necessary,

what meaning can be given

to the contact of the could what has no parts think what has parts, or what has parts think what has none? must identify the circle referred to with mind; for it is mind whose [20] movement is thinking, and it is the circle

parts? Further,

how

We

whose movement ing

is

a

which has be mind. If

is

revolution, so that

movement

this characteristic

the circular

if

think-

of revolution, the circle

movement

movement must is

eternal, there

must be something which mind is always thinking what can this be? For all practical

—

on ess,

for the sake of

and

all

close in the

—

they all go something outside the proc-

processes of thinking have limits

theoretical processes

same way

come

to a

as the phrases in speech

which express processes and results of think[25] ing. Every such linguistic phrase is either definitory or demonstrative. Demonstration has both a starting-point and may be said to end in a conclusion or inferred result; even if the process never reaches final completion, at

never returns upon itself again to its it goes on assuming a fresh middle term or a fresh extreme, and moves straight

any

rate

it

starting-point,

408

BOOK

s

forward, but circular

movement

I,

returns to

CHAPTERS

3-4

637

its

[30] starting-point. Definitions, too, are closed

There

groups of terms. Further, ed,

if

same revolution

the

mind must

repeatedly

is

think the

repeat-

same

object.

Further, thinking has more resemblance to coming to rest or arrest than to a movement; the same may be said of inferring. It might also be urged that what is difficult and enforced is incompatible with blessedness; 407 b if the movement of the soul is not of its essence, movement of the soul must be contrary to its nature. It must also be painful for the soul to be inextricably bound up with the body; nay more, if, as is frequently said and a

widely accepted, it is better for mind not to be embodied, the union must be for it undesirable.

[5] Further, the cause of the revolution of the is left obscure. It is not the essence of

heavens

soul which is the cause ment that movement

— soul —nor

of this circular is

move-

only incidental to

a fortiori, the body its cause. not even asserted that it is better that soul should be so moved; and yet the reason for which God caused the soul to move in [jo] a circle can only have been that move-

Again,

is,

it is

ment was

better for

it

than

rest,

and movement

of this kind better than any other. But since this sort of consideration is more appropriate to another field of speculation, let us dismiss it for the present.

The view we have company with most

just

been examining, in

theories about the soul, in-

volves the following absurdity: they all join [75] the soul to a body, or place it in a body,

which

yet another theory about soul,

is

has commended itself to many as no less probable than any of those we have hitherto mentioned, and has rendered public account [30] of itself in the court of popular discussion. Its supporters say that the soul

harmony

of harmony, for (a)

is

is

a

kind

a blend or

composition of contraries, and (b) the body

compounded out however,

is

of

contraries.

is

Harmony,

a certain proportion or composition

and soul can be

of the constituents blended,

neither the one nor the other of these. Further,

power of originating movement cannot belong to a harmony, while almost all concur in regarding this as a principal attribute of soul. 408 a It is more appropriate to call health (or generally one of the good states of the body) a harmony than to predicate it of the soul. The absurdity becomes most apparent when we try the

and passive affections of harmony; the necessary readjust-

to attribute the active

the soul to a

ment

of their conceptions

[5] in using the

is

difficult.

Further,

word 'harmony' we have one

two cases in our mind; the most proper sense is in relation to spatial magnitudes which have motion and position, where harmony means the disposition and cohesion of their parts in such a manner as to prevent the introduction into the whole of anything homogeneous with it, and the secondary sense, derived from the former, is that in which it or other of

means the

ratio

between the constituents so

blended; in neither of these senses T

[

o] ble to predicate

harmony

it

of soul.

in the sense of the

mode

body

is it

That

plausi-

soul

is

a

of composi-

view

without adding any specification of the reason

tion of the parts of the

of their union, or of the bodily conditions re-

refutable; for there are

quired for it. Yet such explanation can scarcely be omitted; for some community of nature is presupposed by the fact that the one acts and the other is acted upon, the one moves and the other is moved; interaction always implies a special nature in the two interagents. All, how-

and those variously compounded; of what

[20] ever, that these thinkers do is to describe the specific characteristics of the soul; they do

not try to determine anything about the body which is to contain it, as if it were possible, as in the Pythagorean myths, that any soul could be clothed upon with any body an absurd view, for each body seems to have a form and shape of its own. It is as absurd as to say that the art of carpentry could embody itself in [25] flutes; each art must use its tools, each soul its body.

—

bodily part

many

is

a

easily

composite parts

mind or the sensitive or the apmode of composition ? And mode of composition which con-

is

petitive faculty the

what

is

the

each of them? It is equally absurd to identify the soul with the ratio of the mixture; [75] for the mixture which makes flesh has a different ratio between the elements from that which makes bone. The consequence of this view will therefore be that distributed throughout the whole body there will be many souls, since every one of the bodily parts is a different mixture of the elements, and the ratio of mixture is in each case a harmony, i.e. stitutes

a soul.

From Empedocles at any rate we might demand an answer to the following question

ON THE SOUL

63 8

body between the [20] elements: is the soul identical with this ratio, or is it not rather something over and above this which is formed in the parts? Is love the cause of any and every mixture, or for he says that each of the parts of the

what

is

it

in virtue of a ratio

is

only of those that are in the right ratio? Is love this ratio itself, or is love something over and above this? Such are the problems raised by this account. But, on the other hand, if the soul

is

from the mixture, why does

different

it

[25] disappear at one and the same moment with that relation between the elements which constitutes flesh or the other parts of the ani-

mal body? Further, if the soul is not identical with the ratio of mixture, and it is consequently not the case that each of the parts has a soul,

what

is

soul quits the

That the or be

which perishes when the

that

body ?

in a circle,

is

clear

harmony, from what we

[50] have said. Yet that it can be moved inci1 dentally is, as we said above, possible, and

even that in a sense

can move

it

the sense that the vehicle in

moved, and moved by

moved

the soul be

it;

in

itself, i.e.

in

which it is can be no other sense can

in space.

More legitimate doubts might remain as to movement in view of the following facts. 408 b We speak of the soul as being pained or

its

pleased, being bold or fearful, being angry, perceiving, thinking. All these are regarded as

modes of movement, and hence ferred that the soul

it might be inmoved. This, however, follow. We may admit to

is

does not necessarily [5] the full that being pained or pleased, or

movements (each of them ing moved'), and that the movement is thinking, are

a 'beorigi-

nated by the soul. For example we may regard anger or fear as such and such movements of the heart, and thinking as such and such another movement of that organ, or of some other; these modifications may arise either from changes of place in certain parts or from quali[10] tative alterations (the special nature of the

parts

and the

special

modes

of

their

changes being for our present purpose irrelevant). Yet to say that it is the soul which is angry is as inexact as it would be to say that it is the soul that weaves webs or builds houses. It is doubtless better to avoid saying that the soul pities or learns or thinks

man who

and rather

to say

does this with his soul. [75] What we mean is not that the movement is in the soul, but that sometimes it terminates

that

1

it is

406* 30

the

ff.,

b5-8.

s

and sometimes starts from it, sensacoming from without inwards, and reminiscence starting from the soul and terminating with the movements, actual or residin the soul

tion e.g.

ual, in the sense organs.

The case of mind is different; it seems to be an independent substance implanted within the soul and to be incapable of being deit could be destroyed at all, it would be under the blunting influence of old age.

stroyed. If

[20]

What

really

happens

in respect of

mind

age is, however, exactly parallel to what happens in the case of the sense organs; if the old man could recover the proper kind of eye, he would see just as well as the young man. in old

The

incapacity of old age

tion not of the soul but of in

is

due

mind

to

an

affec-

vehicle, as occurs

its

drunkenness or disease. Thus

old age the activity of

soul cannot either be a

moved

409

it

is

that in

or intellectual ap-

prehension declines only through the decay of part; mind itself is impas[25] sible. Thinking, loving, and hating are affections not of mind, but of that which has mind, so far as it has it. That is why, when this vehicle decays, memory and love cease; they were activities not of mind, but of the composite which has perished; mind is, no doubt,

some other inward

something more divine and impassible. That [50] the soul cannot be moved is therefore clear from what we have said, and if it cannot be moved at all, manifestly it cannot be moved by itself. Of all the opinions we have enumerated, by far the most unreasonable is that which declares the soul to be a self-moving number; it involves in the

first

place

all

the impossibilities

which follow from regarding the soul as moved, and in the second special absurdities which follow from calling it a number. How 409 a are we to imagine a unit being moved? By what agency? What sort of movement can be attributed to what is without parts or inis both originacapable of being

ternal differences? If the unit tive of

movement and

itself

moved,

it must contain difference. Further, since they say a moving line generates a surface and a moving point a line,

[5] the

movements

be lines (for a point

of the psychic units is

must

a unit having position,

and the number of the soul is, of course, somewhere and has position). Again, if from a number a number or a unit is

subtracted, the remainder

is

another

num-

and many animals when divided continue to live, and each segment is thought to retain the same kind of soul. ber; but plants

BOOK

410*

I,

CHAPTERS

[10] It must be all the same whether we speak of units or corpuscles; for if the spherical

atoms of Democritus became points, nothing being retained but their being a quantum, there must remain in each a moving and a part, just as there is in what is continuwhat happens has nothing to do with the size of the atoms, it depends solely upon their [75] being a quantum. That is why there must

4-5

639

quence that follows is that the animal must be moved by its number precisely in the way that Democritus explained its being moved by his spherical psychic atoms. it

What

make whether we speak

difference does

of small spheres or

moved

of large units, or, quite simply, of units in

ous;

[10] movement? One way or another, the movements of the animal must be due to their movements. Hence those who combine movement and number in the same subject lay themselves open to these and many other simi-

be something to originate movement in the units. If in the animal what originates movement is the soul, so also must it be in the case of the number, so that not the mover and the moved together, but the mover only, will be the soul. units

to

But how

is it

function

this

fulfil

one of the

possible for

of originating

movement? There must be some

difference be-

[20] tween such a unit and all the other units, and what difference can there be between one

placed unit and another except a difference of position? If then, on the other hand, these psy-

body are different from the points of the body, there will be two sets of units both occupying the same place; for each unit will occupy a point. And yet, if there can be two, why cannot there be an infinite number? For if things can occupy an indivisible place, they must themselves be indivisible. [25] If, on the other hand, the points of the body are identical with the units whose numchic units within the

ber

the soul, or

is

the

if

number

of the points

lar absurdities. It is

—

it is impossible that they should even be attributes of it. The point is clear if the [75] attempt be made to start from this as the account of soul and explain from it

soul

ment and number do not jecture

about the

as

we have

said,

1

that

this

kind of body, is on the other entangled in the absurdity peculiar to Democritus' way of describing the manner in which movement is b

409 originated by soul. For if the soul is present throughout the whole percipient body, there must, if the soul be a kind of body, be two bodies in the same place; and for those

who

call it a

number, there must be many

[5] points at one point, or every body must have a soul, unless the soul be a different sort

number

—

than the sum of the points existing in a body. Another conse-

of

1

b

4 o8 33

ff.

other, that

is,

even con-

properties

of

Such are the three ways ers declared

in which soul has one group of thinkto be that which is most orig-

it

movement because it moves itanother group to be the subtlest and most nearly incorporeal of all kinds of body. We have now sufficiently set forth the difficulties [20] inative of

self,

and inconsistencies to which these theories exposed. It remains now to examine the doctrine that soul is composed of the

elements.

is,

facilitate

derivative

traditionally been defined;

finity of points.

result

e.g.

soul.

are

The

soul,

reasoning, sensation, pleasure, pain, &c. For, 2 to repeat what we have said earlier, move-

body is the soul, why have not all bodies souls? For all bodies contain points or an in-

view, while on the one side identical with that of those who maintain that soul is a subtle

and actions of the

the affections

in the

Further, how is it possible for these points to be isolated or separated from their bodies, [50] seeing that lines cannot be resolved into points?

impossible not only that

these characters should give the definition of

The

reason assigned for this doctrine is that may perceive or come to know everything that is, but the theory necessarily

thus the soul

[25] involves

itself in

many

impossibilities. Its

upholders assume that like is known only by like, and imagine that by declaring the soul to be composed of the elements they succeed in identifying the soul with all the things it is capable of apprehending. But the elements are not the only things it knows; there are many

more exactly, an infinite number of formed out of the elements. Let us ad-

others, or, others,

[50] mit that the soul

knows

or perceives the

elements out of which each of these composites is made up; but by what means will it know or perceive the composite whole, e.g. what God, man, flesh, bone (or any other compound) is? For each is, not merely the ele-

410 a ments of which it is composed, but those elements combined in a determinate mode or ratio, as Empedocles himself says of bone, 2

402 b 25-403*

2.

ON THE SOUL

640

The \indly Earth

in

its

broad-bosomed moulds

1

Won of clear Water two parts out of eight And four of Fire; and so white bones were [5]

formed.

Nothing, therefore, will be gained by the presence of the elements in the soul, unless there be also present there the various formulae of proportion and the various compositions

Each element will indeed know its fellow outside, but there will be no knowledge of bone or man, unless they

in accordance with them.

too are present in the constitution of the soul.

[10] The impossibility of this needs no pointing out; for who would suggest that stone or man could enter into the constitution of the soul? The same applies to 'the good' and 'the

and

so on.

Further, the

word

not-good',

may

it

be used of a

quantum, or

has

Does the

many meanings:

or substance, or of a

of a quale, or of

kinds of predicates [75]

'is'

'this'

any other of the

we have

soul consist of

distinguished. all

of these or

not? It does not appear that all have common elements. Is the soul formed out of those elements alone which enter into substances ? If so, how will it be able to know each of the other kinds of thing? Will it be said that each kind of thing has elements or principles of its own, and that the soul is formed out of the whole of [20] these? In that case, the soul must be a

quantum and a quale and a substance. But all that can be made out of the elements of a quantum is a quantum, not a substance. These (and others like them) are the consequences of the view that the soul is composed of all the elements. It is absurd, also, to say both (a) that like is not capable of being affected by like, and (b) that like is perceived or known by like, for [25] perceiving, and also both thinking and knowing, are, on their own assumption, ways

moved. There are many puzzles and difficulties raised by saying, as Empedocles does, that each set of things is known by means of its corporeal elements and by reference to something in soul which is like them, and additionof being affected or

[30] al testimony is furnished by this new consideration; for all the parts of the animal body

which consist wholly of earth such as bones, 41 b sinews, and hair seem to be wholly insensitive and consequently not perceptive even of objects earthy like themselves, as they ought to 1

have been. Fr. 96, Diels.

410 b

Further, each of the principles will have far

more ignorance than knowledge, for though each of them will know one thing, there will be many of which it will be ignorant. Empedocles at any rate must conclude that his God [5]

is

the least intelligent of

him alone

is

it

all

true that there

beings, for of is

one thing,

which he does not know, while there is nothing which mortal beings do not know, for there is nothing which does not enter into Strife,

their composition.

In general, we may ask, Why has not everything a soul, since everything either is an ele-

ment, or

is

formed out of one or several or all Each must certainly know

of the elements?

one or several or all. [10] The problem might also be raised, What is that which unifies the elements into a soul ? The elements correspond, it would appear, to the matter; what unites them, whatever it is, is the supremely important factor. But it is impossible that there should be something superior to, and dominant over, the soul (and a fortiori over the mind); it is reasonable to hold that mind is by nature most primordial [75] and dominant, while their statement is that it is the elements which are first of all that

is.

who

All, both those

assert that the soul, be-

knowledge or perception of what is, is compounded out of the elements, and those who assert that it is of all things the most originative of movement, fail to take into con-

cause of

its

sideration all kinds of soul. In fact (1) not all beings that perceive can originate movement;

there appear to be certain animals

which are

[20] stationary, and yet local movement is the only one, so it seems, which the soul originates in animals.

against

all

And those

(2) the same objection holds construct mind and the

who

perceptive faculty out of the elements; for

it

appears that plants live, and yet are not endowed with locomotion or perception, while a large number of animals are without dis-

Even if these points were waived and mind admitted to be a part of the [25] soul (and so too the perceptive faculty), still, even so, there would be kinds and parts of soul of which they had failed to give any accourse of reason.

count.

The same

objection

lies

against the view ex-

pressed in the 'Orphic' poems: there it is said that the soul comes in from the whole when breathing takes place, being borne in upon the

Now

this cannot take place in the [30] winds. case of plants, nor indeed in the case of cer-

BOOK

411 b

I,

CHAPTER

tain classes of animal, for not all classes of

41 l a animal breathe. This

fact has

escaped the

If

we must

construct the soul out of the

there

no

is

tion;

suppose

to

necessity

that all the elements enter into

construc-

its

one element in each pair of contraries

will suffice to enable

it

to

know

both that

ele-

it

the curved

its

able

us

—the carpenter's rule enables us —but what curved does not en-

to

is

distinguish

to

either

itself

the

or

straight.

Certain thinkers say that soul

is

intermin-

gled in the whole universe, and it is perhaps for that reason that Thales came to the opinion that all things are full of gods. This presents

some

[10]

when

difficulties: it

Why

does

the

resides in air or fire not

soul

form an

animal, while it does so when it resides in mixtures of the elements, and that although it is held to be of higher quality when contained in the former?

why

(One might add

the question,

maintained to be higher and more immortal than that in animals.) Both possible ways of replying to the former fuestion lead to absurdity or paradox; for it 75] is beyond paradox to say that fire or air is an animal, and it is absurd to refuse the name of animal to what has soul in it. The opinion that the elements have soul in them seems to have arisen from the doctrine that a whole must be homogeneous with its parts. If it is true that animals become animate by the soul in air

it is

some quite other cause?

[5] that

both

whether

41 l b with the whole soul we think, perceive, ourselves, act or are acted upon, or whether each of them requires a different part of the soul? So too with regard to life. Does it depend on one of the parts of soul ? Or is it dependent on more than one ? Or on all ? Or has

[5] ment itself and its contrary. By means of the straight line we know both itself and

test

641 i.e.

move

notice of the holders of this view.

elements,

5

bute of the soul as a whole,

is

drawing into themselves a portion of what surrounds them, the partisans of this view are

Some hold

that the soul

is

divisible,

and

one part thinks, another desires. If, then, nature admits of its being divided, what

can it be that holds the parts together? Surely not the body; on the contrary it seems rather to be the soul that holds the body together; at

any

when

the soul departs the body disinand decays. If, then, there is something else which makes the soul one, this unifying agency would have the best right to the [10] name of soul, and we shall have to repeat for it the question: Is it one or multipartite? If it is one, why not at once admit that 'the rate

tegrates

is one? If it has parts, once more the quesmust be put: What holds its parts together, and so ad infinitum? The question might also be raised about the

soul'

tion

parts of the soul:

What

is

the separate role of

each in relation to the body ? For, if the whole [75] soul holds together the whole body, we should expect each part of the soul to hold together a part of the body. But this seems an impossibility; it is difficult even to imagine what sort of bodily part mind will hold together, or It is

how

it

will

do

this.

a fact of observation that plants

and

cer-

[20] tain insects go on living when divided into segments; this means that each of the seg-

ments has a soul in it identical in species, though not numerically identical in the differ-

bound to say that the soul of the Whole too is [20] homogeneous with all its parts. If the air

ent segments, for both of the segments for a

homogeneous, but soul heterogeneous, clearly while some part of soul will exist

movement. That

sucked in

is

in the inbreathed air,

The

soul

must

that there are

which

it is

some other part will not. homogeneous, or such

either be

some

not to be found. has been said it

knowing

as

is

all

the

now clear that

[25] ent all the parts of soul, and the souls so present are homogeneous with one another and with the whole; this means that the sev-

an attribute of soul cannot be ex-

speak of soul as moved. But since (a) knowand further (b) desiring, wishing, and generally all other modes of appetition, belong to soul, and (c) the local [50] movements of animals, and (d) growth, maturity, and decay are produced by the soul, we must ask whether each of these is an attriing, perceiving, opining,

But,

same, in each of the bodily parts there are pres-

[25] plained by soul's being composed of the elements, and that it is neither sound nor true to

necessary for self-maintenance.

in

parts of the

From what

Whole

time possess the power of sensation and local this does not last is not surprising, for they no longer possess the organs

eral parts of the soul are indisseverable

from

one another, although the whole soul is divisible. It seems also that the principle found in plants is also a kind of soul; for this is the only principle which is common to both animals and plants; and this exists in isolation from the principle of sensation, though there [30] is nothing which has the latter without the former.

ON THE SOUL

642

BOOK

412 b

II

in spite of their

extreme simplicity are 'organs';

e.g. the leaf serves to shelter the pericarp, the

412 a Let the foregoing

our account which have

suffice as

of the views concerning the soul

been handed on by our predecessors;

now

dismiss

them and make

as

us

let

were a com-

it

endeavouring to give a pre-

pletely fresh start,

[5] cise answer to the question, What is soul ? i.e. to formulate the most general possible defi-

nition of

it.

We are in the habit of recognizing, as one determinate kind of what is, substance, and that in several senses, (a) in the sense of matter or that which in itself is not 'a this', and (b) in the sense of form or essence, which is that precisely in virtue of called

that

'a this',

which

and

which

compounded

is

a

thing

is

thirdly (c) in the sense of of both (a)

and

Now

matter is potentiality, form ac[10] (b). tuality; of the latter there are two grades re-

one another as exercise of knowledge. lated to

knowledge

e.g.

to the

pericarp to shelter the fruit, while the roots of mouth of animals, both serving for the absorption of food. If, then, we have to give a general formula applants are analogous to the

[5] plicable to all kinds of soul, we must describe it as the first grade of actuality of a nat-

body. That is why we can wholly dismiss as unnecessary the question whether the soul and the body are one: it is as meaningless as to ask whether the wax and the shape given to it by the stamp are one, or generally the matter of a thing and that of which it is the matter. Unity has many senses (as many as 'is' has), but the most proper and fundamental sense of both is the relation of an actuality to that of which it is the actuality. [10] We have now given an answer to the question, What is soul? an answer which apural organized

—

plies to

its

full extent. It

which corresponds

the sense

Among substances are by general consent reckoned bodies and especially natural bodies;

in

it

is

substance in

to the definitive

formula of a thing's essence. That means that

for they are the principles of all other bodies.

it is 'the essential whatness' of a body of the character just assigned. Suppose that what is

Of

literally

some have

natural bodies not; by

ers

life

we mean

life

in

them, oth-

self-nutrition

and

[75] growth (with its correlative decay). It follows that every natural body which has life in

it is

a substance in the sense of a composite.

But since it is also a body of such and such a kind, viz. having life, the body cannot be soul; the body is the subject or matter, not what is attributed to it. Hence the soul must be a sub[20] stance in the sense of the form of a natural body having life potentially within it. But substance is actuality, and thus soul is the actuality of a body as above characterized. Now the word actuality has two senses corresponding respectively to the possession of knowledge and the actual exercise of knowledge. It is obvious that the soul

is

actuality in the first sense,

knowledge as possessed, for both [25] sleeping and waking presuppose the existence of soul, and of these waking corresponds to actual knowing, sleeping to knowl-

viz. that of

edge possessed but not employed, and, in the history of the individual, knowledge comes before

its

employment

That

is

why

or exercise.

the soul

is

the

first

grade of

ac-

body having life potenThe body so described is a body

tuality of a natural tially in

it.

412 b which

is

organized.

The

parts of plants

body,

its

an

'organ', like

an axe, were a natural would have been

'essential whatness',

and so its soul; if this disappeared would have ceased to be an axe, ex[75] cept in name. As it is, it is just an axe; it wants the character which is required to its

essence,

from

it, it

make

its

whatness or formulable essence a soul; it would have had to be a natural body of a particular kind, viz. one having in for that,

the power of setting itself in movement and arresting itself. Next, apply this doctrine itself

in the case of the 'parts' of the living body.

—

Suppose that the eye were an animal sight would have been its soul, for sight is the substance or essence of the eye

which corresponds

[20] to the formula, the eye being merely the matter of seeing; when seeing is removed

—

is no longer an eye, except in name it no more a real eye than the eye of a statue or of a painted figure. We must now extend our consideration from the 'parts' to the whole living body; for what the departmental sense is to the bodily part which is its organ, that the whole faculty of sense is to the whole sensitive body as such. [25] We must not understand by that which is 'potentially capable of living' what has lost the soul it had, but only what still retains it;

the eye

is

BOOK

413 b

CHAPTERS

II,

1-2

643

but seeds and fruits are bodies which possess

down, and everything that grows

the qualification. Consequently, while waking is actuality in a sense corresponding to the cut413 a ting and the seeing, the soul is actuality

bulk alike in both directions or indeed in all, [30] and continues to live so long as it can absorb nutriment. This power of self-nutrition can be isolated from the other powers mentioned, but not they from it in mortal beings at least. The fact is obvious in plants; for it is the only psychic

in the sense corresponding to the and the power in the tool; the

sight

power of body cor-

responds to what exists in potentiality; as the pupil plus the power of sight constitutes the eye, so the soul plus the body constitutes the animal.

From soul

is

this

indubitably follows that the its body, or at any rate

it

inseparable from

increases

its

—

power they possess. 413 b This is the originative power the possession of which leads us to speak of things as living at

all,

but

is

it

the possession of sensa-

has parts) of them is noth-

tion that leads us for the first time to speak of

ing but the actualities of their bodily parts. Yet some may be separable because they are not the actualities of any body at all. Further, we

which possess no power of local movement but do possess the power of sensation we call animals and not merely living things. The primary form of sense is touch, which [5] belongs to all animals. Just as the power of self-nutrition can be isolated from touch and

that certain parts of

it

[5] for the actuality of

are (if

some

it

have no light on the problem whether the soul not be the actuality of its body in the

may

sense in

which the

sailor

is

the actuality of the

living things as animals; for even those beings

ship.

sensation generally, so touch can be isolated

This must suffice as our sketch or outline [10] determination of the nature of soul.

of self-nutrition

from

all

other forms of sense. (By the power

power of the and animals: Since what

is

clear or logically

emerges from what

more evident

confused but more observable by us, we must reconsider our results from this point of view. For it is not enough for a definitive formula to express as [75] most

now do

in itself

the

mere

is

fact;

must

it

in-

clude and exhibit the ground also. At present definitions are given in a form analogous to the conclusion of a syllogism; e.g. What is squaring? The construction of an equilateral rectangle equal to a given oblong rectangle. Such a definition is in form equivalent to a

One

that tells us that squaring

we mean which

soul all

is

that departmental

common

to plants

animals whatsoever are ob-

served to have the sense of touch.)

What

the

[10] explanation of these two facts is, we must 1 discuss later. At present we must confine ourselves to saying that soul

phenomena and by

is

powers of

the

is

the source of these

characterized by them, viz. self-nutrition,

sensation,

thinking, and motivity. Is

And

each of these a soul or a part of a soul? if

a part, a part in

A

what sense?

part

merely distinguishable by definition or a part [75] distinct in local situation as well? In the case of certain of these powers, the answers to

is

these questions are easy, in the case of others

which is a mean proportional between the two unequal sides of the given rectangle discloses the ground of what is

what to say. Just as in the case which when divided are observed to continue to live though removed to a distance from one another (thus showing that in their

conclusion.

the discovery of a line

defined.

We

resume our inquiry from a fresh [20] starting-point by calling attention to the fact that

what has

soul in

not, in that the

it

from what has

differs

former displays

life.

Now

this

word has more than one

sense,

and provided

any one alone of these

found

in a thing

say that thing

is

is

living. Living, that

is,

we may

mean thinking

or perception or local move-

ment and

or

rest,

movement

in the sense of

[25] nutrition, decay and growth. Hence we think of plants also as living, for they are observed to possess in themselves an originative power through which they increase or decrease in all spatial directions; they grow up and

we

are puzzled

of plants

case the soul of each individual plant before

division

we

so

was

actually one, potentially

many),

notice a similar result in other varieties

[20] of soul, i.e. in insects which have been cut in two; each of the segments possesses both

sensation and local

movement; and if sensaimagination and appeti-

tion, necessarily also

tion; for,

where there

is

sensation, there

is

also

pleasure and pain, and, where these, necessarily

also desire.

We

have no evidence as yet about mind or

[25] the power to think; it seems to be a widely different kind of soul, differing as what is 1

in. 12, esp.

a b 434 22-30, io

ff.

ON THE SOUL

6 44 eternal

from what

is

perishable;

it

alone

is

ca-

pable of existence in isolation from all other psychic powers. All the other parts of soul, it evident from what we have said, are, in spite of certain statements to the contrary, incapable

414 b

served fact; the actuality of any given thing can only be realized in what is already potentially that

thing,

i.e.

in a

From

matter of

its

own

ap-

is

propriate to

of separate existence though, of course, distin-

soul is an actuality or formulable essence of something that possesses a potentiality of being

guishable by definition. If opining is distinct [30] from perceiving, to be capable of opining and to be capable of perceiving must be dis-

and so with

tinct,

all

the other forms of living

some animals possess all these parts of soul, some certain of them only, others one only (this is what enables us to classify animals); the cause must 414a be considered later. A similar arrangement is found also within the field of the senses; some classes of animals have all the senses, some only certain of them, others only one, the most indispensable, touch. Since the expression 'that whereby we live [5] and perceive' has two meanings, just like the expression 'that whereby we know' that may mean either (a) knowledge or (b) the soul, for we can speak of knowing by or with either, and similarly that whereby we are in above enumerated.

Further,

1

—

health

may

be either (a) health or (b) the

body or some part of the body; and since of the two terms thus contrasted knowledge or health or

if

is

we

the

name

so express

—

of a form, essence, or ratio, it

an actuality of a recipient

[10] matter knowledge of what is capable of knowing, health of what is capable of being

made

healthy (for the operation of that which capable of originating change terminates and has its seat in what is changed or altered); further, since it is the soul by or with which it folprimarily we live, perceive, and think: is

—

lows that the soul must be a ratio or formulable essence, not a matter or subject. For, as we 2 said, the word substance has three meanings [75] form, matter, and the complex of both and of these three what is called matter is po-

what is called form actuality. Since then the complex here is the living thing, the

tentiality,

body cannot be the actuality of the soul; it is the soul which is the actuality of a certain kind of body. Hence the Tightness of the view that the soul cannot be without a body, while it can[20] not be a body; it is not a body but something relative to a body. That is why it is in a body, and a body of a definite kind. It was a mistake, therefore, to do as former thinkers did, merely to fit it into a body without adding a definite specification of the kind or character [25] of that body. Reflection confirms the ob111.

12, 13.

2

412*7.

it.

all

this

it

follows that

besouled.

Of

the psychic powers above enumerated 3 some kinds of living things, as we have said, 4 possess all, some less than all, others one only, [jo] Those we have mentioned are the nutritive,

the appetitive, the sensory, the locomo-

tive,

and the power

none but the

first,

of thinking. Plants have

the nutritive, while another

order of living things has this plus the sensory. If any order of living things has the sen-

414 b sory,

must

it

petite

is

also

have the appetitive; for ap-

the genus of which desire, passion,

and wish are the

species;

now

all

animals have

and whatever has a sense has the capacity for pleasure and pain and therefore has pleasant and painful objects present to it, and wherever these are present, one sense

at least, viz. touch,

[5] there is desire, for desire of what is pleasant. Further,

is

the sense for food (for touch

just appetition

all

animals have

the sense for food); the food of all living things consists of what is dry, moist, hot, cold, and these are the is

apprehended by touch; all other senapprehended by touch only [10] indirectly. Sounds, colours, and odours contribute nothing to nutriment; flavours fall qualities

sible qualities are

within the

field of tangible qualities.

Hunger

and thirst are forms of desire, hunger a desire for what is dry and hot, thirst a desire for what is cold and moist; flavour is a sort of seasoning added to both. We must later 5 clear up these [75] points, but at present it may be enough to say that all animals that possess the sense of touch have also appetition. The case of imagi-

nation

is

obscure;

we must examine

it

later.

6

Certain kinds of animals possess in addition the power of locomotion, and still another order of animate beings, i.e. man and possibly another order like man or superior to him, the [20] power of thinking, i.e. mind. It is now evident that a single definition can be given of soul only in the same sense as one can be given of figure. For, as in that case there

distinguishable 3 5

and apart from

is

no

figure

triangle,

&c,

4 a b a b 4 i3 3 2 -4i4 i4 i 3 23-5, i 1-13,21-4. b 18-21); Sense and the Sensi11, in. 12 (434

Chapter

ble, 4.

6111.3,11 (433 b 3 I -434a 7)-

BOOK

415 b so here there

no

is

soul apart

II,

CHAPTERS

from the forms

of soul just enumerated. It is true that a highly general definition can be given for figure

which

will

fit

figures without expressing

all

the peculiar nature of any figure. So here in the case of soul and its specific forms. Hence [25]

it

is

demand which

absurd in this and similar cases to an absolutely general definition

will fail to express the peculiar nature

is, or again, omitting this, to look for separate definitions corresponding to each infima species. The cases of figure and

of anything that

soul are exactly parallel; for the particulars sub-

sumed under

—figures [50]

ries,

the

contains

tially

common name

—

its

both cases

predecessor, e.g. the square

the triangle, the sensory tive.

in

and living beings constitute a seeach successive term of which poten-

Hence we must ask

der of living things,

power the

self-nutri-

in the case of

What

each or-

What man? Why the serial way must form is its

soul,

i.e.

the soul of plant, animal,

is

terms are related in this

415 a the

subject of later examination.

1

But the

power of perception is never found apart from the power of self-nutrition,

facts are that the

—

—

in plants the latter is found isolated from the former. Again, no sense is found apart from that of touch, while touch is found

while

[5] by itself;

many

animals have neither sight,

hearing, nor smell. Again, that possess sense

among living

things

some have the power of loco-

motion, some not. Lastly, certain living beings a small minority possess calculation and thought, for (among mortal beings) those which possess calculation have all the other [10] powers above mentioned, while the converse does not hold indeed some live by imagination alone, while others have not even imagination. The mind that knows with immediate intuition presents a different problem. It is evident that the way to give the most adequate definition of soul is to seek in the case of each of its forms for the most appropri-

—

—

—

ate definition.

2-4

645

der of investigation the question of what an agent does precedes the question, what enables [20] it to do what it does. If this is correct, we must on the same ground go yet another step farther back and have some clear view of the objects of each; thus we must start with these objects, e.g. with food, with what is perceptible, or with what is intelligible. It follows that first of all we must treat of nutrition and reproduction, for the nutritive soul is found along with all the others and is the most primitive and widely distributed power of soul, being indeed that one in virtue [25] of which all are said to have life. The acts in which it manifests itself are reproduction and the use of food reproduction, I say, because for any living thing that has reached its normal development and which is unmutilated, and whose mode of generation is not spontaneous, the most natural act is the production of another like itself, an animal producing an

—

animal, a plant a plant, in order that, as far as its nature allows, it may partake in the eternal

415 b and divine. That is the goal towards which all things strive, that for the sake of which they do whatsoever their nature renders

The phrase 'for the sake of which' is ambiguous; it may mean either (a) the end to achieve which, or (b) the being in whose interest, the act is done. Since then no living thing is able to partake in what is eternal and divine by uninterrupted continuance (for nothing perishable can for ever remain one and [5] the same), it tries to achieve that end in possible.

way

the only

possible to

it,

and

varying degrees; so

success

is

pos-

remains not indeed as the self-same individual but continues its existence in something li\e itself not numerically but specifically one. sible in

it

—

The soul is the cause or source of the living The terms cause and source have many

body.

But the soul

senses.

is

the cause of

alike in all three senses

[10] recognize.

movement,

it is

which we

its

body

explicitly

(a) the source or origin of (b) the end, it is (c) the es-

It is

sence of the whole living body.

That necessary for the student of these forms of soul first to find a definition of each, ex-

It is

it is

the essence being,

the is

and

last, is clear;

for in everything

identical with the

ground of

[75] pressive of what it is, and then to investigate its derivative properties, &c. But if we are

their being

to express what each is, viz. what the thinking power is, or the perceptive, or the nutritive, we must go farther back and first give an ac-

source. Further, the actuality of whatever

count of thinking or perceiving, for in the or1

in. 12, 13.

its

here, in the case of living things, is

to live,

and of their being and them is the cause or

their living the soul in

potential

is

identical

with

its

formulable

is

es-

sence.

[75]

It

is

manifest that the soul is also the its body. For Nature, like mind,

final cause of

ON THE SOUL

6^6

416 b

always does whatever it does for the sake of something, which something is its end. To that something corresponds in the case of animals the soul and in this it follows the order of nature; all natural bodies are organs of the soul. This is true of those that enter into the

belong to the side of formulable essence rather than that of matter. Nutrition and reproduction are due to one

which

sake of which', viz. (a) the end to achieve which, and (b) the being in whose interest,

food that this psychic power is distinguished from all the others. The current view is that what serves as food to a living thing is what is contrary to it not that in every pair of contraries each is food to the other: to be food a contrary must not only be transformable into

anything

the other

constitution of plants as well as of those

enter into that of animals. This shows that that

We

[20] for the sake of which they are is soul. recall the two senses of 'that for the

must here

We

or

is

is

done.

must maintain,

further, that the soul

also the cause of the living

body

source of local movement.

The power

is

as the original

and the same psychic power.

It is necessary give precision to our account of. food, for it is by this function of absorbing

first to

[20]

—

and

vice versa,

it

must

also in so do-

ing increase the bulk of the other. Many a contrary is transformed into its other and vice

changes which constitute growth and decay; nothing grows or decays naturally except what feeds itself, and nothing feeds itself except

versa, where neither is even a quantum and so cannot increase in bulk, e.g. an invalid into a [25] healthy subject. It is clear that not even those contraries which satisfy both the conditions mentioned above are food to one another in precisely the same sense; water may be said to feed fire, but not fire water. Where the members of the pair are elementary bodies only one of the contraries, it would appear, can be said to feed the other. But there is a diffi-

what has

culty here.

motion things.

not found, however, in

is

of loco-

all

living

But change of quality and change of

quantity are also due to the soul. Sensation is held to be a qualitative alteration, and nothing except what has soul in it is capable of sensa-

The same

[25] tion.

holds of the quantitative

a share of soul in

Empedocles in plants

is

is

wrong

in

it.

adding that growth

to be explained,

the

downward

rooting by the natural tendency of earth to 416* travel downwards, and the upward branching by the similar natural tendency of fire to travel upwards. For he misinterprets up and down; up and down are not for all things what they are for the whole Cosmos: if we are to distinguish and identify organs according [5] to their functions, the roots of plants are

analogous to the head in animals. Further, we must ask what is the force that holds together the earth and the fire which tend to travel in contrary directions;

if

there

is

no counteract-

ing force, they will be torn asunder; if there is, this must be the soul and the cause of nutrition and growth. By some the element of fire is held to be the cause of nutrition and growth,

alone of the primary bodies or eleobserved to feed and increase itself. Hence the suggestion that in both plants and animals it is it which is the operative force. A concurrent cause in a sense it certainly is, but [75] not the principal cause, that is rather the soul; for while the growth of fire goes on without limit so long as there is a supply of fuel, in the case of all complex wholes formed in the course of nature there is a limit or ratio which determines their size and increase, and limit and ratio are marks of soul but not of fire, and [10] for

ments

is

it

One

[jo]

is

like.

Another

set of

thinkers assert that like

fed, as well as increased in

amount, by maintain the very reverse, viz. that what feeds and what is fed are contrary to one another; like, they argue, is incapable of being affected by like; but food is changed in the process of digestion, and change is always to what is opposite or to [35]

what

is

b acted

41

set, as

we have

said,

intermediate. Further, food

upon by what

is

nourished by it, not the other way round, as timber is worked by a carpenter and not conversely; there is a change in the carpenter but it is merely a change from not-working to working. In answering this problem it makes all the difference whether we mean by 'the food' the 'finis

ished' or the 'raw' product. If

we

use the

word

food of both, viz. of the completely undigested and the completely digested matter, we can [5] justify both the rival accounts of it; taking food in the sense of undigested matter, it is the contrary of what is fed by it, taking it as digested it is like what is fed by it. Consequently it is clear that in a certain sense we may say that both parties are right, both

wrong. Since nothing except fed,

what

because

it

is

fed

is

what

is

alive can be

the besouled body and just

has soul in

it.

Hence food

is

essen-

[10] tially related to what has soul in it. Food has a power which is other than the power to

BOOK

417*

what

increase the bulk of

what has

forth as

may

increase

what has

its

soul in

is

it is

fed by

II,

CHAPTERS

so far

quantum, food

a

quantity, but

it;

it is

only so far

a 'this-somewhat' or substance that food acts as food; in that case it maintains the being of what is fed, and that continues to be what it is so long as the process as

soul in

it is

[75] of nutrition continues. Further, it is the agent in generation, i.e. not the generation of the individual fed but the reproduction of another like it; the substance of the individual fed is already in existence; the existence of no substance is a self-generation but only a self-

maintenance.

Hence the psychic power which we are now studying may be described as that which tends to maintain whatever has this power in it of continuing such as it was, and food helps it to do its work. That is why, if deprived of food, it

must

[20]

The

process of nutrition involves three

what is fed, (b) that wherewith it is fed, (c) what does the feeding; of these (c) is the first soul, (a) the body which has that soul in it, (b) the food. But since it is right to call things after the ends they realize, and the factors, (a)

end of

this soul is to

like that in

which

generate another being

it is,

the

soul ought to

first

[25] be named the reproductive soul. The expression (b) 'wherewith it is fed' is ambigu-

ous just as ship

hand

is

is

the expression 'wherewith the

steered'; that

may mean

or (ii) the rudder,

moved and

sets in

merely moved.

i.e.

either (i) the

either (i)

movement, or

(ii)

what what

is

is

We can apply this

analogy here if we recall that all food must be capable of being digested, and that what produces digestion is warmth; that is why everything that has

warmth. [30] We have now given an outline account of the nature of food; further details must be soul in

it

possesses

given in the appropriate place.

these distinctions let us now speak of sensation in the widest sense. Sensa1 tion depends, as we have said, on a process of movement or affection from without, for it is held to be some sort of change of quality. Now

Having made

[55] some thinkers assert that like is affected only by like; in what sense this is possible and

41

a

in

what

sense impossible,

we have

ex-

plained in our general discussion of acting and being acted upon. 2 1

2

4i5 b 24, cf. 410* 25. On Generation and Corruption, 323b

647

arises a

of sense ?

that

It is clear

what

is

sensitive

it

so

ablaze.

In reply

we must

recall that

we use the word

[10] 'perceive' in two ways, for we say (a) that what has the power to hear or see, 'sees' or 'hears',

even though

also (b) that

it is

what

at the

moment asleep,

actually seeing or

is

hearing, 'sees' or 'hears'. Hence 'sense' too must have two meanings, sense potential, and sense actual. Similarly 'to be a sentient' means either (a) to have a certain power or (b) to

manifest a certain activity. To begin with, for [75] a time, let us speak as if there were no difference between (i) being moved or affected, and (ii) being active, for movement is a kind of activity an imperfect kind, as has elsewhere been explained. 3 Everything that is

—

acted upon or moved is acted upon by an agent which is actually at work. Hence it is that in one sense, as has already been stated, 4 what [20] acts and what is acted upon are like, in another unlike, i.e. prior to and during the change the two factors are unlike, after it

like.

But we must now distinguish not only between what is potential and what is actual but also different senses in which things can be said to be potential or actual;

up

to

now we

have been speaking as if each of these phrases had only one sense. We can speak of something as 'a knower' either {a) as when we say that man is a knower, meaning that man falls within the class of beings that know or have [25] knowledge, or (b) as when we are speaking of a man who possesses a knowledge of grammar; each of these is so called as having in him a certain potentiality, but there is a difference between their respective potentialities,

the one (a) being a potential knower, because his

kind or matter

is

such and such, the other

(b), because he can in the absence of any external counteracting cause realize his

i8ff.

is

only potentially, not actually. The power of sense is parallel to what is combustible, for that never ignites itself spontaneously, but requires an agent which has the power of starting ignition; otherwise it could have set itself on fire, and would not have needed actual fire to set

and

cease to be.

4-5

problem: why do we not perceive the senses themselves as well as the external objects of sense, or why without the stimulation of external objects do they not produce sensation, seeing that they contain in [5] themselves fire, earth, and all the other elements, which are the direct or indirect objects

Here

* Physics,

20 b 3 1 257b 8. ,

*

4 1 6* 2Q-

b

9.

knowl-

ON THE SOUL

64 8

knowing

This implies a third meaning of 'a knower' (c), one who is already realizing his knowledge he is a knower in actuality and in the most proper [jo] sense is knowing, e.g. this A. Both the former are potential knowers, who realize their respective potentialities, the one (a) by change of quality, i.e. repeated transitions from one state to its opposite under instruction, the other (b) by the transition from the 41 b inactive possession of sense or grammar to their active exercise. The two kinds of tran-

edge

in actual

at will.

—

hends is individuals, while what knowledge apprehends is universals, and these are in a sense within the soul. That is why a man can exercise his knowledge when he wishes, but his sensation does not depend upon himself [25] a sensible object must be there. A similar statement must be made about our knowledge of what is sensible on the same ground, viz.

—

that the sensible objects are individual

A

[5] and the other potential. For what possesses knowledge becomes an actual knower by a transition which is either not an alteration of it at all (being in reality a development into its true self or actuality) or at least an alteration in a quite different sense from the usual meaning. Hence it is wrong to speak of a wise man as being 'altered' when he uses his wisdom, just as it would be absurd to speak of a builder as

being altered when he building a house. [10]

What

is

using his

knowing

in the case of

skill

in

or under-

standing leads from potentiality to actuality ought not to be called teaching but something else. That which starting with the power to

know

knowledge through knows and has teaching either (a) ought not to

power

be said [75]

of

'to

who

actually

be acted upon' at

must recognize two

all

or (b)

we

senses of alteration,

viz. (i) the substitution of

one quality for an-

other, the first being the contrary of the sec-

ond, or quality ity

(ii)

the development of an existent

from

potentiality in the direction of fix-

or nature.

In the case of what first

ex-

later

more appropriate occasion may be

1

found thoroughly to clear up all this. At pres[jo] ent it must be enough to recognize the distinctions already drawn; a thing may be

two senses, (a) which we might say of a boy that he may become a general or (b) in the sense in which we might say the same of an adult, and there are two corresponding senses 418 a of the term 'a potential sentient'. There are no separate names for the two stages of said to be potential in either of in the sense in

we have

potentiality;

different

pointed out that they are

We

and how they are

different. cannot help using the incorrect terms 'being acted

upon or altered' of the two transitions inAs we have said, 2 what has the power sensation of is potentially like what the pervolved.

ceived object

is

actually; that

beginning of the process of

while at the being acted up-

is,

its

on the two interacting factors are dissimilar, [5] at the end the one acted upon is assimilated to the other and is identical in quality with it.

learns or acquires

the agency of one the

and

ternal.

sition are distinct.

Also the expression 'to be acted upon' has more than one meaning; it may mean either (a) the extinction of one of two contraries by the other, or (b) the maintenance of what is potential by the agency of what is actual and already like what is acted upon, with such likeness as is compatible with one's being actual

418-

heard, &c, are outside. The ground of this difference is that what actual sensation appre-

transition

is

due

is

to possess sense, the

to the action of the

male

In dealing with each of the senses we shall have first to speak of the objects which are perceptible by each.

The term

'object of sense'

two kinds of our language, directly perceptible, while the remaining one is only incidentally perceptible. Of the first two kinds one (a) consists of what is perceptible by a single sense, [10] the other (b) of what is perceptible by any and all of the senses. I call by the name of covers three kinds of objects,

which

are, in

special object of this or that sense that

which

parent and takes place before birth so that at birth the living thing is, in respect of sensation, at the stage which corresponds to the posses-

cannot be perceived by any other sense than that one and in respect of which no error is

sion of knowledge.

ject of sight,

Actual sensation corre-

sponds to the stage of the exercise of knowledge. But between the two cases compared [20] there is a difference; the objects that exthe sensory powers to activity, the seen, the

cite

possible; in this sense colour

is

the special ob-

sound of hearing, flavour of

taste.

Touch, indeed, discriminates more than one set of different qualities. Each sense has one [75] kind of object which it discerns, and nev1

ni. 4, 5.

2

417® 12-20.

BOOK

419* er errs in reporting that

what

is

before

II, it

CHAPTERS is

colour or sound (though it may err as to what it is that is coloured or where that is, or what it

is

that

is

objects are

sounding or where that is.) Such what we propose to call the special

objects of this or that sense.

'Common number,

are

sensibles'

movement,

rest,

magnitude; these are not pe-

figure,

culiar to any one sense, but are common to all. There are at any rate certain kinds of movement which are perceptible both by touch and

by

We

speak of an incidental object of sense [20] where e.g. the white object which we see is the son of Diares; here because 'being the son of is

incidental to

the directly visible

white patch we speak of the son of Diares as being (incidentally) perceived or seen by us. Because this is only incidentally an object of sense, it in no way as such affects the senses. Of the two former kinds, both of which are in their own nature perceptible by sense, the first

kind

6 49

same in both and is also found in the eternal body which constitutes the uppermost shell of the physical Cosmos. Of this substance light the activity of what is transis the activity

—

parent so far forth as it has in it the determi[10] nate power of becoming transparent; where this power is present, there is also the potentiality of the contrary, viz. darkness. Light is as it were the proper colour of what is

and

transparent, ly

transparent

whenever the

exists

is

potential-

excited to actuality by the in-

fluence of fire or something resembling 'the

sight.

Diares'

5-7

—that of —constitute

objects of the

special

several

the objects of sense in the [25] strictest sense of the term and it is to them that in the nature of things the structure

senses

of each several sense

is

adapted.

uppermost body'; for fire too contains someis one and the same with the sub-

thing which

stance in question.

We

have now explained what the transparand what light is; light is neither fire nor any kind whatsoever of body nor an efflux [75] from any kind of body (if it were, it would again itself be a kind of body) it is the presence of fire or something resembling fire in what is transparent. It is certainly not a body, for two bodies cannot be present in the same place. The opposite of light is darkness; darkness is the absence from what is transparent

is

—

ent of the corresponding positive state above characterized; clearly therefore, light is just the presence of that.

Empedocles (and with him all others used the same forms of expression) was wrong in speaking of light as 'travelling' or being at a given moment between the earth [20]

The

object of sight

the visible, and

is

what

is visible is (a) colour and (b) a certain kind of object which can be described in words but which has no single name; what we mean by (b) will be abundantly clear as we proceed.

Whatever is visible what lies upon what [50] ble; 'in that visibility

its

own

is is

colour and colour is in its own nature visi-

nature' here

means not

involved in the definition of what thus underlies colour, but that that substratum contains in itself the cause of visibility. Every colour has in it the power to set in movement what is actually transparent; that is

who

and

envelope,

its

movement being unob-

its

servable by us; that view

the clear evidence of

served facts;

if

is

contrary both to

argument and

to the obthe distance traversed were

[25] short, the movement might have been unobservable, but where the distance is from ex-

treme East to extreme West, the draught upon our powers of belief is too great.

What

constitutes its very nature. That not visible except with the help of light; it is only in light that the colour of a thing is seen. Hence our first task is to explain

is what what can take on sound is what is soundless; what is colourless includes (a) what is transparent and (b) what is invisible or scarcely visible, i.e. what is [50] 'dark'. The latter (b) is the same as what

what

is

418 b power is

why

it is

light

Now

is.

there clearly

is

something which

is

in itself

is

capable of taking on colour

is

colourless, as

transparent,

course

when

when

it is

and by 'transparent' I mean what [5] is visible, and yet not visible in itself, but rather owing its visibility to the colour of something else; of this character are air, water, and many solid bodies. Neither air nor water

same substance which

transparent because it is air or water; they are transparent because each of them has contained in it a certain substance which is the

sight

transparent,

is

potentially, not of

is

it

actually transparent; is

now

it is

darkness,

the

now

light.

419 a Not everything that is visible depends upon light for its visibility. This is only true of the 'proper' colour of things.

which

Some

objects of

in light are invisible, in darkness

stimulate the sense; that fiery or shining.

This

is,

things that appear

class of objects

has no

ON THE SOUL

650 simple

common name,

but instances of

it

are

[5] fungi, flesh, heads, scales, and eyes of fish. In none of these is what is seen their own

'proper' colour.

Why we

other question.

At present what

is anobvious is that what is seen in light is always colour. That is why without the help of light colour remains invisible. Its being colour at all means

[10] precisely

its

having in

movement what

in

parent, and, as

what

see these at all

is

it

the

is

power

—

[35] smell

I

say 'in water' because animals

that live in water as well as those that live on 419 b land seem to possess the sense of smell,

and

'in air'

because

man and all

seen, the actuality of

transparent is just light. following experiment makes the necessity of a medium clear. If what has colour is placed in immediate contact with the eye, it cannot be seen. Colour sets in movement not the sense organ but what is transparent, e.g. the air, and that, extending continuously from [75] the object to the organ, sets the latter in movement. Democritus misrepresents the facts when he expresses the opinion that if the inis

The

other land ani-

mals that breathe, perceive smells only when they breathe air in. The explanation of this too will be given later. 2 8

to set

already actually trans-

we have

419 b

Now

let us,

to begin with,

tinctions about

make

certain dis-

sound and hearing.

[5] Sound may mean either of two things (a) actual, and (b) potential, sound. There are certain things which, as we say, 'have no

sound', e.g. sponges or wool, others which have, e.g. bronze and in general all things which are smooth and solid the latter are

—

between. Hence it is indispensable that there if there were [20] be something in between nothing, so far from seeing with greater distinctness, we should see nothing at all. We have now explained the cause why colour cannot be seen otherwise than in light. Fire on the other hand is seen both in darkness and in light; this double possibility follows necessarily from our theory, for it is just fire that makes what is potentially transparent

sound because they can make a sound, i.e. can generate actual sound between themselves and the organ of hearing. Actual sound requires for its occurrence ii) two such bodies and (iii) a space befi, 10] tween them; for it is generated by an impact. Hence it is impossible for one body only to generate a sound there must be a body impinging and a body impinged upon; what sounds does so by striking against something else, and this is impossible without a movement from place to place. As we have said, not all bodies can by impact on one another produce sound; impact on wool makes no sound, while the impact on [75] bronze or any body which is smooth and hollow does. Bronze gives out a sound when struck because it is smooth; bodies which are hollow owing to reflection repeat the original impact over and over again, the body original-

actually transparent.

ly set in

were empty one could

an an impossibility. Seeing is due to an affection or change of what has the perceptive faculty, and it cannot be affected by the seen colour itself; it remains that it must be affected by what comes terspace

distinctly see

ant on the vault of the sky; that

is

—

The same account

holds also of sound and smell; if the object of either of these senses is in immediate contact with the organ no sensation is produced. In both cases the object sets [25]

movement only what

lies between, and this organ in movement: if what sounds or smells is brought into immediate contact with the organ, no sensation will be [jo] produced. The same, in spite of all appearances, applies also to touch and taste; why there is this apparent difference will be clear 1 later. What comes between in the case of sounds is air; the corresponding medium in the case of smell has no name. But, corresponding to what is transparent in the case of colour, there is a quality found both in air and

in

in turn sets the

water, which serves as a 1

4« b 34ff-

medium

for

what has

said to have a

—

movement being unable

to escape

from the concavity. Further, we must remark that sound is heard both in air and in water, though less distinctly in the latter. Yet neither air nor water is

the principal cause of sound.

What

is

re-

[20] quired for the production of sound is an impact of two solids against one another and against the air. The latter condition is satisfied

when

That

is

why

sharp blow, of the

upon does not retreat not dissipated by it. must be struck with a sudden

the air impinged

before the blow, it

i.e. is

if it is

to

sound

whip must outrun

air, just as

—the movement

the dispersion of the

one might get in a stroke

or whirl of sand as

it

at a

heap

was traveling rapidly

past.

[25]

An

echo occurs, when, a mass of

*42i b 13-422"

6.

air

hav-

BOOK

420**

II,

CHAPTERS

7-8

651

bounded, and prevented

reverberate like a horn; the air inside the ear

from dissipation by the containing walls of a by the impinging body and set in movement by it rebounds from this mass of air like a ball from a wall. It is probable that in all generation of sound echo takes place, though it is frequently only indistinctly heard. What happens here must be analogous to what happens in the case of light; otherwise it would light is always reflected [jo] not be diffused and outside what was directly illuminated by the sun there would be

has always a movement of its own, but the sound we hear is always the sounding of something else, not of the organ itself. That is why we say that we hear with what is empty and echoes, viz. because what we hear with is a

ing been

unified,

vessel, the air originally struck

—

blank darkness; but this reflected light is not always strong enough, as it is when it is reflected from water, bronze, and other smooth bodies, to cast a

guishing It is

shadow, which

is

the distin-

mark by which we recognize

rightly said that

light.

an empty space plays

the chief part in the production of hearing, for is the air,

what people mean by 'the vacuum' which is what causes hearing, when

that air

is

movement as one continuous mass; but owing to its friability it emits no sound, being dissipated by impinging upon any sur420 a face which is not smooth. When the surface on which it impinges is quite smooth, what is produced by the original impact is a set in

[35]

united mass, a result due to the smoothness of the surface with which the air is in contact at the other end. What has the power of producing sound is what has the power of setting in movement a single mass of air which is continuous from the impinging body up to the organ of hearing. The organ of hearing is physically united with air, and because it is in air, the air inside [5] is moved concurrently with the air outside. Hence animals do not hear with all parts of their bodies, nor

do

all

parts admit of the en-

trance of air; for even the part

which can be

moved and can sound has not air everywhere in it. Air in itself is, owing to its friability, quite soundless; only when its dissipation is prevented is its movement sound. The air in chamber just to prevent movement, in order that the [10] animal may accurately apprehend all varieties of the movements of the air outside. That is why we hear also in water, viz. because the water cannot get into the air chamber or even, owing to the spirals, into the outer the ear

is

built into a

this dissipating

happen, hearing ceases, as it the tympanic membrane is dam-

ear. If this does

also does

if

aged, just as sight ceases if the membrane covering the pupil is damaged. It is also a test of [75] deafness whether the ear does or does not

chamber which contains

Which

is it

a

bounded mass of air. body

that 'sounds', the striking

Is not the answer 'it is both, but each in a different way'? Sound is a movement of what can rebound from a smooth surface when struck against it. As we have explained not everything sounds when it strikes or is struck, e.g. if one needle is struck against another, neither emits any sound. In order, [25] therefore, that sound may be generated; what is struck must be smooth, to enable the air to rebound and be shaken off from it in one

or the struck? [20]

1

piece.

The

between different sounding in actual sound; as without the help of light colours remain invisible, so without the help of actual sound the distinctions between acute and grave sounds remain inaudible. Acute and grave are here metaphors, transferred from their proper sphere, viz. that of touch, where they mean bodies

distinctions

show themselves only

what moves the sense what moves the sense little in a long time. Not that what is sharp really moves fast, and what is grave, [jo] respectively (a)

much

in a short time, (b)

slowly, but that the difference in the qualities

and the other movement is due to There seems to be a between what is acute or grave to hearing and what is sharp or blunt to touch; what is sharp as it were stabs, while what is blunt pushes, the one producing its efof the one

their respective speeds. 420b sort of parallelism

fect in a short, the other in a

the one

is

long time, so that

quick, the other slow.

[5] Let the foregoing suffice as an analysis of sound. Voice is a kind of sound characteristic of what has soul in it; nothing that is without soul utters voice, it being only by a metaphor that we speak of the voice of the flute or the

what (being without soul) power of producing a succession of notes which differ in length and pitch and timbre. The metaphor is based on the fact that all these differences are found also in voice. lyre or generally of

possesses the

Many animals are voiceless, e.g. all non-sanguineous animals and among sanguineous ani[10] mals fish. This is just what we should exis a certain movement of air. those in the Achelous, which are

pect, since voice

The x

fish, like

^6,

13.

ON THE SOUL

65 2

said to have voice, really make the sounds with their gills or some similar organ. Voice is the sound made by an animal, and that with a special organ. As we saw, everything that makes a sound does so by the impact of something (a) [75] against something else, (b) across a space, (c) filled with air; hence it is only to be expected that no animals utter voice except those

Once air is inbreathed, Natwo different purposes, as the used both for tasting and for articuthat case of the two functions tasting

421 b

Why

they do not [5] or take in air. tion belonging to another inquiry. 2

the distinguishing characteristic of the object of smell is less obvious than those of sound or

The ground

which take

in air.

colour.

for

of smell

tongue

is

lating; in is

necessary for the animal's existence (hence

it

is

found more widely distributed), while

articulate speech

is

a luxury subserving

its

pos-

former case [20] Nature employs the breath both as an in-

sessor's well-being; similarly in the

dispensable

means

to the regulation of the in-

ner temperature of the living body and also as the matter of articulate voice, in the interests of

its

use

possessor's well-being.

indispensable

is

Why

its

former

must be discussed

else-

where. 1

The organ

of respiration

is

the windpipe,

and the organ to which this is related as means to end is the lungs. The latter is the part of the body by which the temperature of land [25] animals is raised above that of all others. But what primarily requires the air drawn in

by respiration is not only this but the region surrounding the heart. That is why when animals breathe the air must penetrate inwards. Voice then is the impact of the inbreathed air against the 'windpipe', and the agent that produces the impact is the soul resident in these parts of the body. Not every sound, as we [30] said, made by an animal is voice (even with the tongue we may merely make a sound which is not voice, or without the tongue as in coughing); what produces the impact must have soul in it and must be accompanied by an act of imagination, for voice is a sound with a meaning, and is not merely the result of any impact of the breath as in coughing; in voice the breath in the windpipe is used as an instrument to knock with against the walls of the 421 a windpipe. This is confirmed by our inability to speak when we are breathing either out or in we can only do so by holding our breath; we make the movements with the breath so checked. It is clear also why fish are voiceless; they have no windpipe. And they have no windpipe because they do not breathe

—

1

On

Breathing, 478* 28;

On

the Parts

of Animals, 642*

a ques-

Smell and its object are much less easy to determine than what we have hitherto discussed;

ture uses

it

is

is

less

of this

is

that our

power

discriminating and in general

[10] inferior to that of many species of animals; men have a poor sense of smell and our

apprehension of its proper objects is inseparably bound up with and so confused by pleasure and pain, which shows that in us the organ is inaccurate. It is probable that there is a parallel failure in the perception of colour

by animals that have hard eyes: probably they discriminate differences of colour only by the presence or absence of what excites fear, and [75] that it is thus that human beings distinguish smells. It seems that there is an analogy

between smell and taste, and that the species of tastes run parallel to those of smells the only difference being that our sense of taste is more discriminating than our sense of smell, because the former is a modification of touch, which reaches in man the maximum of dis-

—

criminative accuracy. While in respect of all [20] the other senses we fall below many species of animals, in respect of all

touch

we

far excel

other species in exactness of discrimination.

That

is

why man

animals. This

is

the most intelligent of

all

confirmed by the fact that it is to differences in the organ of touch and to nothing else that the differences between man is

man in respect of natural endowment are men whose flesh is hard are ill-endowed [25] by nature, men whose flesh is soft, well-

and

due;

endowed.

As flavours may be divided into (a) sweet, (b) bitter, so with smells. In some things the flavour and the smell have the same quality, i.e. both are sweet or both bitter, in others they diverge. Similarly a smell, like a flavour, may [50] be pungent, astringent, acid, or succulent. But, as we said, because smells are much less easy to discriminate than flavours, the names of these varieties are applied to smells only 421 b metaphorically; for example 'sweet' is extended from the taste to the smell of saffron or honey, 'pungent' to that of thyme, and so on. In the same sense in which hearing has for 2

Cf.

On

Breathing, 474 b 25-9, 476* 6-15;

Animals, 669* 2-5.

On the Parts of

BOOK

422*

II,

CHAPTERS

and the inaudible, [5] sight both the visible and the invisible, smell has for its object both the odorous and its

object both the audible

may

be either (a) what has no smell at all, or (b) what has a small or feeble smell. The same ambiguity the inodorous. 'Inodorous'

word

lurks in the

i.e.

through

air or

water

—

add wa-

I

ter,

distance

has any scent. That

if it

why

is

the

following facts constitute a problem for us. All animals smell in the same way, but man smells only when he inhales; if he exhales or holds his breath, he ceases to smell, no difference being [75] made whether the odorous object is distant or near, or even placed inside the nose and actually on the wall of the nostril; it is a disability

common

to all the senses not to per-

what is in immediate contact with the organ of sense, but our failure to apprehend what is odorous without the help of inhalation is peculiar (the fact is obvious on making the experiment). Now since bloodless animals do [20] not breathe, they must, it might be argued, have some novel sense not reckoned ceive

among this

is

the usual five.

Our

impossible, since

it

reply is

must be

scent that

ceived; a sense that apprehends

what

is

is

that per-

odor-

ous and what has a good or bad odour cannot be anything but smell. Further, they are observed to be deleteriously effected by the same strong odours as man is, e.g. bitumen, sulphur, [25] and the like. These animals must be able to smell without being able to breathe. The probable explanation is that in man the organ of smell has a certain superiority over that in all other animals just as his eyes have over those of hard-eyed animals. Man's eyes have in the eyelids a kind of shelter or envelope, which must be shifted or drawn back in order [30] that we may see, while hardeyed animals have nothing of the kind, but at once see what-

of smell

the transparent

422 a mals, uncurtained, while is

in others

which

probably has a curtain over it, drawn back in inhalation, owing to it

the dilating of the veins or pores. That explains also why such animals cannot smell un-

is

tangible.

Hence,

if

we

lived

we

should perceive a sweet object introduced into the water, but the water would not be the medium through which we perceived; our perception would be due to the solution of the sweet substance in what we imbibed, just as if it were mixed with some drink. There is no parallel here to the percepin water,

tion of colour,

which

is

due neither

to

any

blending of anything with anything, nor to any efflux of anything from anything. In the [75] case of taste, there is nothing corresponding to the medium in the case of the senses previously discussed; but as the object of sight is

colour, so the object of taste

is

flavour.

But

nothing excites a perception of flavour without

what acts upon the sense of must be either actually or potentially liquid like what is saline; it must be both (a) itself easily dissolved, and (b) capable of disthe help of liquid;

taste

[20] solving along with itself the tongue. Taste apprehends both (a) what has taste and (b) what has no taste, if we mean by (b) what

has only a slight or feeble flavour or what tends to destroy the sense of taste. In this it is exactly parallel to sight, which apprehends both

what

and what is invisible (for darkand yet is discriminated by sight; so is, in a different way, what is overbrilliant), and to hearing, which apprehends both sound and silence, of which the one is [25] audible and the other inaudible, and also ness

is

is

visible

invisible

over-loud sound. This corresponds in the case of hearing to over-bright light in the case of sense

which

dry as flavours

potentially dry.

matter, and this

sight.

itself in

is

moist. Consequently the organ

can be tasted is always something that can be touched, and just for that reason it cannot be perceived through an interposed foreign body, for touch means the absence of any in[10] tervening body. Further, the flavoured and tasteable body is suspended in a liquid

medium.

take in air

is

is

What

Similarly in certain species of animals the organ of smell is like the eye of hard-eyed ani-

ever presents

come from what

Smells

from what

10

because water-animals too (both sanguineous and non-sanguineous) seem to smell just as much as land-animals; at any rate some of them make directly for their food from a [jo]

653

[5] der water; to smell they must first inhale, and that they cannot do under water.

'tasteless'.

Smelling, like the operation of the senses previously examined, takes place through a

medium,

8-10

As is

a faint

sound

is

'inaudible', so in a

a loud or violent sound.

The word

'in-

and similar privative terms cover not only (a) what is simply without some power, but also (b) what is adapted by nature to have it but has not it or has it only in a very low

visible'

degree, as

low

is

when we

'footless'

say that a species of swal-

or that a variety of fruit

is

ON THE SOUL

654

So too

'stoneless'.

what can be

[30]

taste has as

its

object both

—

and the tasteless the what has little flavour or

tasted

latter in the sense of

a bad flavour or one destructive of taste.

difference between

what

The

and what is not seems to rest ultimately on that between what is drinkable and what is undrinkable both are tasteable, but the latter is bad and is

tasteless

tends to destroy taste, while the former

normal stimulus of

What

is

the

423

s

range between a single pair of contraries, white and black for sight, acute and grave for [25] hearing, bitter and sweet for taste; but in the field of

what

is

tangible

we

find several

such pairs, hot cold, dry moist, hard

soft, &c.

This problem finds a partial solution, when is

it

recalled that in the case of the other senses

more than one

pair of contraries are to be met with, e.g. in sound not only acute and grave

is

[30] but loud and soft, smooth and rough, &c; there are similar contrasts in the field of colour.

tasted is liquid, the perception cannot be either (a) actually liquid or (b) incapable of becoming

Nevertheless we are unable clearly to detect in the case of touch what the single subject is

common

the

taste.

is

object of both touch

drinkable

and

taste.

422 b Since what can be organ for

its

Tasting means a being affected by what can be tasted as such; hence the organ of taste must be liquefied, and so to start with must be non-liquid but capable of liquefaction without loss of its distinctive nature. This is [5] confirmed by the fact that the tongue cannot taste either when it is too dry or when it is liquid.

too moist; in the latter case to a contact

what occurs

is

due

with the pre-existent moisture in

when after a foretaste of we try to taste another flavour; it is in this way that sick persons find everything they taste bitter, viz. because, when the tongue

some strong

itself,

flavour

they taste, their tongues are overflowing with

which underlies the contrasted qualities and corresponds to sound in the case of hearing. To the question whether the organ of touch lies inward or not (i.e. whether we need look any farther than the flesh), no indication in 423 a favour of the second answer can be drawn from the fact that if the object comes into contact with the flesh

stretching

web

is

it

same manner

as before, yet

would

report

plays in touch very

on the

and the

bitter,

(b) secondary, viz.

side of the sweet, the succulent, (ii)

on the side of the bitter, the saline, (iii) between these come the pungent, the harsh, the astringent, and the acid; these pretty well exhaust the varieties of flavour.

It

follows that

[75] what has the power of tasting is potentially of that kind, and that what able ally

what has the power of making what it itself already is. is

what

is

is

taste-

it

actu-

11

Whatever can be

said of

what

is

tangible,

can be said of touch, and vice versa; if touch is not a single sense but a group of senses, there must be several kinds of what is tangible. It is a problem whether touch is a single sense or a [20] group of senses. It is also a problem, what is the organ of touch; is it or is it not the flesh (including what in certain animals is homologous with flesh)? On the second view, flesh is 'the medium' of touch, the real organ being situated farther inward. The problem arises because the field of each sense is according to the accepted view determined as the

at

once per-

is

reported in the

it is

clear that the

organ is not in this membrane. If the mem[5] brane could be grown on to the flesh, the

[10] The species of flavour are, as in the case of colour, (a) simple, i.e. the two contraries, (i)

is

tight over the flesh, as soon as this

touched the sensation

bitter moisture.

the sweet

it

For even under present conditions if the experiment is made of making a web and

ceived.

travel

still

quicker.

much

the

The

flesh

same part

as

would be played in the other senses by an airenvelope growing round our body; had we such an envelope attached to us we should have supposed that it was by a single organ that

we

perceived sounds, colours, and smells,

and we should have taken

sight, hearing,

and

[10] smell to be a single sense. But as it is, because that through which the different move-

ments are transmitted is not naturally attached to our bodies, the difference of the various sense-organs is too plain to miss. But in the case of touch the obscurity remains. There must be such a naturally attached

no living body could be it must be something solid. Consequently it must be composed of earth along with these, which is just what flesh and its analogue in animals which have no true flesh tend to be. Hence of neces[75] sity the medium through which are trans'medium'

as flesh, for

constructed of air or water;

mitted the manifoldly contrasted tactual qualities must be a body naturally attached to the organism. That they are manifold is clear when we consider touching with the tongue; we apprehend at the tongue all tangible qualities as

well as flavour. Suppose

all

the rest of

424

BOOK

a

II,

CHAPTERS

was, like the tongue, sensitive to flavour, we should have identified the sense of [20] taste and the sense of touch; what saves us from this identification is the fact that touch

our

flesh

and taste are not always found together in the same part of the body. The following problem might be raised. Let us assume that every body has depth, i.e. has three dimensions, and that if two bodies have a third body between them they cannot be in contact with one another; let

us

[25]

remember that what is liquid is a body and must be or contain water, and that if

two bodies touch one another under water, touching surfaces cannot be dry, but

their

must have water between, viz. the water which wets their bounding surfaces; from all this it follows that in water two bodies cannot be in contact with one another. The same holds of two bodies in air air being to bodies in air precisely what water is to bodies in wa-

—

[50] ter

—but the

facts are

not so evident to

10-11

to the real

655

organs of touch and

taste, as air

and

water are to those of sight, hearing, and smell. [20] Hence in neither the one case nor the other can there be any perception of an object if it is placed immediately upon the organ, e.g. if a white object is placed on the surface of the eye. This again shows that what has the power of perceiving the tangible

Only with

so

would there be

is

seated inside.

a complete analogy

if you on the organ it is not per[25] ceived, here if you place it on the flesh it is perceived; therefore flesh is not the organ

the other senses. In their case

all

place the object

medium

but the

of touch.

What

can be touched are distinctive qualiof body as body; by such differences I

ties

mean viz,

those which characterize the elements, hot cold, dry moist, of which we have

[jo] spoken earlier in our treatise on the ele-

ments. is

1

The organ

that of touch

for the perception of these

—that part of the body

in

which

our observation, because we live in air, just as animals that live in water would not notice that the things which touch one another in 423 b water have wet surfaces. The problem,

primarily the sense of touch resides. This is that part which is potentially such as its object

does the perception of all objects of sense take place in the same way, or does it not, e.g. taste and touch requiring contact (as they are commonly thought to do), while all

424a something such as it itself actually is makes the other such because the other is already potentially such. That is why when an

then,

is:

other senses perceive over a distance ? The distinction is unsound; we perceive what is hard [5] or soft, as well as the objects of hearing, and smell, through a 'medium', only that

sight,

the latter are perceived over a greater distance than the former; that is why the facts escape our notice. For we do perceive everything through a medium; but in these cases the fact

what we said before, touch were a membrane

escapes us. Yet, to repeat if

the

medium

for

separating us from the object without our observing its existence, we should be relatively to [10]

it

in the

same condition

as

we

are

now

to

water in which we are immersed; in their case we fancy we can touch objects, nothing coming in between us and them. But there remains this difference between what can be touched and what can be seen or can sound; in the latter two cases we perceive because the medium produces a certain effect upon us, whereas in the perception of objects of touch we are affected not by but along with the meair or

[75] dium; it is as if a man were struck through his shield, where the shock is not first given to the shield and passed on to the man, but the concussion of both is simultaneous. In general, flesh and the tongue are related

is

actually: for all sense-perception

of being so affected; so that that

is

a process

which makes

is equally hot and cold or hard and soft we cannot perceive; what we perceive must have a degree of the sensible quality lying beyond the neutral point. This implies that the sense itself is a 'mean' between any two opposite qualities which determine the field of [5] that sense. It is to this that it owes its power of discerning the objects in that field.

object of touch

What

is

'in

the middle'

relatively to either

is

fitted to discern;

extreme

in the place of the other.

can put

it

As what

is

itself

to per-

white and black must, to begin be actually neither but potentially either (and so with all the other sense-organs), ceive both

with,

so the organ of touch must be neither hot nor cold.

had for its what was visible and what was (and there was a parallel truth about

[10] Further, as in a sense sight object both invisible all

the other senses discussed),

2

so touch has

what is tangible and what is intangible. Here by 'intangible' is meant (a) what like air possesses some quality of tangible things in a very slight degree and (b) what possesses it in an excessive degree, as defor

its

object both

structive things do. 1

2

On Generation and Corruption, 42i b 3-6, 422*29.

II.

2, 3.

ON THE SOUL

65 6

We

have now given an outline account [75] of each of the several senses.

424 b

b

424 perature can be lowered or raised. The explanation is that they have no mean of contrary qualities,

and

so

no principle

in

them

The

capable of taking on the forms of sensible objects without their matter; in the case of plants the affection is an affection by form-and-matter

every sense

together.

12

following results applying to any and may now be formulated. (A) By a 'sense' is meant what has the pow-

er of receiving into itself the sensible forms of

things without the matter. This must be conceived of as taking place in the way in which a piece of wax takes on the impress of a signet[20] ring without the iron or gold;

what produces the impression bronze or gold, but stitution

the sense

makes no

we

say that

a signet of

particular metallic con-

its

difference: in a similar

affected by

is

is

what

is

way

coloured or

fla-

voured or sounding, but it is indifferent what in each case the substance is; what alone mat-

what

ters is

quality

it

has,

i.e.

in

what

ratio its

The problem might be raised: Can what cannot smell be said to be affected by [5] smells or what cannot see by colours, and so on? It might be said that a smell is just what can be smelt, and if it produces any effect it can only be so as to make something smell it, and it might be argued that what cannot smell cannot be affected by smells and further that what can smell can be affected by it only in so far as it has in it the power to smell (similarly with the proper objects of all the other senses). Indeed that this is so is made quite evident as [10] follows. Light or darkness, sounds and

what does not these but the bodies which

smells leave bodies quite unaffected;

constituents are combined.

affect bodies

(B) By 'an organ of sense' is meant that in which ultimately such a power is seated. [25] The sense and its organ are the same in

are their vehicles, e.g.

but their essence

fact,

What

not the same.

is

of course, a spatial magnitude, but

perceives

is,

we must

not admit that either the having the

power

to perceive or the sense itself

nitude;

what they

are

is

is

a

a certain ratio or

magpow-

er in a magnitude. This enables us to explain

why

objects of sense

which

possess one of

two

opposite sensible qualities in a degree largely in excess of the other opposite destroy the or[3°] g ans °f sense; if the movement set up by an object is too strong for the organ, the equipoise of contrary qualities in the organ, just is

its

sensory power,

is

disturbed;

which

it is

pre-

concord and tone are destroyed by too violently twanging the strings of a lyre. This explains also why plants cannot perceive, in spite of their having a portion of soul in them and obviously being affected by tangible objects themselves; for undoubtedly their temcisely as

is

what

splits

the trunk of

not the sound of the thunder but the air which accompanies thunder. Yes, but, it may be objected, bodies are affected by what is tangible and by flavours. If not, by what are things that are without soul affected, i.e. ala tree

is

tered in quality ?

Must we

not, then,

the objects of the other senses also

them?

admit that

may

affect

not the true account this, that all bodies are capable of being affected by smells [75] and sounds, but that some on being acted upon, having no boundaries of their own, disintegrate, as in the instance of air, which does become odorous, showing that some effect is produced on it by what is odorous ? But smelling is more than such an affection by what is odorous what more ? Is not the answer that, while the air owing to the momentary duration of the action upon it of what is odorous does itself become perceptible to the sense of smell, smelling is an observing of the result Is

produced ?

BOOK

III

sence of a sense necessarily involves absence of and if (1) all objects that we

a sense-organ;

That

[20]

to the five taste,

touch

there is no enumerated

sixth sense in addition

—

sight, hearing, smell,

—may be established by the follow-

ing considerations: If

we have

actually sensation of everything

which touch can give us sensation (for all [25] the qualities of the tangible qua tangible are perceived by us through touch); and if ab-

of

them are which sense we actually

perceive by immediate contact with perceptible by touch,

and (2) all objects that we perceive through media, i.e. without immediate contact, [50] are perceptible by or through the simple elements, e.g. air and water (and this is so arranged that (a) if more than one kind of sensible object is perceivable through a single mepossess,

BOOK

425 b

II,

11-12— BOOK

CHAPTERS

dium, the possessor of a sense-organ homogeneous with that medium has the power of perceiving both kinds of objects; for example, if the sense-organ

is

made

of

air,

and

air

is

a

425 a the same kind of

sensible objects, as e.g.

CHAPTERS

1-2

657

Cleon's son but as white, and the white thing which we really perceive happens to be Cleon's son.

me-

dium both for sound and for colour; and that (b) if more than one medium can transmit

III,

But

in the

there

case of the

already in

is

common

sensibles

us a general sensibility

which enables us to perceive them directly; there is therefore no special sense required for

water as well as air can transmit colour, both being transparent, then the possessor of either alone will be able to perceive the kind of objects transmissible through both); and if of the

their perception:

simple elements two only, air and water, go to form sense-organs (for the pupil is made of water, the organ of hearing is made of air, and the organ of smell of one or other of these

objects incidentally; not because the percipient

found either in none or an essential condition of and earth either in none or, if all sensibility anywhere, specially mingled with the components of the organ of touch; wherefore it would remain that there can be no sense-organ formed of anything except water and air); and if these sense-organs are actually found in cer[5] two, while fire is warmth being in all

—

—

tain animals;

—then

the possible senses are

all

[10] possessed by those animals that are not imperfect or mutilated (for even the mole is observed to have eyes 'beneath its skin); so that, if there is no fifth element and no property other than those which belong to the four

elements of our world, no sense can be wanting to such animals. Further, there cannot be a special sense[75] organ for the common sensibles either, i.e.

the objects

which we perceive

incidentally

through this or that special sense, e.g. movement, rest, figure, magnitude, number, unity; for all these we perceive by movement, e.g. magnitude by movement, and therefore also figure (for figure is a species of magnitude), what is at rest by the absence of movement: number is perceived by the negation of continuity, and by the special sensibles; for each sense perceives one class of sensible objects. So [20] that it is clearly impossible that there should be a special sense for any one of the

common

sensibles, e.g.

movement;

for, if that

our perception of it would be exactly parallel to our present perception of what is sweet by vision. That is so because we have a sense for each of the two qualities, in virtue of which when they happen to meet in one sensible object we are aware of both contemporaneously. If it were not like this our per-

were

so,

[25] ception of the

common

always be incidental, Cleon's son, where

we

i.e.

as

is

qualities

would

the perception of

perceive

him not

as

of

if

there were, our perception

them would have been

exactly like

what has

been above 1 described.

The

[50] sense

is

this or that special sense,

form

all

senses perceive each other's special

but because

a unity: this incidental perception

takes place whenever sense is directed at one and the same moment to two disparate qualities in one and the same object, e.g. to the bit425 b terness and the yellowness of bile, the assertion of the identity of both cannot be the act of either of the senses;

sense, e.g. the belief that

hence the illusion of a thing is yellow it

if

is bile.

might be asked why we have more senses

It

[5] than one. Is it to prevent a failure to apprehend the common sensibles, e.g. movement,

magnitude, and number, which go along with Had we no sense but

the special sensibles?

sight, and that sense no object but white, they would have tended to escape our notice and everything would have merged for us into an

indistinguishable identity because of the concomitance of colour and magnitude. As it is, the fact that the common sensibles are given in the objects of more than one sense reveals [10] their distinction from each and all of the special sensibles.

Since that

it

we

is

through sense that

are seeing or hearing,

we

it

we

are

must be

aware either

aware of seeing, or by some sense other than sight. But the sense that gives us this new sensation must perceive both sight and its object, viz. colour: so that either ( 1 ) there will be two senses both percipient of the same sensible object, or (2) the sense must [75] be percipient of itself. Further, even if the sense which perceives sight were different from sight, we must either fall into an infinite regress, or we must somewhere assume a sense which is aware of itself. If so, we ought to do by sight that

are

this in the first case.

This presents a sight

is

just to see,

difficulty: if to perceive

and what

(or the coloured), then Ml. 24-7.

if

is

we

seen

is

by

colour

are to see that

ON THE SOUL

65 8

which

sees, that

which

sees originally

must be

[20] coloured. It is clear therefore that 'to perceive by sight' has more than one meaning; for

when we

by sight that

426 b

&c, while

ing,

as

potentialities

one of them

[20] may exist without the other. The earlier students of nature were mistaken in their view

discriminate darkness from light, though not in the same way as we distinguish one colour from another. Further, in a sense even that

was no white or black, no savour. This statement of theirs is partly true, partly false: 'sense' and 'the sensible object' are ambiguous terms, i.e.

which

may

even

are not seeing,

it is

we

sees is coloured;

sense-organ

is

for in each case the

capable of receiving the sensible

object without

its

matter.

That

is

why

even

that without sight there

without

taste

denote either potentialities or actualities:

[25] the statement is true of the latter, false of the former. This ambiguity they wholly

[25] when the sensible objects are gone the sensings and imaginings continue to exist in

failed to notice.

the sense-organs.

voice

voice always implies a concord,

of the percipient sense is one and the same activity, and yet the distinctipn between their

and if the and the hearing of it are in one sense one and the same, and if concord always implies a ratio, hearing as well as what is heard must [jo] be a ratio. That is why the excess of ei-

being remains. Take as

ther the sharp or the

The

activity of the sensible object

and that

illustration

actual

sound and actual hearing: a man may have hearing and yet not be hearing, and that which has a sound is not always sounding. But when that which can hear is actively hearing and [jo] that which can sound is sounding, then the actual hearing and the actual sound are merged in one (these one might call respec426 a tively hearkening and sounding). If it is true that the movement, both the acting and the being acted upon, is to be found in that which is acted upon, both the sound and the hearing so far as it is actual must be found in that which has the faculty of hearing; for

in the passive factor that the actuality

it is

of the active or motive factor is realized; that [5] is why that which causes movement may be at rest.

Now

sound

just

the actuality of that which can sound or sounding, and the actuality of that which can hear is hearing or hearkening; 'sound' and 'hearing' are both ambiguous. The same account applies to the other senses and their objects. For as the-acting-and[10] being-acted-upon is to be found in the is

passive, not in the active factor, so also the actuality of the sensible object

and that of the

sensitive subject are both realized in the latter.

But while

in

some

cases each aspect of the total

actuality has a distinct

name,

e.g.

sounding and

hearkening, in some one or other

is

nameless,

e.g. the actuality of sight is called seeing,

the actuality of colour has

no name: the

but

actu-

ality of the faculty of taste is called tasting,

but

no name. Since the of the sensible object and of

the actuality of flavour has

[75] actualities the sensitive faculty are one actuality in spite

modes of being, and actual sounding appear and disappear from existence at one and the same moment, and so actual savour and actual tastof the difference between their actual hearing

If

426 b (So

flat

destroys the hearing.

also in the case of savours excess de-

and in the case of colours excessive brightness or darkness destroys stroys the sense of taste,

and in the case of smell excess of strength whether in the direction of sweetness or bitterness is destructive.) This shows that the sight,

the sense

That

is

pleasant

a ratio.

why when the

is

also

the objects of sense are (1) sensible extremes such as

acid or sweet or salt being pure

and unmixed

are brought into the proper ratio; then they are

and in general what is blended more pleasant than the sharp or the flat alone; or, to touch, that which is capable of be[5] pleasant:

is

ing either

warmed

or chilled: the sense and

the ratio are identical: while (2) in excess the sensible extremes are painful or destructive.

Each sense then is relative to its particular group of sensible qualities: it is found in a sense-organ as such and discriminates the differences which exist within that group; e.g. [10] sight discriminates white and black, taste sweet and bitter, and so in all cases. Since we also discriminate white from sweet, and indeed each sensible quality from every other, with what do we perceive that they are different? It must be by sense; for what is before us is [75] sensible objects. (Hence it is also obvious that the flesh cannot be the ultimate sense-or-

gan: if it were, the discriminating power could not do its work without immediate contact

with the object.) Therefore ( 1 ) discrimination between white and sweet cannot be effected by two agencies which remain separate; both the qualities discriminated must be present to something that is one and single. On any other supposition even if I perceived sweet and you perceived [20] white, the difference between them would

BOOK

427 b be apparent. What

III,

CHAPTERS

two things are difsweet is different from

says that

must be one; for what asserts this difference must be self-identical, and as what asserts, so also what thinks or perceives. That it is not possible by means of two agencies which remain separate to discriminate two objects which are* separate, is therefore obvious; and that (2) it is not possible to do this in separate movements of time may be seen if we look at it as follows. For as what asserts the difference between the good and the bad is one and the [25] same, so also the time at which it asserts the one to be different and the other to be different

white. Therefore

ferent

is

not accidental to the assertion (as

for instance

do not it

when I now

assert that there

asserts thus

it is

assert a difference but is

now

a difference);

—both now and that the objects

now; the objects therefore must be present at one and the same moment. Both the discriminating power and the time of its exercise must be one and undivided. are different

But,

it

may

be objected,

it is

impossible that

what is self-identical should be moved at Dne and the same time with contrary movements in so far as it is undivided, and in an undivided moment of time. For if what is sweet be the quality perceived, it moves the [50]

sense

or thought in this

determinate way,

427 a while what is bitter moves it in a contrary way, and what is white in a different way. Is it the case then that what discriminates, though both numerically one and indivisible, is at the same time divided in its being? In one sense, it is what is divided that perceives two separate objects at once, but in

another sense

it

does

it

2-3

659

takes the limit as two,

separate objects with

what

in a sense

takes

it

with what single

is

About

to be affected at

one and the same

that sensation

it

moment by

to be the case

and thinking are properly

so de-

scribed.

[10] The answer is that just as what is called a 'point' is, as being at once one and two, properly said to be divisible, so here, that

discriminates in a single

is

qua undivided one, and

moment

which active

of time, while so far forth

twice over uses the same dot

as

it is

at

one and the same time. So far forth then as

divisible

it

is it

divid-

does so

activity a

its

the principle in virtue of

which we

[75] say that animals are percipient, let this discussion suffice.

There are two distinctive peculiarities by reference to which we characterize the soul (1) local movement and (2) thinking, discriminating, and perceiving. Thinking both speculative and practical is regarded as akin to [20] a form of perceiving; for in the one as well as the other the soul discriminates and is cognizant of something which is. Indeed the ancients go so far as to identify thinking and perceiving; e.g. Empedocles says Tor 'tis in respect of what is present that man's wit is in2 creased', and again 'Whence it befalls them from time to time to think diverse thoughts', 3 [25] and Homer's phrase 'For suchlike is man's mind' means the same. They all look upon thinking as a bodily process like perceiving, and hold that like is \nown as well as 1

perceived by

like, as

I

explained at the begin-

ning of our discussion. 4 Yet they ought at the same time to have accounted for error also; for 427 b it is more intimately connected with animal existence and the soul continues longer in the state of error than in that of truth. They cannot escape the dilemma: either (1) whatever seems is true (and there are some who accept this) or (2) error is contact with the un-

one and the same.

the forms of both, assuming

as one,

two

of time.

may

—

it

one and occupies in

moment

well as

be both contraries at once potentially, it cannot be self-identical in its being it must lose its unity by being put into activity. It is not possible to be at once white and black, and therefore it must also be impossible for a thing

discriminates

ed: while so far as

qua undivided; for it is divisible in its being, but spatially and numerically undivided. [5] But is not this impossible? For while it is true that what is self-identical and undivided so

it

like; for that

like

by

[5]

But

is

the opposite of the

knowing

of

like. it is

a received principle that error as

knowledge

in respect to contraries

is

That perceiving and practical thinking are not identical is therefore obvious; for the former is universal in the animal world, the latter is found in only a small division of it. Further, speculative thinking is also distinct from perceiving I mean that in which we find

—

Tightness

and wrongness

—rightness

in

pru-

[10] dence, knowledge, true opinion, wrongness in their opposites; for perception of the special objects of sense ror,

and

sible

is

found

to think falsely

thought

is

Odyssey,

always free from

as well as

found only where there 2

iFr. 106. 3

is

in all animals, while

xvm.

Fr. 108.

136.

4 404**

8-18.

it is

truly, is

er-

pos-

and

discourse

ON THE SOUL

66o

of reason as well as sensibility. For imagination

different

is

from

either perceiving or dis-

[75] cursive thinking, though

not found

it is

without sensation, or judgement without it. That this activity is not the same kind of thinking as judgement is obvious. For imagining lies within our own power whenever we wish (e.g. we can call up a picture, as in the practice of mnemonics by the use of mental im[20] ages), but in forming opinions we are not free: we cannot escape the alternative of falsehood or truth. Further, when we think something to be fearful or threatening, emotion is immediately produced, and so too with what is encouraging; but when we merely imagine we remain as unaffected as persons who are looking at a painting of some dreadful or encouraging scene. Again within the field

428 b

remains therefore to see

It

if it is opinion, be either true or false. [20] But opinion involves belief (for without belief in what we opine we cannot have an opinion), and in the brutes though we often

for opinion

may

find imagination ther, every

belief

we

opinion

never find

belief.

Fur-

accompanied by belief, by conviction, and conviction by disis

course of reason: while there are some of the brutes in which we find imagination, without discourse of reason. It is clear then that imagi[25] nation cannot, again, be ( 1 ) opinion plus sensation, or (2) opinion mediated by sensa-

is

blend of opinion and sensation; both for these reasons and because the content of the supposed opinion cannot be different from that of the sensation (I mean that imagination must be the blending of the perception of white with the opinion that it is white: it could scarcely be a blend [jo] of the opinion that it is good with the perception that it is white): to imagine is there428 b fore (on this view) identical with the thinking of exactly the same as what one in

ment: we must therefore

the strictest sense perceives. But

[25] of judgement itself we find varieties knowledge, opinion, prudence, and their opposites; of the differences between these I must speak elsewhere. Thinking is different from perceiving and

held to be in part imagination, in part judgefirst mark off the sphere of imagination and then speak of judge428 a ment. If then imagination is that in virtue of

which an image

excluding

arises for us,

metaphorical uses of the term,

is

a single

it

faculty or disposition relative to images, in vir-

which we discriminate and are

tue of

error or not?

we do

The

either in

faculties in virtue of

which

this are sense, opinion, science, intelli-

gence. [5]

That imagination

is

not sense

is

the following considerations: Sense

clear is

from

either a

faculty or an activity, e.g. sight or seeing: imagination takes place in the absence of both, as e.g. in dreams. (2)

Again, sense

is

always

present, imagination not. If actual imagination

and actual sensation were the same, imagination would be found in all the brutes: this is [10] held not to be the case; e.g. it is not found in ants or bees or grubs. (3) Again, sensations are always true, imaginations are for the most

part false. (4) Once more, even in ordinary speech, we do not, when sense functions precisely

with regard to

agine

it

some

failure of accuracy in

to be a

its

object, say that

we

im-

man, but rather when there its

exercise.

is

And

[75] (5), as we were saying before, visions appear to us even when our eyes are shut. Neither is imagination any of the things that are 1

never in error: e.g. knowledge or intelligence; for imagination may be false. ill. 7-8.

tion, or (3) a

this is impossible

ine

is

sometimes

false

what we imagthough our contempora-

neous judgement about it is true; e.g. we imagine the sun to be a foot in diameter though we are convinced that it is larger than the inhabited part of the earth, and the following dilemma presents itself. Either (a) while the fact has not changed and the [5] observer has neither forgotten nor lost belief in the true opinion which he had, that opinion has disappeared, or (b) if he retains it then his opinion is at once true and false. A true opinion, however, becomes false only when the fact alters without being noticed.

Imagination

is

therefore neither any one of

the states enumerated, nor

compounded out

of

them. [70] But since when one thing has been set in motion another thing may be moved by it, and imagination is held to be a movement and to

be impossible without sensation, i.e. to in beings that are percipient and to have content what can be perceived, and movement may be produced by actual tion

and that movement

is

its

since sensa-

necessarily similar

in character to the sensation itself, this

ment must be (1)

occur for

move-

necessarily (a) incapable of

[75] existing apart from sensation, (b) incapable of existing except when we perceive, (2) such that in virtue of its possession that in which it is found may present various phe-

BOOK

429 b

III,

CHAPTERS

nomena both active and passive, and (3) such that it may be either true or false. The reason of the last characteristic is as follows. Perception (1) of the special objects of sense is never in error or admits the least possible amount of falsehood. (2) That of the

concomitance of the objects concomitant with the sensible qualities comes next: in this case [20] certainly we may be deceived; for while the perception that there is white before us cannot be false, the perception that what is white is this or that may be false. (3) Third

comes the perception of the universal attributes which accompany the concomitant objects to which the special sensibles attach (I mean e.g. of movement and magnitude); it is in respect of these that the greatest

sense-illusion

is

amount

of

possible.

[25] The motion which is due to the activity of sense in these three modes of its exercise will differ from the activity of sense; (1) the first

from error while the sensation is present; (2) and (3) the others may be erroneous whether it is present kind of derived motion

or absent, especially

is

when

free

the object of per-

[50] ception is far of?. If then imagination preno other features than those enumerated

3-4

661

while impassible, capable of receiving the object; that is, must be potentially identical in character with its object without being the object. Mind must be related to what be,

form of an

is

thinkable, as sense

is

to

what

is

ity.

(by

Thus that in the soul which is called mind mind I mean that whereby the soul thinks

and judges) is, before it thinks, not actually any real thing. For this reason it cannot reasonably be regarded as blended with the body: [25] if so, it would acquire some quality, e.g.

warmth

or cold, or even have an organ like

the sensitive faculty: as

good idea though (1)

a

it is, it

has none.

this description

intellective soul,

this is the

Observation of the sense-organs and their [jo] impassibility of the sensitive

(fyavraala (imagination)