Gnosiology: The Scientific Approach to the Theory of Knowledge

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GNOSIOLOGY The Scientific Approac/1 to tlze T/1eo1')' of K11oii•ledge I

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The Scientific Approach to the Theory of Knowledge BY

TA DEUSZ KOTARBINSKI Translated from the Polish by OLGIERD WOJTASIEWICZ

Translation edited by G. BIDWELL

and

C. PINDER

P ER GAMO N P R ESS O X F O R D · L O N D O N · E D I N BU R G H · N E W Y O R K T O R O N T O · P A R I S · B R AU N S C H W E I G ZAKLAD NARODOWY im. OSSOLIN SKICH. WYDAWNICTWO WROCLAW

Perga1non Press Ltd ., Heading ton H ill Ha ll, O xfo rd 4 & 5 Fitzro y Square, Lo 11 don W. 1

Pergamon Press (Sco tla11d ) Ltd., 2 & 3 Te vio t Place, Ed inburgh 1 Pergan1on P ress Inc., 4 4-01 2 1 s t S treet, Long Island City, Ne w York 1 1 1 0 1 Pergamon o f Canada , Ltd. , 6 Ad ela id e S treet East, T (1ron to , Onta rio Pergan1on P ress S. A. R. L., 24 rtte d es Eco lcs, Pa ris 5 e Fr icd r. Vieweg & Sohn Verlag, Pc)s tfa cl1 1 85 , 3 3 Brre generally, ab::>ut an object) to the effect that that person is an itinerant minstrel composing satirical Latin verse. Hence, if the word or phrase ''N'' is a name that is a saying which can be used as the subjective complement in the structure "A is B'' - then to the question ''what does N mean'?'' we may answer: ''x is N'' means that x is such and such; or: ''x is N'' is a statement of the thougl1t that xis such and such; or: ''N'' can be used as the subjective complement in a sentence which would state concerning an object that it is such and such. In this way we try to cope with questions about the meaning of a given term. But apart from sentences and terms there are other words and phrases wl1ich mean something, and with reference to which we may encounter questions about . · the meaning of ti1e conJunctions e1ther... or...•• ···1 r th en... , etc. In this case, too, we may not reasonably answer that ''either... or ..." means that etc., but we can find our way out in the following manner: the sentence ''either . .

·

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·

,

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. • •

SUCH SEMANTIC RELATIONS AS EXP�ON '' '' '' p or q (where ''p'' and q stand for certain sentences) means that if not

7

p

then q,

and not both p and q. For instance : ''Either the defence will succeed or a wrong will result'' means that if the defence does not succeed then a wrong will result, and not both that the defence will succeed and a wrong will result (here the negation ''not'' refers to the linking of the two sentences by ''and''). In other words, ''eitl1er... '' '' or..." can be used as a conjunction between two sentences ''p'' and q , with which

i t forms a compound sentence which states the thought tl1at if the first sentence is false then the second is true, and that not both sentences are true. Difficulties pile up when from sentences we pass to terms, and from these to other parts of the sentence. We shall, therefore, confine ourselves to a general remark stating that in all those cases when someone asks what a given phrase means, the proper answer is obtained by using the phrase ''means that'', either used directly after the word or phrase to which the question pertains, or somehow implied in accordance with the syntactic function of that word or phrase. Thus the difference between the expressions "means'' and ''states as to content'' is made sufficiently clear. These expressions are not isosemic, and not even equivalent . . An analytic definition of the phrase ''means that'' as applied to · sentences can be built with the aid of the words ''states as to content'' (or ''is a statement as to content'') in '' the following manner: ''The sentence S means that q is the same as ''The sentence '' S states as to content, directly or indirectly, a person's thought that q . This does not in the least contradict the fact that the expressions ''means'' and ''states as to content'' have different meanings, since if for ''states as to content'' we substitute ''means'' then we obtain a malfor1nation : ''S means, directly or indirectly, someone's '' thought that q , whereas by the definition given above and in the light of previous explanations

S

means that q, and does not mean anyone's thought, even if that

thought is precisely the thought that q.

3. DENOTING.

(a)

Terms and their types.

We shall now reflect on denoting. This

is a property of ter1ns, for it is only terms which denote, while all kinds of phrases express, state, mean (something). For to denote a given object in a given language is as it were to supply a term for that object in that language, in other words : a

term usable in that language as a subjective complement in a true sentence of

the type

''A

is

B'' referring to that object (with the primary understanding of the

copula ''is''). In general, to be a term is to be usable as a subjective complement in any sentence

'�A

is

B" with the primary understanding of the .copula ''is''.

A given saying is usable as a subjective complement not only if, when substituted for a

B, it makes the whole sentence a true one, but even if it makes the sentence

meaningful one. That is why, for example, ''came'' i s not a term. There are singular

terms,

which denote one and only orie object, there are general

terms, which denote more than one object, and there are empty terms, which denote no objects at all. For example, the word ''Paris'' is a singular term, since it denotes a certain object, namely the capital of France, and does not denote anything else. Likewise the phrase "the

discoverer of blood circulation''

is a singular term since it

8

REMARKs

ON LANGUAGE

denotes Harvey and him alone, for we can predicate truly about Harvey that he is the discoverer of blood circulation: we build a true sentence of the type ''A is B'', where ''Harvey'' stands for "A'', and the phrase ''the discoverer of blood circulation'' for "B''. If we predicate the same about some other person, we obtain a false sentence. But the term "King of England'' is a general term, for it is true as con­ cerning Henry IV, George V, and many others as well, that he was the King of England. But the term "werewolf '' or the term ''the King of the Swiss Republic'' are empty terms, since it is impossible to formulate a true sentence in which any of these terms would be a subjective complement. For there is nothing and nobody which or who was a werewolf or a King of the Swiss Republic. How then, it may be asked, are they terms at all, if they cannot truly predicate about anything? Is a word which cannot name anything, a term? Can it be said about it that it is usable as a subjective complement in a sentence of the type 'A is B' with the primary understanding of the copula 'is'? This is not an empty term, but not a term at all. Despite appearances, such a protest would not be justified. For to be a term, that is to be usable as a subjective complement in a sentence of the type "A is B'', etc., and to be a term for something, to be a denoting term, to be usable as a subjective complement in a true sentence of the type ''A is B'', are two different things. We can formulate a grammatically correct sentence ''John is a were­ wolf" or "Peter is the King of the Swiss Republic'', where the terms in question function as subjective complements. This proves that they are usable as subjective complements, since they actually perform such roles. Even that is not necessary, since a phrase which never has been and never will be used as a subjective comp­ lement is also capable of being given such a function. Suffice it that if it were used by someone as a subjective complement, the whole would be a syntactically correct sentence of the type ''A is B'', and not an incoherent string of words. For instance, the word ''came'' cannot be used as a subjective complement and therefore is not a term at all; for if we say ''London is came'', we utter an incoherent string of words. Here, however, we face the danger of a misunderstanding. It might be supposed that whenever we have to do with a saying of the type "A is B'' which forms a coherent whole, then the phrase which occupies the place of B in that scheme is always a term; in particular, that every noun or adjective is a term. But that is not so. Let us examine the sentence: "Seniority is a transitive relation''. The whole is not only syntactically correct, but even true. The structure of that whole has the form "A is B''. It would seem, therefore, that ''transitive relation'' is a term, and a non­ empty term at that, which denotes the object otherwise called seniority. But that is only by appearance. We have been led astray by the variety of ways in which the structures of the type "A is B'' happen to be used in English. Sometimes they are used in the primary way, as in the case of the sentence "Uranus is a planet''. Here the word "is" functions in its elementary role of a copula (which does not reflect any tense) between the singular term on the left and some other term on the right. In

SUCH SEMANTIC RELATIONS AS EXPRESSION

9

other cases, the word is used in its secondary, derivative way, for instance in ''The moon is full'', where it has the role of ''is'' in the former example but amplified by the sense of ''now'' or its equivalent. In still other cases we en.counter further sec­ ondary uses of the structure in question. This holds, for example, for the sentence "The whale is a mammal''. Here the term on the left need not necessari ly be a singular term (''whale'' is a general term), and the whole functions as an abbreviation standing for another sentence, which in this case would be : ''Whatever is a whale is a mammal''. There are also other secondary uses of the structure now being discussed, as for instance in the case of the sentence about seniority. Here also the whole is an abbre­ viation, but an abbreviation of a sentence whose structure is much more complicated than that of the sentence about the whale. The sentence the abbreviation of which has the form ''Seniority is a transitive relation'' runs unabbreviated as follows: "If an object is o lder than some other object, and the latter is in tum older than a third one, then that first object is older than the third." In the abbreviated version the word ''is'' stands between words which are not terms, in spite of the fact that both ''seniority'' and "relation'' are grammatically no11ns. The word ''is'' appears here not in its primary, but in a secondary, substitutive role. For whenever we ask: "What i s that?'' with reference to the term ''N'', we must answer by the phrase "N is such and such thing (or person)'' . But if we want to answer the question "What is seniority?'', that method fails. We may answer first of all that ''Seniority'' is the same as "the relation holding between something which came into being earlier and something which came into being later'' ; but to the further question ''What is a relation?'' we are unable to give a correct answer of the type ''It is such and such a thing'', because it is not true that a relation is a thing. Hence we cannot in this way (or in any other way either) subsume ''seniority'' under ''thing''. On the contrary, when we want to answer the question ''What is seniority?'', we must, so to speak, define '' in use by saying, for instance, ''Seniority holds between x and y , which is the same '' as "x came into being earlier than y . Thus in the sentence ''Seniority is a transitive relation'' we have a structure of the type ''A is B'', but in its secondary use, where the word ''is'' has the same form as the copula in the sentence ''Uranus is a planet", it performs a different role and has a different meaning, while the phrases holding the places of A and B are not terms, although they have the appearances of terms. They might be called apparent terms or onomatoids. Thus by an apparent term we shall mean any word (or phrase) which may meaningfully stand for B in a structure of the type ''A is B'', but only if that structure plays not its primary role but the role of a substitute and an abbreviation. There are many such words among nouns. ''Justice'', ''fact'' and ''competence'' are th.e examples chosen at random from among a legion. Of course, such apparent terms are, strictly speaking, not terms, in the same way as false coins are not coins. So much about the apparent terms, as distinguished, on the one hand, from empty terms and, on the other, from phrases which are not terms and have no appearance of being ter111s.

ON LANGUAGE

10

The class of general ter111s suggests other comments. We must warn the reader against confusing the generality of terms with their polysemy. If we call a designatum of a term any object which it denotes - that is, of which it is a name - then every singular term has only one designatum, every empty term has no designatum, and every general terin has many - more than one - designata. This gives rise to the following naive paradox. Let a term

''N'' denote only one object in a given language (or

have one of its meanings in a given ethnic language). It is then a singular term., Let the same term

''N '' in some other language (or in some other of its meanings in the same

ethnic language) denote only one object, different from the former. It is thus a singular term again. Yet, in view of these assumptions it denotes two objects and is thus a general term. We have hence a contradiction. Now it is obvious that there is no contradiction whatever here. The term

''N''

is a singular term with respect to its first

meaning; and also with respect to its second meaning. It is not a general term wit1i respect to any of these meanings, and it does not follow at all from the assump­ tions adopted that it should be a general term. For a given term N ''

''

is general with

respect to a given meaning if and only if with respect to that meaning it denotes more than one object. It is a singular term with respect to a given meaning if and only if with respect to that meaning it has only one designatum. It is empty with respect to a given meaning if and only if the condition is satisfied that it has no designatum whatever with respect to that meaning. Nothing therefore prevents a phrase from being in one interpretation a singular term, in the second a general term, in the third an empty term, and in the fourth not a term at all (but merely an apparent term, or a conjunction, or something else). Thus, for instance, the written word ''ale'' is in English a general term, since it denotes any amount of a special kind of beer, but in Polish it is not a tern1 at all, but a conjunction. Likewise, ''Hull'' has, in its present English usage, at least two meanings : with respect to one of them it is a singular ter1n, being the name of a city, and with respect to the other it is a general term. Thus, obviously, the generality of a ter1n and its polysemy are two different things. A phrase is polysemic if it has many meanings; a ter1n, with respect to a given meaning, is general if with respect to that meaning it has many designata. ·

But generality can equally well be confused with

co/lectiveness, for often i n reply

to the question ''What is a collective term?'' we hear that ''It is a term which denotes a collection of certain objects''. And since a collection of objects is tantamount to many (more than one) objects, then the generality and the collectiveness of a term appear to be the same. But let us take into account that ''the Polish ar111y'', ''the French nation'' and ''proletariat'' are collective terms, and ''wood'' and ''magnet'' are not, in spite of the fact that ''wood'' beyond all doubt denotes a collection of plant cells, and ''magnet'', a collection of molecules. The difference between a col­ lective and a non-collective term consists not in what they denote, but in what they mean, so that a given term may denote a certain collection without being a collective term, and on the other hand there may be a collective term wllich does not denote any collection since it is an empty term. Such a term "N'' will be called collective

,

SUCH SEMANTIC RELATIONS when to the question "What is N?'' we reply:

AS EXPRF.5SION

11

''N

is a collection of such and such objects'', or to the question ''What does N mean?'' we reply: '' x is N'', meaning that xis a collection of such and such objects. Now we would not give such answers to such questions in the case of ''wood'' or ''magnet''. We would perhaps say: ''A tree is a perennial plant having a trunk''; '' x is a magnet means that x is a body that attracts iron at a distance''. On the other hand, we would certainly say: ''The French nation is the totality of Frenchmen''; ''The proletariat is the class of hired workers'', etc. Likewise, ''the Jurassic population'' is a collective term, since it is equivalent to ''the totality of people in the Jurassic period'', although it is an empty term, since there were no men in the Jurassic period. On the other hand, the term ''the French nation'', while collective, is also a singular tern1, for there is only one object about which it can be truly predicated, that is, the totality of Frenchmen. Thus the generality and the collective nature of a tern1 are two different things. (b)

Intension and extension of terms.

It is time now to introduce a new technical

ter111, which will facilitate a further analysis of the relation of denoting, especially in the case of general terms. This is ''connotation''. Now instead of saying that, '' x is ice'' means that x is solid water, we may say that· the term example, for "ice'' connotes the properties of wateriness and solidity. Instead of saying (as is equivalent to the former formulation) that ''square'' is· usable as the subjective complement of a sentence stating someone's thought about something to the effect that that something is plane, bounded, quandrangular, equilateral and equiangular, we may say: the word ''square'' connotes jointly the properties of planeness, bound­ edness,

quadrangularity,

equilaterality and equiangularity. We should make it

a point in this connection not to say that the word ''square'' connotes, for example, planeness, or that the property of planeness is connoted by that word, for by so saying we should suggest that ''square'' is the same as ''plane'', whereas not all that is plane is thereby square. It is true only that ''square'' connotes the combination of certain properties which include the property of planeness, or that planeness is included among those properties which are jointly connoted by the word ''square''. The

properties jointly connoted by a given term form together tl1e intension of that term, or its sense, or its connotation; this must be contrasted with the designata which jointly form the extension of that term, or its denotation. We may thus say that every object which has all the properties jointly connoted by a given term with respect to its given meaning is a designatum of that term with respect to that meaning. In other words, every object which has the intension of a given term with respect to its given meaning belongs to the extension of that term with respect to that meaning. It is obvious that there may be two terms with the same extension and with different in tensions:

for example, two singular terms, ''the victor of Jena" and

"the vanquished of Waterloo'', the only and common designatum of which is Napo­ leon I Bonaparte; or two singular terms, ''the morning star;' and ''the evening star'', which denote one and the same planet Venus; or two general terms, ''NaCl'' and

12

REMARKS ON LANGUAGE

"rock salt'', the extensions of which are the various quantities of the common mineral. It is equally obvious that we may characterize collective terms as those the intension of which includes the property of being a set of certain objects; for example, the phrase ''the French nation'' is a collective term, since its intension includes (and is even exhausted by) the property of being the totality of Frenchmen. The reader will excuse the use of somewhat unnatural formulations, but this is required by the subject matter under discussion. We have thus introduced the word ''connotes'', and by its aid, the words ''inten­ sion" and ''extension''. The latter requires, however, a closer analysis. We shall, namely, examine the relationship between the term ''extension'' and the terms "set'' and ''class''. To clarify that relationship we shall first consider the term ''set'', in doing which we shall firmly emphasize its ambiguity. In its the word is an apparent term, in its

distributive

meaning

collective meaning, a real term. Its role as a dis­

tributive term is defined in use when we say, for example, ''x is an element of the set of M's'' (or ''x belongs to the set of M's'') means the same as ''x is M'' . For instance, mathematicians say ''The number

3

number", meaning thereby that ''The number or, more simply, ''The number

3

is an element of the set of natural

3

is one of the natural numbers",

is a natural number''. Another example, ''Mars

belongs to the set of the planets of the solar system'', means ''Mars is one of the planets of the solar system''. Although that statement about Mars is true, no object is a set of planets in the meaning of the term ''set'' as used here; the string of words ''the set of the planets of the solar system" does not denote anything when used in that context. To use that string in that meaning as a subjective complement in a sentence of the type

"A

is

B'', where "is'' is interpreted i n its primary sense, would be an ,

absurdity, something like "John is came'', etc. The word "set'' must be treated here

in the same way as the word "screw'' in the phrase "to have a screw loose'', although no object - in the sense implied by that phrase - is a screw which is loose. In its second meaning the word "set'' is a true term. "The set of M's'' in this meaning denotes a certain totality consisting of M's, in the same way as a chain consists of links, a swarm of bees, of particular bees, and a heap of sand, of sand grains. A closer analysis reveals that the second meaning is somewhat obscure. In this meaning, by the set of M's we mean such an object Q whose every element either is an M, or at least includes an element of some M which is an element of that object. Thus, for instance, the set of coins in John's purse is a totality charac­ terized by the fact that its every piece includes a piece of this or that coin in John's purse, such a coin being an element of that set. A chessboard is a set of chessboard squares in the sense that whatever part of that chessboard be taken into consideration (be it a single square, or a part of a square, or a square with a part of an adjoining square, or two squares at two opposite corners, or any other part of the chessboard, be it as fantastically cut out as may be) it turns out that it includes anyhow a part of this or that square belonging to the chessboard in question. We had this meaning in mind when we said that such words as ''tree" or "magnet'' have sets as their

SUCH SEMANTIC RELATIONS AS E XPRESSION

13

designata. A particular tree - for instance a particular oak - one of the many designata of the term ''tree'', is a set of plant cells, and a set of filaments, and a set of molecules ; for whatever component (or part, in the most common understanding of that word) we isolate, we obtain something which contains at least some element of this or that filament, this or that cell, or this or that molecule belonging to the oak tree in question. On the other hand, the part of the chessboard obtained by cutting the chessboard along its diagonal is not a set of chessboard squares, since it includes some triangular half-squares, such that the squares of which they are halves do not belong to that part of the chessboard, and hence no element of such a half-square is an element of a square which is an element of that part. The word ''class'' shares the fate of the term ''set'' and inherits, as it were, the amb­ i guity of the latter. A "class'' is the same as "the set of all'' ; more strictly, ''the class of M's'' means "the set of all M's''. As an apparent term it may be defined in use in the following way : ''x is an element of the class of M's'' or ''x belongs to the class of M's'' is the same as ''x is an element of the set of all M's'' or ''x is one of all M's'', which is equivalent to saying directly : ''x is an element of the set of M's'', hence ''x is one of the M's'', briefly ''x is an M'', and thus it is equivalent to the statement ''x belongs to the set of M's''. Consequently, ''The number 3 belongs to the class of natural numbers'' is the same as "The number 3 is a natural number'' ; "Mars is an element of the class of planets of the solar system'' is the same as "Mars is a planet of the solar system''. On the other hand, as a real term the word "class" differs in meaning from the word ''set" understood as a real term. In such an interpretation, "the class of M's'' denotes the set of all M's - that is, the totality consisting of all M's ; for instance a given chain is the class, that is , the set of all its links, but is not just a class of links, because not all links are links of that chain. More precisely, by the class of M's (in the collective sense of the term) we mean the set of all M's, that is an object 0 whose every element includes an element of this or that M and which moreover has the property that whatever is an M is an element of that object 0. In this sense, a tree is not a class of cells, or a class of filaments, or a class of molecules, for although the first condition is satisfied in each of these cases, the second is not ; it is not true that whatever is a plant cell is an element of that particular tree (and the same holds for filaments and molecules). But a given tree is the class of its own cells, its own tissues, its own molecules, etc. ; for instance, the sacred Lithuanian oak tree Baublis is the class of Baublis's tissues, since not only does its every element include at least some element of some Baublis tissue, but whatever is a Baublis tissue is an element of Baublis. Likewise, the fauna of Poland is the class of animals living in Poland (now, in the past and in the future), for on the one hand each of its elements (be it a given animal, or the head of some other animal, or an animal p lus a leg of some other animal, or any other so distin­ guished whole, fantastic as it may be) includes this or that element of an animal living in Poland, and on the other hand every animal living in Poland is an element of the fauna of Poland.

14

REMARKS

ON LANGUAGE

We shall ask now whether a general term denotes the set or the class of its own designata. The answer is obvious if we have in mind the distributive meaning of the terms, if ''set'' and ''class'' occur as apparent te1·ms. In such a case there is no object which would be a set or a class of the designata of a given term. Hence such a term cannot denote any such thing, and cannot predicate about any such thing as a subjective complement in a true sentence. The answer is different if we have in mind the collective sense of the te1·n1s in question. In some cases, a given general term denotes the set or the class of' its own designata, but in some cases it does not. For example, the term ''something which finds itself within tl1e solar system'', whose designatum is every and only every object within the solar system (the Earth, the Moon, a mountain of the Earth, a particular man, etc.), denotes the class of its own designata, since that class, that is, the set of all the objects within the solar system, also is an object within the solar system. On the other hand, the term ''chair'', whose designatum is every and only every chair, does not denote the class of its own designata, because that class is not a chair. Let it be added parenthetically that a singular term, in the collective interpretation, always denotes any set of its designata, and hence also the class of its designata, since any such set, as well as that class, are identical with the · only designatum of that term (for example, the class of the first emperors of the French is identical with Napoleon I Bonaparte, the only designatum of the term ''tl1e first emperor of the French�). On the other, hand, an empty term never denotes any set of its designata since it has no designatum at all. '

When we pass to the word ''extension'', we may state that it is equivalent

to· the phrase ''the class of designata'' in the distributive sense of the term. Hence , to say ''the extension of the term 'N' '' amounts to saying ''the class of the designata of the term

'N' ''

or ''the set of all the designata of the term 'N' '', where the words

"class'' and ''set'' occur as apparent terms.

It follows therefrom that the word

�extension'' also is an apparent term; hence no object is the extension of a given term, and no term denotes its own extension. The use of the word ''extension'' is a consequence of the role of the word ''class'' . We shall therefore say ''x belongs to the extension of the term element of) the

'N' ''

instead of saying ''x belongs to (or is an

class of the designata of the term

to ''x is a designatum of tl1e term

'N' ''.

'N' '',

which is equivalent

We also accept for the time being that if the

term ''N '' is, for example, ''fox'', then the clause ''x is a designatum of the term 'fox' '' is equivalent to tl1e clause ''x is a fox'', etc. We have just stated that ''exten­ sion'' is an apparent term; the same can be stated with reference to the word ''inten­ sion" as applied to terms. This results from the explanations given above in connec­ tion with ''inten�ion'' and ''apparent term'' . (c)

Dual understanding of singular and general terms.

On having considered

what we have said about terms, John, our regular helper, would now like to raise an issue concerning, so to speak, his case. The issue involves what are called proper names. Are they terms in the sense accepted in this book? The natural answer that

SUCH SEMANTIC RELATIONS AS E XPRESSION

15

"John'', ''Peter'', etc., are singular terms involves certain difficulties. Not, above all, because there are many Jol1ns, many Peters, etc., which might suggest that they are general terms, since to that one could reply that we should forget about the baptismal explanation of the name ''Peter'' as the token of the special patronage of the first apostle (in which meaning the word ''Peter'' is a universal term - as are such surnames as Smith, Jones, Dupont or Millier - identical as to extension with the phrase ''the first apostle or a man placed at baptism under the special patron­ age of the first a postle''), since in everyday life we understand in di fferent ways the names of two persons called ''Peter''. When we refer to one Peter, we use his name in a decidedly di fferent meaning - although the difference may be merely one of shade - from when we refer to another Peter : the word proves to be ambi­ guous, but with respect to each of its meanings it is a singular term. Hence the doubts originate not from that alleged generality of the proper names. To realize in what the doubt consists we have to recall the definition of a term, as given above. A term is understood there as a real or potential subjective compte... ment i 11 a sentence of the type "A is B'', interpreted in its .essential sense. Now there arise protests against using what are called proper names in the role of subjective complements. Even Aristotle thought that, for example, this or that can be predicated about Socrates, but Socrates cannot be sensibly predicated about anything ; for according to Aristotle there are "primary substances'', such as Socrates, and "secondary substances'', such as man : the former can have predicates referring to them, but they cannot be predicated with reference to anything, whereas the latter can be predicated about the former (and about the latter as well). When we separate his semantic ideas (that is ideas referring to that aspect of the language which is concerned with meanings) from their ontological cover (Aristotle formulated his thoughts in such a way as to indicate that he did not classify words by their meanings, but various ''entities'') we arrive at the statement that proper names cannot functio n sensibly as subjective complements and that in a structure of the type "A is B'' a proper name can stand o nly in the place of A, that is the place of the grammatical subject, while the place of B must be occupied by a universal term. Moreover, its universality does not consist in having many designata, but precisely in its role as a subjective complement. It would therefore comply with the spirit o f Aristotle's intentions if we were to mean by a universal term what we have meant above simply by a term. We thus find two opposing systems of using the technical terms ''term'', ''uni­ versal term'' and "singular term'' : the Aristotelian system and the system we have used above. In Aristotle's approach, a term is a saying (a word or a phrase in general) which can stand as subject, or an utterance which can stand as subjective complement in the structure ''A is B'', understood in the primary meaning. A singular term is a term which can stand o nly as subject, a universal term is a term which can stand also as subjective complement. According to Aristotle, universal terms can also stand as subjects, but when we make our analysis more subtle and prove that then •

16

REMARKS ON LANGUAGE

the entire structure of the type

''A

is

B''

plays a subsidiary role, and the word ''is''

has some secondary, derivative meaning, we arrive at the opinion which holds that a universal term can stand only as a subjective complement. From that point of view the use of a singular term (for example, ''London'') as subjective complement, or the use of a universal term (for example, ''city'') as subject in the structure

''A i s B '',

understood in its primary meaning, would yield nonsense, a semantically incoherent whole, as though someone said ''Came is a city'' or ''London is came''. Further, from that point of view the universality of a term does not depend on the number of its designata, for there are universal terms with many designata (for example, "animal''), with one designatum (for example, ''that planet of the solar system which has a ring''), or with no designatum at all (for example, ''a bird with h11rnan head''). In this system, a singular term (its singular meaning being given) is a name of at most one object, but it would be difficult to call that object its designatum, if by a designatum we mean the object concerning which a given term can be truly pre­ dicated. This is so because from that point of view a singular term cannot be pre­ dicated of anything, and although it is a name, it does not have as its designat11m even that of which it is a name. Moreover, there may be no object of which it could be a name. For instance, the singular term ''Polyphemus'' has no object of which it is a name. This is no contradiction, since from that point of view the singularity of a term does not consist in the uniqueness of the object of which it is a name; it consists in its being meaningfully used only as a subject, on the fact that it can be sensibly used in the structure in the place of

A,

"A

is

B'',

understood in its essential meaning, only

and never in the place of

B.

The opposite interpretation has been exhaustively described above, and there is no need to repeat it here. We shall only emphasize that from that opposite point of view any term may always be used as subjective complement and as subject as well, and conversely any phrase that may be used as subject may be used as subjective complement too, so that both ''John'' and ''London'' may be subjective complements (for example, in the sentences ''That man is John" and ''The city we are approaching is London'') and ''lake'' and ''the worm born by spontaneous generation'' may be subjects. But if the subject is not a singular but a universal or empty term, then if the structure

''A

is

B''

is understood in its primary role we

obtain a whole which is meaningful but false. Consequently, the sentence ''A town is a human settlement'' is a nonsense in the first system, if the copula "is'' is understood in its primary meaning, and in the second system it is a sentence, but a false one also, if the copula ''is'' is understood in its primary meaning. This is so because in the first system a universal term cannot function meaningfully as grammatical subject in the structure

''A

is

B'', lJnderstood

in its primary meaning, and in the second system the result i s not nonsense but a falsehood, since while any term may sensibly stand as subject in such a structure understood in its primary meaning, only a singular term can yield a true sentence. Likewise, from the point of view of the first system the formulation ''That man

,

SUCH SEMANTIC RELATIONS AS E XPRESSION

17

is John'' is nonsense, since a singular term occurs here as subjective complement, but in the second system this is quite admissible and nothing prevents such formula­ tions from being meaningful and even true : if we say ''That man is John'' and point to John, and not to Peter, we build a true sentence, and if we say the same sentence while pointing to Peter, and not to John, we build a false sentence. Aristotle's approach to the interpretation of the relations under discussion has the drawback that it requires indication as to how to recognize that a given phrase may stand only as a subject, and some other only as a subjective complement. The number of designata cannot serve as the criterion, and analysis must go deeper and probably seek the difference in the ways of defining, which are different for these two kinds of terms. Moreover the Aristotelian system results in greater con­ straints in the handling of terms than does the opposite system : we must here renounce certain, natural as it would seem, formulations (for example, ''This man is John'') and resort to more complicated and artificial forn1ulations (for example, "This man is identical with John''). On the other hand, the opposite system deviates, as it would seem, from a traditional and current interpretation of ''singular term'' and ''11niversal term''. It can be felt that the difference here does not consist in the n11mber of designata, but in something which can be known before these designata are counted. It is felt that in such a current interpretation ''Polyphemus'' is a singular term, and ''the voter who handed in a blank voting paper'' is a universal term, although the former has no designatum, and although it may occur that only one person, or none, hands in a blank voting paper. In the conflict between these two systems, a conflict which remains acute to this day, we have chosen the system which is opposed to Aristotle's, because it is clearer and simpler to use. The controversy about singular and l1niversal terms concludes the analysis of issues more intimately connected with denoting. What remains for discussion is replacement and representation. 4.

REPLACEMENT AND REPRESENTATION.

Replacement and representation belong

to relations between phrases, which cannot be said of expressing, denoting and meaning. For it is not true that what a given phrase expresses, that is, someone's experience, is itself a phrase ; and what a given phrase denotes, the designatum of a term, as a rule is not a phrase (for example, London, Manchester, Birmingham, Liverpool, designata of the term ''city in Great Britain'', are themselves not phrases but human settlements). This is so in special cases only, when we refer precisely to phrases : for instance, ''labour'', ''honour'', etc. - designata of the term ''an abstract noun ending in -our'' - are themselves words, that is, linguistic entities. It would not be true to assert that what a given phrase means is itself a phrase, for example, that the meaning of a term, a system of properties jointly connoted by that term, is a string of words. On the other hand, a given phrase replaces only some other phrase, and a given linguistic term represents only some other linguistic term. Those phrases

replace

one another which can be used interchangeably - that

is, without affecting their meanings. These include synonyms in a given language,.

18

REMARKS ON LANGUAGB

that is, words which have the same meaning in a given language and di ffer as to their form, such as "motor car'' and ''automobile", "last will'' and ''testament", etc. Pairs of expressions which have the same meaning but belong to di fferent ethnic languages (and hence in most cases di ffer as to form) also replace one another (cf. "order'' and ''Ordnung'', ''rana'' and ''frog'', "to eat'' and ''manger'', etc.). But within one ethnic or artificial language, any two phrases replace one another if one is a definiens of the other (see p.

26 below) or if both have a common definiens, for instance ''an even number'' and ''a number divisible by 2'', and ''the intersection of the classes A and B'' and ''the product of the classes A and B''

(the common definition of the last two phrases being "the greatest class included in both

A

and

B''). Very often we pay attention to such

a

replacer of a given phrase

as is defined by that phrase and at the same time is its abbreviation or a shorter equivalent (compare ''i.e." and "e.g." which are abbreviations of ''that is'' and ''for instance'', and ''aspirin'' which stands for ''acetyl-salicylic acid''). The existence of replacers with an illusory structure is of particular importance for the logical criticism of language. The reader will recall what has been said above, in connection with apparent terms, about replacer phrases which include nouns which only appar­ ently are terms (cf. ''bay'' i n the phrase ''to keep at bay'', or ''set'' in ''to be an element of a set'') or such cases in which the whole has the form ''A is

B'' but performs a sec­

ondary function which does not correspond to the essential function of that struc­ ture (cf. such phrases as ''a whale is a mammal'' or ''the relation of seniority is transitive''). In the light of this i nformation it is obvious that whenever we commonly say that one phrase ''means the same'' as the other or ''is equivalent'' to the other, we refer to phrases which replace one another. .,

We shall, finally, speak of

representing only with reference to variable symbols and what are called their values. To explain the terms used here let us compare a very simple sentence, for example, ''Etna is a volcano'', with a corresponding sentential function, for example,

''A

is

B''. The latter formulation is called a sentential function

because, while not a sentence, it has the property that if we substitute any terms

''B'' we shall always obtain a sentence, true or false, but anyhow a sen­ tence. If, for instance, for ''A'' we substitute ''London'' and for ''B'' ''the capital for

''A''

and

of England'', we obtain the true sentence ''London is the capital of England''; if

''B'' ''a plant'', we obtain the false sentence ''iron is a plant''; if for ''A'' we substitute ''Etna'' and for ''B'' ''a volcano'', we have the

for

''A''

we put ''iron'' and for

.true sentence, written above, ''Etna is a volcano'', etc. Likewise, ''if p then q'' also i s a sentential function. It is not a sentence, since a sentence is a phrase stating some­ one's thought that something is so-and-so, and the formulation given above does not state anyone's thought, either directly or indirectly. It includes the symbols ''p'' and ''q'' which - like empty places left by missing units of type - do not mean anything and, as it were, make the whole structure incomplete, so that it ceases to have any meaning whatever. But while not a sentence, the formula is built so that if for ''p'' and ''q'' we substitute any sentences (sentences, and not terms !) we obtain

SUCH SEMANTIC RELATIONS AS E XPRESSION

19

a whole which i s a sentence. For certain substitutions we obtain a true sentence, '' '' for other substitutions, a false one, but even so a sentence. Thus, if for p we put, '' '' for i nstance, ''6 i s divisible by 3'', and for q '' 1 2 i s divisible by 3'', we arrive at the implication, ''If 6 i s divisible by 3, then 1 2 is divisible by 3'', which is certainly '' '' true. But if for ''p'' we put ''bats have wings'', and for q ''bats are birds'', we obtain the false implication ''If bats have wings then bats are birds''. '' '' '' '' Whatever we substitute for p and for q , provided the substituted phrases are sentences, the resulting whole will be a sentence, even if the substituted phrases are fantastic. The saying ''John i s older than Peter x Peter is older than John'' yields a sentence whe11ever for ''x'' we substitute a sentential connective. If for ''x'' we put ''or'', we obtain the true sentence ''John is older than Peter or Peter i s older than John'', and if for ''x'' we put ''and'', the resulting sentence is a false one, but i n all cases we obtain a se11tence. Thus we see that sentential functions differ as to the kind of variables : tl1ere are term variables, sentential variables, conjunction variables, etc. Consequently, a general interpretation of sentential variables may not be specially connected with terms. To interpret the term broadly enough, we shall say that ''sentential variable'' i s the same as ''an inscription containing variables and built so that on substituting for those variables any constants from appropriate categories we obtain a sentence''. An analogous definition might be adopted also for speech. For instance, all terms are constants for a term variable, all sentences are constants for a sentential variable, etc. Now a variable represents all constants o f the appropriate category ; hence a term variable represents all terms ; a sentential variable, all sentences, etc. Since it has become tl1e usage to call the constants represented by a variable the values of that variable (which has its source in the language of mathematics, where numerical variables are used, for example, in the case of the sentential function ''x = 2y'', where the ''names of numbers'' form the range of x and y), it can also be said that a variable represents all its values. It must, however, be taken into account that the word ''value'' is more general than the word ''constant'' (or ''constant symbol''), for every constant (from the category of the given variable) is a value (of that variable), but not vice versa. In a given sentential function we may substitute for a variable not a constant but a func­ tion, thus obtaining a whole which is not a sentence, but a function, so that the whole yields not a sentence but a sentential function. For instance, if in the senten­ '' '' '' '' q we substitute for p the sentential function r and t'' tial function ''if p then '' '' '' and for q the sentential function ''s or v , we obtain ''if r and t then s or v'', which i s not a sentence, but a new sentential function with the sentence with the '' '' '' '' sentential variables r , ''t'', ''s'' and v . If, on the other hand, we begin with the form ''A i s B'', we can obtain new sentential functions by substituting for the term variables ''A'' and ''B'' what are called term functions, that is, neither terms nor constants, but phrases with variables so built that on substituting for them constants of appropriate categories tl1ey become terms. For instance the formulation "' C who pushed D'' i s a term function, since on substituting ''the man'' for ''C '' and 3

REMARKS ON LANGUAGE

20

''the cart'' for ''D'' we obtain the term ''the man who pushed the cart'', and on substitu­ ting other terms for ''C'' and ''D'' we always obtain a term, whether singular, uni­ versal or empty, but nevertheless a term. Hence such term functions may be substi­ tuted freely for ''A'' or ''B'' in the sentential function ''A is B'', and we shall always obtain a new sentential function. Let us substitute for ''A'' ''C who pushed D'', and for ''B'' ''the agent of E '' ; this yields the sentential function ''C who pushed D is the agent of E'', from which we may obtain in turn, for instance, the following sentence : ''The man who pushed the cart is the agent of the move''. In a word, the value of a given variable is not confined to those constants which may be substituted for that variable, but also covers sentential, term and other functions which may be substituted for the variable. In the first case, we speak of a constant value ; in the other, we might speak of a variable value. But we consider that both the values of the first kind (constant values) and those o f the second kind (variable values) are represented by the variable symbol for which we may substitute them. ''May'' means here that as a result of substitution we obtain a meaningful whole, and not a meaningless string of words ; this is guaranteed if we substitute values belonging to appropriate categories - that is, if for sentential variables we substitute only sentences or sentential functions ; for term variables, only terms or term functions, etc. These explanations concerned with the relation of representation, will prove necessary in the discussion of the formulae of formal logic. J. S. Mill, System of Logic, 6th ed., London 1 865, Vol. 1 , p. 3 1 .

t

2 S. Lesniewski, Podstawy ogolnej teorii mnogosci (Foundations of General Set Theory), Moscow 1 91 6, Vol. 1 , p. 1 1 . Our definition of the ''set of M's'' is an attempt to formulate more clearly the definition of the ''set of objects m'', as given in that work. See also 0 podstawach matematyki (The Foundations of Mathematics), Pt. 2, by the same author (in Przeglqd Filozoficz11y, Vol. XX.XI, 1 928, No. 3, p. 270), which includes a definition of the ''set of objects a'', which is an analogue of the above-mentioned definition of the ''set of objects m''. 3 Concerning the interpretation of the ''class of M's'' as the set of all ''M's'' and concerning the interpretation of the ''class of M's'' in the collective sense (see below) cf. Lesniewski's Pod­ stawy . . (notes to Part One, 2), p. 12, and 0 podstawach (notes to Part One, 2, on p. 264). 4 Aristotle, Categories, Chapters 2 and 3 . s As an example of systems in which the said distinction i s made as between terms that may be used as subjects and those which may be used as subjective complements we may mention the system built by Peano (cf. C. Burali-Forti, Logica matematica, 2nd ed., Milan 1 91 9, p. 5), and as an example of systems in which no such distinction is made, the system of Lesniewski's ''onto­ logy'', described in Part III of the present book. 6 Cf. ''Supplement'', item 1 , ''On the Classification of Names''. 7 Cf. ''Supplement'', item 2, ''A Survey of Logical and Semantic Problems''. .

.

.

.

_

CHAPTER II

DEFECTIVENESS IN LANGUAGE, AND DEFINITIONS AS A MEANS OF AVOIDING MISUNDERSTANDINGS AND FICTIONS ORIGINATING IN S UCH DEFECTIVENESS

5. AMBIGUITY.

On considering the distinctive characteristics of the various relations

between different language phrases and /or between language phrases and something else, it is to the point to write down some important observations pertaining to the criticism of language and to reflect on the ways of avoiding the defects of speech r evealed by the criticism. First of all, we must point out the

ambiguity

of the various formulations. When

the owner takes out of his wardrobe a suit which he bought a year ago but did not use at all, he will call the suit old, but a friend of his may say that, on the con­ trary, the suit is still quite new. Such a difference of opinion, as to whether the suit is old or new, is purely verbal, since it disappears following the explanation that each of the disputants is using the term ''new'' in a different meaning: in the lang­ uage of the first person ''new'' means ''recently made'', whereas in the language of the second person ''new'' means ''little used''. Such verbal controversies are likely to arise when the meanings involved are close to one another ; if they are remote, the situa­ tion is clear: for instance, when we have two sentences, ''He sat with set teeth'' and ''The bracelet was set with diamonds'', no one is likely to confuse the two different meanings of the word ''set''. But when we read that ''the author reduces one thesis to the other'', a misunderstanding may arise : the writer, for example, wants to say that the author in question proves that the first thesis follows from the second, whereas the reader may think that he considers both theses as equivalent or that they both mean the sa1ne. But even after it has been established that reference is made to the fact that one thesis is a consequence of the other, and vice versa, and not to the same meaning of both theses, there is still some room for a verbal con­ troversy, since it is possible to mean either simultaneous truth and simultaneous falsehood of both theses, 01· the fact that one thesis can be deduced from the other, and vice versa. In such cases, the mistake called

equivocation 21

is also likely to occur. It consists

22

ON LANGUAGE

in using, in some reasoning, a given formulation in two different meanings, although for the sake of correctness that formulation should be used in the same mea11ing. For example, someone reasons as follows : Antigone was bound to obey Creon and she knew it ; since whoever is bound to do something and knows it, but consciously does not do it, acts in opposition to his conscience, hence Antigone by consciously not obeying Creon acted in opposition to her conscience. Here the error of equi­ vocation consists in that ''is bound to do something'' means either that one is re­ quired to do so by an order of the authorities (and in that sense of the phrase Antigone was bound to abstain from burying her brother), or that one should act in such and such a way according to one's own sense of equity (and in that sense of the phrase Antigone would have acted in opposition to her conscience if she had left her brother's body unburied). Now that this difference of meanings is made clear, the reasoning proves obviously incorrect, since it would be thus : Antigone was ordered by Creon to obey him and she knew it, and since whoever should do some­ thing according to his sense of equity and knows it, but consciously does not do so, acts in opposition to his conscience, hence Antigone by not obeying Creon acted in opposition to her conscience. Among those cases in which we readily fall victims to ambiguity, it seems ad­ visable to mention those involving what is called occasionality, that is situations in which the meaning of a word varies according to the occasion. The words ''I''� ''here'' and ''now'' are striking illustrations of occasionality, as also are such adje­ ctives as ''my'', ''local'' and ''present''. The words ''I'' and ''my'', the meanings of wl1ich, to put it freely, have a certain personal shade, vary relatively as to their meaning according to by whom they are used ; the words ''now'' and ''present'', , the meanings of which have a temporal shade, vary relatively as to their meaning according to when they are used ; and the words ''here'' and ''local'', the meanings of which have a certain spatial shade, vary relatively as to their meaning according to where they are used. For instance, ''I'' used by Peter has such a meaning that it denotes Peter, and used by John has such a meaning that it denotes Jol111. When someone says in London that ''Smith lives here'', the word ''here'' often means that whoever is said to live ''here'' lives in London, and vice versa ; when someone says the same sente11ce in New York, the word ''here'' often means that whoever lives ''here'' lives in New York, and vice versa. Wl1en a person says in January, ''Now it is winter'', he has in mind some time i11 January, and when a person says in July ''Now it is summer'', he has in mind some time in July. This may give rise to misunderstandings, as in the case of the deceptive sign­ board in a shop : ''Tomorrow on credit, today for cash''. On reading that, a customer might be inclined to come on the next day so as to be able to buy goods on credit, but then the owner would point to the signboard and refuse to sell on credit. The text on the signboard preserves its form, but changes its meaning every day. Hence the trick resorted to by the shop owner is not honest : he makes consecutive state­ ments which contradict one another, in doing which he avails himself of the fallacy

DEFECTIVENESS IN LANGUAGE

23

that two sentences which have the same form always mean the same. But this alleged principle does not hold when it comes to sentences tl1at include occasional ex•

press1ons. There is also another case of veiled ambiguity, very important from the logician's point of view. Reference i s made here to the

role of words,

''ordinary'' , ''fo1·mal'' and ''material''

which was distinguished even by mediaeval theorists. There is no

need to enlarge upon the ordinary role

(suppositio simplex). The formal use of a term

(suppositioformalis) occurred when that term arose as an apparent term of a ''general concept'' o r ''universal object'' or ''universal''. For instance, the word ''dog'' in its ordinary role i s a term for any bulldog, greyhound, etc., and it i s used in that role when we say that Bob i s a vicious dog. But when in classical logic we say that ''dog'' i s a species for ''animal'', and that ''animal'' is the genus for ''dog'', the words ''dog" and ''animal'' are used i n formal supposition. Likewise, it is said in tradi­ tional logic that there are concepts with extensions which do not overlap, for example, ''man'' and ''horse''. On the other hand, a given word in material supposition denotes either only itself or itself and any word of the same form. For instance, the word "dog'', written here in quotation marks, has been used to draw attention to that word, as the name of precisely that word ; in other cases, for instance when we say that '' 'dog' is spelled 'd', 'o ', 'g', in that order'', we have in mind all the words with the same form. When we say that ''Copernicus revived the idea of Aristarchus of Samos that the Earth revolves around the S11n'', the word ''Copernicus'' occurs

in

ordinary supposition, but when we say '' 'Copernicus ' is a Silesian surname'',

the word ''Copernicus'' appears in material supposition. To put it generally, a given expression ''N'' i s used in material supposition if and only if it is used in the meaning which corresponds to a definition of the type : ''N'' is the same as ''the expression built so . . . '' (where the dots are replaced either by an expression o f the same form as

''N'' quoted

in extenso

or by a specification of the graphic or phonetic elements

of which ''N'' consists). The following jocular paralogism also results from the confusion of the ordinary and the material role of words : ''The mouse is gnawing at a book, but the mouse i s a syllable, hence a syllable is gnawing at a book." The equivocation i s revealed when we realize that the word ''mouse'' was first used in ordinary, and next in mate­ rial supposition. The same applies to the following reasoning : and one, and since

3

''3

is the sum of two

i s a figure, hence a certain figure is the sum of two and one."

To avoid the errors which in that respect threaten the various subtler forms of reasoning, we should make a distinction as between the use of an expression in ordinary supposition and its use i n material supposition ; in the latter case, the expression concerned should be placed in quotation marks or written in italics, etc. In the examples given above, ''mouse'' and

''3 ''

should be written without quota­

tion marks when they occur for the first time, and in quotation marks when they occur for the second time. These measures used in writing would have their coun­ terpart in speaking in the word ''word'', or ''phrase'', or some other equivalent

24

REMARKS ON LANGUAGE

�

formulation, preceding tl1e w rd or phrase used in material supposition ; inciden­ tally, there i s nothing to prevent us from resorting to this measure i n writing, too. Consequently, it would be safer to formulate the above in the following manner :

"3 is the sum of two

and one, and since the sign

'3' is a figure, hence a certain figure

i s the sum of two and one''. In sucl1 a formulation, the difference between ordinary and material supposition i s immediately brought into relief. We would also have to distinguish formal and material supposition in some similar way. In spoken language, this is done fairly well by putting the word ''concept'' before the word in question. In writing, quotati on marks are usually used, which, however, does not eliminate the possibility of confusing formal and material supposition . Since in writing, too, the word ''concept'' is usually added, misunderstandings are, as a rule, avoided.

6. BLURRED MEANINGS (UNCLEAR, INDISTINCT AND VAGUE UNDERSTANDING OF E XPRES­ SIONS). In addition to the ambiguity of expressions, unclear, indistinct and vague un­ derstanding of expressions i s often a source of trouble. All this can best be explained by way of the example of terms. ''I understand a given term clearly'' means that I so realize what properties contribute to its connotation that whenever I notice the presence of those properties in an object I correctly recognize in it a designatum of that term ; and conversely, I correctly state that a given object is not a designatum of that term whenever I notice that it lacks any of these properties. We usually clearly lJnderstand such terms as ''horse'', ''sparrow'', ''penny'', ''cigarette'', and many others. It i s true that i n some cases it is difficult to decide whether a given bird is a sparrow or some other represent­ ative of the passerine family, but then the difficulty is due not to unclear understanding of the term ''sparrow'', but to the lack of sufficient information about the bird in question. We just do not see at a distance what its feathers are like, and so on, and hence do not notice wl1ether it has the properties which contribute to the connotation of the term. Once we notice those properties, however, we correctly recognize in the bird one of the designata of the term. On the contrary, such terms as, for instance, ''organism'', are frequently not understood clearly. There have been long discussions as to whether a colony of protozoans with differentiated functions i s an organism, whether human society is an organism, etc. Very often we understand a term clearly, but we do not understand it

distinctly.

This probably occurs most frequently with reference to terms denoting objects of everyday use.

A

term is distinctly understood by the person who knows how to

specify all the properties contributing to its connotation (or, in other words, as we shall shortly see, knows how to formulate its analytic definition). Now it very often happens that we unerringly refer a given term to certain objects, and yet we are u11able to specify those properties by which we identify certain objects as des­ ignata of the term in question, and by the lack of which we recognize that certain other objects are not designata of that term. This shows beyond all doubt that we do not know how to analyse the meaning of sucl1 a term, and are unable to formulate

,

DEFECI1VENESS IN LANGUAGE

25

its analytic definition. Even a simpleton understands clearly the word ''money'', and yet does not understand that term distinctly. Every reader certainly knows the type of an ''arrogant fellow'' and identifies such a man after a few minutes' talk, but if he tries to analyse what that term actually n1eans, he soon realizes that this is an exceptionally difficult task. Thus, tl1ere are terms which we understand clearly, but which we d o not understand distinctly. But it occurs very often that the lack of distinctness in understanding a tern1 involves a lack of clarity as well, so that these two shortcomings quite commonly accompany one another. They also quite frequently find a third companion in vagueness of understanding a given terrn. We often have to do with a set of objects which share a certain property in a varying degree, and moreover, when we pass from one such object to another, that property increases or decreases gradually and imperceptibly. Further, the connotation of the term in question incl11des the property of sharing that given property - in a current expression, ''to a small degree''. In such cases we find it extremely embarrassing to decide whether a given object is, or is not, a designatum of the term, and we fail to realize how we should distinguish the designata from the other objects. Thus understanding of a term may be unclear and indistinct, but it may also be vague, if we hesitate in trying to classify a given object and find it difficult to take a definite stand on the issue. As examples of tern1s which commonly are vaguely understood we may quote ''young'', ''old'', ''new'', ''vast'', ''large'', ''giant'', ''small'', ''crowd'', ''light'', ''loud'', etc. How many people are needed to make a crowd? Let us ask ourselves whether one person makes a crowd, whether two persons make a crowd, etc., and we shall grasp by way of this example what it means to understand a term vaguely. We also know that a certain pigmentation mark is on the cheek, and the other on the nose, but what about the third? Is it still on the cheek, or is it on the nose? Here is another example of a vague under­ standing of the term ''cheek''. The problem is the same as in the case of a ''crowd''. Let it be added that, mutatis mutandis, the concept of an unclear, indistinct and vague understanding may also be applied to other expressions - namely those which are not terms. All these shortcomings may be collected under the name of blurred meanings ; let us oppose to them clearness, distinctness and definiteness in understanding expressions, let us realize that these shortcomings often account for verbal controversies, and finally let us search out some methods of eliminating the shortcomings. 7. DEFINITIONS : LEXICAL, SEMANTIC, AXIOMATIC. The above considerations concerned with blurred meanings of expressions lead us to the conclusion that the building of definitions, which determine the meanings of expressions, must be a very valuable remedy against the shortcomings discussed in the preceding section. Definitions make our speech become clear, distinct and definite, because definitions are answers to questions as to what given expressions mean. We distinguish, 011 the one hand, lexical, semantic, and axiomatic definitions, and on the other, analytic and synthetic definitions.

26

REMARKS ON LANGUAGE

A lexical definition is of the type ''A means the same as B'' (or : ''A is equivalent to B'', and the like). Examples : ''travail/er'' means the same as ''to work'' ; ''p apilio'• mea11s the same as ''butterfly'' ; the word ''aber'' is an equivalent of the word ''but'' ; the phrase ''to send him to Coventry'' means the same as the phrase ''to refuse to associate with him''. This kind of definition is called lexical because it prevails in lexicons or dictionaries. Both the definiendum, or the expression being defined, and the definiens, or the defining expression, occur in the above examples in quotation marks, in material supposition. This, however, is not essential ; what is essential is that both the definiens and the definiendum are here indicated by means of their terms as designata of those terms. In order better to understand that point let us consider the following example of a lexical definition : the third word in the second line on page 1 in the 1 925 edition of Whitehead's Enquiry concerning the Prin�iples of Natural Knowledge means the same as the word which is the fifth item on page 1 84 in the third edition of Chodiko's Polish-English Dictionary. In fact, the word ''answer'' means the same as the word ''odpowiedi''. Now in the latter, brief formulation we say about a certain word that it means the same as a certain other word ; or we say of these two words that they mean the same thing. In stating that about those two words we have used the names of these words, namely the word ''answer'', or briefly ''answer'', and the word ''odpowiedi'', or briefly ''odpowiedi''. These names include (and their shorter versions precisely consist of) words which have the same form as the words in question, the words ''answer'' and ''odpowiedi'' used in material supposition. On the other hand, in the lengthier version of the definition, which also states that the two words mean the same thing, we have used two other names : ''the third word . . . " , and ''the word which is the fifth item . . . ". These names do not quote the phonic or the visual form of the words of which the sameness of meanings is stated. These have not been used in material supposition, neither has their phonic or their visual aspect been described. The words in question have not been used in material sup­ position. They are represented by certain descriptive formulas, which differ from them as to form ; these descriptive formulas resemble the case in which Wellington is referred to as ''the victor of Waterloo''. The words ''answer'' and ''odpowiedz" have been used here neither in their formal nor in their ordinary supposition : they simply do not belong to the definitions themselves and are merely designata of certain terms. So much for lexical definitions. Semantic definitions are of the type ''A means that p'' or ''A can be used as the statement of the thought p'', etc. For instance, ''to send to Coventry'' means to refuse communication with ; ''it is going to rain'' means that indications are accumu­ lating which announce the coming of rain ; ''John is crazy'' means that John behaves in an irresponsible or incalculable manner. The difference between this type and the former consists in that in semantic definitions only the phrase to be defined (the definiend11m) occurs in quotation marks in material supposition (or is in some other way represented by its name), whereas the definin g phrase (the definiens) '

IN LANGUAGE

27

i s used i n ordinary supposition. We have called such definitions semantic (that is, referring to meaning) because the definiens brings out the meaning of the definien­ dum in the most pertinent, as it \Vere direct, manner. A11d as both these definitions and the lexical ones are formulated by the use of the word ''means'', hence both type s might be called semantic. Should we adopt sucl1 a convention, we should have to distinguish between semantic definitions - first, lexical definitions and, second, semantic non-lexical definitions, or semantic definitions in the narrower sense of the term.

Axiomatic definitions

may be opposed to both the former groups . As an illus­

tration we shall quote 11ere the axiomatic definition of the word ''between'' as applied to points on a straight line. Suppose that a person wants to be informed about the meaning imparted to that word in a given system of geometry. To his question, what does the word ''between'' mean in that system, he will not receive any answer which would fall i1nder the scheme : it means the same as, or, under the scheme, it means that ; but he will receive an answer in the form of a number of statements, in which the word in question occurs in ordinary supposition. They may be, for instance, the following statements : ( 1 ) If

A, B,

C are points on a straight line, and

between A and C, then B is also between C and A . (2) Among any three different points on a straight line there is exactly one point which i s between the two remaining ones. (3) Among any three different points on a straight line one is between the if B is

remaining two if and only if they are in the different parts of the straight line into which it divides that straight line. Such an answer does in a way inform as to the meaning of the word ''between''. This is essentially the same method as the ''Berlitz method'' of teaching foreign languages, and which is used in explaining to children the meaning of some word, for example, ''to peck'' ; we say that : the hen pecks, the sparrow pecks, the pigeon pecks, etc. By observing the use of a given word in several cases we somehow grasp the meaning in which it is used. It must, however, be admitted that this is not the proper answer to the question as to what does a given word ('lto peck'', ''between'') mean. Hence it i s not a definition in the strict sense of the term, but rather a substitute for a definition, something like a definition, a pseudo-definition. It would, therefore, be safer to call it not axiomatic definition, but axiomatic pseudo-definition. After all these explanations the term ''axiomatic definition'' will, perhaps, give rise to no misunderstandings. Let it be emphasized once more that in this method of defining we do not speak about the word being defined, but we use that word i n statements : it occurs in ordinary supposition as part of a statement or statements. In the example above, we do not say of the word ''between'' that it means this or that, but we use the word in statements about points on a straight line. In the second example, we also do not say of tl1e word ''to peck'' that i t means such and such, but we use it in ordinary supposition in a

number of statements about the hen, the sparrow, the pigeon, etc. We can, however, perform our task by making only one statement in which we

use the word being defined. If that statement has a definite structure, to be discussed

•

28

REMARKS ON LANGUAGE

below, we shall then obtain, as a special case of an axiomatic definition, an

mathematical definition

ordinary

(or, rather, a pseudo-definition).

We can thus define the conj unction ''either . . . or . . . " in one of its current meanings if, by stating that something i s either s o and s o or something is such and such we want it to be understood that, and only that, these two possibilities are mutually exclusive (so that one of them may occur, or the other may occur, or neither of them may occur, but they cannot both occur). We have i n mind that meaning in which one of the two tenderers for an exclusive right to deliver certain goods might say to the other : ''Of us two, at best either you will get the j ob or I shall '' or, briefly, ''Either you will fail or I shall fail''. What i s meant here i s that neither one of them need succeed with his o ffer, or at the most one of them may succeed, but in no case may both of them succeed. Now for that meaning the foilowing definition ' ' would be satisfactory : ''For all constant values of the sentential variables p and 'q' a true sentence is obtained from the following s entential function : 'either p or q ' if and only if not q or not p ." Another example of a mathematical definition is o ffered by the definitions of the phrase ''is included in'' as applied to classes : the class of M's is included in the class of N's if and only if whatever is an M i s an N. For brevity's sake we have dropped the introductory formulation : ''For all constant values of the sentential variables 'M' and 'N' a true sentence i s obtained from the following sentential function.'' In that sense mathematicians say that the class of

2 is included in the class of odd numbers (since every prime number greater than 2 i s an odd number). In the same sense it may be said prime numbers greater than

that the class of Calvinists i s included in the class of Protestants (since whoever is a Calvinist is a Protestant). It is said of some horses that they amble. To the ques­ tion, as to what does it mean, one could reply with the following pseudo-definition (here too the stereotype introductory formulation is omitted) : ''x ambles if and only if x moves by raising both right or both left legs simultaneously''. Here we have a definition of a verb, and in the preceding cases, definitions of a sentential conjunction and of a predicative plrrase. But a term can also be defined i n this way : ''x is a xerophyte if and only if x is specifically adjusted to an arid environ­ ment." All these examples given above were marked by a certain constant structure. The beginning consisted of an explicit or implicit schematic formula of the type : ''For all the constant values of the variables . . . a true sentence i s obtained from the following sentential function." It would be superfluous to add that such a formula should have preceded the example of an axiomatic definition of the preposition ''between'', given above, and the earlier examples of definitions, if we used an expanded formulatio n with variables. This is not, i11 pri11ciple, a characteristic of all definition s. Should a speaker have to quote a long sentence only once in his lecture, he might in advance adopt the convention (to be included in preliminary information about abbreviations, given before the text proper) that he would re­ place that sentence by an abbreviated symbol of a specified fo1·m. In general, however, we define symbols that are to be used many times in situations that cannot

DEFECTIVENESS IN LANGUAGE

29

be specified i n advance, and that is why we usually have to use variables in defini­ tions. · What distinguishes the structure of ordinary mathematical definitions among the entirety of axiomatic definitions can be formulated under two points. definitions are

equivalences.

( 1 ) Such

Tl1ey are hence usually of the type ''p i f and only if q '',

which i s reversible, s o that the thesis ''q if and only if p'' is equally true. Consequently, i t i s not only that ''The plant x i s a xerophyte if and only if the plant x is specifically adjusted to an arid environment'', but also conversely, ''The plant x is specific­ ally adjusted to an arid environment if and only if the plant x i s a xerophyte." (2) In such definitions, the phrase being defined occurs only once. Both these prop­ erties are shared by ordinary mathematical pseudo-definitions with both lexical definitions and semantic definitions (there, too, the phrase being defined occurs only once and means the same as the phrase by which it i s defined, and hence is equivalent to it). The difference, as indicated above, consists ii1 that the phrase being defined occurs here in

to,

ordi11ary

supposition, whereas there it is only

referred

either not being quoted at all in its visual or phonic form, or being quoted in

material supposition ; moreover, the definition is rendered not by ''means that'' or ''means the same as'', etc., but by ''if and only if'' or by equivalents of the latter phrase.

8.

PRELIMINARY ISSUES CONNECTED WITH E XPLANATION OF THE ESSENCE OF THE CLAS­ SICAL DEFINITION. We have to deal now with the classical definition. But to understand its spirit well, we must first deviate from the topic and consider a number of preliminary issues. We shall : (a) analyse the intentions included in the question ''What i s (this or that)?'' and i n the reply to that question : ''(This or that) i s (this or that)'' ; (b) examine the meaning of the formulation ''the essence of (this or that)'' ; (c) consider the issue of the existence of what are called ''universals''. (a)

.that''.

Interpretations of the question '' What is N?'' and of the reply ''N is this or First of all, what is the meaning of the question ''What is this or that?'' Such

questions are often asked in which an object is indicated by a gesture. For instance, at an industrial exhibition a visitor is puzzled by a device witl1 a cylinder, the use of which he cannot guess and asks : ''What is this?'' If the question is asked by a child i t often suffices to answer, ''This is a roneo'', since a child o ften asks such a question in order to be told the ordinary name of the object in question. For a child, ''What is this?'' frequently means ''What is the name of tl1is?'' But a criti­ cally-minded visitor at the exhibition i s satisfied only wl1en told that the object he asked about i s used for duplicating letters, circulars, etc. He may not even stop at that but only consider himself satisfactorily informed when it is explained to him how the device functions or how it is to be operated. In a word, a description of the object concerned in this or that respect will be required, according to the intention of the person who asks the question, an intention veiled by the schematic formulation of the question. In other cases we hear questions such as ''What is society?'', ''What is a poison?'', ''What actually i s money?'', etc. Here no object

REMARKS ON LANGUAGE

30

is indicated by a gesture, but the copula ''is'' i n the question is followed by some general term, as if an attempt were being made to show something by its means. What is concerned in such cases is the description of the extension of the term by some specific properties - that is, properties which are attributes of all its designata and of its designata only. Sometimes the point is to indicate certain properties which are of particular importance for a given ability or a given purpose, which has aroused the interest of the person who asks the question. This is the way a child understands the question ''What is a snail?'' when he or she answers ''It is for crushing." In other cases those properties which we want to know are those which are partic­ ularly useful in explaining other properties of the objects o r concepts discussed. In other cases we want to know from what certain objects have developed, or o f what and how they are built o r consist of. Such is the case when t o the question "What is air?'' we reply ''Air is a mixture of nitrogen, oxygen and other gases." In still other cases, we are concerned with those properties which form the connota­ tion of a given term witl1 respect to its received meaning. This is so because one can understand a given term clearly but not distinctly enough, and therefore one can desire fully to realize its meaning. This is usually so, for example, with the term ''society''. We all use it with the feeling that we mean the same, but discussions reveal that we cannot formulate what we mean. Therefore we ask ''What is society?'' when we actually want to ask what that term means. Finally, we often ask ''What is a palimpsest?'' or ''What is DORA?'', when we encounter the term in question in some spoken or written text and do not understand it. M oreover, we ask ''What is it?'' not only with respect to terms, but usually with respect t o any new and incomprehensible word or phrase - for instance, when we for the first time hear or read a word or phrase i n a foreign language, which we do not understand : ''What is ''What is

haud?'',

xveie iAirJaov ?''

''What is

meinetwegen ?'' ,

''What i s

yvwfft aeav7:6v?'',

We are then satisfied if someone gives us in reply an

equivalent of such a word or phrase in a language which we know and understand, either by means of a lexical, or semantic, or even classical definition. ''Palimpsest'' means the same as ''a manuscript text revealed by erasing of another manuscript text written on it'' ; ''DORA'' means the same as ''the Defence of the Realm Act'' ;

haud

in Latin means the same as ''not'' in English ;

the same as ''know thyself'' ;

xvete lAirJaov in

yvwff i aeav7:6v

i n Greek means

Greek means the same as ''Lord,

have mercy''. In all those cases, the use of the phrase ''What is this or that?'' has its counterpart in the use, in reply, of tl1e phrase ''This or that is this or that'', so that the entire ambiguity of the former is inherited by the latter. In this connection, it is important to note that among the various uses of those phrases we can distinguish a and a

semantic

real group

group. The former includes those cases in which the point is t o

give the name of a certain indicated object, or to characterize i t i n a given respect, or else to characterize the extensio11 of a given term, that is, the class of des­ ignata of a given term ; the latter includes those cases in which the poin t is to reveal

DEFECIIVENESS IN LANGUAGE

31

the meaning of a given phrase. These two groups overlap, for in such cases, as with ''society'', ''poison'', "money'', we want to achieve both things : to characterize the extension of a given term by indicating tl1e properties that contribute to its received meaning. (b)

Analysis of the meaning of the phrase ''the essence of (this or that) . "

Issues

of the type '' What is . . . ?'' (''What i s a point?'', ''What is one?'', ''What is an eclipse?'', ''What is quadrature?'', ''What is virtue?'') gave birth to the doctrine to the e ffect that a definition informs about ''the essence'' of what is being defined, ''the essence'' of the thing being defined (that essence being supposedly always a secondary being, or a general object, or a universal). It i s extremely difficult to unravel the ossified knot of intentions integrated in that very hazy term whicl1 is the equivalent of the Greek

essentia.

ovala

and of the Latin

It seems correct to suppose that the Greek thinkers who endeavoured to

realize of what proper replies consist to the questions of the type ''What i s this o r that?'' (Socrates, Plato, Aristotle), felt the need to explain why just any pert­ inent characterization of the extension of a given term does not suffice, but a specific characterization is required. They \Vere not satisfied with the super­ ficial explanation that the characterization required should pertain to that aspect which is of special interest to the person who asks the question, or the aspect which leads to an answer most fertile in consequences of interest for the person who wants to know the specific nature of the extension of the given term, or the aspect with respect to which the characterization of the extension of the given term grasps best the received meaning of the term which has hitherto not been quite clear. They guessed that not just any pertinent characterization suffices because the person who asks for a definitio11 wants to be informed about the essence of what is being defined. And here haze and confusion supervene. Does the person concerned mean the essence of a given perceivable object falling under a general term? Or the essence common to all the designata of that term? Or the essence of the universal corre­ sponding to that term? Aristotle tells us about some ''form'' which is shaping ''matter'' and is precisely the essence of the thing shaped by it from that matter ; this might be so, perhaps, since the shape intended by the sculptor is that to which the material of which 11is statue i s made strove, and whicl1, as it were,

guided the trans­

formations of that material. This is supposedly the essence of the statue, since it became a statue only when it acquired that shape, and will cease to be a statue as soon as it loses that shape. In the light of these remarks, we may understand the traditional formula which says that the essence of a given object is that without which it would not be what it is. Now all the issues in connection with which one asks about ''the essence'' of this or that, if that ''essence'' be understood in the sense of old Greek and mediaeval speculations, should, in our opinion, be effaced as wrongly formulated. On the other hand, we do not renounce the use of the words ''essence'' a11d ''essential'' in definite phra­ ses, their meanings being defined in each case. For instance, we may formulate the title

32

REMARKS ON LANGUAGE

of a paper to be ''On the Essence of Inner Experience'' instead of writing ''What is the Meaning of the Expression 'Inner Experience' ?'' Or, when above we asked several times what is a defi11ition, we meant such an understanding of that question as in the case of the example of ''society'' discussed above. In still other cases, by what is ''essential'' in a given issue we shall understand what is important to it, to be distinguished from what is irrelevant to that issue ; in particular cases, what i s especially important to the i ssue. Further, by properties which are ''essential'' to the elements of a given extension, we often mean those properties which enable u s to find out comparatively the greatest number of important points, specific to the extensio11 of the term in question. Finally, by the properties which are ''essential'' to the extension of a given ter1n we also, and most frequently, mean those properties which form its connotation.

Stands adopted on the issue of the existence of universals : realism, conceptu­ alism and nominalism. We now pass on to the third issue of those specified on p. 29 (c)

above. What do the believers in the existence of general objects (or universals) mean by that term when they, for example, state that the task of a definition consists in revealing the essence of a given general object? It i s usually difficult to obtain an answer, the more so since they differ remarkably in their views on ''the sphere and the mode of existence'' of those alleged objects. Do they exist in the minds of those persons who understand general terms , or outside those minds, in the per­ ceivable designata of those general terms or outside them? These are the questions which, formulated by Porphyry in his introduction to Aristotle's century

A. D.),

Categories (third

tortured mediaeval thinkers for many centuries and have for many ,

not ceased to be of topical interest. The ways of answering these questions are usually classified as radical realism, moderate realism, conceptualism and nominalism. The realists of both types agree that the universals exist ''outside human minds'', but according to radical realists they exist ''outside things'' (outside the designata of given general terms), while moderate realists admit only the existence of universals ''in things''. Radical realism is

conventionally

called

Platonic ;

moderate, Aristotelian.

The

conceptualists

insist that universals exist exclusively ''in minds''. Finally, the nominalists reject the existence of universals at all . Thus, according to a ''triangle in general'',

radical realists there exist, for instance, a ''man as such'' , a ''dozen in abstracto'' (such and similar phrases being used

to emphasize that reference is made to a universal, and not to any ''particular'' man, triangle, or dozen) ; moreover, they exist ''outside minds'', so that even i f all the persons who think anything about any of those universals should perish, man in general, triangle

in abstracto,

and dozen as such would not cease to exist.

According to radical realists, they would continue to exist if there were no partic­ ular men, particular triangle, particular dozens, since they allegedly exist ''outside things''. To the question,

where they exist, the radical realists reply that such a ques­

tion with reference to the universals is unreasonable, in the same way as it would

DEFECTIVENESS IN LANGUAGE

33

b e unreasonable to ask what the universals eat. A similar answer i s given to the question, lvhen the universals exist : it is said that the question is nonsensical, since the universals are extra-temporal. In the face of such an approach it could not, of course, be asserted that a triangle in ge11eral would ''continue'' to exist even if all thinkin g perso ns had perished ; b11t it could be said that a triangle in general would exist even if there never, nor during a given period of time, had existed any perso n who would think anything about a triangle. The supposedly extra-temporal existence of the universals does not depend on which and when particular per­ ceivable things come into being or cease to exist. Hence the peculiar ''durability'' of universals, hence further the guarantee of durability and consequently of the certainty of knowledge about them, since they are supposedly changeless . For a radical realist, the statement, for example, that ''The sum of the inner angles of a triangle is equal to the sum of two right angles'' (reference being made to a triangle in general), or the statement that '' 1 2 is divisible by 3 '' (here, too, reference being made to a dozen as such, and not, for in&tance, a dozen of apples or buttons), are good examples of theorems about universals, theorems which, as certain Greek thinkers would add, are permanently true because they refer to something which i s n on-temporal and therefore changeless.

The moderate realist

need not go so far. But for him, too, the universals are

something more durable than the particular perceivable objects, and hence for many of them knowledge about the universals i s more permanent. A particular man, for instance, i s changing, growing, ageing, etc., but as long as he remains a man, there ''inheres'' in him a universal, always identical and the same i 11 every respect : ''man

in abstracto '' ,

a general object which we can distinguish ''in'' John or Peter

by appropriately concentrating our attention on that whicl1 characterizes each of them as a man, and by disregarding what in John i s secondary and what in Peter i s i ncidental (for instance, that he is married, that he is a locksmith, etc.). In a word, according to moderate realists a universal can, as it were, be brought out by abstrac­ tion, or by mentally detaching it from its substratum . The phrase ''as it were'' indi­ cates that in describing those doctrines we resort to metaphors, and not to precise �

formulations. But it would be otherwise impossible to summarize the views which i n themselves are built of metaphors. The moderate realists, however, hold the opinion that even if there were no beings which think of man as such, triangle

abstracto,

in

dozen i n general, etc., yet man as such, triangle in abstracto, dozen in general,

etc., would exist anyhow, since they do not exist ''in the mind'' of the person who thinks about them, but i ndependently of such a mind. It i s otherwise with the

conceptualists.

True, they accept the existence of uni­

versals, but only ''mental'', ''ideal'' ones, as opposed to the ''real'' ones claimed by the realists. This is to indicate that they exist only in (someone's) mind, as does a castle i n the air, of which a person dreams, or a hero of a novel. Contrary to the realists, the conceptualists are inclined to consider the universals to be products of the mind of the person who thinks about them, whereas the realists are inclined

REMARKS ON LANGUAGE

34

to claim that such a person only perceives them in things or outside them. Often, too, the conceptualists prove i 11clined to consider the universals as something psychic, as 've sometimes consider as psychic the events of which we have dreamt. But once the state of imagining sometl1ing as an ''act'' is distinguished from what is the content of s uch an act, or an ''imaginary object'' or ''illusory object'', that tendency usually disappears, and it i s then said that acts are something psychic, but their content is not. •

Let it also be admitted that the term ''conceptualism'' is used very ambiguously and, moreover, in meanings which are likely to be confused. Conceptualism as it is most commonly understood - for example, i n the sense used by Locke, etc. will di ffer essentially fro 1n the doctrine here described. It i s rather the belief that although general objects do not exist, general concepts (and, of course, general terms) do. For apart from the interpretation of realism, conceptualism and nominal­ ism whicl1 is given in tl1is book, there is another i11terpretation according to which the doctrines called by those i1ames form the foilowing series : realism recognizes the existence of general objects (universals), general concepts and general terms ; conceptualism rejects the existence of general objects, but recognizes the existence of general concepts and general terms ; and nominalism rejects the existence of general objects and general concepts, and recognizes merely the existence of general terms (Berkeley). But let us revert to the interpretation from which we started. Enough has been said of conceptualism, as the doctrine maintaining that the universals exist but only in the mind. A few words must now be added about

nominalism,

which

maintains that there are no universals at all. Indeed? an opponent will ask, is there then no truth in such statements as ''Tl1e sum of the internal angles in a triangle is equal to the sum of two right angles'',

'' 1 2 is

divisible by

3'',

''A sage is free from

superstitions'', etc., and are these not statements about universals, with dropped or implicit ''in general'', ''as such'' or similar additions after tl1e words ''triangle'',

'' 12'' and ''sage'' ? If so, then there must exist some general objects, whether in mind or outside mind, in things or outside thi11gs, since certain statements about those general objects are true. Illusion ! These and similar statements are abbreviations, which sta11d for fully expanded sentences in which general terms no longer occur in the role of full grammatical subjects. And that use of general terms in the role of full grammatical subjects most probably was the principal cause (and remains to this day one of the main causes) of surmising the existence of universals. The abbreviated form ''A sage i s free from superstitions'' stands for the sentence ''Who­ ever is a sage, is free from superstitions'' , etc. This also attempts to explain the use of such phrases as ''as such'', ''in general'' in such formulations as

''A

as such i s

in abstracto, and

B'', etc. They have, however,

other shades of meanings too. In particular, concerning the phrase ''as such'', so fondly used in tht> papers of those who philosophize, it is well to remember that ''A as such is

B'' often means ''From the fact that something is A it follows that that s ome-

35

DEFECTIVENESS IN LANGUAGE

B too'', or ''From the definition of the term A it follows that 'if something i s A then it i s B too ' ''. thing is

So much for the controversy about the mode and sphere of existe11ce of uni­ versals. But we have still not said what the term ''universal'' means. Who knows whether all the co11troversy would cease in the eyes of critically minded people if an agreement had been reached about that term and other terms involved in the formulation of conflicting doctrines. Such, however, is usually the fate of purely conceptual controversies. Yet in the discussion about the universals there were no good definitions of terms. Two formulations, the Platonic and the Aristotelian, both of them misleading, prevailed i n the past and continue to haunt us to this day. In the Platonic interpretation, a universal is the same as an idea. And an idea is an object - not perceivable by the senses - which can be mentally imagined, changeless and independent of changes in those objects - perceivable by senses which participate in it. Nearly as many metaphors as there are words. For Aristotle, a universal i s the same as a ''secondary substance'', and a secondary substance is wl1at is predicated about something else and about which sometlling else is predi­ cated. It would seem, therefore, that secondary substances are certain words, since a word is something which can be predicated about something else and about which something else can be predicated. But it follows from the contexts that what is meant here i s not a word but something else. It is supposed that in the sentence ''Man is a rational being'' something is predicated about man in general, in the same way as i n the sentence ''Socrates i s a sage'' something is predicated about Socrates. And since in the sentence ''Plato is a man'' the same seems to be predicated about Plato, about which it was predicated in the first sentence that it is a rational being, hence the conclusion suggests itself that ''man in general'' is precisely something about which something else can be predicated and which can be predicated about s omething else. IIg wr:ov

'ljJeiJoo�

(the prime error), as the Greek used to say, consists

i n treating the meaning of such sentences as ''Man is a rational being'' strictly in the same way as such sentences as ''Socrates is a sage'', although (according to what we have said above) the sentences of the former kind, with a general term as the grammatical subject, are merely abbreviations which stand for (usually conditional) sentences in which general terms no longer occur as grammatical subjects. Thus the Aristotelian formulation i s very vague, but - and this is the worst of it - has the appearance o f definiteness. If we want to base the criticism o f realism and conceptualism from the nominalist point of view on a clear understanding of the term ''universal'' we must look for a better definition. And in searching for such we find at least two possible definitions, wl1ich, by the way, are not equivalent : term

''N''

( 1 ) P is a u11iversal for the designata of the

is the same as : P i s an object which has only those properties that are

connoted by the term

''N'' ; (2) P is

a universal for the designata of the term

''N''

is

the same as : P i s an object which has only those properties that are common to the designata o f the term

''N'' . 4

REMARKS ON LANGUAGE

36

Now it turns out that whether we adopt the former or the latter interpretation, the universals cannot exist, since they would 11ave to be contradictory obj ects. Let us take into account the former definition. Let the term erties a,

b

and

c

''N'' connote the

prop­

(and it must be borne in mind that a term can connote only a fmite

nun1ber of properties) ; now should an object have those properties, it wo11ld have to possess other properties as well, since properties are not independent of 0 11e another but one involves an infinite number of others. Hence, whatever has the propertJ a must also have the properties

''N''

P be ice as such, let the tern1

m, n, r,

and many others. Let, for instance,

be the word ''ice'' ; the designata of the term

''N''

will therefore be all pieces of ice, past, present and future. Let the term ''ice'' connote the properties : being a structure of molecules of water

(a),

and solid consistency

(b). It is obvious then that whatever has the property of being a structure of molecules of water has, as a result, many other properties which chemistry sl1ows to be in­ separably connected with the molec1tles of H2 0 - for instance, a characteristic specific weight (ni) , a definite fo1·m of crystallization (n), a definite electric cond11ctivity

(r),

and many others . He11ce there cannot exist an object whicl1 would have only

the properties a and

b.

Similar results are obtained when we turn to the second definition. This ca11 even be done in two ways. Here is the first. Let an object X be one of the designata of the term

''N''. It must have a certain specific property which distinguishes it from

all other objects. Let it be symbolized by

t, and let us

state that any otl1er designatum

of the term ''N'', for instance the object Y, does not have that property, si11ce \Ve 11ave assu1ned that only the object X has it. Conseque11tly, the object Y possesses the lack of the property

t,

which may be symbolized by

versal P has tl1e property

t. If it has, this

t ' . We now ask whether the u11i-

leads to a co11tradiction, since by assun1ption

it should 11ave only those properties wl1icl1 are common to all the designata of the term ''N'', and tl1e prope1·ty

t

is not comn1011 to them ; but, on the contrary, it dis­

tinguishes only one designatum, nan1ely X. But if the u11iversal P does not possess the property t it must possess the lack of that property, that is

t'

(this in view of tl1e

''ontological principle of excluded middle'', for which see below) . But this too leads to a contradiction, since the property of the term

''N'' :

t'

also is not common to all tl1e designata

that property is the attribute of all the designata otl1er than the

object X, which does not have it. Thus it is obvious that if so1nething '''ere a uni­ versal it would be a contradictory object. Thus the assumption tl1at universals exist leads

ad absurdum.

For tl1e sake of illustration , we may substitute : ''volcano in

general'' for ''P '', ''volcano'' for Bay'' for

'' t'' ,

''N'', ''Vesuvius'' for ''X'', ''lying in the Neapolitan

and ''Etna'' for '' Y''.

And here i s the second way. Let res1)ect to tl1e term

''N'' - that

u

stand for tl1e property of generality with

is, the property of havi11g only those properties

wl1ich are com1non to tl1e desig11ata of tl1e te1·m

''N' ',

and let us ask whether an

arbitrarily chosen d esignatu111 of that tern1, for instance the desig11atum Z, possesses that pro perty. Obvi o11sly i t d oes not, since being d isti11ct fro1n all other designata

�

DEFECTIVENESS IN LANGUAGE

37

''N'' i t must have some property, let it be v, which those other designata do not have. But the universal P, general with respect to the term ''N'', as such has exactly that property of generality with respect to the term of the term

''N'' - that i s, the property u. Hence it has a property (in this case u) which i s not common to all the designata of the term ''N'', and this

the property yields a con­

tradiction. This i s how the nominalists refute the hypothesis of the existence of universals, by reducing it to a contradiction. But, obviously, the efficiency of such refutations depends o n the adoption of appropriate definitions of the ''universal'', and on appropriate answers to the question as to what the term ''universal'' means. Objec­ tions are occasionally raised that in the case of other definitions, which grasp some of the semantic intentions of that term as it was used in the past (this refers to the Greek term

To xatf6J.ov and the Latin term universale),

no contradiction can be

arrived at. Yet it must be stated here that no such definitions are known to us (if we confine ourselves to those definitions which are not blurred).

9. CLASSICAL DEFINITION. We can now pass to an analysis of the classical (cf. p . 29). For illustration let u s recall, for instance, the definition of

definition the term

''amber'', which is ''Amber is petrified resin''. By analogy, ''a xerophyte is a plant specifically adjusted to an arid environment'' and ''an Amazon is a female warrior''. All these definitions are of the type

''A

is

BC'',

where

''A'', ''B''

and

''C''

stand for

terms. The reader will easily recognize here the classical kind of definition, as used i n schools. Almost always when in traditional education reference i s made to def­ initions, (a) they are usually built by means of the copula ''is'' or its equivalent ; (b) examples of definitions are definitions of terms (or at least such are ordinarily the intentions) ; (c) the definition is constructed by connecting a noun with an attrib­ utive adjunct ; (d) it is required that the definition should be reversible ; (e) there i s a warning against the vicious circle in defining. It is now necessary to comment on those five principles of the traditional theory of definition .

(a) Misunderstandings due to the structure of the type ''N is . . . ", characteristic of the classical definition. Now it has become customary to ask for a definition of a term i n the words ''What i s this?'' It has also become customary to reply ''This i s . . . " (or, of course, by the equivalents of that formulation in tl1e various languages). That habit i s frequently the source of grave errors and misunderstandings i n con­ ceiving the task of a definition. Tl1is is so because it suggests that a definition is not an answer to the question what does a given phrase mean, but an answer to the question,

what is a given thing;

what i s being defined i s therefore, supposedly,

something different from the words wl1ich form the grammatical subject of that definition. Moreover, a definition i s to point to some essence of that thing - namely, the essence of the supposed universal which corresponds to the grammatical subject of a given definition. In that view, what is being defined by the definition ''Amber is a petrified resin'' is not the very word ''amber'', nor any tangible piece of amber, but some amber in general ; the same holds for other definitions : a xerophyte in

38 \

REMARKS ON LANGUAGE

general, a sage in general, etc. Tl1us, we always have to do with some universal or general object. It angered even Socrates, as described in Plato's works, when to a question of the kind ''What is a just man?'' someone tried to answer by naming those persons who deserved to be called just, or to the question ''What is 'beautiful'?'' described in reply a beautiful woman, a beautiful horse or a beautiful amphora. Such an individual was then criticized for "fragmenting the issue'', in the sense that instead of giving a general answer he tried to substitute for it a conglomerate of partial ans­ wers. Socrates - supposedly the first to do so - required that in clarifying discus­ sions, definitions be given in the form of ''general'' answers, that is, answers of the type ''A is . . . ", where ''A'' stands for a general term (in the predicative sense), such as ''sage'', ''just'' or ''the beautiful''. It is now difficult to decide whether it was he

or Plato who was the first to assert that general objects, universals, have an exist­ ence of their own. Usually that doctrine is ascribed to Plato. This resulted, in Aristotle's works, in the placing in opposition of real definitions, which are supposed to point to the essence of the things they define, and nominal definitions, which are only to give more comprehensible equivalents of certain ·

words or phrases which are not understood well enough. To us, who adopt the nominalist stand, the issue appears much simpler, because not every question of the type ''What is this?'' is a question that asks for a definition, and not every answer of the type ''This is this or that'' i s a definition. If the thing indicated, or the extension of a given term is merely

characterized,

we simply have

to do with a characteristic, or a description referring to specific properties. It is only when we explicitly or implicitly reply to the question "What does this phrase mean?'' that we o ffer a definition. Hence among definitions we do not distinguisl1 between real and nominal ones :

all definitions are nominal.

The classical definition does not in the least refer to the essence of some universal, or to the essence of the designata of the term that corresponds to that universal. It i s a veiled answer to the question ''What does the term 'N' mean?'' In its simplest form, the answer should be : " 'N' means the same as however, its form is :

"A

is

'BC' ''. Since,

BC'', its meaning, one of the many possible for such

formulations, i s often veiled, and either a simple characteristic of the extension of a given term or an individual case of a mathematical pseudo-definition can only too easily be taken for a classical definition. In the first case, that phrase is equivalent to the phrase ''Every A is and

BC and conversely'', the meanings of the terms A , B

C having been previously established by a tacit understanding or certain def­

initions. In the second case, the phrase means the same as ''If x is A then x i s

BC, and conversely'', the meanings of the terms A , B and C not being previously defined : they are to be defined by the adoption of the given thesis as an axiom. So much for the copula ''is'' as it occurs i n tl1e classical definition. (b)

The classical definition applied to terms.

A few remarks must now be made

on the issue as to whether in the classical definition the definiendum (''A'') and the

DEFECTIVENESS

IN

LANGUAGE

39

definiens (''BC'') are tern1s. It would not be exact to claim that traditional logic gives definitions of real terms only, since we may encounter such definitions as : ''Justice i s the virtue of judging on merits and demerits'', or ''Botany is tl1e discipline concerned with plants''. Now, ''justice'', ''botany'', ''virtue'' and ''discipline'' are, we dare to assert, apparent terms or onomatoids. Moreover, we may encounter defini­ tions i n which the definiendum is a verb (''To limp is to walk lamely'') or an adverb (''Laconically is briefly, sententiously''). Such definitions, however, which are quite often met with i n conversation, are exceptional in traditional Jogic and are difficult to confine within the framework of traditional views on the nature of definition. It is only the examples with terms which adequately comply with that tradi­ tional view. From that point o f view, a definition is usually understood as a judgement concerning a concept, or a judgement concerning a term, or a judgement concerning a thing (concerning an alleged general object, or ''universal''). Generically, reference is perhaps made to a ''term''. Now the corresponding Greek word is used by Aris­ totle to indicate the subject or the complement i n the structure ''A is B'' (though Aristotle prefers, when expounding his formal logic, to say that ''B [beta] is an attri­ bute o f A [alpha]''). Thus ''A'' and ''B'' prove to be, almost exclusively, general terms. This can easily be a source of ambiguity, since some interpret the ''term'' as the word itself (phonic or written), others as the content it connotes, still others (of whom a good deal has been said above) as some general object supposed t o correspond to it (for example, ''horse in general'', ''sage i n general'', and not this or that particular object), and finally others as the extension of the word. But i n all these formulations, one thing remains constant : that what is meant here somehow pertains to a term. It is not important whether it pertains to the term itself, o r to its content, or to its extension, etc. Be that as it may, anyhow i f not the term itself is involved, then its content or extension, etc., is. The form of the question to which a definition replies suggests such limitations, for it is usually not ''What does such and such a phrase mean?'' but ''What is A ?'', ''What is B?'', etc., where ''A'' and ''B'', etc., are terms. The scope of examples of Aristotelian defini­ tions also corresponds to tl1at style. We mean here the definitions o f ''unit'' (the number

1),

''day'', ''eclipse'', ''magnanimous'' and many others.

And yet it is beyond doubt that definitions pertaining not to terms but to other kinds o f phrases (sentences, conjunctions, etc.) are also needed and used. Tl1ere are plenty o f such examples i n mathematics (and certainly in current speech as well), and many of them have been q11oted above. That is why, even if now there is nothing wrong i n saying that all definitions refer to terms, this is explained by a stretching of the use o f the word ''term'' beyond its original extension. At present ''term'' means the same as ''symbol'', ''sign'', ''word or phrase'', so t11at we speak of ''constant terms'' and ''variable terms'' in the sense of ''constant syn1bols'' and ''variable sym­ bols'', of ''primitive terms'' as the signs adopted without definition i n a system (they may be signs o f mathematical or logical operations, such as plus, the negation

REMARKS ON LANGUAGE

40

symbol, etc.), and :finally of ''technical terms'' in a discipline as the words and phrases peculiar to that discipline. Now this confinement to ter111s (and with many authors even exclusively to general terms, in the sense of their predicative function) marks the narrowness of the classical theory of definition.

The traditional formulation : definitio fit per genus proximum et differentiam speci.ficam. We finally have to consider what traditional logic has to say o n the (c)

bi-elemental nature of the complement of two terms,

''BC''. It consists, as has been said above,

''B'' and '' C'', the latter being an appositive adjunct to the former.

The former has the nature of a noun, the latter, of an adj ective. Why i s this so? This can best be understood if we become acquainted with the five Aristotelian technical terms specific

difference

proprium),

(eloo�, species), (eloonoi6� oiacpoea, differentia speci.fica), peculiarity (ioiov, (

t'

I•

I

I i ·I

4

I

I ,

I I J

••

CHAPI'BR

I

NOTIONS

1 . PERCEPTUAL, REPRODUCTIVE

AND

PRODUCTIVE IMAGES. It is usually believed that

all science i s i n any case a certain system of true judgements, distinguished for their i mportance, related by their content, and correctly founded ; and that a judgement consists i n some way of representations, that is of images or ideas, and as the con­ dition of truth must have some objective value for those component representations. In order to understand what is really stated in such a formulation, let us reflect o n images, ideas and judgements. Distinction is commonly drawn between the image itself, also called an act of imagining, the content of the image and the object of the image. Frequently, however, that content of the image, and sometimes also the object of the image, are briefly called image, too, which gives rise to misunderstandings. On the other hand, instead of ''an act of imagining'' the term ''imagining'' is sometimes used. Among images we distinguish

primary

and

secondary,

or derivative. Primary

images are perceptive, secondary images are either reproductive (based on memory}, o r productive (based on fantasy) . Images are not only visual, but also auditory, tactile and so on, and also mixed. The perceptual, reproductive and productive nature of the images is interpreted in two ways : subjective, or psychological, and objective, or genetic. In the

subjective i nterpretation,

an image is this or that, according to the specific

nature which is proper to the content of that image. Hence, an image is perceptual whenever its content has the nature of reality, well known to everyone. I have a perceptual image of an oak when I l ook at it and see it ; I have a per­ ceptual image of a tune when I listen and hear it as it is being played. But the hal­ lucinations of a madman, and also many dreams will, in this interpretation, have to be classified as perceptual images.

An image is reproductive whenever its content has the nature of a reminiscence,

which is also universally known. A productive image, i n the subjective interpretation, is an image, the content o f which bears the stamp of unreality, without, however, having the nature of a rem­ iniscence ; it i s such an image as those which fill our imagi11ation when we read the stories of the Thousand and One Nights.

61

PROBLEM'S OF GNOSIOLOGY

62

But then we shall have to classify as such those images which are experienced by psychasthenics under the influence of stimuli from the environment, that i s i n cases i n which normal people experience perceptive images. They state that they lose the sense of reality, and that it incessantly seems to them that everything they see, hear, etc., is but illusion only. This is not an obsession with them, but a persistent feeling of fantasy, combined with the content of an image when other people have the sense of reality.

Objective

classification does not in the least coincide with the subjective. It

maintains that an image is perceptual when it is a direct response to a stimulus acting on sense organs when, in the expression used, it i s conditioned peripherally. It is reproductive when it is a repeated response to that stimulus and develops as a result of a reproduction in the central parts of the nervous system of a stimulus which previously proceeded from receptors, and now does not. An image is pro­ ductive when it is neither perceptual nor reproductive, and that is its principal characteristic. In such an ii1terpretation, hallucinations are not classified as perceptual images, although they are combined with a sense of reality ; likewise, in the case of para­ mnesia an image is not reproductive, although the stamp of something known appears here. In both these interpretations it is difficult to suppose that one who keeps in his memory things formerly perceived, with all the inter-associations, can have certain purely perceptual images, without reproductive and productive elements, o r purely reproductive, without productive elements ; and it is generally agreed that, in both interpretations, productive images always include reproductive com­ ponents. Hence, as it seems, every image experienced by a thinking person must

be

a synthesis of the various elements (from the point of view of this classification),

and should we desire to classify such an image under a given heading, we should probably have to be guided by what prevails in such an image : seeing (or hearing, etc.) with admixtures of reminiscences and fantasy ; reminiscences modified by fantasy ; or fantastic fiction not without elements bearing the nature of reminiscences. To both these interpretations of the perceptual, reproductive and productive nature of images, we may oppose a third,

relativistic,

the exposition of which must

be preceded by an analysis of such formulations as ''the image of a lion'', ''the image of a Cyclops'', etc., where the word ''image'' is followed by a genitive of some noun. Such formulations can in turn be interpreted immanently or transcendently. Now, in the immanent interpretation, John has an image of something round, shining and goldish if and only if it seems to him that something round, shining and goldish is before him. Not in the sense that he experiences the conviction : ''Something round, shining and goldish is before me'', but in the sense that it s o happens to him that were he asked ''What i n your imagination i s the thing in front of you like'?'' and was required to give an answer inv11Jnerable to criticism, he would have to reply : ''It is round, shining and goldish." Likewise, ''John has an image of a lion'' means

NOTIONS

63

the same as ''It seems to John - in the same sense of the word as above - that a

lion i s before him'' ; the same, analogously, as an image of a Cyclops, etc. The

same also refers to auditory, tactile, etc., images, with the only difference that then it does not necessarily seem to John that something is before him ; it just seems to him that something somehow i s in his environment. This is so in the interpretation which we have called immanent. In the transcendent i nterpretation, ''John has an image of something'' (where niost frequently a singular name is put in the place of ''something'') means the same as ''John responds with an image (directly or indirectly ; see p .

67

below) to that something as a stimulus." For instance, ''John

has an image of the face of his son'' means tl1e same as ''John responds with an image to the face of his son'' (that is, when he consciously l ooks at the face of this son). Tl1e intentions i n the two cases are quite different. The second is interpreted by reference to that at which one looks or has looked (or, by analogy, what one touches etc . , for other senses) ; the first, by reference t o what something seems to be like. In the transcendent interpretation, a person may have an image of several parallel lines, crossed askew by a number of shorter parallel lines, but need not have such an image i n the immanent interpretatio n : in the latter i nterpretation, he may have an image of converging straigl1t lines crossed askew by a number of shorter parallel ones. Or else, in a transcendent interpretation, a person may have an image of a lump of sugar, white and shining, and yet in the immanent interpre­ tation, he may not have an image of anything white and shining, if his image i s purely tactile and gustatory. The terms just introduced also enable us to classify images roughly into perceptual, reproductive and productive. In the immanent interpretation, an image of something is perceptual if the person who has that image is at the same time consciously looking at something whicl1 is such as the thing imagined, that is, if he also has an image of something like that in the transcendent interpretation. For instance, John has at a certain moment a perceptual image of a lion if something before him seems to him to be a lion and if he is looking at a

lion. Reproductive and productive images share the property that in both cases

one is not looking at the object of which one has an image in the immanent sense. But in the case of a reproductive image one has previously had a perceptual image o f such an object, whereas in the case of a productive image one has not. The classi­ fication thus arrived at will be called relativistic or relative, because in order to place an image under a given heading we must first settle whether - or that - it is an image of something ( I ) in the transcendent interpretation,

(2)

in the immanent

interpretation. We must thus relate a given image to what i s stated in a verbal for­ mulation by the addition of a genitive after the word ''image''.

2. T HE OBJECT AND THE CONTENT OF AN IMAGE. The expression ''John has an image o f something'', in its immanent interpretation, has its counterpart in the expression ''that which John imagines'', or briefly, ''the object of John's image'', also in the immanent interpretation. Hence if John has, for instance, in the immanent inter­ pretation, a genetically productive image of a mountain range, then to the question

•

64

PROBLEMS OF GNOSIOLOGY

''What does John imagine?'' or ''What is the object of John's image?'', in the immanent interpretation of those questions, we have to answer ''John imagines a mountain range'' or ''The object of John's image i s a mountain range," where the words ''the object of the image'' are understood in the immanent sense too. On the other hand, the expression ''John has an image of something'', in the transcendent interpretation, has its counterpart in the expression ''that which John imagines'' or, briefly, ''the object of John's image'', also i n the transcendent interpretation. Hence if John has, for instance, a genetically perceptual image of a watch lying before him, i n the transcendent interpretation - that is, if he i s looking at that watch consciously - then we can say, also i n the transcendent sense, that ''John imagines the watch lying before him'', or that ''The object of John's image is the watch lying before him." Usually, in the analysis of genetically productive images we use the words ''the object of an image'' i n the immanent sense, and i n the analysis of genetically per­ ceptual images, in the transcendent sense, unless a special reservation to the contrary is made. In the analysis of a productive image it would, by the way, be difficult to find the transcendent object, although such an object always exists. But it consists of fragments, scattered i n time and space, to which one has once responded directly, but separately, with perceptual images ; at present, repetitions of those fragments combine to make a productive image. In the case of a genetically reproductive image the transcendent object i s that to which we now respond indirectly, and to which we have previously responded directly by a perceptual image, of which the present reproductive image is, as it were, a repetition. But the formulations ''What does John imagine?'' and ''That which John ima­ gines'' are sometimes understood in a different way, the stress being laid n ot o n the object but on the

content of the image i n question . In such

a case ''that which John

imagines'' means then ''the content of John's image'', and i n this sense, when we ask about ''that which John imagines'' we ask about ''the content of John's image'' . What i s concerned here is an alleged inner picture which one, as it were, has in oneself whenever one experiences an image. It is supposed, if the picture is ''visual'', to be a combination of colours, shapes, etc., But it is not necessary that that content must be a visual picture. It is claimed that, apart from colours, etc., elements of content may also be tunes, pressures, smells, tastes, etc. Thus, when I recall, or imagine reproductively, the face of a man I have once seen, then to the question, what is the transcendent object of that image, I ought to answer : ''that face at which I have once looked'' (a physical body which existed in the past and of which the present face of that man is a continuation) ; to the question, what is the immanent object of that image, I ought to answer as if I were describing what that something which seems to be before me looks like, for example, by saying ''a swarthy, long, pleasant face'', etc. ; to the question, what i s the

content

of that image, the person

who asks would expect an answer of the kind : ''an inner visual picture consisting of such elements : light flesh-like colour above, darker flesh-like colour below, such and such patches in the centre, such and such shapes and lines, etc.".

NOTIONS

65

Various issues arise in connection with the terms introduced above and their di fferent meanings. We shall concentrate only on those which have played a signal role in the history of epistemology - that is, human reflections focused around the problem of the nature of truth. Now, pride of place in that field belongs to the problem of the relation between the transcendent object of a perceptual image and the content of that image, or, in other words, the problem of the objective value of the content of a perceptual image. When we speak here of a perceptual image we mean that sense of that term which might be called mixed (see p. 62 above) and according to which we call perceptual any such image which, while being a synthesis of a perceptual, a reproductive and a productive image in the genetic sense, predominantly consists of a genetically perceptual image. The issue mentioned above is the field of controversy between idealists and realists of various shades. 3. IDEALISM, ITS vARIATIONS AND ARGUMENTS USED. The term ''idealism'' comes from the word ''idea'', understood not according to the oldest tradition, dating back to Plato, but as used commonly by Locke, the English philosopher who lived at the turn of the 1 7th century (principal work : An Essay Concerning Human Under­ standing) and who was one of the main redevelopers of epistemology in modern times. In accordance with that usage, by an idea we mean any element of the content of an image or a combination of such elements. As examples we may mention col­ oured patches (briefly, colours) which form part of our visual ''inner pictures'', sounds which form part of the content of our auditory sensations, pressures which can be distinguished in the content of our tactile, muscular, etc., images. It would not be proper to maintain the use of the word ''idea'' in that role, since its ambiguity is a very disturbing factor. In contemporary language, by an idea we often mean an opinion (for example, when we refer to great political ideas) or a conception (for example, when we say that a person developed the idea of a new invention). Moreover, in the professional literature of epistemologists we find still alive the memory of Platonic ''ideas'', and also of the Hegelian ''ideas'', which owe their origin to the for1ner. As a general term for colours, sounds, pressures, etc., the word ''sensation'' would recommend itself strongly (being a counterpart of the German word Empfindung). But we are warned, and rightly so, against such a ter1ninological usage, since the word ''sensation'' would give to our examples a psychological tinge and would thus distort, if they had to be described in such terms, the meaning of certain doctrines. That is why we prefer to follow that advice and to use the indifferent word ''element'' as an abbreviation for ''an element of content''. But in doing so we do not want to suggest any association with some simple, indivisible components of content : when saying ''element'' we might in the same sense speak of ''component'', without deciding in advance whether it is something simple, or in turn consists of components. On the other hand, the names of the theoretical trends, to be discussed below, will be left, although they include that ambiguous term which is ''idea''. What do then the idealists expo11nd? < t > Now they assert that what is seen

66

PROBLEMS OF GNOSIOJ..OOY

(at which one looks), what is touched, etc., and in general all what we should call the transcendent object (or, in plainer terms, the external object) of a perceptual image, is a combination of elements of the content of that image. Such idealism will be called epistemological. Ontological idealism' goes farther, since it claims that every object is a combination of elements of content : thus, it does not confine itself to those objects which are outer objects of someone's images, but asserts something about every object and does not predetermine whether the elements of content, of which a given object consists, are elements of content of anyone's image. Both ontological idealism and its special case, which is epistemological idealism, have two variations - subjective and objective. According to subjective idealism, any element of content is an element of content of someone's image, and the extreme wing of subjective idealists assert unequivocally that every element of content is something psychic. Objective idealism does not assert the first statement, and a fortiori the second ; in its more cautious form it simply abstains from expressing its opinion on that point ; in its extreme form it states that there occur elements of content which are not elements of content of a11yone's images, and a fo1·tiori are nothing psychic. Thus, for any idealist the face of the friend at which he is looking is a whole consisting of coloured patches distributed in a certain definite way ; when a person shakes his friend's hand, the object being shaken is a certain combination of elements of content, elements which are tactile, muscular, thermic, etc., in nature ; the tea which I am drinking is a combination of thermic, tactile, olfactory, gustatory, etc., elements. As a result, the idealist identifies the outer object of a perceptive image with its content. He does not do that merely by whim, but explains that he has certain reasons for doing so. First of all, he draws attention to the fact that those who hold different views are mistaken in confusing the conditions prevailing in the case of reproductive images with those applicable to the case of perceptual images. In the former case, there is, of course, a di fference between the inner picture which we have at the moment of recollection, and that past object which we recollect through the intermediary of that inner picture. But in the latter case, no such duality exists, and to suggest that would be to draw an unjustified analogy with reproductive images. In this case, there is no difference between the picture of the object seen and that object itself, between the content of the image and its outer object. Moreover, the term ''outer object'' is in this case clumsy, when considered from the idealist point of view, since someone might think that the outer object is opposed to tl1e inner picture as something from the outside of the sphere of elements of content to something from that sphere. Now from the idealist standpoint there are simply no outer ob­ jects of perceptual images, so understood: every object being seen, smelt, etc., is ''inner'' - that is, consists of elements of content and, as the subjectivists would have it, is also inner in the sense of being psychic. The duality in the sphere of reproductive images, as mentioned above, is explained not by an opposition between

NOTIONS

67

the content of a reproductive image and some object being recollected, which exists outside content, but by an opposition between the content of the reproductive i mage and some other, previous content wllich is precisely the object being re­ collected. For an idealist, that at which I am looking is identical with that which I am seeing, the latter being understood as an inner picture, a combination of elements of content ; he holds that everyone will at once agree to that if he reflects on his own perceptual images directly, and not through the intermediary of a fictitious analogy with reproductive images. If one does so then one realizes - and that is the second argument of the idealists - that the content ai1d only the content of images is ''immediately given'', in the case of both derivative and primary images. Tl1at whicl1 I am seeing (am visually imagining perceptually) is a combination of coloured patches, is for an idealist experienced, found in experience, given in experience, and immediately given at that, and not through the intermediary of a conjecture. And it is only a conject­ i1re that there exists something else, at which I am looking. Now - and this is the third argument - such a conjecture does not deserve recognition either because (as some say) it is absurd, or because (as others put it) it is unfounded and superfluous. Absurdity is said to co11sist in that we assume some­ thing which is seen and which is not a visual content ; but what else can be seen if not a visual cnntent? The same applies, by analogy, to hearing, tactile perception, etc. Such a conjecture is said to be unjustified because it cannot be correctly concluded from that which is immediately given, or from any truth that would be obvious without experience. And if it is not jt1stified, then it could be assumed at most as a hypothesis, should such prove necessary. But the idealists assert that we can quite \veil do without it. For instance, the stamp of reality, which so commonly accompanies perceptual images and is usually explained by saying that we respond directly by those images to an outward object, can also be explained by saying that the content of images consists of strong and weak elements, and that the stamp of reality is an attribute of those contents which at least in part consist of strong elements. And it is of such elements that the contents of perceptual images consist, at least for the most part, and in this way the term ''perceptual images'' is defined - analytically, in the broad­ e r sense of the word. No answer is given to the question as to what is the origin of that di fference between strong and weak elements of content, and why some images have contents which consist of weak elements only, some of both weak and st1·ong, and still others perhaps of strong alone, since it is claimed that one is entitled to assume such truths without explanation as primitive. We have to start from some point ; why not do so from the self-evident differences as between the various imme­ diate data? Likewise, the specific regularity of the course of perceptual images is also assumed as primitive, it being held that opponents also will have to assume ,som e such regularity without explanatio n, the difference being that the opponents assume that regularity for conje ctured outer objects, and the idealists, for the imme6

68

PROBLEMS OF GNOSIOLOGY

diately given contents of images. Such are the most important arguments of the idealists. Ontological idealism draws particular attention to the fact that since we can make reasonable conjectures about those objects which we do not see, do not touch, do not smell, etc., only by analogy to what we notice in those objects which we have seen, touched, smelled, etc., therefore it will be most circumspect and most correct to think not only of those objects which we see, touch, smell, etc. - that is, the outer objects of images - but also of all other objects that they are combinations of elements of contents (to which epistemological idealism confines itself). The additional argument in favour of that standpoint i s the obvious conjecture that certain unperceived objects exist in the temporal and spatial gaps between perceived (that is, seen, touched, smelt, etc.) objects and that these two worlds incessantly pass from one into another and vice versa. The relationship between seen, touched, etc., objects and u11seen, untouched, etc., objects is, in the view of ontological idealists, so close that once the former are recognized to be combinations of elements of content, the latter cannot be anything else. Obviously, ontological idealism usually pays for that harmonious unification with the necessity of renouncing subjectivism, understood as the thesis that any element of conte11t i s an element of content of someone's image. We say ''usually'' because there might be an ontological idealist who would maintain that every object is a combination of elements of content, but would not in the least assume the existence of an object that would not be an outer object of some image. More­ over, he might even assert that everything which has ever been noticed by anyone has been an object of someone's perceptual image. Yet in general, ontological , idealisn1 is associated with recognitio11 of the existence of objects at which no-one is looking, which no-one is touching, etc. Now to assert as regards such an object that it is a combination of elements of content of someone's image would be to admit the existence in relation to someo11e's image contents which are not seen, not heard, etc., even by the persons of whose image they are contents. The propounders of ontological idealism attempt to bridge the gap within idealist views between objectivism and subjectivism by treating those elements of conte11t of which, according to them, consist the objects that are not seen, touched, etc., by anyone, as ''potential elements of content'' of someone's images. For instance� that side of my watch at wl1ich I am looking but which

I am not touching consists

of the elements of conte11t of my visual perceptual image (light patches distributed in a ce1·tain way), and also of other elements of content (pressures, coolness, etc.) which are i1ot elements of conte11t of my image, but are ''potential elements o f content'' of a possible tactile perceptual image which

I would have if I took the

watch i11to my hand. This means that they might be elements of content of that tactile image ; in other words, should someone touch that side of the watch, his tactile perceptual image would have those elements as its co1nponents. On the other hand, the inside of the watch, its mechanism hidden behind the dial, consists exclu-

NOTIONS

sively of such ''potential elements of content''

69

of a11 i1nage, be they visual or

tactile. < 2 > B y contrast, epistemological idealism is usually associated with a clear tendency t o subjectivism. The epistemological idealist by-passes the issue of the structure of those objects which are not perceived by anyone, and expresses his opinion only concerning those objects which are being seen, touched, etc. ; he is usually inclined to believe that those objects co11sist exclusively of elements that belong to the con­ tents of their perceptual images. Moreover, we notice a certain extremism in sub­ jectivism - namely, a tendency to recognize those elements of content as something psychic. Do not, it is argued, those components of objects perceived, those colour patches, tunes, pressures, smells, tastes, hotnesses and coolnesses, possess the specific properties of something psychic? They can be perceived by that person, they are immediately given only to that person, of whose image they are elements of content : for they are always someone's elements of content, they are conditioned by the structure of the sense organs, etc. Hence they may well be recognized as something psychic, and called feelings ; hence also it may in turn be asserted that every object of a perceptual image i s a combination of feelings of the person who perceives it. 4.

REALISM VERSUS IDEALISM.

Yet idealism, whether objective or subjective, whether

ontological or epistemological, i s at variance with common sense, which usually adheres to realism. < 3 > And the latter asserts, contrary to idealism, that no outer object of any perceptual image i s a combination of elements of content, but i s something di fferent from such a combination of elements of content. Hence for a realist the thing perceived i s not to any degree identical with an ''inner picture i n the mind of the person who is perceiving it'' . On the contrary, a realist opposes those things which are being seen, touched, etc. , as reality grasped in images, to contents of images, as something which exists only in mind and is somehow related to that reality. A friend 's face, which he i s seeing, i s for a realist not in the least a configuration of colour patches, is i n general not a combination of elements of

content, and a

fortiori

is not a combination of elements of content of anyone's

image ; in particular, it is not a combination of anyone's sensations. Even if i t be true, argues the realist, (a) that a face i s swarthy, it does not follow i n the least that a swarthy tinge i s an element of it ; even if it be true that the full moon i s round, shining and goldish, it does not follow that the moon consists of the sensations of roundness, glitter, and goldish colour. He proceeds by saying (b) that the object seen and the content of someone's image o f that object are two d i fferent things ; this can immediately be see11 if we become observers of a person's image and, at the same time, of the object that person i s looking at. For i nstance we observe John who i s looking at a running horse. But that horse does not co11sist of elem.ents of the content of John's image : those elements are not there where the horse is, they are not galloping a score of yards away from John. There are realists who assert that an image together with its content exists in the head of the person looking. But the idealists rightly reject

70

PROBLEMS OF GNOSIOLOO Y

such an ''introjection'', or an inconsiderate location of content in the observer's head. But the realist does not need any introjection, for even if we do not want to risk the claim that the contents of the observer's image are in his head, we may calmly assert that they are not there where the horse is galloping, either. For they develop (he asserts, and the idealist cannot reasonably refute that) according to the state of John's visual organs which are located in his body. Does the horse really change its colour every ti1ne he appears to John lighter or darker, which depends on the colour of the objects it is running past? Does tl1e horse really increase or decrease in size according to the size of the area of John's retina which has been stimulated? Does the size of the horse double whenever John squints and sees two horses instead of one? All this pertains to the content of the image developed by John, but does not occur in the horse looked at, whose fortunes depend 011 many factors, but not in the least on the changes in the eyes and the brains of the persons looking. Thus, the object seen and the content of the perceptual image experienced by the looker at that object are two di fferent things. Should the idealist here i11terpose that nothing prevents the horse in question from being, while not a combination of elements of content of the image experienced by the looker, 11evertheless a combination of some elements of content, the realist will ask ''Whose?'' If the idealist specifies the person, the argumentation will be as above, since it is inessential whether someone believes that horse to be the content of an image experienced by John or by Paul. Anyhow, the idealist would have to explain how the adventures of the horse galloping far away from the person concerned, depend on the states and changes of that person's sensory receptors. This can hardly be accepted. And if the idealist replies that the component parts of the horse may be not elements of content of anyone's image, but simply elements of content not associated with any person, the realist will first state that his opponent is not a propounder of subjectivism, and next will protest against the assumption, peculiar to objective idealism, that there exist such elements of content not associated with anyone. He will do so because he does not know such elements from experience and does not see any reason to suppose that they exist. Moreover, he suspects that it would be absurd to assume the existence of tastes which no-one senses, smells which no-one encounters, colour patches which no-one imagines visually, etc. Of course, discussion is here concerned not with such physical stimuli as particles of volatile oils, a vibrating electromagnetic environment, etc., but with such alleged elements of content as tastes, smells, pressures, tunes, etc. But even the very peculiarities of t11e content of perceptual images prevent the realist from being converted to idealism. The first reason (c) i s that stamp of reality which is usually the attribute of such peculiarities and which is usually connected with some strong, intense nature of elements of content in the case of perceptual images, as distinguished from the derivatives. It does not suffice to rest satisfied, as the idealists do, with the explanation that there exist strong and weak elements, and that the former are usually accompa11ied by a stamp of reality, whereas the

NO"IlONS

71

latter are not. And when we try to explain why this i s so, it immediately seems self-evident that there is no better explanation than to assume that the elements of content of perceptual images owe their strength and the stamp of reality to the fact that they differ from the thing perceived - that is, from that to which they are

an

immediate response.

The presence of the thing perceived can, according to the realist, explain (d) the high degree of dependence of perceptual images on a free intervention by the person who experiences them.

A normal person can easily imagine fantastic things

if he guides his imagination in a given direction ; he can also easily recollect various things, if he wants to ; but in order to

see

the Eiffel tower, if he wants to see it, he

must go to have a look at it. In such a case it does not suffice to strain one's will ; one has to go to a specified place, raise up one's eyes, etc. This is obvious : we are masters of our fantasy, but we cannot so easily master those things on which the content of our perceptual images usually depends (the latter being here understood in the subjective sense, cf. p.

66 above).

The significant regularity (e) in the sequence of certain perceptual images also finds an explanation in the assumption of the existence of things which are per­ ceived (seen, touched, etc.), but are not combinations of elements of content. Whatever we do, dawn comes every day at a certain time and then at a certain time it grows dark ; a flash of lightning is followed by a clap of thunder after a certain interval ; and when we wake up after a sleep we find that the hands of our watch have moved in proportion to the time we have slept. Is this not so because those hands in fact move proportionally to time and because they exist objectively, and are not in any way contents of our images? And because the Earth (not any combination of elements of content) rotates around the Sun (which also really does not consist of anyone's sensations), and the light waves propagate much more quickly than the sound waves, and do so with complete indifference in regard of any contents of anyone's images. In particular, the inertial durability of the solids that surround us is said best to explain the perseverance of the contents of our everyday perceptual images. Every day, we see the same configurations of things, unless we rearrange the furnit11re in our fiat or take some other steps, not with respect to any contents, but with respect to things from our environment. Such are the arguments used by the realists against the idealists. Yet a common attitude towards idealism does not prevent certain controversies with realism, where we distinguish, above all, two groups of opi11ions called, re­ spectively, naive realism and critical realism.

5. CRITICAL REAi.ISM VERSUS NAIVE REALISM. The not particularly creditable terin "naive realism'' is being used in at least three meanings. In its first meaning, naive realism implies that ''images are copies of reality'' or, strictly, that the contents of perceptual images are copies of the outer objects of those images. In the second meaning, it holds that the objects perceived are always such as they appear to be to those who perceive them. In the third meaning, it maintains that perceivable

72

PROBLEMS OF GNOSIOLOGY

objects have, as their attributes, sensory qualities. We shall 11ow briefly discuss each of these three variations of ''naive realism''. As mentioned immediately above, according to the first variation the contents of perceptual images are to be copies or replicas of the objects perceived (seen, touched, etc.). The relation meant here i s that which is described by such compar­ isons as an original picture and its copy, or a face and its photograph. Like a paint­ er's copy or a photograph, the content of a perceptual image may be good or not quite good, so that we have to do with a replica which is better or worse, but is anyhow a replica. Critical realism, in its corresponding variation, raises here its objection by questioning the relation between original and copy. How do we ascertain, it is asked, that a given copy is a good copy of the original? We observe both the original and the copy, and develop perceptual images which have as their outer objects, respectively, the original and the copy. Now if and only if the contents of these two images are in certain respects the same, we say that the copy is good. Should the relation as between the copy and the original hold be­ tween a given perceptual image and its external object, then in this case too we should be able to ascertai11 whether the given content is ''good'' or not. But that we cannot do, for we can11ot observe the content of an image in the same sense as we observe an original and its copy. In that sense we can observe only the external objects of our images : only at them can we look, only them can we touch, only to them can we respond immediately with perceptual images that have definite contents. But should we even so extend the interpretation of the word ''to observe'' as to make conte11ts of images observable too, that method, the critical realist asserts, would have to fail : were it to be effective in the case when the copy is good, we should have to respond to the two objects observed together (the original and the copy) by images that have contents which in essential respects are the same. Now for a critical realist it is impossible to admit that the content of any image of the content of another image could in esse11tial respects be the same as the content of the image of the external object of that other image. To put it briefly, he believes that the content of an image cannot be compared by observation with the external object of that image, and that that content can11ot in any way appear the same as that external object ; the same applies to the tactile perceptibility of the content of tactile images, etc. This is so because the contents of images and the external objects of those images belong to entirely different worlds. Yet it would be difficult not to remark in this con11ection that in maintai11ing all this tl1e critical realist ultimately assumes what he was supposed to prove - namely, that there cannot be sufficient likeness between tl1e content of an image and the external object of that image, and that it would be superfluous to consider the possibility of cl1ecking whether a given content is a ''good'' copy of a11 external object or not. For the naive �alist (in the sense now being discussed) does not claim that the contents of per­ ceptual images happen to be, or usually are, or always are good copies of the external objects of those images ; he merely states that they are copies ; moreover, the relation

NOTIONS

73

as between copy and original might hold even if it could not be confirmed by obse1·­ vation . and comparison.

naive realism in the second interpretation and critical realism in the second interpretation. As mentioned

We shall now have to reflect on o n its antithesis - that is,

above, the former suggests that the external objects of perceptual images are always such as they appear to be. The latter denies that. In detail, the arguments adduced by the critical realists against naive realism so understood are approximately as follows :

(1) The formation of given elements of content depends on the persons perceiving, for i f an athlete lifts a 20 kg weight, his perceptual image includes the element of a mild tension , whereas if the same weight i s lifted by a young boy his perceptual image include s the element of an intense effort. (2) A given person develops a certain element of content i n accordance with chemical changes within his body : the person who has taken i n some santonin sees everything yellow, and the person who has had an effusion of bile has the i m­ pression that everything he tastes is bitter.

(3) One and the same person develops in his perceptual image eleme11ts of content which depend on elements of content i n his other previous or simultaneous images. For instance, there i s the Jaw of simultaneous contrast which consists in that, for instance, when two complementary colour patches are placed side by side, the colours seem to be more intense - for example, green seems more green, and red more red, than the colour patches which are viewed separately. The law of subsequent contrast is also at work. If we first look at something which i s bright red i n colour, and then at a sheet of paper which normally seems white, the content of our image will include not white, but green colour. Likewise, if we look for a long time at the flowing waters of a river and then shift our eyes to the bank, we shall see, contrary to expectation, that the bank (apparently) moves in the opposite direction. Thirdly, the contents of our perceptual images are subject to what is called adaptation - that is, when a stimulus preserves its intensity, the sensation weakens after some time (this applies, for instance, to pressures and smells). Fourthly, elements of content which are genetically reproductive, and as such are based on memory, coalesce so strongly with those elements which i n the content of a perceptual image are genetically perceptive, that they result as it were i n alloys, so that new elements of content result from the synthesis of the two. An example of such a synthesis is o ffered, for instance, by the content of a perceptual auditory image formed when we are listening to someone talking ; this explains why i n our native language we are able to understand even very indistinct pronunciation or the words spoken by an actor wl1ich reach us only in fragments, and why a foreigner, even if he has a book knowledge of our language, finds it at first very difficult to understand \vhat is being said on the stage. In the former case, the content of the perceptual image is combined with

elements retrieved from memory and a whole is formed, of which the listener i s

PROBLEMS OF GNOSIOLOGY

74

a co-author. In the latter case, actual perceptual image is not so completed by past experience. That is why, also, we find it easy to read in our native language, and difficult in a foreign language, and we find it much easier to read a certain text for the second time than for the first. This guesswork goes so far that when we are listening or reading we put correct sounds or letters in the place of wrong ones, actually spoken or written, and when we are reading proofs we therefore leave printing errors unnoticed. The present author, after twenty years of friendship with a person who used often to repeat a Polish proverb in which the surname ''Kornacka'' occurs, realized with extreme astonishment that that was the real sound of that surname, since it had always seemed to him that it was ''Kownacka'' (the difference of pronunciation in Polish being much greater than it would be if these two words were spoken by an English-speaking person who does not know Polish).

A different kind of a synthesis of what is perceived

with what is remembered is the way in which people see three-dimensional objects : there is a marked difference between those who, born blind, have been restored to sight following an operation, and those who have always enjoyed normal sight. The former see some flat patches which seem to be just in front of them, whereas the latter have the feeling of three dimensions and of distance as elements of the contents of the corresponding perceptual images. Psychologists explain it by a synthesis of purely visual sensations with tactile and muscular sensations resulting from the movements of the eyeballs and similar tactile and muscular sensations which we experience when we handle three-dimensional objects aro11nd us. (4) It is argued, in connection with the objections already raised, that the same thing- for example, a drawing - looks different to us according to the way in which we concentrate our attention on it, which in turn depends both on our wishes and aspirations and on our habits. If we concentrate our attention appropriately, we see water in the river as flowing, and the bridge as standing unmoved; if we con­ centrate attention in a different way, it seems to us that the bridge is moving and the water is standing still. The same cloud seems to us to be a boat with sails or a winged angel. In the same two-dimensional drawing of a cube one person sees only a com­ binatio11 of lines on a plane, another person sees a solid turned askew to the left, and still another, a solid turned askew to the right. In every image, percept11al images included, the content seems to be shaped somehow, according to our attitude, and hence, the critical realist argues, it would be difficult to consider that specific shape of the content of an image to be an attribute of the object perceived.

(5)

But the naive realist is really at a loss when he has to defend his position

against the penetrating arguments which the critical realist draws from the psy­ chological law of ''the specific energy of the senses''. That law states that the content of a perceptual image depends on the kind of sensory receptor. If one's eyeball is struck strongly, one ''can see the stars'' (which is the Polish saying describing the specific visual sensations caused by a direct irritation or stimulation of visual recep-

NOTIONS

75

tors), which implies that one will have certai11 visual sensations ; if one is struck strongly on the ear, one will hear sounds. Conversely, if the eye is stimulated by electric current, or struck, or irritated by light, in all these tliree cases we respond with elements of content which include light as their component. If the tongue is stimulated with electric current, we feel an acid taste, as if the tongue had been irritated by some acid liquid. In general, a given stimulus, when applied to different organs, induces different elements of content in the perceptual image, and different stimuli, when applied to one and the same organ, induce different elements of content, too. How then could such or other elements of content be attributed to the external object itself? In recent times, that argument played an important role in propagating the critical realist approach among the natural scientists. The law of the specific energy of the senses is also known as Johann Miiller's law, and Helmholtz, the eminent physicist and physiologist, based on it the justification of his critical realist approach. (6) The elements of content of a perceptual image also depend on the exact spot at which and the way in which a given receptor has been stimulated, so that the same object appears in different ways, according, for instance, to the angle at which i t is seen - that is, according to the area of the retina stimulated by the light rays that come from that object, and according to whether the mapping of the object being perceived, as formed on the retina, is distinct or blurred. A more remote ob­ ject, which in fact is greater than the closer one, seems to be smaller than the latter ; of two circles of the same size the white one will appear greater than the black one (probably because of irradiation or stimulation by light which radiates upon the neighbouring points on the retina from those places on the retina on which light from the circle falls). (7) Finally, the environment through which objects are perceived, is not indiffer­ ent. The sun, as seen through dust and mist, seems to be red ; a distant forest, seen through a thick layer of air, appears blue ; when we are looking through dark glasses everything looks dark, too, etc. And after all is the entire nervous system which works as receptor not an element of the environment that separates an external object from its perceiver? May we not legitimately compare our eyes, ears, etc., with coloured spectacles which, according to their colour, make things appear to be this or that while they are not so in fact? Naive realism in the third interpretation asserts that sensory qualities are attri­ butes of perceivable objects. To understand that we must consider the meaning of the formulation given above. Reference is made there to perceivable objects. Now by a perceivable object, we understand in this case an object which is being perceived (seen, touched, etc.), and as such is the external object of some perceptual image, or (because this is assumed too) which while not being actually perceived might be perceived (as a stone which is not being touched might nevertheless be touched). But what is meant by the statement that a given element of content is an attribute of a given object? For instance, there is said to exist an element of content

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which is called lustre, and when we say that lustre is an attribute of a mirror, we say simply that a mirror i s lustrous ; there i s said to exist an element of content called whiteness, and when we say that whiteness i s an attribute of snow we want merely to say that snow is white ; there i s said to exist an element of content called coldness, and when we say that coldness is an attribute of ice we want only to say that ice is cold. The formulations to the e ffect that the mirror is lustrous ; snow, white ; ice, cold ; do not mean i n this case that the mirror when being looked at evokes lustre in our imagination, that snow when being looked at evokes in us the feeling called whiteness, that ice when being touched evokes, in the person who touches it, the content called ''coldness'' ; they mean, according to the speaker's intention, that the mirror i s lustrous ; snow, white ; ice, cold ; i n the same way as, for i nstance, the Earth is spherical, the horse I am riding is animate, and the stick i s inanimate. The word ''is'' plays here the essential role, not being an abbreviation of anything. In general, ''The element of content e is an attribute of the object O'' means the same as ''The object 0 is E'' (where the relation between ''E'' and ''e'' i s the same as between ''lustrous'' and ''lustre'', ''white'' and ''whiteness'', ''cold'' and ''coldness'', etc.). And since elements of content, either all or, more frequently, those which are essential or basic, have come under the impact of their most common, psychological, interpretation, to be called ''sensory qualities'', therefore we may often encounter the statement, formulating the opi11ion held by the naive realists, that ''sensory qualities are attributes of external objects''. By external objects in this case are meant perceivable objects in the sense outlined above. This yields the formula : ''Sensory qualities are attributes of perceivable objects. '' That view i s often described as ''recognition of objective importance'' (or, in a different terminology, objective value) of se11sory qualities. In further analysis, however, we prefer to eliminate that inessential psychological tone and to use the formula which i s more pertinent to the whole of that type of realism - that is the formula : ''Elements of content are attributes of perceivable obj ects." This is opposed by critical realism in the third interpretation. It is claimed that it is not true that elements of content are attributes of perceivable obj ects. The arguments need not be adduced here in any greater detail, since we should have to repeat those which have been described above in the discussion between critical and naive realism in the previous interpretation. They can be reduced to attempts to justify the assertion that the contents of our perceptual images depend not only on what i s the external object of a given image, but also on the state and condition of the perceiving person, and this i s believed to be sufficient circumstantial evidence to prove that no element of content can be an attribute of any object, even that actually being perceived, not to me11tion those which are merely perceivable. Con­ sequently, i n the eyes of a critical realist a lemon, whether one being perceived by someone or 011e closed i n a case, i s yellow in the (physical) sense that if sunshine falls on it then it will absorb other rays and will reflect only rays of a certain wave.; length, and also in the sense that whoever is looking at it has i n the content of his

NOTIONS

77

image the element, yellow colour, though it is i1ot yellow in the essential se11se, analo­ gous to that i n which we say that it i s oval or ripe. Moreover, many critical realists are of the opinion that i n general no-one ever states about a11ything that it is yellow,

i n such a mysterious third meaning of the formulation ; a fortiori, he cannot admit that we encounter true statements to that effect. On the contrary, i11 the opinion of a critical realist, external objects have, as their attributes, such objective properties as definite extension i n space, definite duration, definite movements, definite mass, definite distance from other external objects . Thus, tl1e lemon i n questio n is oval, became ripe a month ago, i s now rolling on the table, weighs fifty odd grammes.

In

general, according to the critical realist, external objects have geometrical and

physical properties - more strictly : spatial, temporal, and dynamic. Critical realism thus sees an abyss of difference between two groups of subjective complements predicated about external subjects : between the subjective ones, such as ''yellow'' and ''acrid'', and objective ones, such as ''one foot long'', ''weighing five grammes'', ''vibrating'', ''ripe'', etc. The former can only apparently be predicated about external objects i n true sentences, whereas the latter can truly be predicated about them i n fact. For the sake of caution, attention must here be drawn to the systemic ambi­ guity of numerous subjective complements, wl1ich i n one sense belong to the for111e r, and i n the other, to the latter group. For i nstance, we have a feeling of pressure which ;ve experience when we lift a solid by hand. But that solid has a weight of its own, which presses our hand i n conformity with the well-known gravitation formula. The realist will say that although i n both cases we put it that the given solid is ''heavy'' (or very heavy, or heavier than some other solid), a dis­ tinction must be made here, because i n the former case we refer to a subjective property, and i n the latter, to an objective property. The same applies to shapes. The same wording is used to ascribe to an external object both a sensory quality, a subjective property (as we experience certain elements of content), and an objective property. For there are said to exist such impressions of shape, impressions of size, etc. , as there exist colour patches, tastes and smells. Their nature can perhaps best be grasped when we compare them with impressio ns of time. We feel how long the various objects have existed ; we have, as it is expressed, i 11tuition of time ; in some persons it i s even extremely acute. And yet these are two quite different things : to say that something was longer ago than something else, and to say, in the same words, that more time has elapsed, i n the physical sense of those words, from the former than from the latter. The same is alleged to 11old for spatial impres sions as distinguished from objective geometrical properties . If that distinc tion is not suffi­ ciently clear for anyon e, let him realize that the distance between the Eartl1 and the Sun i s some 1 50,000,000 kilometres, and that the giant Jurassic reptiles became extinct millio ns of years ago : n o specific impre ssions i n the conte11t of our images corres pond to those distances i n space and time. Whe n we tl1ink of them we have certain quite misle ading impr essio ns of great distance and some equally naive impressions of the

PROBLEMS OF GNOSIOLOGY

78

remote past, which we experience when we look at very distant objects and recollect very old events. Now, critical realists have i n mind those objective geometrical properties when they oppose geometrical (including physical) properties to sensory qualities.

6. EPISTEMOLOGICAL AND METHODOLOGICAL PHENOMENALISM.

yet precisely at that

point critical realism encounters an attack by phenomenalism, which i n the last analysis is also a kind of realism, though it is even more critical than critical realism as discussed above. It is a realism, since i t recognizes the existence of obj ects which are not combinations of elements of content - that is, external objects ; it is ''more critical'' than critical realism since i t refuses objective validity even t o those subjective complements which are accorded such validity by critical realism. It i s the last resort of combatted ''naiveness'' - subj ective complements referring to space, time and movement - that falls a victim to critical analysis. Phenomenal­ ism questions that allegedly essential di fference between those subj ective com­ plements and those corresponding to sensory qualities, if that difference were to consist in an objective validity of the former and the lack of such validity in the latter. Empirical phemomenalism sees counterparts of the wholes consisting of certain visual and tactile elements of content even i n those subjective complements, referring to geometrical and dynamic properties, which are objective for a critical realist. In doing so phenomenalism o ften resorts to ''potential'' elements of content. In this way, such subjective complements as ''by ''extinct i n the Jurassic epoch'', ''weighing

1000

1 50,000,000

kilometres distant'',

kilogrammes'' would, according

to that opinion, misleadingly suggest that some combinations of elements of content are attributes of those objects to which such complements refer. Since, however, elements of content are subjective, such complements also cannot have objective validity and may not be predicated truly about external objects. On the other hand, a

priori phenomenalism, in the Kantian style,

does not consider spatial, temporal

and dynamic properties to be sensory qualities or syntheses of sensory qualities. The propounders of that trend i n epistemology believe that certain elements of con­ tents of our perceptual images develop as a result of experience - that is, as a result of the influence exerted o n us by external objects, colours, tunes, tastes, etc. - where­ as some are developed, as it were, by the perceiving person himself, since he adds them to the content of tl1e image as a result of his own structure. These are said to include : ordering i n space, ordering in time, and causal, that is, dynamic, rela­ tionships. In the terminology of that school it i s said that space and time are ''sub­ jective forms of the phenomena'', and their subjective nature i s proved by pointing to the fact that truth about spatial and temporal relations i s acquired, i n the field of the appropriate disciplines (geometry and arithmetic), by reflection alone, without the need to see or touch anything. Be that as it may, that variatio n of phenomenalism also denies to external objects the possession of spatial, temporal and dynamic properties. What then, from the phenomenalist point of view, may truly be pre­ dicated about external objects if these do not share even tl1ose properties which

',

NOTIONS

are

79

accorded them by critical realism? Nothing is left at all. At1d the phenomenalists often, i n trying to be consistent, assert just that, thereby admitting agnosticism with respect to the external objects : they maintain tl1at external objects cannot be known, and nothing can truly be predicated about them. It would seem therefore that for a phenomenologist science cannot exist. But this is not so. He agrees that he would have to draw such a desperate conclusion if he thought that scientific statements pertain to external objects, ''things in them­ selves''. But i n fact, in his opinion, they pertain only to plienomena. By a "phe­ nomenon'' we usually mean the same as by an ''event'', pl1enomena (events) being opposed to things (solids, bodies, persons). But in the pl1enomenalist terminology a ''phenomenon'' means something else : it is opposed to an external object, or the thing i n itself, to something which exerts influence upon the perceiving person. And a phenomenon is understood as something that consists of elements of content. A priori phenomenalism adds that a phenomenon is shaped by the mind of the perceiving person, wl10 has grasped those elements in an appropriate form (he has mentally ordered them in space and time, etc.) and has thus, as it were, become the co-author of that phenomeno11. For a Kantian the objects of scientific research are the work of the researcher's mind, and he11ce reference is often made to the ''Copernican revolution'' which Kant was supposed to perform in epistemology. An ''anti-Copernican revolution'' would be a more appropriate term, since Kant introduced, rattier than eliminated, a specific anthropocentricism. Thus, for a phenom­ enalist science is possible ; what is impossible, is scientific metaphysics. Strange, indeed, has been tl1e fate of that word - metaphysics. In one of the old­ est, ancient Greek editions of Aristotle's works certain books, of varyi11g content, were placed after his studies in natural science - that is ''after the physical ones''. From the Greek -ra µs-r:a ra But, first of all, what is the association of images? Now if a person experiences an image with a certain content together with another image with another content, especially if that occurs several times, then that person, on experiencing once more an image whose content is more or less identical with the content of that former image, develops a tendency to experience once more the image whose content would be more or less identical with that of the latter image. The sound of the siren recalls to us the picture of a ship, the sight of the face of a friend of ours makes us imme­ diately recall his name, the smell of a box shrub recalls to our view the courtyard where we often used to be and where we were conscious of such a smell. Aristotle, the first European psychologist, noted the law of the association of images and tried to reduce all such associations to similarity, contrast and contact. Appreciation , of the fact that contrast is a special case of similarity (since the opposite, ter111i nal elements of a series recall one another simply by their ter111inal position) and dis­ tinction as between contact in space and contact in time led to the later classification of all associations of images into associations by similarity, by contact in space and by contact in time. Examples of the first are provided by the numerous rhymes which come to a capable versifier's mind when he hears a given word. Association by contact in space occurs when, for example, a well-known mon11ment is associated with the sight of the surrounding trees which appear in the same field of vision. Finally, the examples given above of the so11nd of a siren, the name of a friend, and many others may serve as illustrations of the association of images by contact in time. It seems that all cases of association can be explained by contact in time. For if an association occurred following a contact in space in a field of vision or a field of hearing or a field of tactile sensation, then both elements associated with one another must have been seen, heard or touched at the same time. And if the image of the object A has become associated with the image of the similar object B, then (as it is claimed by those in favour of the reduction of all the types to contact in time) there must be some element C con1mon to both these images, since otherwise '

IDEAS

91

they would not be similar. Hence the image of the object A may be considered to be the image of some CD, and the image of the object B, the image of some CE. Now D is contemporaneous with C and the latter with E, so that D is associated with E by the reiterated relation of contemporaneity. If, for instance, A, the view of John's face, recalls to someone B, the view of Peter's face, who resembles John by the cut of his mouth, then that cut of the mouth, common to both, plays the role of that C which is being perceived contemporaneously with D, the remainder of John's face, and contemporaneously with E, the remainder of Peter's face. Hence these ''remainders'' are associated with one another, too. This takes place indirectly, through the intermediary of C, for apart from direct associations there are also indirect ones, when the first image is associated with the second, the second with the third, and as a result the first becomes associated with the third. It is super­ fluous to add that longer chains of associations may form, too. It is interesting to note that it often happens that when the first image recurs, then our imagination switches not to that which is directly associated with it, but to some remoter link in the chain, with the omission of the intermediate ones, which do not stand out in one's memory. The psychologists explain that phenomenon either by the fact that the apparent gap is filled by some stimulation of the physiological traces of the latent links - a stimulation which suffices to evoke furtl1er links - or by the supposition that the intermediary links were repeated, yet not in one's consciousness, but in subconsciousness. We should have an example of such a latent intermediary link, if a person who recalled the Houses of Parliament in London were directly to develop the auditory image of sound of Big Ben ; the suppressed link would be the visual image of Big Ben. But enough has been said about the general mechanism and the special cases of association of images. Let it rather be emphasized that not only images associate with one another, but other psychic experiences (certain specific moods, etc.) can associate one with another and with images as well ; moreover, arrested and performed gestures may join the association pattern, too. The ability to train animals may be explained by developing in them such mixed associations. The vast expanse of the field to which the laws of association of images pertain, and the plenitude, variety and length of the chains of associations explain the fact that a special trend, called associationism, has developed ; its representatives have attempted to expla.in the course of psychic events above all by the laws of association of images. Thus David Hume ( 1 8th century Scottish philosopher, cf. his Enquiry Into Human Understanding), referring to the frequent observations showing that a given effect follows a given cause (for example, a ball, when struck, moves), explains the emergence of the conviction that there is a connection between cause and e ffect, a connection which he describes as ''necessary consequence''. Likewise Herbart (German philosopher, author of Psychologie als Wissenschajt, 1 824) attempts to base recommendations for rational teaching methods on the laws of association of images, and builds on them as it were the whole mechanics of the manner in which definite contents drag in another contents.

92

PROBLEMS OF GNOSIOLOOY

Now the fact that linguistic phrases have meanings is explained by the associa­ tionists by the association of images. ''A word or a phrase means this or that'' is for the associationist the same as ''Such and such images have become associated with the sound or picture of that word or phrase.'' Thus, according to that opinion, the meaning of the word ''storm'' includes images of lightning and thunder, elements combining to form the picture of a violent wind, etc. And since a given person has with the sound of that word developed associations other than those developed by other persons, therefore a given word means for one person something different from what it means for another. But, since in a group of persons speaking the same language, associations become fixed which are very similar in their composition, hence people can distinguish that which is common to them. This, as it were, public component of individual meanings forms the meaning of a given phrase ''in the language of a given nation'' . To explain ambiguities in a given ethnic language or the cases of polysemy of words belonging to di fferent languages which a given person speaks alternately, one has to refer to the fact that the combinations of contents associated with a given phrase vary according to what the speaker is concentrating upon or according to the context in which a given phrase occurs. When we hear the words ''the shoemaker's last'.', we associate with ''last'' the image of a wooden device used in making shoes, but when we hear the words ''the last will'', we associate with them the image of a docu­ ment, the idea of imminent death, possibly the office of the executor, etc. But it is difficult to agree with the associationists when they claim that the meaning of a word and the content imagined and associated with that word are one and the same. For it seems fairly certain that English-speaking people usually associate with the word ''thunder'' not only an auditory picture of a cacophony of noise, but also a visual picture of a sudden flash ; likewise, with the word ''lightning'' they often associate not only that visual picture of a sudden flash, but also an auditory picture of a cacophony of noise. And yet everyone will admit that the meaning of the word ''thunder'' does not include that visual content, and the meaning of the word ''lightning'', that auditory content. The decisive factor is that which we want to communicate by means of the word in question. When we say that ''it thunders'' we want to say that there is specific noise in the sky, and not that there are flashes in the clouds. And conversely, when we say that ''it lightens'' we want to say that there are flashes in the clouds, and not that there is a specific noise in the sky. It would be difficult to deny that with the word ''bird'' we associate, as a rule, the image of a vast space with an object flying high in the air. But the sentence ''Penguins are birds'' does not mean in the least that penguins are accustomed to fly high in the air ; hence the property of flying high in the air is not an element of the meaning of the word ''bird''. A fortiori, an inner picture of something flying high in the air is not such an element. In general, when a person says that meanings consist of properties, we are ready to take that as truth, with the assumption in favour of the speaker that a correct idea is concealed behind the metaphorical and hypostatic

IDEAS

93

form of the statement. But when we are told that meaning consists of inner pictures associated with a given word, we cannot find any correct idea in that formulation. A11d that is how the associationists usually put it. In our opinion, the mechanism of association of images and of formation of associations in general plays an extremely important role i n the formation of the semantic function of languages, but neither suffices to explain everything in that field, nor is the essence of that function. A given phrase means that : it is so and so - is the same as : a given phrase can adequately be used to communicate to someone the idea that it i s so and so (cf. p. 6 above). In particular, the properties a, b, c constitute the meaning of a given term is the same as : a given term may adequately be used as a sub­ jective complement in a sentence intended to communicate to someone the idea that a certain object has the properties a, b, c. To put it briefly, reference to the intention to communicate something, reference to the fact that a given phrase is adequately used to communicate something - for example, to predicate something by means of a given term - belongs to the essence of meaning. The fact that a given content of an image associates with a given word does not in the least prove that we want to communicate that content by means of that word, or that we want to predicate that content about an object by means of that word (for what would be meant by ''to communicate some content of an image'' or ''to predicate some content of an image about some­ thing''?). It al'io does not in the least prove that we want to predicate by means of that word some property of being such as would correspond to that content. That i s why ''the meaning of the phrase 'A ' '' and ''the content of the image associated with the phrase 'A ' '' are not equivalent terms. And since we have agreed that ''the meaning of the phrase 'A ' '' is the same as ''the content of the concept corresponding to the phrase 'A' '', we must conclude that ''the content of the concept corresponding to the phrase • A' '' and ''the content of the image associated with the phrase •A' '' also are not equivalent terms. I11 particular, with reference to terms it is true that ''the content of the image associated with the term 'A ' '' di ffers from ''the content of the concept corresponding to the term 'A ' '' (that is, ''the meaning of the term 'A' ''). So much about associationism and its encroachments into semantics and hence, indirectly, into the field of analysis of the term ''the content of a concept''. 1 0. THE OBJECT OF A CONCEPT. When passing in turn to ''the object of a concept'' we must state that that term, used in discussing the concepts corresponding to terms, is endowed with different meanings. Frequently, (1) ''the object of the concept of man'' is interpreted as ''man in general'' - that is, as the universal corresponding to the term ''man''. In general, the object of the concept of M is interpreted as ''M in general'', or the universal corresponding to the term ''M''. On the other hand, (2) in the case of singular terms the object of the concept corresponding to a given term i s interpreted to be the only designatum of that term. Thus, for instance, the object of the co11cept of Paris would be, in that interpretation, the city of Paris itself. That phrase is also used in the sense (3) that the object of the concept corre­ sponding to a given term is each of its desig11ata (of course, with respect to a given

94

PROBLEMS OF GNOSIOLOGY

meaning), so that if a given term in a giv·en meaning 11as many designata, then there are many objects of the corresponding concept. In that interpretation, every criminal is an object of the concept of criminal, and there are as many objects of the concept of criminal as there are criminals, past, present and future. But there is still another interpretation (4) of the object of a concept - namely such that the object of the concept corresponding to a given term is that about which we speak when we use that term as the subject in a sentence. In many cases, the object of a concept, so understood, is identical with the object of a concept understood as the designatum of a singular term ; for instance, when a person says ''Paris lies on the Seine'', the designatum of the term ''Paris'', used in that sentence, is precisely that city and the sentence refers to that city. But when it is said, for instance, that ''Jove is the king of Olympic gods'', then these two meanings diverge : the terin ''Jove'' is empty, has no designatum, since there is no object about which it could be predicated truly and literally that it is Jove ; and yet to the question as to what a person speaks of when he makes such a statement we shall obtain the answer, which in a sense is correct, that l1e speaks ''about Jove''. Evidently that which is spoken about is u11derstood to be some "intentional object'', something to which the speaker somehow refers in a way similar to that in which he refers to ''what he imagines'' (that phrase being interpreted in the immanent sense, cf. p. 64 above). Thus, here, the object of a co11cept is interpreted analogously to the immanent object of an image. It is said in that immanent sense that, for example, "the red swan is the object of a productive image which I am experiencing now'', and in the analogous intentional interpretation as applied to concepts it is said that ''Jove is t11e object of a concept''. The similarity consists in that as a rule empty terms are quoted as the names of such alleged objects - the immanent object of an image and the inten­ tional object of a concept. The difference lies in that to the question, what is the immanent object of an image, I am told that such is what I am imagining (in the sense recorded on p. 64 above), and to the question, what is the intentional object of a concept, I an1 told that that is what I am thinking about (in the sense in which I am thinking about Jove when I say ''Jove is the king of Olympic gods''). One remark more : ''that which is referred to'' in a given sentence often means just ''the designatum of the term which is the subject of that sentence". With that interpretation, we come back to the third interpretation of ''the object of a concept''. A special case of the intentional objects in the sense of ''that about which one is thinking'' is, according to some philosophers, the class of certain specified objects (5). When we reflect on general sentences, for1nulated after the scheme ''all M are N'' (or ''every M is an N'', or briefly ''M's are N's''), then to the question, to what do they refer, we obtain an answer which seems to be natural : ''They refer to M's". Hence the incautious conclusion that the intentional object corresponding to the term ''M's'' is the class of ''M's'', the term ''class'' being here treated not as an ono­ matoid, yet understood not as a whole of which the various i11dividuals are parts�

IDEAS

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but as something else, such that when we refer to it we indirectly refer to each individual embraced by it. Now, for instance, when it is said that ''Birds are ver­ tebrates'', the a11swer to the question, to what does that sentence refer, would prob­ ably be ''To birds'', or, in a more erudite form, ''To the class of birds'', and ''the class of birds'' would be considered here to be the object of the concept of ''birds'' . And the class would here be interpreted not as a whole of which each bird is part, but as something else, such that when one refers to it one thereby indirectly refers somehow to each bird (in this case, one states that a bird is a vertebrate). Moreover, the distinctio n between ''the content of a concept'' and ''the object of a concept'' is not al\vays scrupulously respected, so that we may encounter cases in which the formulation "the object of a concept'' is used in the sense of ''the conte11t of a concept'' (6), which contributes still further to the ambiguity of the term ''the object of a con­ cept''. In view of that ambiguity, we should recommend, unless special reservations are made in special cases, one of the interpretations described above - namely, that according to which the object of the concept corresponding to a given term i s any designatum of that term. If the term is empty and has no designatum, then the corresponding concept has n o object, nothing is tl1e object of such a concept. Such terms as ''centaur'', "Hephaestus'', ''active volcano in England'', etc., can serve as examples. If a term has many designata (with respect to the same meaning), then the corresponding concept has many objects, for instance ''man'', ''bird'' or "criminal''. If the term has only one designatum, then that designatum is the only object of the corresponding concept - for instance ''Paris'', ''Julius Caesar'', "the Earth''. The interpretation of tl1e phrase ''the object of a concept'' as adopted above is the third o n the list analysed previously ; the second is its special case, but we see no reason to use that phrase in so narrow a sense. On the other hand, the remaining interpretations differ from these two since in many cases it is said ''N is an object of such and such concept'', although 11othing . is an N and the statement is not to the point. As we already know (cf. p. 36 above), universals do not exist. But the same applies to such alleged objects of concepts, such alleged objects, to 'vhich it is said that references are made, as ''Hephaestus'', "active volcano in England'', etc., and, in general, in many cases the same further applies to what i s called "intentional objects''. This is obvious, especially when the subject of a given sentence is marked by an inner contradiction, as in the case of the sentence "The son of the childless mother was born in 1928 ''. And the fact that ''reference is made to them'' does not suffice to admit that st1ch objects exist, although one may easily succumb to sucl1 argumentation as follows. When John is thinking of Hephaestus, he is in a certain relation to Hephaestus, as when he is leaning against a railing he is in a certain relation to that railing. If that is so, then there must be something to which he is in that relation, hence, the railing, when he is leaning against it, and Hephaestus, \Vhen he is thinking o f him. We can free ourselves from that illusion when we realize that we are using •

•

96

PROBLEMS OF GNOSIOLOGY

here non-literal, substitutive formulations. ''To refer to the M'' or ''To refer to the M's'' is the same as ''to pronounce comprehendingly the term 'M' as the subject of a sentence'' (''M is N'', ''all M 's are N's'', etc.). So much for the alleged ''inten­ tional objects''. And as concerns in particular the ''classes'', we have here to deal, in the case of the interpretation described above, with some kind of onomatoid, the proper role of which should be explained by a definition in use by those authors who use that term in such an enigmatic sense. Instead of ''the object of a concept'' we may say ''that which is represented con­ ceptually'', and instead of ''this i s the object of tl1e concept which John has'' we may say ''John represents this to himself conceptually''. Now the question arises here as to whether one imagines all that which one represents to oneself conceptually. The answer is emphatically, No. This is obvious, above all, in those cases when a given object is represented conceptually as one of the many designata of a general term. For instance, I understand the term ''a drop of water'', and hence every drop of water, as the designatum of that term, is thereby an object of my concept of the drop of water, is somehow co11ceptually given to me, and I somehow represent it to myself. But I certainly do not imagine every drop of water ! That is why, whenever there is a controversy as to whether all that is represented conceptually is always imagined, that controversy practically pertains only to those cases in which reference is made to a concept corresponding to a singular term or some other term treated as if it were singular. For instance, I visualize the Eiffel tower, and hence I imagine it reproductively. But at the same time I understand the term ''the Eiffel tower'', I understand what it means, and hence I conceptually represent to myself the designatum of that term, that is the tower i11 question. Thus, in this case what is conceptually represented is also imagined. But is it always so? Not in the least. I am bending over the map, I see a circle near a line, and the inscription ''London'' . I understand that term and at this moment I represent to myself that city concep­ tually, but I do not imagine it at all. Instead of London I imagine, perceptively in this case, that circle on the map, which is accompanied by the feeling, rather mysterious as to its psychological composition, that properly speaki11g the circle is not London, but it somehow corresponds to London, etc. Likewise, when I hear the words ''La Marseillaise'', and I hear them comprehendingly, I conceptually represent to myself that well-known song, but I do not hear it, nor do I recall it auditorily ; in general, I do not imagine it at all. The role of the substitute for the image of ''La Marseillaise'' is played in that case by the image of the word itself, which is its name, also surrounded by an aura of feelings with a complicated psychological structure, feelings of differences, unity, directional trends, etc., which we shall not analyse here. The reader interested in those proble1ns is referred to Twardowski's paper On the Essence of Concepts < 2 > and is encouraged to think over the penetrating suggestio11s contained therein. We shall rest satisfied, in view of the examples given above, with the state1nent that what is represented co11ceptually need not necessarily ¢

IDEAS

97

be imagined. On the other hand, it seems that reverse situations occur too : we see something, hear or touch something, or imagine something reproductively, and yet do not represent it conceptually, because we do not comprehend some term. In such a case we imagine that something, but do not represent it conceptually. 1 1 . RELATION BETWEEN THE INTENSION AND THE E XTENSION OF A CONCEPT. The relation between the intension and the extension of a concept is supposed to be governed by the law which states that whenever the intension increases, the exten­ sion decreases, whenever tl1e intension decreases, the extension increases, and conversely, whenever the extension increases, the intension decreases, and when­ ever the extension decreases, the intension increases. Yet that temptingly simple formula conceals several traps. First of all, let us bear in mind that scholas­ tic logic, when referring to concepts, means terms, that is, appellatives, which can occur as subjects or subjective complements in sentences, or else means some semantic correspondents of those terms, which are moreover treated as universals or something of that kind. In any case, it refers only to terms, and not to any phrases. The use of the words ''extension'' and ''intension'' might be broadened so that they would cover not only terms, in conformity with the interpretation of the word ''concept'' outlined above ; but in the traditional approach the thesis quoted above, apparently formulated so as to refer to all kinds of concepts, in fact pertains only to term concepts. But even when so restricted it is not correct in toto, and above all it is not cleat. For \Vhat is meant by the statement that the intension, or the ex­ tension, of a given concept increases or decreases? We know already that both ''intension'' and ''extension'' are onomatoids, and that, strictly speaking, such objects do not exist. If then we are not to reject the entire formula, we must guess behind it a dictionary of substitutive formulations, with respect to which it would no longer be a description of illusions. Sucl1 a dictionary is used. A part of it has been given above (cf. p. 14). Moreover it is said that a given term has its extension if at least one object is its designatum. Thus, for instance, there is an extension of the term ''sparrow'' since at least one object (in this case of course much more) is its designatum ; but there is no extension of .the term ''phoenix'' since no object is its designatum. If the extension of the term ''M'' is greater (broader) than that of the term ''N'', that means that every object which is a designatum of ''N'' is also a designatum of ''M'', and moreover at least one object which is not a designatum of ''N'' is a designatum of ''M''. For instance, the extension of the ter1n ''vertebrate'' is greater (broader) than the extension of the term ''bird'', because every bird is a vertebrate, but in addition there are vertebrates which are not birds. Conversely, the extension of the term ''bird'' is smaller (narrower) than that of the term ''vertebrate'' ; in general, the converse convention about ''smaller extension'' is built in an analogous way. It would not suffice to confine ourselves to the statement, apparently satisfactory, that the extension of the term M is greater than that of the term N (or that of the term M with respect to its new intension) if and only if there are more M's

PROBLEMS OF GNOSIOLOGY

98

than N's - for instance, if there are more vertebrates than birds. This does not suffice for two reasons. First of all, we should have to admit that if the term M has five designata (for example, the name ''a finger of John's right hand''), and the term N has two designata (for example, the name ''Peter's eye''), then the extension of the term

M is greater than that of N. But such an interpretation would not

correspond to the sense of the formula in question. To preserve its sense, we must consider that such a term

M has a greater extension than the term N, which among

its designata has all the designata of N and some others besides. If both terms have some designata in common, but in addition the term

M has certain designata

of its own, as also so has N, we do not say that the extension of one term i s greater than that of the other, even if the set of the designata of the former is more numerous than that of the latter. In such a case we say that

the extensions of those terms in­

tersect or overlap. If they have no designata ii1 common, we say that the two terms are ''not comparable''. Secondly, it must be borne in mind that when it comes to infinite sets, that set which includes all the elements of the other set and has some elements of its own besides must not necessarily be more numerous. It is claimed that the set of the natural numbers is equinumerous with the set of the even numbers, although the former includes all the even numbers and the odd numbers in addition. And yet in that case, too (if we treated ''names of numbers'' as real terms, and not as onomatoids), we should say that the extension of the term ''natural number'' is greater (broader) than that of the term ''even number'', since we consider it sufficient that the set of the designata of the latter term is a part proper of the set of the designata of the former (which means that every element of the latter set is an element of the former, but not conversely). And it does occur in the case of , infinite sets that a proper part is equinumerous with the whole. Now that we have adopted such an interpretation of the phrases ''greater (broader) extension'' and ''smaller (narrower) extension'', we must state that the extension of a given ter1n has become greater (broader) or has increased following a change in intension, if and only if its extension with respect to the new content is greater that its extension with respect to the old intension. If we now approach the issue from the aspect of content, we confine ourselves to the following explanation. The content of the term

M is narrower (less com­

prehensive) than the content of the term N if and only if to say about something

A and a an A, a B

that it is an M means the same as to say about it that it is an

B, and to

say about something that it is an N means the same that it is

and a C,

where ''C'' differs in meaning fi·o1n

''A'',

and from''B'', and from ''A and B'' ; the

same principle holds by analogy for other subjective complements. Now in such an interpretation of the technical terms involved it proves true that when the exten­ sion becomes broader the intension either cl1anges qualitatively (for example, from

A

into

D,

the latter meaning something else than

A),

or becomes narrower, but it

does not prove true that the converse holds. It is true that in some cases when the '

intension becomes broader the extension becomes narrower, or when the intension

IDEAS

99

becomes narrower the extens ion becomes broader, but there are also cases in which the extension remains the same although the intensio n has become broader or narrower. Let, for i nstance, ''man'' mean the same as ''two-handed mammal'', and ''human male'' the same as ''male two-handed mammal'' ; let us put ''man'' for

''M'', ''human male'' for ''N'', ''mammal'' for ''A'', ''two-ha11ded'' for ''B'', and

"male'' for '' C'' ; this illustrates all the four cases usually considered to be normal. But if i n the language of an amateur ornithologist ''stork'' means ''a migratory, red-billed, carnivorous bird'', and if for another amatem· ornithologist it means "a migratory, red-billed, carnivorous, clattering bird'', then i n the latter case the intension of the term ''stork'' will be broader than i n the former case, but the exten­ sions will be the same. The same holds if to the content of the ter1n ''cuckoo'', defined as ''the bird whose call i s 'cuck-koo' '' we add that it has two toes of each foot turned backward or that it i s insectivorous ; we also increase the intension of the term, but its extension remains the same. So much for concepts. 1 S. Szober, Zarys jfzykoznawstwa (An Outline of Linguistics), No. 1 , Warsaw 1 924, pp. 4-22 ; M. Niediwiecka-Osso\\

'', i.e., ''if. . . .

then . . . . ''), and only the symbols of negation, alter11ation and implication are used to formulate the axioms. These axioms are given below, the universal quantifier of all tl1e variables being omitted in all cases (which does not disagree with Russell who does not think it necessary to introduce quantifiers into the sentential calculus) ; moreover, the set of axioms i s here reduced from five to four since, as has been demonstrated by Lukasiewicz, < 3 > the remaining axion1 i s superfluous in the system. First comes the definition of the implication symbol :

(p -+ q) dJ" ( "' p v q)

(D. 1 )

The axioms of the system are as follows :

(p v p) --+ p q --+ (p v q) (p v q) --+ (q v p) (q --+ r) --+ [(p v q) --+ (p v r)]

(A.

1)

(A. 2) (A. 3 ) (A.

4)

'

1 65

THE LOGICAL RELATIONSIIlPS BETWEEN SENTENCES

These axioms and this definitio11 are used to deduce in that system a number of theorems ; next the definition of the conjunction symbol ('' A ''), read as ''and'', i s joined to the systen1 and used in deducing further theorems, a11d finally the def­ inition of tl1e equivalence symbol ( ' = '' ) , read as ''if a11d only if'', is joined also, and used in deducing the last group of theorems. These two definitions are as follows : '

(p

A

q) df "' (

"'

p

(p :::::: q) df [(p --+ q)

V

A

,....,

q)

(D. 2)

(q --+ p)J

(D. 3)

Of these for1nulas, the axioms are included in the formulas Nos. 1 -46, discussed above : Axiom 1 is covered by No. 2, Axiom 2 by No. 1 0, Axiom 3 by No. 1 4, and Axiom 4 by No. 4 1 . Definitions did not occur there, since they were represented by corresponding equivalences ; they become definitions in Russell's system, and as equivalences they occur in all the systems that are equivalent to the latter. These counterparts of Russell's definitions differ from them only in that they have the symbol '' = instead of ''-;;1 and are easily identified as No. 29 (counterpart of D. 1), No. 2 1 (counterpart of D. 2) and No. 1 3 (counterpart of D. 3). ' b) Rules and formal proofs in the sentential calculus. Theorems are proved on ( the strength of appropriate axioms and definitions ; for that purpose the operations of substitution, definitional replacement, and detachment are used. Substitution consists in that instead of variables in a given formula we place arbitrary functions ; thus, sentential variables (that is, letters) in the formulas belonging to the senten­ tial calculus are replaced by formulas, such as p --+ q , p v q, r, etc. All these are sentential functions, since they change into sentences whenever the letters are replaced by sentences. Consequently, if for instance an axiom states that the for1nula (p v q) --+ (q v p) turns into a true sentence whenever any sentences are placed i n it instead of letters, provided that the same sentences are substi­ tuted for the same letters, then it will turn into a true sentence also if, for example, instead of q we place a sentence that has the form of an implication. Hence, we are right in accepting as correct the formula obtained from the former by the substi­ tution, for instance, of r --+ s for q - that is, the formula [p v (r -+ s)] --+ [(r -+ --+ s) v p]. In this case we apply what is called the rule of substitution, which might be formulated as follows : if a given formula belongs to the system, then it is permis­ sible to build a new formula belonging to that system, by placing instead of varia­ bles in the existing formula any appropriate functions (hence, in the case of the sentential calculus, sentential functions instead of sentential variables), provided that the same variables are replaced by the same functions. It is superfluous to add that the letter 'p as also the letter ''q'', is itself a sentential function, so that, by the rule of substitution, it is legitimate to substitute, for instance for ''p'' , a single letter, for instance ''q''. Hence the formula (p v q) -+ (q v p) may yield the correct formula (q v q) --+ (q v q), etc. Definitional replacement consists in that a part of a for1nula which has the form of the left side of a definitional formula may be replaced by the right side of ''

''

"'

'

'',

ELEMENTS OF FORMAL LoGIC

1 66

the latter formula, and vice versa, which the reader will probably accept as obvious. For i11stance, if we have a formula which includes as its part the function p --+ q, we may replace that p - q in that formula by p v q in view of the fact that the former is the left, and the latter is the right side of the definitional formula of the implication symbol (cf. No. 29 above). The corresponding rule of definitional re­ placement is : if a given formula belongs to the system, a new formula belonging to that system may be built by placing, instead of a function which the former for­ mula includes, its definitional equivalent. Detachment consists in that in a given formula which belongs to the system and has the form of an implication or an equivalence, we may omit the antecedent (or one side of the equivalence) if it already belongs to the system. For instance, from the formula (p v p) - (p - p) we might obtain the formula p - p by omitting, or detaching, the formula p v p, previously included in the system. The rule of detachment may be formulated so : if both a given implication (or equivalence) and, separately, its antecedent (or one side of that equivalence) belong to the system, we may build a new formula of that system by taking as that new formula the consequent of tl1at implication (or the other side of that equivalence). The above rules of transforming formulas in such ways as is permissible in proving theorems, cannot be expressed in the symbolism of the sentential calculus ; they are, therefore, often called ''spoken rules''. Now that we know them, we un­ derstand the structure of proofs in sentential calculus. A few such proofs must now be examined by way of example. Let us consider the theorem : q - (p - q) (cf. No. 1 1 above). To prove it, it suffices to refer to Axiom 2 (A. 2), that is, q - (p v q), and to apply to that axiom in turn the rules of substitution and definitional replacement. First, we sub­ stitute p for p, which yields q - ( ,....., p v q). Now we notice that the consequent p v q, is the right side of the formula of the implication thus obtained, namely which is the definition of the implication symbol (cf. No. 29 above), while the left p v q by p -+ q, then we obtain side of that formula is p - q. If we now replace q -+ (p - q ), which was to be proved. In order to demonstrate the usefulness of the rule of detachment, let us try to prove the law of ordinary hypothetical syllogism - that is, hypothetical syllogism with conjunction. We do it at that stage of the construction of the system when both tl1e law of importation (cf. No. 35) and the law of conjunction-free hypothetical syllogism (cf. No. 38) have been proved and included in the system. As the starting point we take the law of importation : [p --+ (q - r)] - [(p A q) --+ r], to which we apply first the rule of substitution and put p - q for p, q -+ r for q, and p --+ r for r. This yields : ,.....,

,.....,

,.....,

,.....,

,.....,

,.....,

{(p - q) - [(q - r)

-+

(p

-+

1·)]} - { [(p -+ q)

/\

(q --+ r)] --+ (p - r)} .

The left side - that is, the antecedent - of that entire implication, which we have legitimately introduced into the system by applying the rule of substitution,

THE LOGICAL RELATIONSHIPS BETWEEN SENTENCES

1 67

that is, (p - q) - [(q - r) - (p ....:.+ r)], is nothing else than the law of conjunction­ free hypothetical syllogism. We therefore disregard it in conformity with the rule of detachment, and as a result we obtain the right side of the entire implication, which right side is precisely the form of the ordinary hypothetical syllogism (with conjunction) : [(p - q) A (q - r)] - (p - r) (cf. No. 37). We have thereby proved the law of ordinary hypothetical syllogi sm. The choice of rules is, within broad limits, arbitrary, but they must be such that they will always lead from true sentences to true sentences. Thus, for instance, a rule permitting the introduction into the system of a reversed form of an implication already given in that system (that is, to introduce q - p, when p - q belongs to the system), would be wrong. Moreover, the rules must be adjusted to the symbols used in the system : for instance, the rule of detachment would have no application in a system in which neither implication nor equivalence would be used. In the sentential calculus, the rule of replacing a given sentential function by its equi­ valent turns out to be very convenient (in this case we mean not necessarily a definitional equivalent, but an equivalent obtained on the strength of any for­ mula which establishes equivalence for the function in question). It can, however, be llSed i n proofs only when the appropriate equivalence has been introduced into the system. In Russell's system, it is ,...., p v q that is the definitional equi� valent of the i mplication p - q, but that implication has several other ordinary equivalents - that is, formulas connected with it by the equivalence symbol ('' = '') : p = (p A q) ; q = (p v q) ; ,...., (p A ,...., q) ; etc. (cf. Nos. 27, 28, 30). Now, by that additional rule we may, in sentential calculus, replace the implication p - q by any of these formulas. If we have, for instance, the formula ,...., p - (p - q) (No. 1 2), we may obtain the for1nula ,...., p - ,...., (p A ,..., q) through replacing p - q by ,....,

(p

/\

,...,

q).

.

The reader may be sure that if he proceeds to transform any of the correct for­ mulas given above in accordance with the rules explained in this section he will always obtain a correct formula, either new or one already listed. In this way, it is possible to associate in one's mind many of these formulas with one another, which makes it much easier to remember them and increases knowledge of rela­ tionships as between the various forms of reasoning. For instance, from the implica­ tion (p v p) - p, contained in No. 2, we obtain by substitution the for1nula ( ,..., p v ,..., p) -+ ,..., p. Formula No. 29, also by substitution, yields (p -+ ,...., p) = = ( ,..., p v ,..., p). If in the formula obtained directly from No. 2 we replace ,...., p v "' p by p -+ ,...., p, or its equivalent from the last formula, we obtain the formula (p - ,...., p) - ,...., p, or one of the formulas of reductio ad absurdum (No. 7). Likewise, Formula No. 1 5 by the substitution of q for p and p for q yields (q -+ p) = = ( ,...., p -+ ,...., q). If we in turn replace, in Formula No. 23, the left side of this equivalence by its right side, we obtain Formula No. 26. In the same way, from No. 20 we obtain, by substitution, the formula ,...., (p " ,...., q) = [ ,...., p v ,...., ( ,...., q)] ; 11 la No. 4), we have ,...., (p A ,...., q) = if we next replace ,..., ( ....... q) by q (by For1u

•

E LEMENTS OF FORMAL LoGIC

1 68

( p v q). If 11ere the left side is replaced by its equivalent on the strength of No. 30, we obtai n Formula No. 29. Very many similar relationships can be established by means of tl1e transforma­ tions described above. But it must be borne in mind that if a new theorem is to be proved in a given system one may resort only to such theorems as have been proved without the help of the theorem to be proved now. Hence, when building a system, one has to remember at every moment what has already been built. This requires a special concentration on the subject ; the same applies to a detailed study of the full store of theorems known in sentential calculus. Whoever is to be satisfied with the knowledge of elements only, can best prove a theorem by resorting to the zero-one verification method, or by replacing a full proof by deducing the desired formula from any formulas which he knows to be correct ; i n doing so, he must apply the rules described above, including the additional rule recently referred to� (c) Remarks on implicationa/ and inferential consequence. The knowledge of rules will prove helpful in understanding what is consequence, which will be discussed now. The formulation ''follows from'' has, it seems, three principal meanings. The first is extra-logical and is concerned, roughly speaking, with the e ffect of some cause, and corresponds, in everyday parlance, to "results from''. The remaining two meanings are logical ; they are : implicational and inferential. They have already been mentioned above, on pp. 1 40- 1 . Let it be recalled here that in the implicational sense we say that "q follows from p'', or ''the sentence q follows '' from the sentence p whenever we want to say that if p then q. Strictly speaking, this covers a gamut of meanings, one of which - namely, the implicational meaning in the narrower sense of the term - we have in mind when we read the implication , symbol in logical formulas such as "if then . . . ". In the inferential sense, we say that '' '' "q follows from p or ''the sentence q follows from the sentence(s) p wl1enever we mean that the sentence q can be obtained from the sentence(s) p by such trans­ formations as, when applied to a true sentence (or a set of true sentences), always give as a resul t a true sentence. Such metl1ods of tra11sformation are established, for instance, by the rules of substitution, definitional replacement, and detacl1ment. In this sense, we may say that the law of hypothetical syllogism with conjunction follows from the laws of importation and conj unction-free hypothetical syllogism. It will certainly be to the point to draw attention to the fact that a given sentence follows (implicationally or i nferentially) from a set of given sentences, regardless of whether anyone realizes that or not. Consequence is entirely determined by the structure of sentences (for a given meaning of the constant logical symbols, such as sentential connectives, which they include). From the sentences (1) ''If he bought the ticket No. 1 0 then he won the chief prize'', and (2) ''He bought the ticket No. 10'', the sentence (3) ''He won the chief prize'' follows inferentially owing to the structure of those sentences alone. The first sentence is of the type p -+- q, where p stands for tl1e second sentence, and q, for the third. Now q follows from (1) p -+- q, and (2) p by the rule of detachment, for if we assume p -+- q, that is an implication with =

,.....,

. • .

THE LOGICAL RELATIONSIIlPS BETWEEN SENTENCES

1 69

the antecedent p, then if we also assume that antecedent, we are entitled to detach it, so that the consequent q remains. Likewise, from the sentences (1) ''If he goes there, he will fall into an ambush'', and (2) ''If he falls into an ambush, he will be killed'', the sentence (3) ''If he goes there, he will be killed'' follows in the implica­ tional sense, regardless of whether that is realized or not. It suffices that these sentences give the form of reaso11ing wl1ich is called hypothetical syllogism with conjunction - namely, the form [(p ---+ q) A (q ---+ r)] ---+ (p -+ r) , if for p we substitute ''He goes there'', for q, ''He will fall into an ambush'', and for r, ''He will be killed''. The sentences ( 1 ), (2) a11d (3) yield (4) : ''If: if he goes there, he will fall into an am­ bush, and if he falls i11to an ambush, he will be killed ; then : if he goes there, he will be killed." This is an iinplication, the antecedent of which is the conjunction of the sentences ( 1 ) and (2), and the consequent, the sentence (3). Hence (3) fol­ lows implicationally from (1) and (2), regardless of whether that is realized, on the strength of the structure of those sentences alone. Should anyone see a difficulty in this, let him take into consideration that q follows implicationally from p not only when someone has built the true sentence ''If p then q'', but also if anyone built the sentence ''If p then q'', that sentence "'ould be true. And q follows inferentially from p not only when someone has in fact obtained q from p, for example, by way of a combination of substitutions, definitional replace1nents and detacl1ments, but even when that can be done. And it can always be done whenever p and q have definite structures. For instance, in the case analysed above, not 011ly does the sentence (3) follow implicationally from ( 1 ) and (2), but also : (a) the sentence (4) follows inferentially from the law of hypo­ thetical syllogism with conjunction ; and (b) the sentence (3) also follows inferentially from the conjunction of ( 1 ) a11d (2) and the implication (4) which holds between ( 1 ) and (2) on the one hand and (3) on the other. Concerning (a) : it is so, since the sentence (4) can be obtained from the formula of hypothetical syllogism with con­ junction on the strength of the rule of substitution (here extended so that not only sentential functions but sentences as well may be substituted for sentential variables). Concerning (b) : it is so, since if we assu1ne the implication (4) and also assume the conjunction of (1) and (2), which is the antecedent of that implication, we may obtain the consequent alone by the rule of detachment. Here, too, no reference is made to anyone realizing the consequence in question. This does not prevent correct intuition from developing in those who have co11siderable experience in reasoning and are versed in the matters which it concerns. Intuition tells them then what follows from what. Thus, consequence does not consist i11 intuition, but intuition often helps one to realize that consequence occurs, before a regular proof is carried out. Moreover, in everyday reasoning we often co1npJetely rely on such intuition, and sometimes it would not even be possible not to rely on it, for instance, when we are pressed for time. We may now add to the justification of the statement that formal logic is con­ cerned with forms of reasoning (cf. p. 1 3 1). We are entitled to ascribe that function

1 70

ELEMENTS OF FORMAL LOGIC

to it not only because its numerous formulas for any substituti o11s of formulas for variables turn into true hypothetical statements, and each hypothetical stateme11t expresses a conditional judgement, and each conditio11al j11dgement is a certain reasoning. We may call for1nal logic, for instance, a theory of forms of reasoning because it also formulates rules for the transformation of sentences, on applying which we obtain from given sentences other sentences which follow infe1·entially from the former. Now, passing in one's mind from given sentences to those which follow inferentially from the former is also a form of reasoning, and the rules tell us how to perform it. To put it briefly : to formal logic ca11 correctly be ascribed the functio11 of being concerned with for1ns of reasoning because tl1e task of formal logic is also to indicate the methods of a certain kind of reasoning - that is, passage in one's mind from given sentences to other sentences whicl1 follo\v inferentially from the former. As we shall later see, there are also other reasons why formal logic may be considered tl1e theory of forms of reasoning. In concluding our remarks pertaining directly to consequence we shall add that what follows is also often called consequence, and that from wl1ich it follows is called reason, so that if the sentence q follows from the se11tence p, the sentence p is the reason of the sente11ce q, and tl1e sente11ce q is the consequence of the sentence p. This way of speaking inherits, of course, all the ambiguities of the words ''to follow'' and ''conseque11ce'', with the reservation that the word ''reason'' is now not used in its extra-logical sense - that is, in those cases in wl1icl1, when by ''follows from'' we mean a causal nexus (cf. p. 1 68). (d) The possibility of a different axiom system of the sente11tial calculus. Tl1e structure of the system of the sentential calculus suggests that certain additional explanations may be useful. Fo1· instance, in the system expounded above, defini­ tions (pp. 1 64-5) of sy1nbols take ''if. . . then . . . " and ''and'' as adopted. Let us recall the definition of that ''and''. It goes : ''p and q means the sa1ne as : it is not true that : it is not true that p or it is not true that q'', or, more briefly, ''p and q 111eans the same as : not : not-p or not-q ''. Hencethe expression (a) : ''I a1n ill and I lack n1oney'' would mean the sa1ne as the expression (b) : ''It is not tr11e tl1at : I am not ill or I do not lack money''. Now one feels bound to raise the objection that in ordi11ary parlance the connective ''and'' does not have that meaning, although it is true tl1at whenever there occurs what is stated in the sentence (a), there also occurs \vhat is stated in the sentence (b), and vice versa. But tl1e fact that whenever I an1 ill and I lack money, it is not true that : I am not ill or I do not lack mo11ey, and that whe11ever it is not true tl1at : I am 11ot ill or I do not lack money, then I am ill and I lack money, results 011ly in tl1e equivale11ce of the sentences (a) and (b), but 11ot i11 their identity of meaning. Why then say that the word ''and'' means wl1at in fact it does not mean? The reply i s that we are concerned here not with the role of a give11 connective i11 received everyday language, b11t with its role i n a11 artificial technical language. The makers of that language do not intend fully to comply, in their choice of definitions, with the current nieaning of connectives, but 011ly intend to preserve,

THE LOGICAL RELATIONS.HIPS BETWEEN SENTENCES

171

to a certain extent, the limits of tl1eir usage. It is also so in ou1· case ; t1·t1e, we usually do not use the wo1·d ''and'' in tl1e sense determined by tl1e definition oftered by Russell and Wl1itehead, but it must be adn1itted that as a rule in tl1ose cases i11 wl1ich we use ''a11d'' as a sentential con11ective i11 the expressions of the type ''p and q'' we should also agree to say, \vith equal correctness, ''Not : not-p or not-q'', and vice versa. T11e same applies to the connective ''if. . . tl1en . . . " . Probably very few people '' use i t in the sense adopted by Russell who assumes tl1at ''If p then q mea11s the '' same as ''It i s not true that p, or q'', or briefly ''Not-p, or q . But that connective i s often used i n sucl1 a sense that if we assume that if p then q, then we must assume, with equal correctness, tl1at it is not true that p, or q, and vice versa. For instance, if we say sometimes (a) : ''If the weather is fine, we shall go to the mou11tains'', we do not have in n1i nd the meaning suggested by (b) : ''It is not true that the weather will be fine, or we shall go to the mountains'', but (a) results in (b), and vice versa. Hence Russell, while taking into account the extent of usage of the sentential con­ nectives whicl1 he defines (indicating a certain connection between his system of the sentential calculus and everyday speech) - that is, while striving, in general, for those and only those sentences to be true for his meaning of a given connec­ tive whicl1 are true for the principal everyday meaning of that connective - does 11ot care i n the least about retaining, i n his definitions, the current meanings of the connectives he defines (in which his system deviates from naturalness, as prob­ ably do all the other systems). He does so for technical reasons wl1ich we need not discuss 11ere. We shall only bear in mind that logicians as a rule impart to con11ectives meanings which differ markedly from the everyday usage, but which are more or less adjusted to the range of their usage, so tl1at although meanings differ greatly from current usage, there is mucl1 less disc1·epancy as between the logical a11d the current usage of sentential connectives. A jarri11g exceptio11 here is the way the implication symbol is used, as has been explained above. Tl1ere is also co11siderable arbitrariness in the cl1oice of the primitive terms and axioms. For i nstance, Russell takes as his primitive terms the symbol of negation ( ), the symbol of alternatio n ( v ), and the symbol of definitional equivalence (d1), which 11e then uses to define the symbols of implication ( � ), co11junctio11 ( A ), and equivalence ( = ) . There is nothing, however, to prevent us from building an analogous system in which tl1e symbol of co11ju11ctio11 wot1ld be a primitive term, along witl1 tl1e symbols of negation and of definitional equivalence, and in which the symbo l of alter11ation would, on the other hand, be introdt1ced by definitio11. In q) (cf. No. 2 1 and Def. 2 sucl1 a system, the equivalence (p A q) = ( p v above) - which in Russe ll's system defines tl1e symbol '' A '' by means of the symbols '' ,...., '' and ' v '' - woul d appear as an ordi11ary tl1eorem whicl1 must be proved. On the other hand , the equivalence (p v q) = ,.._, ( p " ,...., q) - which can easily be obtained fi·om D e Morgan's second law (cf. No. 22) and tl1e law of simple transposition (cf. No. 1 5) - migh t in sucl1 a system be adopted as the defi.11ition of the symbol of alternatio n by the symbols '' '' and '' A ''. This would be more "'

,.._,

,.._,

'

,.._,

,.._,

•

172

ELEMENTS OF FORMAL Lootc

natural - that is, would come closer to current meanings of the connectives involved. In such a case Russell's definition of implication would become an ordinary theorem (p � q) = ( ,..,., p v q), and the role of the definition of that symbol might be taken, for instance, by the theorem (p � q) = (p A q) (cf. No. 30). That, too, would probably be more natural, for the interpretation ''If p then q means the same as : it is not true that both p and not-q (or : it is not true that p without q ; or : no p without q, etc.)'' comes closer to one of the current meanings of the connective ''if. . . then . . . '' than does the following one : ''If p then q means the same as : not-p, or q." The reader will certainly 11ave noticed that we have used the first interpreta­ tion to explain theorems of the sentential calculus. This was a concession to natural­ ness at the expense of faithfulness to Russell's system. The disharmonies discussed above can be explained by the origin of recent formal logic, which developed neither to serve epistemology, nor to se1·ve the needs of general education or the requirements of teaching practice, but to help to improve the foundations of mathematics. And in that field naturalness is less important, while at the same time technical values are more prized. Hence the difficulty of adjusting the results obtained by the sentential calculus to the aims which the present book is primarily intended to serve. And here is an example of endeavours to i11crease the technical merits of the system. It has been observed that the number of the primitive terms and of the axioms is reduced to a minimum. It has been noticed that if a new primitive term is introduced the foundations of the system are simplified ; that primitive term i s a symbol which i s to be read ''not both . . . and . . . ", or '' . . . excludes . . . " . The idea, originated by C. S. Peirce, American philosopher of the turn of the 1 9th century, , and afterwards forgotten, was rediscovered by H . M . Sheffer, contemporary Ameri­ can logician, who introduced the symbol ''/''. This symbol may be called the symbol of non-coincidence or the symbol of alternative denial. Hence the correct forn1ula q) will be read : ''If not both p and q (otherwise : if p excludes (p/q) � ( ,..,., p v q), then either it is not true that p or it is not true that q." In Nicod's system (Jean Nicod, a French 20th century logician) that symbol is adopted as the only primitive term beside the symbol of definitional equivale11ce, and is used to define the symbols of 11egation, implication, alternation; and equi­ valence. Here are the definitions : ,..,.,

,..,.,

,..,.,

read : not-p is the sa1ne as : p excludes p ; (p/p) p d f ,..,., (p � q) df (p/ ,..,, q) read : if p then q is the sa1ne as : p excludes not-q ; (p v q) df ( "' p/ ,..,, q) read : p or q is the same as : not-p excludes not-q ; (p " q) df ,..,, (p/q) read : p and q is the same as : it is not true that p excludes q. Now that the symbols of conj unction and implication have been defined it is possible to define the symbol of equivalence as a conjunction of specified implica­ tions. Thus the only primitive ter111s are the symbols of alternative denial (non­ coincidence) (/) and of definitional equivalence (d1). Instead of Russell's four axioms,

THE LOGICAL RELATIONSHIPS BE'I'WEEN SENTENCES

1 73

one axiom suffices here to build a system of the sentential calculus ; that axiom, complicated i11 for1n, need not be discussed here. In Nicod's system, the rule of detachment di ffers from that which occurs i n the system of Russell and Whitehead. It states that ''If the formula p is already included in the system, and the system also includes the formula p/(q/r), tl1en we may introduce into the system the formula r." This is obvious : if the sentence p excludes the exclusion of r by q, and is itself true, then r is not excluded by q (that is, it is not true tl1at not both q and r), and hence it is true that both q and r, and consequently it is true that r. 6. SENTENTIAL CONNECTIVES NOT INCLUDED IN TI-IE SENTENTIAL CALCULUS. In view of all that has been said above, it is clear that the sentential calculus may be called the theory of the correct use of sentential connectives. But we have to do only witl1 a very small number of those connectives. The question arises - why have we disregarded other sentential connectives in use? To answer that question we must first undertake a review of those other connectives. First of all, there are connectives which are merely stylistic or phraseological variations of those analysed above ; tl1ey need not be discussed here since it may be assumed that they have the same functions as their analoga included in the system. (This remark applies more to Polish than to English, but we might also imagine someone saying ''p together with q'' in the sense of ''p and q'', etc.) Further, there are connectives which do not belong to sentential calculus because when they are used to connect component sentences, the truth of the compound sentence thus built does not depend solely on the truth of those component sentences, '' as is the case of the connectives discussed so far (for example, ''p or q is true when at least one of the component sentences is true, ''p and q'' is true when both are true, etc.). Various considerations here come into play, different in different classes of connectives. We shall briefly analyse such connectives as ''although'', ''yet" and ''because''. As regards ''although'', the following definition will perhaps be accepted : ''p although q is the same as : q and p, and the fact that q suggests that not-p'' ; for example, John likes Mary although Mary is John's stepmother, means the same as : Mary is John's stepmother and John likes Mary, and the fact that Mary is John's stepmother suggests that it is not true that John likes Mary. As regards ''yet'', the following defi11ition is o ffered : ''p yet q is the same as : p and q, and the fact that p suggests that not-q''. It turns out that in these definitions we have to do with such words as ''suggests'', etc., which is not admissible in the formulas of the sentential calculus. A similar difficulty would arise in connection with that­ clauses, in the case of which the truth of the entire compound sentence depends not on the truth but on the content of the that-clause. Tl1is refers to such sentences '' as ''John knows that p , or ''John guesses that p''. As regards ''because'' and the like, they have no place in the sentential calculus since they do not yield wholes which are true or false, that is, do not yield statements (sentences) in the logical sense o f the word, although they express some inference of proof. A person may

1 74

ELEMENTS OF FORMAL LOGIC

infer and prove correctly or incorrectly, but he cannot infer and prove truly or falsely. And, as we know, i n the sentential calculus every formula, when its variables are replaced by sentences, ought to become a sentence - that is, a whole which is either true or false. The fact that the sentential calculus does not analyse the sentential connectives discussed i n this paragraph does not by any means imply that they should not be investigated from the point of view of formal logic. On the contrary, may that happen as soon as possible. This concludes information on the sentential calculus. We have been concerned with building a system of formulas each of which is a form of correctly combining sentences by means of sentential connectives. Whatever sentences be substituted for the sentential variables in any correct formula of the sentential calculus, provided that the same sentences are substituted for the same variables, always a true compound sentence results which is built of the sentences joined by sentential connectives. All the formulas of the sentential calculus have the property that the only con­ nectives they include are sentential connectives (including the negation symbol, whicl1, strictly speaking, is hardly a connective), and the only variables they i nclude are sentential variables, and that any sentences, whether simple or compound, regardless of their inner structure, may be substituted for those variables. Hence, the sentential calculus is concerned solely with relationships between sentences, and investigates those for1ns of reasoning which are determined exclusively by such relationsl1ips between sentences. But there are other forms of reasoning, which are additionally determined by relationships within sentences, for example, relationships between the subject and the subjective complement of a simple sentence. The corresponding formulas include not only sentential, but also term connectives, and also term variables, for which only terms may be substituted, regardless of the degree of their complexity. The next chapter is devoted to the study of those for1ns of reasoning, some of which are very important in everyday practice. 1 J. Lukasiewicz, Logika dwuwartosciowa (Two-valued Logic), in Przeglqd Filozoficzny, Vol. XXIll, 1 921 (Jn honorem Kazimierz T»>ardowski), p. 200f. 2 A. N. Whitehead and B. Russell, op. cit., p. 96f; D. Hilbert and W. Ackermann, Grund­ ziige der theoretische11 Logik, Berlin 1 928, p. 22f. 3 J. Lukasiewicz, Demonstration de la compatibilite des axiomes de la theorie de la deduction in Anna/es de la Societe Polonaise de Mathematique, Cracow 1 925, Vol. 3, p. 1 49. 4 A. N. Whitehead and B. Russell, op. cit., p. xvi.

'·

'

CHAPTER II

THE LOGICAL RELATIONSHIPS BETWEEN SENTENCES AS DEPENDENT ON THE INTERNAL STRUCTURE OF SUCH SENTENCES CATEGORICAL SYLLOGISM

7. GENERAL CHARACTERISTIC OF FORMULAS OF TRADITIONAL LOGIC. We now pass to the second branch of formal logic, which is the calculus of terms. Formulas here i nclude only term variables - that is, variables for which we may legitimately substitute only tern1s if we want to obtain a sentence and not a meaningless string of words. One such formula is, for instance, ''If all A is B then some B is A'', where A and B are term variables. If we substitute ''grain'' for A and ''seed'' for B, or ''town'' for A and ''health resort'' for B, or any other terms for A and B, we shall obtain a sentence. Should we, however, substitute ''it rains'' for A and ''the sun shines'' for B - that is, sentences, and not terms - we should obtain not a sentence but a meaningless string of words. The modern calculus of terms has developed on the ground of the old Aristo­ telian logic, cultivated by Mediaeval schoolme11. We shall therefore first explain the achievements of traditional logic, and then pass to the modern form of the calculus of terms. We must now pay attention to the forms of direct inference and categorical syllogism, which almost entirely exhaust traditional formal logic. They 11ave the shape of p---+ q, where always one categorical sentence stands i n place of q, and one sentence or a conjunction of two categorical sentences (that is, sentences neither of which is a combination of sentences by means of sentential connectives) stands for p. These categorical sentences must be of the type : ( 1 ) ''All S is P'' (general affirmative sentence : S is the initial of subiectum, ''the (grammatical) subject'', and P is the initial of praedicatum (''the subjective complement''), or briefly SaP (where ''a '' is the first vowel in affirmo, ''I affirm''), or simply a ; (2) ''No S is P'' (ge11eral negative sentence), S e P, or e (''e'' is the first vowel in nego, ''I deny'') ; (3) ''Some S is P'' (particular affirmative sentence), or S i P, or i (where i is the second vowel in a;fjirmo) ; and (4) ''Some S is not-P '' (particular negative sentence), or S o P, or o (where ''o'' is the second vowel i n nego). ''

1 75

''

1 76

ELEMENTS OF FORMAL LooI C

The function of the component parts of these formulas i s as follows : (1) Terms are substituted for S and P. It must be borne in mind that the traditional theory stands valid if tl1e range of variability of those variables is limited : (a) no empty terms (ter1ns which denote nothing, such as ''the son of an issueless mother'', ''a square circle'', ''centaur'', etc.) may be substituted ; (b) no universal terms, that is, those under which any object falls (for example, ''object'', ''something'', and co ­ extensional) may be substituted. (2) The sentences S e P and S o P (negative, in wl1ich the negation is placed before the copula) have the same meaning as, ai1d hence are equivalent to, the corresponding affirmative sentences in which the negation stands befor also lie outside the field of the sentential calculus and the calculus of ter111s, although in formu1ating and proving theorems of those calculi we have resorted to those laws. So far, there has been no need to analyse such laws, since we have confined ourselves to the formulas in which the universal quantifier implicitly preceded all the variables or in which the inner quantifiers could very easily be eliminated by means of appropriate definitions of abbreviations

(sub, ex, sol,

etc.). We shall now give the most important laws of handling the quantifiers. Let us consider the sentential function : ''x is a plant'', and let us write the true '

sentence : L'x (x is a plant). Now the relationship holds : L'x (x is a plant) .- (x is a plant)], and also the analogous relationship : Jix (x is a ,..., (x is a plant)]. The former is read : for some x,

= plant) =

.....,

......

[llx [Ex

s is a plant, is equivalent to : it is not

true that for all x it is not true that x is a plant. It is superfluous to add that this relationship is not specific to the example in which ''plant'' is the subjective comple­ ment, but holds for any subjective complement. The subjective complements ''animal'', ''man'', ''extensive'', ''liquid'', etc., could stand there equally well. We could therefore for1nulate all this in a more general manner, by taking the variable A as the subjective complement : for any A ,

{L'x (x est

A)

=

,..., [llx ,..., (x

est

A)] } .

The quantifier ''for any A'' can of course be symbolized as IIA . The second, anal­ ogous, relationship can also be generalized i n the same way and written as : lIA

{Jix (x est A) =

,..,

[L'x ,..., (x

est A)] } .

But these relationships can further be general­

ized, since i t is irrelevant whether in the brackets we find x x

om

est

A , or x

sub

A , or

A, etc. Nothing will be changed if we place here any sentence containing x.

Let us symbolize such a sentence as fx, and the two relationships will be :

,

THE

LOGICAL RELATIONSHIPS BETWEEN SENTENCES

207

Ilf{Ilx(fx) = - [Ex - (fx)]}, Ilf{Ex(fx) = - [Ilx - (fx)]} . The former of the two is read : for any f, for any x, f of x, is equivalent to : it i s not true that for some x it is not true that f of x. In other words, whatever the structure of the sentential function containing tl1e term variable x, to state that that sentential function yields a true sentence for any substitutions for x, is equiv­ alent to stating that it is false that it yields a false sentence for some substitution. But we can proceed still further in this generalization, since these relationships hold with respect to term variables, to sentential variables, and to any other variables belonging to other semantic categories. Should we interpret the above formulas in this way, then the first of them would have to be read : whatever the structure of a sentential function containing a given variable x of any semantic category, to state that that sentential function yields a true sentence for any substitutions for x, is equivalent to stating that it is false that it yields a false sentence for some substitution. These relationships show that the existential quantifier both in the sentential and in the ter1n calculus can always be eliminated by means of the univer­ sal quantifier and the symbol of negation (and conversely, the universal quantifier can always be eliminated by means of the existential quantifier and the symbol of negation). If the reader has grasped what 11as been explained above he will also easily read the following relationships between quantifiers which we formulate without, at the beginning, everywhere writing out the quantifiers for p and /:

p v Ilx(fx) = Ilx(JJ v fx). Whatever the sentence p (on the condition, however, that it does not contain the variable x) and whatever the sentential function f, containing the variable x, the alternation of that sentence p and of the sentence stating that the sentential function f holds for any substitutions for x (that is, the sentence Ilx(fx)), is equiv­ alent to the statement that the sentential function which is an alternation of that sentence p and that sentential flJnction j holds for any substitutions for x. To put it briefly, the universal quantifier may be shifted from before the second element of an alternation so that it precedes the entire alternation, a11d vice versa. The same holds, by analogy, if the quantifier occurs before the first element of an alternation, while the other element is free - that is, when we have Ilx(fx) v p. In the same way, we may shift the existential quantifier :

p v Ex(fx)

==

Ex(p v fx).

The same holds for conjunction ; he11ce we have : p A

Ex(fx)

p

Ilx(fx)

A

==

==

Ex(p Ilx(p

A

fx),

A

fx),

208

EI.EMENTS OF FORMAL LoG1c

where, too, it is indifferent whether the quantifier stands before the first or the second element of conjunction. But this is not indifferent in the case of implication. Here the universal and the existential quantifier may be brought before the entire implication from before the consequent (or conversely), in accordance with the theorems :

[p --+ Ilx(fx)] = Ilx(p --+ fx), [p --+ L'x (fx)] = L'x (p --+ fx), but we may not do so with the quantifier which stands before the antecedent; in the latter case, the universal quantifier, when shifted, ought to be changed into the existential quantifier, and vice versa, in accordance with the theorems :

[Ilx(fx) --+ p] = L'x (fx --+ p), [L'x(fx) --+ p] = Ilx(fx --+ p). This becomes immediately obvious when it is taken into account that (p --+ q) = ( "'P v q) so that [Ilx(fx) --+ p] = { ,..., [Ilx (fx)] v p} = [.Ex- (fx) v p] = = {.Ex[ "' Suppose, for instance, that John knows that Goethe is t11e author of Faust, but does not know that Goethe is the author of Hermann und Dorothea. Consequently, a person inferring so : John knows that Goethe is the a11thor of Faust, but ''the author of Faust'' and ''the author of Hermann und Dorothea'' are names with the same extension, hence John knows that Goethe is the autl1or of Hermann und Dorothea, would infer incorrectly. Tl1e reader is warned against such replacements in subordinate clauses which express the content of a person's knowledge, intention, desire, advice, etc. - that is, in the clauses that follow the connectives ''that'', ''in order to'', etc. Apart from that, as many knowledge-forming rules can be built as there are formulas in formal logic ; many of them, if sufficiently simple, would correspond to certain intuitive methods o f finding consequences for given reasons, methods which are actually in use. Let us take De Morgan's law : "' (P /\ q) � ( "'P v ,..., q ). We may base on it the following rule : on having built the negation of a conjunction of two sentences we build an alternation of the negations of those sentences, and next infer by this rule : it is not true that the public prosecuting counsel is right and the counsel for the defence is right, therefore either it is not true that the public prosecuting counsel is right, or it is 11ot true that tl1e counsel for the defence is right. The same applies to other formulas. =

224

0unINE OF

TIIB

GENERAL METHODOWG¥ OF SCIENCE

Yet the formulas of formal logic can serve the cause of inference not only because we can use them to formulate transfor1nation rules that lead from reason to consequence, but because they can be used in another way : theorems of for1nal logic, which state that a given formula hoJds true for all permissibJe substitutions of constants for the variable, may function as premisses. We have had an example of that in the case of ''it makes sense to resist'', and other similar examples might easily be quoted. But, on the other hand, however paradoxical it might seem, we have to admit that there are also many examples of correct inference in which no thesis of formal logic occurs as a premiss, and no rule used is built according to any formula of for1nal logic. Such, for instance, is the following inference : if a person has published a libellous item, he is bound to withdraw it (in other words : if x has published a libellous item, x is bound to withdraw it), therefore if the editor of Public Opinion has published a libellous item, the editor ofPublic Opinion is bound to withdraw it. Here the only premiss is the for1nal implication from the field of law, and not from the field of formal logic, and the only rule used is the rule of substitution which, in contradistinction to the rule of detachment that can be based on the formula called modus ponendo ponens - cf. No. 1 6 on p. 1 47-cannot be built according to any for1nula of formal logic. So much for the examples of inference, the rules used in them, the premisses used, and the role of formulas of formal logic as elements of inference. Let it also be added further that the ability to infer can be improved in the following ways. First, we may increase the range of premisses- that is, simply increase our knowledge in the various fields, including those relationships which are grasped by the theorems of formal logic. In earlier times, those who engaged in eristic sought to list those theses which could be used as auxiliary premisses in all disputes. They were called loci communes, which, because of their triviality, in some languages gave rise to derogatory terms. A discouraging result thus discredited an intention which was reasonable in principle, even if the main point is not to memorize such theses as could be used on every occasion. Theses from the various fields containing miscellaneous factual knowledge are undoubtedly more important. Secondly, we may increase the number of transformations- that is, the ways of finding consequences for reasons ; in other words, we may infer on the strength of a wider range of rules, even if they be used in an auxiliary manner only, in the same 1nanner as we can draw the same shape with various turns of the hand, even if we only intuitively realize the order of our movements. Thirdly, we may

acquire better and better self-knowledge concerning the structure of any inference, whether done by ourselves or by other people. Fourthly, we may improve meth­ odological criticism of the various instances of. inference performed. The point is to know whether a given conclusion actually follows from the adopted premisses on the strength of the rules applied, and whether it is at all deducible from those premisses - that is, whether it is obtainable from them at all by some knowledge­ forming rules. Hence the striving for the discovery of the least possible number

REASONING

225

of lucid rules by means of which it might be possible to check the correctness of inference by showing that tl1e conclusion really follows from the premisses. The following set of rules : the rule of substitution, the rule of detachment, and the rule of definitional replacement, are usually considered as universally sufficient. I t must further be mentioned that the term ''inference'' is also often used in a sense different from that ascribed to it in the classification of reasonings now under discus sion. First of all, we must specify that sense, different from that now being considered, in which it is indifferent whether we assert the reason first, and the consequence next, or whether we do not assert the reason, but only assume all its factors, or at least assert some of tl1em, and assume the rest. In that interpretation, the term ''inference'' comes to mean the same as the ter1n ''deducti on''. I make an inferential statement in that broader sense (but make no inferential statement in the sense used s o far) when I say : suppose that 28 is divisible by 6 ; then, since every number which is divisible by 6 is divisible by 3, 28 is divisible by 3. The reason consists of the thesis ''28 is divisible by 6'' (which we only assume, as we often do in the case of notoriously false theses when we prove by reductio ad absurdum), and the thesis ''every number divisible by 6 is divisible by 3'' (which we assert) ; the conclusion consists of the thesis ''28 is divisible by 3'', which we do not assert either. In that enlarged sense, the following will be inference, too : let it be true that eve1·y thesis implies its own negation ; then : if potatoes grow in Poland then potatoes do not grow in Poland. The conclusion was obtained by substitution from the only premiss, assumed but, of course, not asserted. We sometimes also call inference any thought formulated in a conditional sentence ; in this sense, a person infers if he thinks (with conviction or not) that whoever is vaccinated against smallpox is thereby protected against contracting that disease. In this sense, any conditional sentence can be used as an illustration of an inferential statement. We had this in mind and we believed that inference so conceived is a special case of reasoning, when we often called the formulas of formal logic formulas of for1ns of reasoning. Finally, when it comes to purely external operations, we call inference a system of actions which consists in writing new inscriptions, in accordance with adopted transformation rules, when certain given inscriptions are taken as the starting point. In this sense, we have to do with inference if someone, having the inscription ''For any p and for any q : (p -+ q) -+ "" (p A "'q)'' and the inscription (definition) ''For any p and for any q : (p -+ q) = ( ""P v q)'', obtains the following new inscription ''For any p and for any q : ( ""P v q) -+ "" (p A ,..., q)'', by applying the following transfor1nation rule : on having written an inscription, we write a new one by replacing in the former any component inscription which has the same form as the left side of a definitional inscription, by another, which has the same form as the right side of that definitional inscription. It is obvious that such a build­ ing of inscriptions is not, strictly speaking, any reasoning, but only a certain external manipulation which replaces reasoning in the same way as operating a compto­ meter replaces the mental operations of computation .

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6. VERIFICATION. We shall now consider verification. In accordance with the definition already adopted, it consists in finding a consequence, previously accepted as true, for a given reason. The reader is warned against the illusion that the verifica­ tion of a given sentence, so understood, is the demonstration of its truth or of its being completely well founded (see pp. 235 f below). Verification usually provides only a partial foundation of the sentence in question : the sentences by which it is verified speak, as it were, in defence of its truth. For instance, we suppose that the number 10219 is prime - that is, it is not divisible except by one and by itself. Hence it follows, we continue, that it is not divisible by 3, and the fact that 1 0219 is not divisible by 3, we 11ave previously accepted as true. An indictment i s verified by a judge who establishes that the facts confirmed by the investigation follow from what is stated i n the indictment. For instance, a person has been accused that on January 10, 1926, at noon, when driving a car he knocked down a pedestrian, and the police investigation has shown that at that time the accused was not at home, that shortly before he was seen driving a car near the place of the accident, etc. But it is not essential for verification, so understood, that the truth of the conse­ quence found be revealed before that consequence is obtained from a given reason. On the contrary, there are often cases involving the reverse order, whenever the consequence found is a guess concerning the future. For instance, a pl1ysician notices suspicious symptoms and consequently supposes that the child suffers from German measles ; he then states that if this is a case of German measles, tl1en a small rash will appear in a few days ; then in a day or two - that is, after finding a conse­ quence for a reason - he confirms by observation the truth of that consequence. Quite often, in order to establish tl1e truth of the consequence selected, we have to employ some operation, whicl1 is frequently physical in nature. I do not know whether John has fever and I reason that from the assumption that Jol1n has fever it follows that the column of mercury in the thermometer will rise above 37°C. But to make sure that the thermometer will show such a rise in temperature, I must perform a measurement. That is why the term ''verification'' is very often (perhaps even in the majority of cases) used to denote such an operation, required to reveal the truth of a conse­ quence selected for the reason being verified. The measuring of temperature, the weighing of a patient who is supposed to have lost weight, the immersion of the litmus paper i n a liquid and the examination of how its colour has changed (when we want to verify whether the liquid is acid, or not) - all such operations, pro­ vided they are performed with some purpose in view, are usually called verification. Sometimes verification is understood as a wl1ole consisting of a reasoning of the type described above and of some such operation. In this sense, tl1e whole which consists, for example, of the following steps : stating that from the assumption (and from selected tl1eorems of optics and from theses about the position of the Sun, the direction of its rays, etc.) it follows that the disc of Venus passes through phases as does the Moon ; the making of a telescope ; observation, by means of that telescope,

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of the authenticity of that phenomenon - may well be called a verification of the formerly controversial issue, as to whether Venus revolves around the Sun. Finally, a reflection on the relation between verification and inference in the broader sense of the word. It is obvious that verification in its essential meaning is a particular case of inference understood as finding a consequence for a reason that is, understood as deduction in general is understood in the classification of reasonings here adopted. 7. E XPLANATION. Among the reductive forms of reasoning we shall first be concerned with explanation - that is, finding a reason for a given consequence, previously accepted as true. For instance, we notice small mounds of fresh soil on a meadow, and we explain to ourselves their origin so that we guess that they were turned out by the moles. The decomposition of light in a prism into the spectrum series is explained by the choice of the thesis concerning the different wavelengths of the rays which together form white light. The apparently strange phenomenon of sailing against the wind is explained by guessing that the resultant force which pt1shes the boat consists of the force of the wind and the resistance of water - for the appropriate directions of those forces (this is so as when a set square is placed on a billiard table with its hypotenuse along the cushion and pressure is exerted on one of the shorter sides ; the set square, squeezed between the cushion and the pressing object, slips away moving ''against the wind''). Changes in pressure in heated and cooled gases which retain the same volume are explained by guessing that the reason is that the higher the temperature of the gas, the more violently are the walls of the container bombarded by more rapidly moving molecules of the gas. The presence of shells on mountain tops is explained by the guess that these places at one time were at the bottom of the sea. There is a plenitude of cases of explanation in the various sciences ; they include all the guessings of such and such Jaws of nature. The corresponding theses are precisely those reasons which we select for the given consequences of such theses - that is, for the descriptions of facts observed. A clear distinction must be made as between the three relations which are so easily confused by beginners : (1) the relation between the reason and the conse­ quence ; (2) the relation of cause ; (3) the relation of suggesting an idea. The thought that there is hoarfrost on the roofs suggests the idea that at night the temperature fell below zero. But the hoarfrost on the roofs was not the cause of the low temperature, but conversely, the low temperature was the cause of the hoarfrost. Yet in spite of the fact that low temperature caused hoarfrost we may not from the thesis that last night the temperature was below zero deduce the thesis that tl1ere is hoarfrost in the morning (for there are low temperatures without hoarfrosts), but conversely, from the thesis that there is hoarfrost we may deduce the thesis that last night the temperature was below zero (for there are no hoarfrosts without low temperature). Hence the thesis ''there is hoarfrost'' is the reason of the thesis ''last night the temperature was below zero'', and the latter is the consequence of the former, a111.l 16

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not conversely. The guess that John had fever suggested to the observer the idea that the thermometer would record more than 37°C. Fever caused the column of mercury to go beyond the 37°C mark, but nevertheless the thesis ''the thermometer showed that John's temperature was over 37°C'' is the reason (strictly : an element of the reason) of the thesis ''John has fever''. No wonder, then, that we have called those observations consequences, and the theorems formulating the laws of nature we have called reasons, for we are concerned here with the relation of logical consequence, and not with the suggestion of ideas. It is true that observations suggest to us ideas of laws of nature, but the relation between reason and consequence operates the other way round : not ''facts'' are reasons of ''laws'', but ''laws'' are reasons of ''facts''. This will astonish nobody who realizes that by asserting this we do not assert that laws cause facts, for that would be something quite different. Let it be mentioned, too, that we often say that facts cause facts. All such forn1ula­ tions, however, are substitutive abbreviations, which we do not intend to analyse here, and which we mention only in order to avert frequent misunderstandings as to what, in the case of explanation, is reason and what is consequence. Consequence, in the logical sense, as that which follows inferentially from reason, is not the same as a sequel in the temporal sense, and a fortiori not the same as a consequence in the causal sense - that is, effect, and not the same as consequence in the process of thought, understood as what is being thought at a later moment under the influence of earlier thought. Hence, explanation includes all the cases of building hypotheses in natural science, since in natural science the boundary between hypotheses and laws practic­ ally vanishes. This fully agrees with the interpretation of explanation we are 11ow discussing, an interpretation which does not in the least require that the reason chosen be previously known to us as true. For however paradoxically it may seem, both in science and outside science we often explain what is known by what is only being guessed. There is also, however, a narrower and stricter interpretation of explanation, to the effect that we explain only if we select a true reason for certain given conse­ quences, previously accepted as true. Hence, althougl1 numerous observational data follow inferentially from the hypothesis of the existence of absolutely elastic aether (combined with some other theses), yet in that narrower and stricter sense these data cannot be considered as explained by that hypothesis, because other facts show tl1at it is false. On the other hand, a subfebrile condition and cough, even in that stricter terminology, will be explained by a physician as resulting from a considerable enlargement of the bronchial glands, if such a swelling enlargement always results in the same symptoms and if it really takes place in a given case (as may be confirmed by an X-ray examination). There is also an intermediate interpretation in wl1ich the explaining reason is not necessarily required to be true, yet it i s also not the case that just any thesis is accepted as a reason provided only that given consequences follow from it. The

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evident falsehood of the explaining reason i s excluded, and that reason is required to have · certain methodological merits : it must be true, or it must be probable, or all the known facts must follow from it and it may not be refuted by any known fact, or those predictions which can be more easily inferred from that reason than without it should later prove true, or it should suggest new and valuable ideas of discoveries or inventions, etc. Finally, methodologists of natural science under­ stand ' 'explanation'' in the sense that if any hypothesis has some of the methodolo­ gical advantages (for instance, inventive fertility or suitability to deduce from it all the data in a given field), then this suffices for its acceptance as ''explaining'' these data even if it be notoriously false. Such a hypothesis (or the thesis selected as the reason of given consequences), in which we are interested not because of its presumable trutl1, but for its fertility or importance in making further work easier, is called a working hypothesis. A working hypothesis which is notoriously false is called a fiction (in the methodological sense of the word). 8. PROVING. The remaining variation of reduction is proving. In the sense accepted in this book, to prove is the same as to find a reason, previously accepted as true, for a given consequence. For instance, the plaintiff proves the thesis that the defendant ought to pay a specified sum ; he proves it by choosing for that thesis another thesis, from which the former follows ; in this case it is a conjunction consisting of the thesis that the defendant has signed a promissory note, and the thesis that the person who has signed a promissory note must pay the sum specified in that note. In that sense, a person proves a geometrical theorem by selecting, from the store of theorems already accepted, that one from which the theorem to be proved can be obtained through transformations in accordance with knowledge-forming rules. I prove the thesis that the year 1928 was a leap year by referring to the fact that 28 is divisible by 4, and that every year in the date of which the figure consisting of t11e last two digits is divisible by 4 is a leap year. I formulate that by saying : "The year 1 928 was a leap year because (for, since, etc.) . . . " Likewise, the physician states that the dog which has bitten the patient was rabid, because the patient has hydrophobia (and it remains implicit that hydrophobia is characteristic of rabies and can be transferred only by a bite, and the patient was bitten by that dog only). Usually, however, as we must admit, the term ''proving'' is interpreted other­ wise - namely, as selecting a reason, previously accepted as true, for a given conse­ quence, the truth of which was not known to us before, together with the inference consisting in deriving that consequence from that reason. That inference is a test of the derivability of that consequence from that reason. Moreover, quite often, only the process of deriving a given consequence from the selected reason is called proving. Thus, all these interpretations are in circulation, sometimes with the ad­ ditional modification that it is not necessary that a given consequence be not known beforehand as true ; also, inference is often interpreted as a purely graphical trans­ formation of inscriptions, and hence not as reasoning, but as an outward form of reasoning. •

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It is only in the light of the most comprehensive interpretation of ''proving'', formulated at the beginning of the foregoing paragraph, that we can fully under­ stand the distinction, made by certain thinkers, as between progressive and regres­ sive procedure in proving. In fact, the distinction pertains rather to the methods of teaching than to the methodology of proving, since it consists in a difference in informing about the process of proving rather than in the proving itself, understood as a form of reasoning. The progressive procedure corresponds to deductive reason­ ing, from reasons to consequences, and the regressive procedure, to reductive reasoning, from consequences to reasons. Now proving, in its most comprehensive interpretation, has two stages : the first consists in selecting, for a thesis given as the consequence, some other thesis which, so to speak, would be a serious candidate for its reason, and the second consists in deriving the given consequence from the thesis so selected. The first stage, in the essential sense following from the classification here adopted, is a reductive procedure ; the second stage, which in the last analysis is a certain reasoning i n one of the senses distinguished above, is a deductive procedure. Hence, strictly speaki11g, any exhaustive description of prov­ ing, understood in the most comprehensive manner, should include both the regressive and the progressive part, in the same way as full proving is both re­ ductive and deductive. It has, however, become usual to distinguish the progres­ sive and the regressive procedure acco1·ding to which stage is formulated explicitly, and which remains implicit. For we may pass over in silence the manner in which we have selected a reason for a given consequence and confine ourselves to stating how that consequence is derived from that reason (progressive procedure), or we may state how we have come to select just that reason for a given consequence, and pass over in silence how we derive that consequence from that reason (regres­ sive procedure). Frequently, also, the procedure is called regressive if it covers both parts, that is, begins with regression, and is called progressive if it covers only the progressive part. In textbooks, the exposition of the subject is often progressive because that suffices to convince the reader of the truth of the theorem being proved. In fact, for that purpose it is not necessary to relate how one has come to select, from among the theorems of which one has prior knowledge, the thesis on which a given theorem can be based, if it is possible to demonstrate that it may really be based so. In many cases, however, the exposition is progressive because it is difficult to realize how one has come upon the idea of referring precisely to that thesis, and not to any other. Yet it is very useful for the pupil if that procedure can be described too, if it has been perfo1·1ned in accordance witl1 a certain system that can be repeated, for then the proving reasons will not seem to the pupil as obtained in some miraculous way, and moreover, when he has to recall what reasons have been used, he need not rely exclusively on some fallible mnen1onic tricks. We can satisfy this require­ ment if from a given consequence we go back to such a reason as is also a conse­ quence - that is, if we go back to a thesis which is i nferentially equivalent to the

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consequence in question, for then we can proceed systematically by auxiliary in­ ference · in accordance with knowledge-forming rules. Here, too, we need some ingenuity, which cannot be systematized, in choosing substitutions and detach­ ments, but sl1ch ingenuity seems after all to be mo1 e disciplined than that which i s needed when reasons for given consequences have to be grasped immediately. Here i s an example of such a regressi'.'e procedure in the exposition of proving. We have to prove that there exist circles which are tangent to two straight lines intersecting at a given angle (it being assumed that the circles and the lines lie on the same plane). Let us suppose that such circles do exist. Each such circle, if it i s tangent to those . straight lines, has its centre distant by its radius from both these lines, and hence is situated on the bisector of the angle between those lines. The truth of the statement as regards the existence of such circles has already been accepted. But that, while being necessary, is also sufficient, and so every circle the centre of which is situated in the bisector of a given angle and the radius of which is equal to the distance from the centre to the sides of the angle, is tangent to two straight lines intersecting at the given angle. Hence such circles do exis�. TI1e structure of this proof is as follows. At first, for the given thesis we select another thesis by inference (understood here without the ass11mption of the truth of the thesis given originally) ; that other thesis is such that, while being a conse­ quence of the form.er, it is also its reason, because the two are equivalent. Hence we select thereby a reason for the given thesis. T11is is the reductive and regressive part. Next, from the thesis selected (as to the truth of which we have foreknowledge) we derive, by inference, the given thesis. This is the deductive and progressive part of the proof. The given thesis : there exist circles tangent to two straight lines which intersect at a given angle. The selected thesis : there exist circles with the centres on the bisectors of straight lines intersecting at given angles and with radii equal to the distances of such centres from either of tl1e two straight lines. Distinction is also frequently made as between direct and indirect proof; the latter is also called apagogic, which means the same as ''by abduction'', and is characterized by the fact that we first prove the falsehood of the negation of the given thesis, and hence only infer as to the truth of the given thesis. In such cases we usually demonstrate the falsehood of the negation of the given thesis by deducing from that negation something contradictory. Such a forn1 of indirect proving is called proving by reductio ad absurdum. From a given sentence we may deduce something contradictory in various ways : by deriving from a given sentence its negation ( p from p) or by deriving from a given sentence some other sentence and its negation (q /\ ,..., q from p), or by deriving from a given sentence the equi­ valence of some otl1er sentence and its negation (q = ,...., q from p), or in still another way. Usually we derive a contradiction not from the negation of a given sentence alone, but from that negation and some auxiliary sentences previously accepted as true. 9. INDUCTION. Having reflected briefly on the elements of the classification of •

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reasonings into deductive, which include inference and verification, and re­ ductive, which include explanation and demonstration, we shall now be concerned with a special case of explanation, namely inductive reasoning, or induction. By induction we often mean such an explanation (or such a selection of a reason for a given consequence, previously accepted as true), in which the consequence has the for1n of a conjunction of singular sentences with a common subjective comple­ ment, and the reason has the form of a general sentence with the same subjective complement and a subject wllich includes the subjects of those singular sentences. Thus the scheme of the consequence is : A 1 is B and A 2 is B and A3 is B . . . and An is B, and the scheme of tl1e reason i s : every A is B. Induction is exhaustive if the designata of the subjects of the sentences which are elements of a given consequence exhaust all the designata of the subject of the reason ; it is non-exhaustive if it is not so. Here is an example of exhaustive induction : Denmark is a democratic state, and Sweden is a democratic state, and Norway is a democratic state, and Finland is a democratic state, and Iceland is a democratic state ; the reason hence is : every Scandinavian country i s a democratic state. And an example of non-exhaustive induction : Argentina is a republic, Brazil is a republic, Uruguay is a republic ; reason : every independent Latin American country is a republic (we have disregarded Bolivia, Columbia, Peru, Chile, and other independent Latin American countries). Usually, however, "induction'' is interpreted much more broadly. First of all, it is extended so as to cover those cases in which the copula ''is'' does not occur in its essential role characteristic of singular sentences, the role in which it may occur in a true sentence only after a singular name, but when a sentence of tl1e type 'M is N'' functions as an abbreviation of the sentence ''whatever is an M, is an N'', and when, consequently, ''M'' may be a general name, without detriment to the truth of the sentence concerned. Here is an example of such non-exhaustive induction : the cow is an ungulate animal, and the goat is an ungulate animal, and the sheep is an ungulate animal ; hence every ruminant is an ungulate animal. This should run strictly : whatever is a cow, is an ungulate animal, etc., hence any ruminant, etc. Such examples were meant by Aristotle when, as the first man to do so, he analysed in his Analytics the inductive reasoning, to which he gave that name (Greek lnaywy�. which was rendered into Latin as inductio, and was in the latter form taken over, slightly modified, into French, English, etc.). Here is an authentic example of allegedly exhaustive induction, taken from Aristotle : man is longaeval, and the horse is longaeval, and the mule is longaeval, hence every animal which has no bile (sic !) is longaeval. On the other hand, the form ''M is N'' is not in any way observed in those cases which nevertheless are quoted as examples of induction. The following also will be induction : Mercury moves along an ellipse and Venus moves along an ellipse, hence every inner planet moves along an ellipse. The sentence "Mercury moves along an ellipse'' is not of the M-is-N type, even if it may be transformed into a structure which would at least closely resemble a sentence of that type. There are other examples in which the sentences i nvolved are probably '

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still more remote from the M-is-N structure. For instance : chloroform has an anaesthetizing effect on John, and chloroform has an anaesthetizing effect on Peter, and chloroform has an anaesthetizing effect on Paul, hence chloroform has an anaesthetizing effect on every man. Such sentences, too, might be made to resemble more closely the essential scheme by being transformed into : John responds to chloroform by falling asleep, etc., hence every man responds, etc. (here the subject is singular, and further transformation can turn this into a M-is-N structure). If we now want to expand the concept of induction so that it may cover such a common interpretation, we have probably to formulate the issue thus : Induction consists in selecting for tl1e conjunction of the sentences : f(A i), f(A2), f(A3), , f(An), a gen­ eralization of those sentences - that is, the sentence f(a11y A), where the name . ''A'' incl udes the names ''A 1 '' , ''A 2'' , ''A 3 '' , , ''A n'' , and ''f(A 1 )'' s tands C'1or any sentence in which the name ''A1'' is involved in a definite manner ; accordingly, ''f(A2)'' stands for the sentence which differs from the former in that A2 stands in the place of A i , etc. We only exclude those cases in which the name An would be involved in the sentence after such connectives as ''that'', ''in order to'', etc. But both the latter, broader, interpretation and the former, traditional, one go beyond the limits of ''induction by simple enumeration'', wl1ich is the term of those reasonings in which generalization is reached by the consecutive enumeration of those cases on!y which fall under that generalization. Induction so understood finds itself in opposition to more complicated concepts of induction, in which given consequences include theses with different content, and the reason selected for them is not, strictly speaking, a generalization of all those consequences. But the analysis of inductive reasonings in such a modified sense must be postponed to a later moment : we shall be concerned with them only after having reflected on the importance of the types of reasoning, distinguished so far, for the foundation (or justification) of the theses selected. But first a few words must be said about the opposition as between deduction and induction. Traditional logic, when discussing the problems of inference, distinguished deduction and induction. The former was characterized as inference from the general to the particular, and the latter, conversely, as inference from the particular to the general. But such an interpretation is erroneous for two reasons. First, many cases of inference in accordance with the rules of formal logic could not be classified as deductive reasoning, since in those formulas the consequents are not more particular than are the antecedents. This holds, for instance, for the conversion of the general negative sentence (if all A are not-B then all B are not-A), for the conversion of the particular affirmative sentence (if some A is B then some B is A), for the formulas of transposition ((p -+ q) -+ ( -q -+ p)) and the negation of conjunction ( "' (P v q) -+ ( -p A -q)), and many others. In general, whenever we infer from a sentential structure and as a result obtain some sentential structure, there is no transition from the general to the particular, since only a categorical sentence may be more general or more particular as compared with some other •

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categorical sentence. Now the formulas of the sentential calculus are precisely such schemes of inference from a sentential structure to some sentential structure. Secondly, we encounter difficulties when we try to treat inductive reasoning as inference (in the sense of selecting a consequence for a reason). It is only in the case of exhaustive induction that the generalization follows from the given sentences, since it is inferentially equivalent to their conjunction. But it is not so in the case of non­ exhaustive induction. When we Jet the generalization extend beyond the range of the specified objects we proceed by a rule which may in no way be considered as knowledge-forming, for it often happens that all the given sentences are true, and yet the generalization is false - for instance, if we reason as follows : gold is heavier than water, silver is heavier than water, copper is heavier than water, hence every metal is heavier than water. And yet there are metals which are lighter than water, for example, potassi11m. On the contrary, the ''premisses'', each of them separately and all of them taken together, follow from the inductive generalization, and hence the generalization is the reason, and the premisses are the consequence. That is why inductive reasoning is to be classified as explanation, and not as inference. 1 0. REASONING BY ANALOGY. The erroneous traditional way of distinguishing in­ duction from deduction easily leaves room for reasoning by analogy, which Aristotle analysed as reasoning by ''example'' (naea q. In particular the round and square brackets which enclose the various elements of the fonnula, and the sentential connectives inserted between sentential '' v between p and q, ''--+- ' between q v ) (p and functions ('' A '' between p [ "'P A (p v q)] and q) impart to the formula a structure that can easily be grasped. And yet this method of notation is passing into disuse in specialist works, because the placing of functors (here : sentential connectives) betlveen the arguments (here : sentential variables) gives rise to difficulties when it comes to precise transforma­ tions of formul as, if only for the fact that it requires the introduction of punctua­ tion symbols in the form of brackets or their equivalents ; but in such cases it is imposs ible always to obtain, from a given formula, a new formula by pure substi­ tution . For instance, new brackets must appear, and, moreover, tl1ose previously o ccurri ng in the formula have to change their shape or at least size, if the clarity of the formula is to be retained. Should we, in the above formula, substitute (r A s) for p, and (s v t) for q, we should have to write the result of such a substitution as follows : { ,...., (r A s) A [(r A s) v (s v t)]} --+- (s v t). Thus, this would not be a ,....,

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simple substitution, but a substitution combined with a transformat ion of the sys­ tem of brackets, and hence the application of some highly complicated rule. No wonder, then, that in striving for the simplicity of rules, and also for the strict and precise observance of such rules, methodologists of the deductive systems prefer some symbolism which is perhaps less clear, but marked by the advantage of man­ oeuvrability. For instance, Lukasiewicz in his system of the sentential calculus places the functors directly before the fiJnctions to which they pertain ; consequently, he places the negation symbol (N) not after the sentential function to which it pertains, but immediately before it ; he places the implication symbol ( C) not between the antecedent and the consequent, but immediately before them, etc. Consequently, the three for1nulas which he adopts in his system of the sentential calculus as the only axioms take the form : (1) CCNppp, (2) CpCNpq, (3) CCpqCCqrCpr, in which we can easily recognize the following formulas written in the symbolism used throughout this book : (1) ( "'p -+ p) -+ p ; (2) p -+ ( "'p -+ q) ; (3) (p -+ q) -+ [(q -+ -+ r) -+ (p -+ r)]. Now in the way Lukasiewicz writes his formulas, brackets become superfluous, since the order of the component symbols deter111ines the structure of the formula. Since all punctuation symbols are done away with, the rule of substitution can be used in its pure form : if, for instance, in the second formula we substitute Crs for p and Cst for q, we obtain the formula : CCrsCNCrsCst, whereas in the quasi-algebraic notation the same substitution would yield the formula : (r -+ s) -+ [ "' (r -+ s) -+ (s -+ t)], which looks clearer, but has require� apart from substitutions, certain changes in punctuation - namely, a transformation of the framework of brackets. 14. DEFINITIONS IN A DEDUCTIVE SYSTEM. Tl1e symbols chosen are used to formulate the theses of the system - that is, axioms, definitions and theorems. As for the definitions, the question immediately arises whether they really belong to the system, or whether they only seem to belong to it. The system includes only those sentences which contain, apart from quantifiers, variables and punctuation signs, only primi­ tive terms of the system and defined terms. But definitions include such formula­ tions as ''means the same as'' or ''is equivalent to'', and also names of the symbols being defined. Take, for instance, ''the inscription 'p /\ q' means the same as the inscription ( P v "'q)''', ' ' 'p = q' is equivalent to ' (p -+ q) /\ (q -+ p)' '', etc. Both these definitions, which define terms belonging to the sentential calculus ('' A '' and '' = ' ) , include specified formulations which have a semantic content and which are not covered by the terms belonging to the theory of deduction (the sentential calculus) since they are neither sentential connectives nor definitional equivalent of formulas built exclusively of sentential variables, sentential con­ nectives, quantifiers, and punctuation symbols. Hence these definitions cannot themselves belong to the sentential calculus ; the same holds for other definitions of many deductive systems. If definitions are then included in a given deductive system in which defined terms occur, this is done only on the condition that in such cases such sentences ' "'

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as those analysed above are not called definitions. What are meant there are mathe­ matical pseudo-definitions. These are equivalences introduced, like axioms, without proof, but differing from axioms in having a definite structure which guarantees their truth. For every proper definition, we can choose such a corresponding pseudo­ definition as belongs to the system, whereas the proper definition itself remains outside the system as a not indispensable comment concerning the sameness of meaning of some two inscriptions belonging to the system. Here is an example : the proper definition of the symbol of conjunction by the symbols of negation and alternation would be : ''A formula of the type 'p A q ' means the same as a forrnula of the type ' - ( -p v -q)'," which has its equivalent in : ''For any p and q, (p A q) = = -( p v "'q)." What is contained in the second pair of double inverted commas belongs to the system of the sentential calculus ; what is contained in the first pair, does not. Yet it is the latter thesis that is usually called a definition (although it is only a pseudo-definition), which is marked by the addition of the words ''ex def." or the like. Similarly, for instance, the proper definition" ' 3' means the same as '2 + l ' ' remains outside arithmetic, while the sentence ''3 = 2 + l , written on the strength of that definition, which is marked ex def, or def or df, belongs to arithmetic. What then is the role of the proper definitions in the building of deductive systems? First of all, they provide information that a given symbol may be used to replace another given symbol in the process of inference. For what is called the rule of definitional replacement (replacement of the definiens by the definiendum, or vice versa) is often applied in inference, and hence also in proving (in the second or third meaning of the term, cf. pp. 229 f). In this connection, information is also provided as to which symbols are the definiens and which are the definiendum, and this is precisely stated by definitions in the words : ''A'' means the same as ''B'', or the like. In purely formal transformations a formulation of the kind ''A is a graphical substitute of B'' would suffice. Such definitions might be called graphical. But usually we have to do with semantic definitions formulated by means of such phrases as ''means the same as'' or ''is the same as'', etc. Such definitions, apart from providing information about permissible substitutions, also provide the in­ formation that he who formulates them associates the same meaning with the definiendum as he does with the definiens. This is important in communication, if the listener or reader is to understand the sentences of the system in the same sense as does their author or expounder. For if understanding is established as to the meaning of the primitive terms, then through the inter1nediary of definitions it is also established as to tl1e meaning of the derived terms, and thus becomes complete. 1 5. AXIOMS IN A DEDUCTIVE SYSTEM. We now pass to axioms, and the question immediately arises what are axioms. In Aristotle's works, ''axiom'' (Greek a�lroµa) means the same as a thesis which is accepted without proof and which does not require proof. H ere, by axioms we mean those basic sentences of a deductive ,....,

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system which are not definitions. The last provision is necessary only if we include pseudo-definitions in the system and call them definitions. By basic sentences we mean here sentences accepted without proof as elements of the system. This concept of axiom does not assume its being ''self-evident'', its ''absolute certainty'', ''the fact that it does not require proof'', etc. - that is, those properties which tradition has considered essential for that concept. That requirement of being ''self-evident'' reflects the Cartesian ideal of building science more geometrico, an ideal shaped as a subtler form (as is often the case with ideals) of the model of deductive systems which was offered by the exposition of geometry in Euclid's Elements, where only self-evident statements were taken as the foundation of the system. < 3 > We encounter there at the outset such definitions as ''A point is something which has no parts'', ''A line has length but no thickness''. Probably, however, they were not intended to introduce derived terms by referring them to primitive ter1ns. In Euclid's intentions, ''point'' and ''line'' themselves seem to be treated as primitive terms. Stress was laid rather on teaching, on directing attention to certain specified properties of ''poi11ts'' and ''lines'', on agreeing, outside the system, as to the meaning of those terms. Next follow the assumptions of the system, in the form of the group of ''postulates'' and the group of ''universally accepted ideas''. It would be difficult to decide what is the specific difference between the two, since the former also belong to those statements which everyone would always accept. The term itself (Greek ai-rrJµa, Latin postulatum), by its etymology and in accordance with the explanations offered by Aristotle, who had used it before Euclid, means ' 'something the acceptance of which must be required (from the listener or reader)'' : in order to continue the exposition of the subject one must have the agreement of the listener (reader) as to a given assumption. And only that is to be required which is not included among the statements that need no proof. But then it is difficult to understand why some basic assumptions are classed by Euclid as postulates, and the rest are placed in the other group. Perhaps he considered postu­ lates to be those sentences to which everyone who is to engage in geometry must give priority among those universally accepted. Or perhaps the essential difference was that the postulates, and postulates only, were statements about the possibility of carrying out certain constructions (for example, drawing a circle through a given point and with a given centre). But then also not everything would hold, since one of the postulates states only that all right angles are equal. In a word, the issue is not clear. No wonder then that the differentiation as between the postulates and the other fundamental assumptions of a deductive system has not withstood the test of time, and today we speak only of axio1ns, witl1out making any distinctions within the statements of that class. But contemporary methodologists of deductive systems do not consider it necessary that axioms should be self-evident, not to mention that simplicity is also not considered an indispensable property of axioms. In accordance with those

•

247

THE DEDUCTIVE MEIDOD

methodologists it might be said that, even in Euclid's opus, being self-evident does not suffice for a statement to be classed among the basic theses of his system, since he proves - that is, classes as a theorem, and not as an axiom - the various very simple and self-evident staten1ents, such as that vertical angles are equal. Like­ wise, in Russell's system the thesis stating that

p

�

p

is proved as a theorem (and

i n a fairly complicated way at that). Thus certain theses have to be proved in a given system in spite Gf being self-evident ; then some statement may perhaps reasonably be accepted without proof in spite of not being self-evident. This is in fact being done by the various contemporary builders of deductive systems. Here, for instance,

is the only axiom in Nicod's system of the sentential calculus He formulated five methods which cover the various forms of inductive reasoning. Thus, we reason by the method of agreement whenever we observe the following scheme : a fJ 'Y AB C a fJ - that is, the situation in which a person only imagines wl1at would occur should certain circumstances be changed. For i11stance, Galileo imagined that a given animal became greater and greater while retaining the shape of its body, and concluded that the pressure of the flesh on the bones would grow so much that it would ultimately break the animal's osseous structure (which made him conclude further that the anatomy of animals must differ according to the size of the animals in question). It is obvious that such cerebrations are not experiments as we understand them, for i n such cases we do not evoke anything in fact, nor do we observe what follows, but only make conjectures. The fact that some people call it experimentation can probably be explained by the fact that they consider as specific to experime11tation, the introduc­ tion of changes i11 something and the subsequent study of concomitant variations in some other thing, or in the same object in another respect. For here too, be it only mentally, we introduce such changes and we examine what accompanies them. In making experiments in our interpretation of that term we usually have two objectives in view : we often want to have support for the thesis that there is a given relationship as between A and B, and for that purpose we want to see what values of the factor B accon1pany given values of A under definite conditions. An experi­ ment which confirms such a relationship is called positive. In other cases, however, we want to have support for the thesis that there is no such relationship between A and B. For that purpose it suffices if under definite conditions we obtain a given value of the factor A not accompanied by a certain specified value of the factor B. An experiment denying such a relationship is called negative. When we warm a metal bar and observe how it grows longer, we make a positive experiment. When, in a constant temperature, we place that bar at first along the compass needle, and next at a right angle to it, and state that the le11gtl1 of the bar does not change, we carry out a negative experiment. When we rub amber against cloth and observe how it then attracts pieces of paper, we perform a positive experiment. When we rub a piece of wood against cloth and then see that it does not attract paper, we carry out a negative experiment. Testing technological installations is also to be classed as making negative experiments. The point is always to achieve some-

THE INDUCTIVE METHOD

301

thing without an accompanying undesirable phenomenon - for i11stance, glow without melting (in electric bulbs), flame without explosion of gases (in Davy's lamp), soap without an unpleasant sn1ell, etc. A positive experiment never proves the relationship being studied in a defu1itive, irrefutable manner. It does not follow, l1owever, that a11y result of a positive experime11t is equally in1portant for the inductive foundation of a given relationship. The purpose of Mill's methods, etc., is precisely to provide indications concerning a proper selec­ tion of data. They are often called methods of experimentation. Yet it would be erroneous to conclude that they can only be applied to experiments, and not to data obtai11ed from ordinary observations. That crowing is a specific property of cocks can be founded very strongly, be it by the method of agreement, or by the method of difference, by observing and comparing the behaviour of cocks, which do crow, with objects that are not cocks, which do not crow, without resort­ i11g to any experime11ts. But Mill's methods are correctly called methods of experi­ mentation if by this we mean that the data obtained from experiments can rationally be selected by those methods. It has been noticed in this connection that not all the methods are equally well suited to guide experiments. First of all, the method of the only difference i s better s uited to that purpose than the method of the only agreement, for it is easier, while selecting a new observation, to leave all the releva11t circumstances as they were, and to change only one of them (for instance, to rub amber against cloth), than to leave only one as it was a11d to change all the remaining ones ( for instance, to change, when we want to find out the cause of frequent head­ aches, a patient's way of life, his place of residence, his sleeping habits, his pl1ysical exercises, etc., and to keep as before his diet only). That peculiar suitability of the method of the only difference for experimentatio11 purposes accounts for the fact that it has often been wrongly considered the only experimental method, which agrees with the oft-propounded, but - in our opinion - too narrow, interpretation of the essence of experiments as the introduction or elimination of a single selected factor. On the other hand, a negative experiment settles the question by abolisl1ing the hypothesis of some supposed relationship or by demonstrati11g the possibility of something without something else, which is to be avoided. Hence the paradoxi­ cal formulation that only a negative experiment is successful. It looks as if this i s wrong, since it suggests that an experiment succeeds 011ly if it does 11ot succeed. In fact, the idea is sou11d : only a negative experiment can be of decisive importance for the problem in question.

J. S. Mill, op. cit., p. 427f. ; E. E. C. Jones, A Primer of Logic, London 191 3, p. 66f; concern­ ing Bacon cf. T. Kotarbinski, Mys/ przewodnia metodologii Franciszka Bacona (T/1e Guiding Idea of Francis Bacon's Methodology), in Przeglqd Filozojicz11y, Vol. XX.IX, 1927, No. 3/4. 1

302

OUTLINE OF

TIIE

GENERAL METIIODOLOGY OF SCIENCE

C. Sigwart, op. cit., p. 493f; J. Ve11n, E111pirical Logic, London 1 907, pp. 403-35 ; N. R. Camp­ bell, Pl1ysics : tlie Ele111ents, Cambridge 1 920, pp. 94-104. 3 E. Godlewski, Mys/i przewod11ie fizjologii rosli11 ( Tlte Guidi11g Ideas in tlze Physiology of Pla11t�;) , Warsaw 1 923, Vol. 1 , p. 226f. 4 N. Cybulski, Fizjologia przewodu pokarrnowego (The P/1ysiology of tlte Ali1ne11ta1·y Tract), i11 Fizjologia czlowieka (Huma11 Physiology), ed. by Beck and Cybulski, Warsaw 1 9 1 5, Vol. 2, p. 246. 5 E. Godlewski, op. cit., p. 99f. 6 W. E. Johnso11, Logic, Cambridge 1 924, Vol. 3, Chaps 2 and 3 ; J. Nicod, Le probleme de logiq11e de l'inductio11, Paris 1924 ; J. Hosiasson, Definicja rozu1no1va11ia i11duf,cyj11ego (Indttctive Reasoni11g Defi11ed), in Przeglqd Filozoficz11y, Vol. XXXI , 1 928, No. 4. 7 W. S. Jevons, Tl1e Principles of Scie11ce, 2nd ed. , London-New York 1 877, p. 487f. s For111ulations in this spirit include, e. g., the paper of R. Avenarius, Philo�·opl1ie a/s Denke11 der Welt geniiiss de111 Prinzip des kleinsten Kraftma.sses, 31·d ed., Berlin 1 9 1 7. 9 B. Russell, Mysticis1n and Logic, 4th ed., London 1 92 1 , chapter entitled ''011 the Notion of Cause''. 1 0 M . Verwor11, Kausale und ko11ditio11ale Welta11schauung, Jena 1918. 1 1 S. Zaremba, 0 stosu11k11 wzajer11nyn1 fizyki i mate1natyki (Or1 tire M11t11al Relatio11ship Bet­ wee11 Pltysics a11d Mathematics), i n Poradnik dla Samouk6w (A Guicle to 5'elf-Education), Vol. 3, Warsaw 1 923, p. 1 35f. 1 2 H . Vaihinger, Die Pl1ilosophie des Als ob, 6th ed., Leipzig 1 920. 1 3 The issues of measurement are discussed in detail by W. S. Jevons, op. cit., Book Three, and more briefly by J. Venn, op. cit., Chap. 1 8. 1 4 W. Witwicki, op. cit., pp. 77-88. 1 5 W. S. Jevons, op. cit., p. 390f; E. M ach op. cit., cl1apter entitled ''Das pl1ysische Experime11t u11d drew attention to the fact that not every selection of classes serves equally well the needs of theoretical studies, and that above all such a selection is needed which would make it possible to build, with reference to a given class, a general thesis establish­ ing a causal nexus characteristic of the elements of that class. Genetic classifications are usually very fertile in that respect, whereas other classifications do not war­ rant such a selection of classes. For instance, a classification of trees into such whose leaves John likes, and such whose leaves John does not like, would be of little value in botany, since, as it seems, neither of the classes so distinguished reveals any natural relationships which would be specific to its elements and import­ ant for botanical research. 3 1 . A REVIEW OF THE REMAINING ISSUES OF METHODOLOGY. The time has come to pass to the remaining issues of methodology. Since they cannot be exhausted here even in outline, we must rest satisfied with a cursory review of types of problem. There -

306

OUTLINE OF TliE GENERAL METHODOLOGY OF SCIENCE

are methods of invention - that is, methods of developing new ideas, val11able for their truth or probability, or for their explicative iinportance, or for their fer­ tility in bringing about new discoveries or inventions. Such methods of i nventio11 i11clude, for it1Stance, the search, in a given field, for a systen1 of relations similar to one found in a related field - that is, recourse to analogy. Further, there are methods of foundation, with whicl1 we have been co11cerned for some time, such as formal proofs in mathematics. Notl1ing prevents, incidentally, a method of founda­ tion from being at the same time a 1nethod of invention, as is tl1e case of the b11ilding of hypotheses by induction (in the sphere of natural science). There are also methods of self-teaching - that is, either methods of acquiri11g skill in operatio11s by which we discover or found something, or methods of assi111i­ lating and memorizi11g knowledge received, accumulated by others or developed by ourselves. This would include the methods of mnemonic technique, today in­ correctly co11sidered as bei11g of little value - that is, the tecl1nique of memorizing ample data : this may consist in composing a verse, building a word from the initial letters of important words, devising a visual model of a system of relations, etc. Many people have been able to fix in memory the first digits of the i1umber represent­ ed by ll sin1ply by memorizing a m11emonic, such as the following :

Que j'aime a faire apprend1·e Un 11ombre utile aux hommes . . . i11 which the number of letters i11 the consecutive words stands for tl1e consecutive digits of the approximate value of ll which is 3. 1 4 1 5926536 Finally, tl1ere are teaching methods, some of them studied by school practice. It must, however, be borne in mind that the study of teaching methods goes much further and covers, for instance, the methods of good description, among them the method of economical description, which makes 011e observe the degree of generality of theorems and statements and formulate, as is often recomme11ded, ge11eral reversible staten1ents, which are the most general possible. Foundation itself has in it something of teachi11g : the point is to indicate a way of convincing a person who knows that p, that q. Hence the methods of foundation are teaching methods as well. And it can be said in general that in methodological research the study of teachi11g methods i11ter­ twines with the study of methods of invention and methods of foundation. A given scientific method can be described, criticized and planned. This gives rise to a wealth of methodological issues. Examples can be found i11 the present book, both i n this and in other parts of it. In the part co11cerned with language we have to a large extent dealt with methodological issues (for example, the descrip­ tion and the critical analysis of the Socratic method of forming analytic definitions). The very analysis and classification of the variety of methods used, whether in a planned man11er or not, in the building of science, by consideration of the origin of tl1ose methods - tl1at is, the history, or rather history and historiosopl1y, of metl1ods, whicl1 might also be called historical methodology - i s a discipline .

. .

SOME OTHER METHODOLOGICAL QUESTIONS

307

with very broad prospects. Herschel, Whewell, Jevons and Mach - are the names of some of those thinkers wl1ose works may introduce one i11to the atmosphere of that discipline. Of course, there may be other trends in methodology : scientific methods may be i nvestigated with a view to findi11g out wl1at is general i11 them, or else the stress may be laid on discovering wl1ich metl1ods are characteristic of a give11 discipline. The first of these leads to a general methodology of sciences, wl1ich turns out to be a special case of a te11tative science of metl1ods of 11uman behaviour, since engag­ i ng i n scientific research is a special case of being active in general . There have been attempts at such an analysis. < ''aware''). (4) But not only nominal expressions occur as predicates in sentences. In general, the expressions of a given language can, with respect to a given meaning, be clas­ sified into terms and non-terms, and by a term (cf. Aristotelian 8eo�, which in the sense used in the Analytics means : the subject or the predicate of a simple categorical general affirmative sentence, a general negative sentence, a particular affirmative 3 < sentence, or a particular negative sentence) > we mean an expression which can be used as a subject or a predicate in a sentence. Hence such words as ''John'' and "shoemaker'' are terms, but such words as ''to smoke'' are terms, too, since it is possible to formulate such sentences as ''to smoke is pleasant''. Thus there are nominal terms and non-nominal terms. Nominal terms include collective terms, which we distinguish by reference to the set of properties connoted j ointly - that is, to connotation, or to content. By a collective term we mean such a term as connotes composition from certain elements, hence one the analytic definition of which has the form ''X is M is the same as X is a set of N's''. For instance, ''crowd'' is the same as ''the set of persons gathered in a limited space'', ''team'' - ''a set of people striving jointly for a specified objective'', ''orchestra'' - ''a set of persons playing musical instruments together'', "Moslems'' - ''the set of the believers in Islam''. It is worthwh ile pointing out that it is useless to try to define analytically ''collective term'' by reference to its designata, and not to its connotation, for instance ''a collective term is a name of a compo11nd object . . . '' or '' . . . object consisting of analogous parts'' etc. In view of such definitions the term ''iron key'' would also be a collective term, since every iron key consists of molecules of iron ; the same would hold for the term ''hat'', since every hat is a compound object. It would even be difficult to find a term which would not denote a compound object or objects.

ON THE CLASSIFICATION OF NAMES

391

The ambiguous use, · in many languages, o f the nominative plural necessitates a distinction as between terms in the plural used collectively , wl1ich in a given case are collective terms, and terms in plural used distributively, which in a given case are non-collective terms. Both a term which i s collective in the singular and a term which is non-co llective in the singular may in the plural be used in both ways. The sentence ''The apples in this box weigh together 100 pound s'' (which means ''The

totality consist ing of apples . . . ") and the sentence ''The competing choirs appeared together on the stage'' (which means ''The group consisting of the competing choirs . . . ") are examples of a collective use of the non-collective term ''apple'' and the collective ter1n ''choir'', where the plurals ''apples'' and ''choirs'' are collective terms. The sentence ''The apples in this box are russets'' (which means ''Every apple in this box . . . '') and the sentence ''The choirs in turn sang their songs'' (which means ''Every choir in turn . . . '') are examples of a distributive use of those ter1ns . Hence the collective nature of a term is not to

be confused with its collective use ;

nor i s the non-collective nature of a term to be confused with its distributive use.

(5) After these general considerations we shall proceed to make other distinctions as between names. For the purpose of this analysis we adopt the convention that

by a name we mean a nominal term in the nominative singular. The distinction as between genuine and apparent names is of extreme importance. Apparent names are such whose function reduces to participating in substitutive formulations ; be they abbreviations, be they metaphors, be they set phrases, be they still something di fferent, they are always substitutive. When such substitutive formulations are eliminated by being reduced to the basic for1ns, which are not substitutive, the apparent names vanish, and only genuine names are left (or words which are their declensional forms). If we take for instance ''He was at bay'', this is a substitution for the rather artless formulation ''He could not escape'' ; ''bay'' here is an example of an apparent name (which vanishes after a reformulation) . Likewise, ''The departure of the train was delayed'' is substitutive for ''The train departed later than scheduled''. ''Train'' is a genuine name, whereas ''departure'' is an apparent name. We have taken the liberty to call apparent names ''onomatoid s''. (6) From quite another point of view, a distinction i s being made as between

general, singular

and

empty

names : it is the number of the designata which is here

taken into account. A given name i s singular with respect to its given meaning (sense, content) if it h as one and only one designatum - for example, tl1e name ''Paris''. It i s general if it has more than one designatum, for example, ''town''. It is empty if it has no designatum at all, for example, ''the horse's horn'', ''the son

of a childless mother''. This gives rise to a number of misunderstandings. People occasionally take a given equivocal name to be general if it has one and only one

designatum with respect to one of its meanings, and one and only one designatum with respect to another meaning. Yet it is evident that in such a case we do not have

to do with a general name : a name is general with respect to a given meaning if in that meaning it has more than one designatum. And here is another issue : is it not

392

SUPPLEMENT

inconsistent to adopt empty names? It might seem correct to believe that any name, as such, is a name of something. How then can a name be empty? It would then be a name of nothing. The reply is that to be a name it suffices, by definition, to be suitable, when in the nominative singular, to be a term. And a given ex­ pression may function as a term in an affirmative false sentence, and not be a term in any possible affirmative true sentence. Precisely in such a case it is an empty name. It is a name, although it is not a name of anything, by which we mean that no object is its designatum, about which that name could be predicated in a true sentence. Finally, there is the issue of the degrees of generality of the onomatoids. Are they, too, classified into general, singular and empty, in the sense of these terms as described above? In our opinion, of course not. Evidently, no onomatoid has any designatum, since it cannot be predicated truly about anything as an subjective complement of a sentence i n its basic, and not substitutive, form, since such a sen­ tence includes only genuine names, and an onomatoid is not such. To that extent, then, an onomatoid resembles a genuine empty name. The di fference consists in the fact that a genuine empty name, when made to replace a genuine general or singular name in a true sentence, yields a falsehood, whereas an onomatoid after such an operation yields nonsense, if the essential, non-metaphorical, sense of the copula ''is'' be preserved. Thus, no onomatoid is singular or general, if singularity and generality are understood as above. But are there between them no di fferences in generality if generality i s understood in a modified sense? Yes, there are di ffer­ ences in generality between onomatoids, but not with respect to extensions, not with respect to generality, interpreted - as above - in terms of extensions, but with respect to the intention revealed in content. A similar distinction will apply to the genuine empty names. (7) ''Zeus'' is a

ge11uine name with a singular intention, and ''centaur'' is a genuine name with a general intention, though both are empty names if their extensions are considered. This is so because the content of the former includes a reservation of singularity, since the meaning of the name ''Zeus'' i s realized as the meaning of the name of the only common father of the Olympic gods. O n the other hand, the name ''centaur'' i s felt to be a ge11eric name of a kind of fictitious creature. In its co ntent, there is no reservation of singularity ; on the contrary, we feel the meaning of that na1ne to be such that, should it turn out that there are many cen­ taurs, there would be no misunderstanding whatever. Moreover, in the sphere of such names, we should be ready to admit of a certain hierarchy of generality : for i nstance, we feel the name ''young centaur'' to be less general than ''centaur''. These are not differences of extensions, since both names are empty, but there is a di fference in content. The content of the name which i n tl1is inte11tional interpretation is felt to be ''less general'' i s richer than the content of the 11ame which is felt to be ''more general'', since in addition to all the components of the latter it includes the property of ''youngness''. Similar distinctions as to generality may be applied to onomatoids too (consider, for instance, ''perfection'' and ''eternal perfection'').

,

ON THE CLASSIFICATION OF NAMES

393

•

(8) Further, i n the sphere of the genuine names a distinction i s made as between

individual

and

general

names. * The problem arises as to what is the relationship

between this distinction and the distinction as between the singular and general1 names, o n the one hand, and the names with a singular and a general1 intention, on the other. This is an old distinction, which has recently acquired importance again. Even Aristotle singled out ''sometl1ing about which we may speak, but which we may not say about anything'' , by which 11e certainly meant the proper names o f individual entities. To these names he opposed what may be predicated about s omething else all the sciences into particular disciplines and philosophy. In philo­ sophy he distinguished logic (with methodology and epistemology), history of philosophy (understood as a universal history of science), and metaphysics (sub­ divided into ethics, aesthetics, philosophy of religion, and the like) ; this division does not contribute anything which might be called essentially new and valuable. Novel ideas, on the contrary, can be found in the division of the real disciplines, which remains after elimination of the formal disciplines (that is, the various bran­ ches of mathematics) from the totality of the particular disciplines. Now those real disciplines are divided into natural and 11umanistic, and either of these groups (and here comes the novel idea) is subdivided into three classes : phenomenological disciplines, which mainly search for a causal explanation of processes and for the laws governing those processes ; syst,.:matic disciplines, which describe objects ; and genetic disciplines, in which the concept of development plays the mai11 role. Among the natural disciplines, physics may be quoted as an example of the phenomenological, mineralogy of the systematic, and the history of the evolution o f organisms, of the genetic ; among the humanistic disciplines, psychology may represent the phenomenological ones, jurisprudence the systematic ones, and eco­ nomic history the genetic ones. Wundt's classification paves the way for an exposition of a broad system of the methodology of sciences. It is an example of such a classi­ fication of sciences as serves to plan out the enormous and variegated amount of data provided by that vigorous and rapidly developing discipline. This field also regularly gives rise to special issues of classification, con11ected with often profound differences of opinion concerning the various kinds of scientific cognition and the tasks of the various disciplines. Let us recall the controversy about the place of formal logic in the system of scie11ces : is it to be classed in psycholo­ gy (Sigwart), or is it to be considered as somethi11g like algebra (Husserl versus Sigwart ; others also previously protested against such an interpretation as Sig­ wart's)? Or take the controversy about the nature of history : is it nomothetic (or, in Karayev's better terminology, nomological), that is, intended to discover the laws of becoming, or is it rather idiographic (Windelband, Rickert), that is, intended to rest satisfied with what is specific in the various elements of the past?

478

SUPPLEMENT

In Poland, Tatarkiewicz does not accept the idiographic character of history. To nomological disciplines he opposes typological ones, which he divides into historical (where temporal characteristics of the types in question come to the forefront), typographic (where above all spatial characteristics are brought out), and systematic (where abstraction is made from both temporal and spatial characteristics).< 1 5> It would be a sheer impossibility to s11m up all those systems which for some reason deserve attention : more than 1 50 suggestions have been published so far. The greatest effort and professional interest in this connection has been shown on the part of bibliographers, bibliologists, librarians and experts in the library sciences, and hence a mention is due to \Vhat they have done. French librarians are particularly renowned in this connection. They developed a system of catalogue­ writing not later than in the middle of the 1 7th century, at first for commercial, and later for more sophisticated purposes. In the hands of Jacques-Charles Brunet it developed in 1 809 into 1 8 pages of two-column print, and has since undergone many improvements. Epistemologically, it is somewhat artless (its five principal sections are : theology, law, history, philosophy and literature), but it is said to have proved practical, and it has become traditional in France. For instance, the National Library in Paris is in part arranged according to that system ; the same refers to the municipal library there, and the British Museum Library also bears traces of that system. But in the English-speaking countries, three-quarters of all libraries, and in the Soviet Union nearly all Russian libraries use the decimal system, promoted princi­ pally by Melvil Dewey ( 1 8 5 1 - 1 93 1 ), head of the New York State Library. In its most mature form that system is known as Classification Internationale Decimate, sponsored by the Federation Internationale de Documentation, and owes its triumphs to a group of excellent bibliographers from Brussels, and of course also to its inter­ national character and the simplicity of the decimal system in all its applications (paradoxically enough, France, which is the country of origin of the decimal sys­ tem of measures, not adopted by the English, strongly resists the decimal system of catalogue classification, having introduced in its libraries the Brunet system). The notation in the decimal system is as follows : the first figure stands for the main section, the second for its subsection, the third for the subsection of a subsection, and so on : the details of punctuation used are disregarded here. There is some re­ semblance to Ampere's system, the di fference being that Ampere divided each section into two subsections, and here each section is divided into ten subsections. This is an obvious violation of the natural system of connections between the various disciplines. Tl1e first ten main sections are as follows : 0 - general works ; 1 - philo­ sophy ; 2 - religion ; 3 - sociology ; 4 - philology ; 5 - natural science ; 6 - prac­ 16) < tical skills ; 7 - fine arts ; 8 - literature ; 9 - history. We need not engage here in the explanations as to how this system was arrived at (epistemologically the classification is hardly satisfactory), and what measures and tricks are used to subdivide each section into exactly ten parts. Let us not complain too much

THE CLASSIFICATION OF SCIENCES

479

about the shortcomings of the decimal system,( 17) but let us be satisfied with the fact that it has proved practical, tl1at its popularity makes it easier to publish in­ ternational bibliographies, and that it contributes to international contacts. So much for the history of the systems of classification of sciences (and, indirectly, books). Both the motives underlying their formulation and tl1e benefits to be derived from them have varied widely. And it must be added by way of conclusion that the idea of a planned co-operation in research has now raised many new issues of classification, issues which are of primary importance. Thus, J. D . Bernal has worked out a table of relatio11s between sciences based tS) on the variety of the tasks facing institutions engaged in researcl1.( The basic division by subject matter yields the three princ:pal sections : physical, biological and social ; this intercrosses with a division by the stages of collective research processes, the latter being accompanied by a classification of institutions engaged in research. For instance, academies of sciences are engaged in fundamental research, both analytic (theory of electricity, theory of colloids, and the like) and descriptive (oceanography, stratigraphic geology, anatomy, anthropology, etc.), while insti­ tutions concerned with technology are engaged in applied sciences, which produce either basic raw materials (mining engineering, metallurgy, paper industry, forestry and timber industry) or consumption goods (light industry, pharmaceutical industry). In addition to these, numerous special laboratories and local research stations work on the various specialized problems. All this is so complicated that it would need a three-dimensional model, the more so since more or less indirect relationships probably connect all the elements with one another. In Bernal's interpretation, the humanities are not treated satisfactorily. The whole shows convincingly that : (1) in a modern state, even if it be not a great power, scientific research cannot any longer be left exclusively to self-regulating action by the scientists themselves ; (2) any rational organization of co-operation among scientists must be based on some classification of sciences ; (3) the organization of scientific life should be extremely flexible, so as to make possible contacts between any disciplines, whether following directives from the authorities or as a result of some initiative on the part of the scientists themselves ; (4) bad organization of collective scientific life must result in damage at least as serious as are the advantages implicit in good organizat1on. •

Sayers-Berwick, A Manual of Classification for Librarians and Bibliographers, London 1 947, p. 96. 2 Ibid. 3 Uberweg-Heinze, Grundriss der Geschichte der Philosophie des Altertums, Berlin 1 894, pp. 1 64, 1 66, 1 70-1 72, 2 14-2 1 7, 224, 231-235, 262-263. 4 S. Kot, Zarys dziej6w wychowania jako funkcji spolecznej (An Outline of the History ofEduca­ tion as Social Function), Warsaw 1 947, pp. 54, 57. s Sayers-Berwick, op. cit., p. 103. 6 Ibid., pp. 1 04 1 05. t

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7

Cf. M .

Ornstein, The Role of Scientific Societies in the Seventeenth Century, Chicago 1 928,

p. 92. 8 I. Halpern, Rzekoma i prawdziwa klasyfikacja wiedzy d'Alemberta (D'Alembert's Alleged and True Classification of Sciences), in Przeglqd Filozoficzny, 1 919, No. 1-2. 9 W. Wundt, Logik, Vol. 2, Stuttgart, 1907, p. 87. 10 Cf. W. M. Kozlowski, Klasyfikacja umiejftnosci ze stanowiska potrzeb wyksztalcenia og6/­ nego (A Classification of Sciences from t/1e Point of View of General Education), Warsaw 1 895, p. 1 0 (kinematics is there termed phoronomy). The same author later published (Cracow 1 902) his Klasyfikacja umiejftnosci na podstawach filozoficznych jako wstfp do wyksztalcenia og6lnego (A Classification of Sciences on Philosophical Foundations as an Introduction to General Education). 1 1 Cf. W. M. Kozlowski's publication quoted as first in Footnote 1 0. 12 Cf. F. Engels, Dialektika prirody (The Dialectics ofNature), 1 948, p. 201 . See also B. M. Ke-

drov, Engels i estestvoznaniye (Engels and Natural Science), 1 947, p. 370. 1 3 Cf. B. M. Kedrov, op. cit., Chap. 4. The quotation from Engels is on p. 369. 1 4 Cf. W. Wundt, op. cit., pp. 89-100. 1 5 W. Tatarkiewicz, Nauki nomologiczne a typologiczne (The Nomo/ogical Versus the Typolo­ gical Sciences), in Sprawozdania PA U (Procedings of the Polish Academy of Leaming), Vol. 46. No. 1-5, 1945. 16 Sayers-Berwick, op. cit., Chaps. XI and XIII. 11 Strongly criticized by H. E. Bliss in his article The System of the Sciences and the Organisa­ tion of Knowledge, in Philosophy of Science, 1935. See also the earlier work by the same author, The Organisation of Knowledge and the System of Science, New York 1 929. t s J. D. Bernal, The Social Function of Science, London 1 944.

THE HUMANITIES WITHOUT HYPOSTASES* AN A'l"IEMPT TO ELIMINATE HYPOSTASES FROM THE DOMAIN OF THE HUMANI'l'IES

THE TASK OF THE PRESENT ANA.LYSIS is to try to formulate the subject matter of the humanities from the point of view of somatism, which states that there are no other entities, and hence no other objects of cognition, than physical bodies. Human beings, animals, plants, microbes, inanimate solids, electromagnetic fields - and component parts of such - are examples of physical bodies in this interpretation. From that point of view, there would be no reason to intervene, should the humanists accept universally that the common subject matter of their research involves, above all, human beings, and also things connected with human beings, and the distinct characteristic of the humanities consists in that with which these disciplines are concerned when it comes to human beings and the things connected with them. Human anatomy is not a humanistic discipline, for it is interested in how human beings are built ; the history of art is a humanistic discipline, for it is concerned with what some human beings have produced and how they wanted to influence other human beings by their products. For classification purposes, it does not suffice, of course, to specify the tasks of the humanities by way of example, but that is a different issue. The important point is to agree that human beings and certain things (products, materials, physical elements of a physical environment) are the only objects of humanistic cognition. Yet very often we hear and read statements which at least apparently are in disagreement with the above. It is said that psychology studies fatigue, pain, intel­ ligence, and psychic phenomena in general, dispositions to experience and to act, psychic acts, and contents of such acts - for example, inner hypnagogic images, after-images, etc. Anyone who might claim that any item in this list is something physical, would j ustly be blamed for misunderstanding the meanings of the words involved. Likewise, linguists, philologists, and theorists of literature often make state­ ments which might suggest that they take as objects of their investigations the vario·us entities which are not physical bodies, such as paradigms, forms of sentence structure, meanings of words, and fictitious personages from literary works, the latter being understood not as physical objects. Further, from historians, sociologists and lawyers we hear that they investigate historical facts, culture phenomena, social systems, legal institutions, and the like. It would be ridiculous to ask whether a cul* First published in Mys/ Filozoficzna, 1 952, No. 1 (3).

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ture phenomenon is a physical body, or whether a legal system is characterized by good electric conductivity or other physical features. We are thus facing the problem : how can we bring somatism into agreement with all that is correct in the statements quoted above? Many of tl1em are simply self-evident, for it is true that psycl1ology studies pain, linguistics meanings of words, legal history legal systems, and literary historians have various things to say about the cyclops Poly­ phemus and about Gulliver's stay with the Lilliputians, although no such creatures can be met anywhere and altl1ough they do not exert any physical influence upon any object in the world. If somatism is correct, then all such correct statements made by humanists may be accepted only on the condition that their sense is metapl1orical, secondary and substitutive, and that is just what we shall try to demonstrate. Let us begin with the issues of psychology. For instance, a psychologist studies the affect of anger. What does that mean? It means that he tries to find out how people get angry. The object of study is a given man who is angry. He changes specifically, and the point is to find out how he changes. Although we put it in that way, it is not a person's anger which irritates, or shocks, or terrifies us, for it is not anger which emits stimuli to our receptors. It is an angry man (or animal) which makes us feel so. And it is thus whenever it is said that we study psychic acts, psychic actions, or psychophysical actions. There is then a person who is experiencing somehow, a person who is moving somehow and straining his body, but there i s no object, other than himself, which would be a process of experiencing or a process of action, unless by the existence of a process of action we mean simply that some­ one acts, that there exists someone who acts. So much for the alleged existence of acts. For a closer analysis, we shall adopt as the point of departure the common opinion that an act can be characterized only by indicating what is its content. First of all, let us examine the existence, one by one, of what we state when we name as an existing object the content of an image, of a concept, of a judgement. Let us first consider the content of an image - for instance, a productive visual image in the genetic sense. Let it be what is called an immanent fancied hypnagogic image - for instance, the face of a stranger, which sometimes appears to our imagination ''as if it were alive'', when we are about to fall asleep. It might seem that we have found a striking example of a non-physical object. The same might hold of an inner landscape which we see in our imagination when, with open or closed eyes, we recall a place we have visited in the past. The same also applies to our own image in a mirror. None of these objects which exist (as we would have to say in accordance with the common opinion), extensive though it may be, is located in any place, determined by definite distances from the bodies taken as the points of practical orientation in our environment, none of them is subject to the force of gravitation, none of them absorbs or emits thermal or light waves, none of them conducts electricity. These objects, specified by way of example, exist, it seems, in time, and share this characteristic with physical frag-

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ments of reality, but differ fron1 them by the lack of location in real space, and by the lack. of physical properties. This is an average popular interpretation. What will somatism say to that? To be consistent, it must adopt the attitude of radical realism and state tl1at, strictly speaking, 110 immanent images exist and that the assumption of such objects (existence in the fundamental sense of the word) is untenable. When imparting precision to this reply and interpreting it in one of the many possible ways we shall adopt the assumption that we can make about something a true observation statement that that something is qualitatively such and such, if that something acts upon our sensory receptors as a stimulus. Hence we can state in this way about a leaf we are looking at that it is green, but we cannot state i n this way about an alleged immanent leaf that it is green, for it is obvious that no alleged immanent image satisfies that condition : it does not emit any waves or rays to our receptors, it cannot be perceived by senses, we can neither touch it nor look at it in the way we look at houses and trees, and we cannot react to it in any way as we should if we perceived it by the senses. That is why we claim what follows : in view of these assumption it is simply impossible to make observation statements about immanent images. The opinion, as outlined above, may at first seem to be a challenge to common sense, which states firmly that when we are half-dreaming we see certain fantastic faces, that we see landscapes in our reminiscences, that we see our own image in the mirror. But somatism does not deny such facts ; it only interprets in its own way the meaning of the sente11ces in which we state them. Everyone will admit that they are metaphorical sentences. For instance, the phrase ''in the mirror'' cannot be taken literally here : it should rather be ''on the mirror'', if we mean the surface reflecting light rays, or ''behind the mirror'', if we mean the place where a person who is looking at a mirror seems to stand. But this is a superficial side-issue. In our opinion the metaphorical character of the statements in question is deeply rooted. We think about a person who sees something (about ourselves or any other person), we say how he sees the various things outside himself, how they seem to him to be, but we formulate all this in the same manner as if we thought about his alleged immanent images. When Mickiewicz, in his well known sonnet, describes the psychic state of a voyager on board a sinking ship he says ''The blood-red sun is setting''. He says that in order to convey what was the visual content of that trav­ eller (as the matter would be formulated in a popular and metaphorical way), but in fact he wants to describe what happened to that traveller-among other things, what he saw. He does this in the way of placing himself in the position of that traveller with respect to his environment and makes the statement which that trav­ eller would make if asked what he sees. And the latter, if he is to give a correct answer, does not speak of any immanent images ; he speaks of the blood-red sun, he speaks of what he is looking at, and describes it as blood-red, in this way properly expressi ng what he perceives. This was a fictitious case of a description of obser­ vational vision ; the situation is similar in the non-fictitious cases of such a description. 32

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There is no other way of informing ''about the content of an observational image" of that part of the city which our guest is just visiting than to describe it in the way our guest would do. The same applies to reminiscences. ''Do you remember X?'' "Oh, yes. Stoops slightly, and has a big, sq11are head." That is the sort of answer the person will give, informing about ''the content of his reproductive image'', if he does not engage in theoretical speculations. In an analogous way, he will answer the question about what were his dreams : he will speak in the same manner as if he spoke in his own name at the moment when he dreamt, and will describe ex­ ternal objects as if they were being described by someone looking at them and stating what he sees. In our opinion, it is always so. Speaking non-metaphorically, we shall never make a statement in the form of a sentence of which the subject would be what is called a name of content (such as ''immanent image'', ''inner image'', "immanent red patch'', etc.). In each case, the subject of such a sentence will be a name of a thing : the object we are looking at, or the object we have been looking at, or the object which is just before us and which seems to be so and so when we are day-dreaming, our eyes closed. It i s probably needless to add that the explanations given above hold not for vision only, but apply to all the senses alike. While in the psychology of perception we have to do with contents of images, in the psychology of thinking there are in addition contents of concepts - that is, the various meanings of names and other expressions, properties, relations, what are called abstract objects in general, including the universals, etc. This i s indeed a nest of hypostases, or at least a multitude of opportunities for hypostatizing. But what is meant whenever we state that a person realizes the conceptual content of, for instance, a general term? What is meant is that the person understands that term. And when does a person lJnderstand a general term? When he at least intuitively knows what the object about which that term is predicated in a given language should be like. I realize the conceptual content of the term ''tenement house'' if I know that it may be predicated about any and every such object which i s a brick-built house with cheap flats for letting. Often we for1nulate this as follows : a person understands a general tern1 if he knows which properties are by means of it ascribed to an object (in this case, the property of ''being a house'', ''being brick-built'', etc.). In simpler cases we encounter such phrases as ''the property of extensiveness'', ''the property of redness'' ; such phrases may be useful, since they serve to abbreviate expressions. This brief analysis shows what is the attitude of the somatist with respect to ''conceptual contents''. He considers it nonsensical to accept an object of this kind, to accept the existence of abstract terms. Yes, we think in terms of abstractions, we generalize, we understand general terms, and all this is extremely important for the progress of hl1man knowledge, but it does not mean that we have contacts, in practice or in the process of cognition, with any general objects, abstract objects, objects called ''meanings'' ; the same holds, of course, for the ''contents of judgements'' - that is, meanings of sentences. We

often hypostatize when we imagine a separate object in the form of what is called

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a logical judgement - that is, the meaning of a declarative sentence. The sentence ''every beginning is difficult'' means that whenever a person begins to do something which he has not done before he finds it difficult to do. We understand that sen­ tence well, and we know that we may answer such and such to the question as to what that sentence means. And for that purpose we need not at all imagine the existence of any special object which would be the meaning of that sentence, a ''being so and so'', in this case the ''difficulty of every beginning'' . We shall make only a brief reference to the contents of non-intellectual acts, such as emotions, feelings, etc. The somatist does not accept the existence of ''feelings'' and ''emotions'' as objects. The words in inverted commas may occur in substitutive formulations, towards which we have an obvious inclination. Instead of speaking with precision : ''X is moved in various ways : he becomes anxious, he becomes excited, he becomes irritated, etc.", we shall say : ''X experiences the various emotional states : unrest, enthusiasm, irritation, etc." The nominalization of phrases makes our formulations briefer and more plastic, but also gives rise to illusory conjectures about the existence of such objects. ''Since we have the noun 'enthusiasm' there must be something of which it is a name'' (this is how we imagine). This reasoning is as faulty as the following : since a person was kept at bay there must be an object which is the bay where the person was kept. If all that is true, then how shall we interpret the correct thesis that a true thought is a mapping (in other words, a ''reflection'') of reality? The somatist rejects the popular interpretation according to which, when we examine the things around us, immanent images and conceptual contents begin to exist in our head ; these are qualitatively similar to the things in question : if the leaf we are looking at is green, its immanent image in our head is green too ; if juiciness is inherent in apples, then the content ''juiciness'' inheres in the head of the person who thinks about apples i n general. For the somatist, the very acceptance of the existence of such objects bears the stigma of nonsense. That nonsense i s multiplied by its own value if the ''immanent image'' is located in someone's head. In which part of the head should be located the ''immanent landscape'', alleged to be in the head of the traveller who i s surveying the vicinity with his eyes? While rejecting that oft-encountered interpretation the somatist accepts the thesis that thought maps reality (of course through the intermediary of the brain). That mapping is interpreted as follows : I am looking at a fresh leaf of lilac, it is green, ovate, shining. And I so experience that to the question how I experience I answer : ''I feel so : there is before me a thing which i s green, ovate, shining." I cannot introspectively describe myself at the moment of observation otherwise than by describing the external object as such as it seemed to me at the moment of observation. And if I observed it carefully, I shall have described it as it was in fact. Our thoughts map reality : this means that things are such and such, and we react to them - perceptively or through the interme­ diary of some objects, such as traces, signals, signs and instruments - so that these things appear to us, directly to our eyes or indirectly through signs, etc., such

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and such. And if we are observing carefully and under favourable conditions, if we draw proper conclusions from explicit sig11s, then we map reality correctly, things appear to us as they are, we think truly, we acquire knowledge about reality, and make true statements. After acts and contents of acts, comes the turn for the objects of such. A dis­ tinction is made between an external object of an act and an intentional object. A tool, a particular man - these are examples of external objects, and the somatist would be glad to encounter such examples only, since these are physical bodies. A difficulty arises whenever the process of an event (the passage of a meteorite, or a dance) is indicated to be an external object of an act. What are called names of events must be considered by the somatist to be onomatoids ; he must also con­ sider as nonsense the acceptance or existence of such objects as passages, dances, etc. I do not see the passage of a meteorite, but a passing meteorite ; we do not admire a dance, but a dancing person, etc. And how easily do we slide down the inclined plane of certain words from the world of things to the pseudo-worlds of processes, and vice versa. Take for instance the word ''current'' or the word ''wave''. On one occasion we interpret ''current'' as "flow'', and ''wave'' as ''vibration'', while on another occasion ''current'' is for us the Gulf stream, a moving mass of water which warms us, and ''wave'' is a moving wall of water which has almost capsized us. As a result of such shifts of meaning "processes'' in our cognition acquire attributes of physical stimuli, of bodies which are stimuli. Yet there is no object called ''sunrise'' or ''sunset'', although in a calendar we may find the entry, which is quite correct in so far as it is treated as an abbreviation : "December 5, sunrise at 8.22 a.m., sunset at 4.28 p.m." Another controversy arises as a result of alleged intentional objects. The external object of an act is always some stimulus (as when we see something) or something towards which we turn (as when we like something or someone, which is a form of the desire to come close to that something or someone). An intentional object is that alleged object towards which we tum in our acts wl1en such are aimed in a vacuum. When we think of the cyclops Polyphemus, who hurled rocks at Odysseus's boat, ''we tum mentally'' to a fictitious personage. Since that personage is fictitious, then there is no such object in the past, present or future reality. And yet, in the opinion of many theorists of literature, a literary work consists just of such objects. This is connected with the very controversial issue as to what is a literary work. The issue is always of topical interest. The catch-word of the philologists is that they should study the work, and not anything else : not the author, not the reader, not the experiences of the author and not the experiences of the reader, are to be investigated by literary historians and theorists, but the works themselves. But at the same time the interpretation suggesting that a literary work is just a quantity of printed paper is usually rejected. And as the philologists do not find any other physical bodies which might pass as literary works, they seek such among alleged non-physical entities, built at least in part from meanings of words, from immanent

487 images which are contents of productive images, and finally of imaginary things, perso ns, and events. The reader will see immediately that the somatist must firmly protest against all that. He has, it seems, only three ways out. One is to consid e r a literary work to be a sequence of words, where words are interpreted as physic al entities - for instance manuscripts, of course having a semantic function - i n the same way as we consider as a banknote a printed piece of paper, which is i11-

�

significant if we take into account its gravitational force, but powerfu functio nally, since it i s provided with meaning. It is also in the same way as we unhesitatingly consider the

to be the work of Leonardo da Vinci. The difficulties con­ nected with this interpretation are well known . Is every copy of Hamlet the work

called

Mona Lisa

And what about the various casts of the same statue? We recall some of these penetrating questions which try to undermine the rationality of the

Hamlet ?

possibility now under consideration. These objections can be rather easily dismissed by making a distinction as between an original and a reproduction or copy, and by considering the original, and the original only, to be the work of a given author, while all the reproductio ns are considered to be imitative works by reproducers, whose authorship is reproductive only, and not creative. Yet there remains the question as to whether a lyrical poem came into being only when it was external­ ized - for example, in the form o f a manuscript - or when its author forn1ulated it in his mind, wben he felt as if he heard that poem recited by himself or by someone else. Here the somatist theory i s assisted by the second possibility. The somatist,

if he admits the existence of works, will not say that a work is an experience of its author, for he does not accept the existence of objects which are experiences, or any objects which are processes. He also may not accept as a work either any auditory content, or any inner words, since such objects do not exist. The truth is only that the author felt in a way the result of which is that he might relate as fol­ lows : it sounded as if someone said : (and here comes the relation of what he alleg­ edly heard). Where, in such a situation, are we to seek a physical object? It i s the author himself who i s such an object, and his work will be the whole consisting of parts of himself, parts of his body ; that whole i s characterized by the fact that a person built so and moving so feels just so. This interpretation of the ter1n ''literary work'' has this drawback that it is not intersubjective, for only the author himself, having as it were become in part his own work, has any knowledge of that work, until he externalizes it by writing or reciting it. But it must be admitted that in some respect that interpretation complies best with common sense. For if we ask on what a poet i s working when he i s composing a poem, we have to admit that the poet's work is inner and that, when composing a poem, he works on himself, and not on any other material. But there i s still the third possibility : to conclude that, in the last analysis, there are strictly speaking no literary works, as there are no works when people talk with one another or when they perform physical exercises. There are people who

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narrate. It is sensible to ask what they narrate, but this is not a question about any ''work''. This is not the same as when we ask - what does a jeweller produce? and we answer : rings, bracelets, etc. To answer the question as to what Homer narrates, we have to resort to such composite forms as : Homer narrates the exploits of Achilles and Odysseus, etc., or strictly : narrates how Achilles fought at Troy, or what Odysseus experienced when coming back from Troy (and here would usually follow what we call a summ ary of the Odyssey). But a summary is not a description of the work concerned, not a description of a physical object, and hence not a description of any object at all. To summarize a poem rather means to feel imitatively, after the poet, more or less as he felt, and hence as it were to reproduce that poet. We say to reproduce, and not to describe, as we describe a mineral or a tool; we say to reproduce, but not in just any respect, to reproduce him simply as a person composing poems and to express oneself somehow analogi­ cally to the manner in which he would express himself when he was composing a poem. And he, when composing a poem, spoke of Achilles, of Odysseus, etc., for he felt as if such heroes were fighting and experiencing various adventures right before his eyes. We may, therefore, agree that a literary historian studies literary works, which means, if we adopt the first interpretation, that he studies the text, the tissue of words ; in doing so he is interested in their meaning in that language in which they were used by the author, interested in how the author felt when he expressed him­ self through his text, in that respect in which, when he is to be imitated, we have to say ''that it was so and so'' about certain fictitious personages about whom the author narrated that this and that happened to them. In the somatist's opinion, the literary historian has no objects of study other than texts and their fragments, their authors and their readers, and if the literary work is to consist of some other elements, then the search for such an object is a search for a non-entity. But an opponent will say : those fictitious personages do somehow exist ; indeed, they influence readers, and affect their attitudes and behaviour. After all, two nov­ els differ one from another in the persons of their heroes, and hence they differ by something, and not by nothing. The authentic king, Alexander the Great, imitated the Homeric semi-divine Achilles, and the recollection of Hamlet has induced numerous people to eschew indecision. These observations are correct, but not perhaps literally, if we are to accept them as true. For what is meant by saying that fictitious persons influence readers? We shall reply by resorting to an example. Shakespeare narrated and showed on the stage that he imagined a certain husband, called Othello, who driven by jealousy smothered his beloved wife, and those who formed the audiences to the play in the theatre were induced, when the actor pretended to behave in that way, to decide that they would not so give way to jealousy. In the last analysis, the influence was exerted by Shakespeare, and the actors, and not by Othello. The latter somehow existed ''in Shakespeare's imagination'', but that existence was in a derivative and metaphorical sense. ''The object A existed in the imagination of '

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WITHOUT HYPOSTASFS

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the person B'' means the same as : the person B imagined as if something were the object A . When using such a metaphorical, derivative language we may say that ''a literary work embodies the fictitious fortunes of personages imagined by the author''. Hence the appearance that there is such an object as a literary work consisting of such fragments, in the same way as a concrete pavement consists of slabs of concrete. But it is only apparently so. ''The famous novel by Cervantes consists of such and such adventures of Don Quixote'' nleans only that Cervantes imagined that one named Don Quixote attacked windmills and engaged in a fight with millers whom he took to be his enemies, etc. But why have we paused for so long a time over the concept of the literary work? For analogous questions arise with respect to all works in which the word acts as an intermediary. What objects are, for instance, a give11 ''discipline'', geometry, zoology, economics, etc.? What object is called a legal code? Mutatis mutandis, we shall have to repeat what we have said with reference to poems, novels and dramas. There are texts, there are authors of those texts, and there are readers of those texts. It is only among them and their component parts that we may seek the objects which are ''works'', ''sciences'', or ''systems of norms''. And moreover the nouns in inverted commas, and their equivalents, may legitimately be used as elements of substitutive formulations, interpreted in a derivative, metaphorical way. A given legislator ordered that under given circumstances people should act in a specified way ; he also ordered that under other circumstances they should act in some other specified way ; this was laid down as the proper behaviour in certain standard cases, and a ''legal system'' emerged. We formulate all this in terms of generalities, but after all that has been said above the reader will surely \1nderstand our intention clearly. There are no objects which would be wholes consisting of meanings of sentences, since there are no such objects as meanings of sentences. Hence if a person demands that the humanities should study the history of sciences, of philosophical systems, and of legal syste1ns, and understands this in the sense that these are the subject matter of the humanities in the same way as minerals, plants and animals are the subject matter of natural science, he falls victim to an illusion and commits a hypostasis. A humanist historian studies men and things of the past, including the things somehow shaped by those men. But he is interested in men only in so far as he can learn how to fill in the dots after ''that'' or ''to'' in the sentences ''X thought that . . . ", ''X strove to . . . ", or the dots after ''produced'' in the sentences of the type '' X produced . . . ", etc. And if John thought that A is B, and Peter thought that A is B, and Paul thought that A is B, and there was a Jarge number of Johns, Peters and Pauls, then ''the thought that A is B'' was a mass phenomenon. In such a case, the humanist often ceases to be interested in who thought that A is B, and is interested solely in ''they thought that such and such'' or in ''they wanted such and such to occur''. We then say tl1at the humanist studies the content of human thoughts, sciences, ideologies, human aspirations, the dominant trend of cultural and social movements, and so on.

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And society - is that a hypostasis too? Not at all. Society is a whole consisting of human beings. The same holds for the nation, the social class, etc. Human beings are understood here in an ordinary way, as John, Peter, Paul, Mary, Ann, etc. ''Man'' in history and sociology is the same being as ''man'' in medicine, but he is studied in other respects. Such human beings, plus certain things, combine to form institutions : factories, offices, banks, universities, states. And institutions differ one from another by their functions and the relationships between those functions, and by the dispositions on which those functions depend. Function, institution, disposition - so many occasions to commit hypostases. No object is a function. ''X has the function of a typist in the bank'' means the same as : X systematically types letters according to the instructions of her superior, a bank executive. Every institution has its structure, and is linked by definite dispositions : all this means that its component parts, and hence also the human beings who belong to it, are disposed in such and such a way : a subordinate is ready to do as he is told by his superior, every specialist is ready to work when required to do so. ''Disposition'', ''link'', ''structure'' - there is certainly no need to add that for the somatist all these are onomatoids. True, there exist different ''forms'' and ''systems'', but they exist in a secondary, derivative, substitutive and metaphorical way. In the strict, fundamental meaning of the word, there exist only groups of human beings institutionalized so and so, functioning collectively so and so, because of specified dispositions of human beings and other component things, including certain specified convictions and aspirations (see above). This is how we imagine the humanities without hypostases from the point of view of somatism ; we do so in the conviction that somatism represents the common sense approach. Somatism means materialism, and the constant concern of material­ ism is not to fall into the narrow trap of the mechanist viewpoint, to know how to cover the tasks and the actual \\'Ork of the humanists. We have endeavoured to solve that problem in a way which seems to us to be the only one for materialists who want to be consistent in their opinions. By way of conclusion, let us add a few defensive words to forestall objections resting on misunderstanding of our intentions in some important points. First, our picture of the world is often interpreted as if the totality of physical bodies were exhausted by separate individuals. Not in the least. In our opinion, the solar system does exist, as do the planets which form it ; a swarm exists as do the bees. A swarm and t11e solar system are compound bodies. Institutions, it should be emphasized, are similar compound bodies, consisting of human beings and of such instrumental bodies as buildings, vehicles, files of documents, etc. And the elements of institutions are linked by relations, not in the sense that there exist entities called relations, such as dependence, leadership, etc., but in the sense that the various elements of institutions are somehow related one to another, that some depend on others - for instance, some of them behave in such a way because the others behave in such a way, etc. The fact that a given institution - for instance,.

'flrn

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a firm - continues to exist although in a hundred years all its staff has changed, does not contradict the fact that at one time it consisted of some people, later on it consisted of some other people, but it always consisted of people (and some instrumental things) and never was an immaterial entity. A firm continues to exist following certain changes of human beings and things and certain changes in rela­ tions between them, while following some other changes in them it ceases to exist and gives place to some other compound object(s). Which of the two happens in a given case is a question of genetic identity of a compound object, a problem of which the analysis goes beyond the limits of the subject discussed in the present paper. The second point is that of the alleged mechanism of our view. ''You are a mech­ anist, since you reduce everything to bodies.'' Yes, I do reduce everything to bodies (defined as above), but somatism is not mechanism. A mechanist is a person who claims that everything that happens to bodies, whether animate or inanimate, whether active and thinking or merely vegetating, can be fully explained by reference to the laws of mechanics - that is, the laws of the science whose range of terms is confined to the world of centimetres, grammes and seconds. And that does not result in the least from the assumptions adopted in the present analysis. Hence the onus probandi falls on those who groundlessly raise the cry of mechanism against the system of theorems here expounded. Having dealt, as far as possible, with the objections we have heard about, we may still mention a certain other possible objection. When striving to eliminate hypostases from the sphere of concepts we should perhaps have attacked anthro­ pomorphism first, and stigmatized such a mental approach to institutions, human groups, etc., as if they were individuals. True, people are guilty of personalizations, but personalization is not a hypostasis, but a deformation, which is often joined to hypostases and thus completes the measure of delusions.

"

ON DISREGARDING THE EVOLUTIONARY APPROACH IN THE METHODOLOGY OF THE HUMANITIES*

WHOEVER IS INTERESTED in the dynamics of progress must indirectly also be in­ terested in the disregard of evolutionism, which is growing in the present century. Half a century ago, the most progressive natural scientists and thinkers were fasci­ nated by the idea of progress and by the study of everything from that point of view. That idea dominated both the biological sciences and the humanities, and even became the guideline of philosophy. But at the turn of the 1 9th century things took a different course. To realize that it suffices to read a dozen important books and articles on philosophy and culture. There do exist, later than the turning moment referred to above, works which are permeated by the idea of evolution. Ex­ amples are provided by Spengler, and by ever-vigorous dialectics. But in the science of culture, anti-evolutionism has come to dominate a number of leading minds and has formulated its own assumptions. Such assumptions have been formulated by the functionalists. What is, in fact, demanded by their spokesman, the ethnologist Malinowski? The local cultures of exotic peoples are vanishing and dying out, he says. If we do not examine them carefully now, afterwards it will be too late. It is, therefore, not the time for a genetic explanation of the institution of marriage among the inhabitants of the Triobriand Islands, or for explaining their complicated system of division of gardening products. All attention must be focused on description, and that will be effective if it demon­ strates the role of a given ingredient of a given culture in the collective life of a given society. There is, for i11stance, the system of co-ownership of boats, in \vhich the various participants have different prerogatives : we have to investigate how that system functions as an organization of fishing. This requirement does not, of course, imply a denial of evolutionism. But if we read further, we encounter more radical opinions - for instance such as this : Enough of searching for relics, which is being done by the evolutionists who expect that from those relics they may succeed in reconstructing bygone stages of the various institutions. In the course of the wedding ceremony the bridegroom pretends to abduct the bride. Hence the conclusion that in that society marriage in the past was concluded per rapti1m. The publications written by the evolutionists abound *

First published in Mys/ Wspolczesna, 1949, No. 1 -2. 492

ON DISREGARDING

THE

EVOLUTIONARY APPROACH. . .

493

in such conjectures, and the functionalists blame them for two transgressions.

First, incomprehension of the fact that every culture element which is called a relic actually performs some function, though not the one from which it had originated. That searching for origins distracts us from the more important task, which is finding out that actual function. Secondly, all attempts to explain empirical data by putative past events are essentially vitiated, for it is not a sound procedure to explain what is certain by what is merely hypothetical, and to explain what is evident by what is veiled by the mist of the past. Of particularly little value is the explanation of facts by doctrines, resorting to vague generalities and distorting the picture of reality, which proclaim the lJniversal nature of such or another law of historical development - for instance, by Spencer's laws of universal evolution as applied to history. Before becoming a pioneer of :fieldwork and theoretical research in cultural anthropology, Bronislaw Malinowski took university courses in mathematics, physics and philosophy. At that time, people used to sail under the flag of the Ger1nan variation of positivism - stick to pure empirical data and shun all meta­ physics like the plague. These general requirements determined the problems and the methods of research. There were also more detailed indications : for instance, metaphysics was discovered, after Hume, even in guessing the existence of permanent substances underlying the combinations and sequences of sense data, and also in all forms of ontological anthropomorphism. For instance, to ascribe independent existence to some necessary nexus between events (which is suggested by what we experience and what we call the feeling of e ffort) was discredited as anthro­ pomorphism. Hence the boycotting of causality : to inquire into causes and to o ffer causal explanations of events - these were considered relics of past naivety. The only task of science was supposed to consist in providing descriptions, as eco­ nomical as possible, of the various phenomena. The general nature of the laws in natural science was saved by general laws being declared to be condensed (and therefore economical) descriptions of phenomena. The flexible concept of economy as an attribute of a proper scientific description served to replace the classical conception of truth as agreement with reality, a conception which was boycotted in the same way as causality was. For the concept of reality was being boycotted too. As can be seen, the positivist broom of that time was used vigorously to sweep away from human minds all which might savour of existence not experienced by anyone, and hence of metaphysics. We are, however, not concerned here with that campaign against metaphysics, conducted by the Kirchoffs, Machs, Petzoldts and other similarly-minded thinkers. The important point for us was the requirement of pure description, with the abandoning of inquiry into causes, and hence inquiry into the causal dynamics of development. Both these requirements have tl1eir coun­ terpa1is in the methodology of functionalism. The first is strictly reproduced, pro­ vided that the meaning of the ter1n ''description'', used by Kirchho ff in the physical sciences, must be adjusted to the sphere of the social sciences and culture. As for

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causality, tl1e functionalists do not renounce it and even state that certain specified actions serve certain specified purposes, and yield certain specified results in a given cultural system. But the functionalists refuse to offer any explanations of systems by reference to putative past stages. They are interested neither in origin nor i n historical causes, and their indi fference to the laws of development is just a special case of that more general indifference. May we, therefore, state only an analogy of attitudes, or are we rather to see in Malinowski's minimalism a certain element inherited from tl1e minimalism of the said methodologists of natural science inter­ preted in a purely physical way? It would be difficult to answer this question which, however, may at least legitimately be posed. It might have been so, and it might have been otherwise. Minimalism is frequently encountered as an attitude in research, and in many cases it is due directly to the conditions of work of cautious researchers. They simply prefer to rest satisfied with tangible things, which does not mean that they are against broad syntheses, com­ prehensive comparative generalizations, and descriptions of the dynamics of pro­ gress. They do not consider such attempts to be misconceived in principle, to be attempts to solve wrongly formulated problems, to be distortions of the state of things, etc., but, either in general or with respect to themselves at the present moment only, they are diffident about their possibilities and therefore prefer modest but practicable tasks to magnificent but risky enterprises. They think that a bird in the hand is better than two in the bush, and they accordingly engage in sociography instead of sociology, dialectography instead of a general theory of language, philo­ logical textual criticism instead of a comprehensive interpretation of literary currents, etc. The minimalists do not accede to any doctrinal system, and hence would not sacrifice themselves for any form of evolutionism. Further, the minimalists differ among themselves in the degree of abstention. Some of them admit loyally that such or other assumptions concerning the dynamics of progress may nevertheless reasonably be adopted as provisional working schemes. Others avoid making even such assumptions. We may be thankful that there are researchers who are so cautious, but it would be unfortunate if only such tempers were attributes of scientists. Anti-psychologism, combined with the interpretation of the humanities as the sphere of intentional contacts with works, is a quite separate source of anti­ evolutionary inspirations. As long as the world of logical judgements, legal norms, poetic fictions - in a word, the world of what is called spiritual culture - was considered as the sphere of psychic life, research was naturally directed to the psychic creative process taking place in real time. Pride of place was given to genetic research : questions were posed as to who imitated whom, who underwent what kind of in­ fluence, which personal experiences of authors were reflected in certain details of their works, how their works reflected changes in social conditions. Many researchers tried to formulate general principles by seeking certain regular relationships ­ for instance, the dependence of literature on the milieu, and the like. But at a certain point a sudden illumination came. People came to realize, in the various spl1eres

ON DISREGARDING THE EVOLUTIONARY APPROACH. . .

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· of research, that what they had taken for acts of consciousness and psychic ex­ periences were nothing of the kind ; hence people turned their backs on psychology and on genetic explanations, and the evolutionary point of view lost its all attrac­ tiveness. A special example of this occurred in the field of formal logic. While Sigwart still held it to be part of psychology, Husserl - wl10 at first also studied ''the psycho­ logy of arithmetic'' - led a revolution and told his readers that formal logic is not psychology, that nothing is founded there by generalizing observations of the temporal process of a person's thinking, and that the discipline in question is not concerned with thinking and psychic experiences. Husserl directed human minds to objects of abstract thinking, intentionally given, but not psychic in nature, in the same way as numbers and the relations between them are not psychic. He was not the only one to do so. The spirit of the time brought with it, especially in the then most i nfluential German methodology, a revival of Platonic, Hegelian, Bolza­ noan tendencies, a revival of objective idealism. Husserl's phenomenology, under­ stood as an inquiry into the essence of ideal obiects, covered with its influence the theory of legal systems, the theory of literature, etc. It came to be allied in practice with Dilthey's idea of the distinct nature of cognition in the field of the humanities. According to the latter thinker, the humanist ought first of all to strive to understand the work he is studying. But that study should consist not in finding out its origin, but in grasping penetratingly the meaning of the work in question. It was concluded that the origin of a literary work tells little about its proper meaning, and that this applies both to the origin of that work within the life story of its author and to its origin in the succession of centuries. People therefore ceased to study - in the field of literary history - the biographies of poets and novelists, and their sufferings in private life ; the study of influences was abandoned, the triumphant catchword was the demand to study the (literary) work alone, and to disregard the past and the experiences of readers. Moreover, formalism restricted the analysis of literary works to that which is specific to a given work qua literary work (style, structure, forms of expression, etc.), disregarding even its intellectual content if the latter is not an element of its literary characteristics. It has been an unquestionable merit of all those allied trends that they made people realize the distinct nature of problems not sufficiently brought out before, that they opened vistas to issues pertaining to products of culture and yet neither psychologi­ cal nor genetic in nature. Neglected issues came to be privileged, and at the same time problems of genetic and evolutionary explanation , previously privileged, came to be completely neglected. The unwillingness to treat man and his culture as subject to the universal laws of evolution has also marked the attitude of the traditionalists. The assertion that spiritual culture is autonomous with respect to Nature has proved to be the meeting ground of the traditionalists with certain representatives of independent thought. For instance, nothing is more alien to Florian Znaniecki than the search for the laws of evolution of compound objects, laws such as those expounded in Spencer's

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First Principles

(progressing differentiation of elements, progressing separation of

elements from the whole, progressing complication of relationships between ele­ ments, etc.). Such laws would have to cover both the evolution of the stellar world, and the evolution of living animals and the evolution of society and spiritual cul­ tures. Znaniecki did not deny progress, just as he did not deny the process of decline ; nor was he indifferent to the issues of origin and history. But, dominated by the con­

sciousness of a creative, and hence not automatic, course of evolution in the matter relating to man, he showed very little interest in general dynamics of development,

in studying its forms and regularities, even if these are merely relative. And if we have to speak of dynamics of development, we should rather, i n his opinion, do so with respect to the individual branches of spiritual culture. But the forces of development which have shaped the system of geometry and those which have shaped polyphonic music have, in Znaniecki's opinion, s o little i n common that it would be difficult to speak of any common principles of evolution. Znaniecki's assumptions were burdened by Bergson's conception of development. The mechanist assumes that everything which happens later has been fully and univocally deter111ined by the laws of mechanics and the position of microelements of the world at a given moment in the past ; consequently, it i s to the limitations of the cognitive faculties of h11man beings that he ascribes the difficulty of discov­ ering the iron laws of becoming. By contrast, the followers of Bergson and his ideas concerning creative revolution hold that i t is essentially impossible to draw from the past a correct conclusion about the future, because there are no iron laws of becoming, although the future emerges somehow from the past. And regularity i s not a principle of the universal course of events, but a marginal phenomenon, which occurs where creative tension subsides. We do not declare ourselves i n favour of either doctrine. It must only be stated that the former rather encourages the human mind to search for the laws of development, while the latter, even though assuming development and the wealth of its unexpected forms as a fact, rather dissuades its followers from searching for such laws. Even if Znaniecki later on abandoned the principles of Bergsonism, and even occasionally so11nded a fatalistic note, yet the Bergsonian component of his early studies could not but leave fairly permanent traces i n his works ; and it probably largely explains the weakness of his inclinations to adopt a general evolutionary view in the theory of s ociety and the theory of culture. A similar weakness of evolutionary tendencies can be seen in the followers of the Baden school of llistoriography. The concept of history as an idiographic discipline, the concept by which history remains itself and at the same time i s fully a science if i t confines itself to studying what i s specific in the various things and events, has fully developed precisely through opposition to the demand that histori­ ans justify the laws of the historical process . In this interpretation, history may be concerned with group characteristics of things and events from a given period and a given territory, but justification of any laws which are temporally and spatially

ON DISREGARDING THE EVOLUTIONARY APPROACH. . .

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universal, like the laws of physics, remains outside the sphere of history as a discipline. The idiographic programme includes genetic explanations of, and inquiries into, the developmental processes of individuals, groups, styles, institutions, etc. ; indeed, it even includes appraisals of the importance of given changes from the point of view of progress, but it repudiates any attempts to discover and justify any laws of historical development - for instance, such as are modelled on the laws of ontogenetic development of living organisms. Hence, it is not that the evolutionary point of view is neglected in the metl1odology of the Windelbands and the Rickerts : in their methodology there is no place for evolutionism. But apart from those mentioned above, there is a current which is decidedly hostile to the idea of progress in the historiosophical sense of the term. It suggests that we should not strive for progress and should not consider the history of man's inner culture in terms of progress. It is thus a trend directed against evolution and against evolutionism. It is formed by the methodological reflections of art histor­ ians and by the personalist interpretation of the essence of education. Compare the image of history as seen by a historian of painting or sculpture or music, with that seen by the historians of mathematics, physics, chemistry, technology, biology, medicine, insurance, trade, etc. The latter are struck by immense changes, consisting in a vertiginous progress in knowledge, efficiency, level of difficulty of problems solved, increasing mastery in processing materials, improving for1ns of organization and co-operation. On the contrary, the forn1er sees a fluctuation of styles, each of which creates masterpieces of its own. May it then be stated with a sense of responsibility that later styles represent better art, more advanced as compared with earlier periods, that, for instance, Renaissance art means progress when con­ fronted with Gothic art, and so on? Within a style it is possible to state technical progress, but it is impossible, they assert, to state progress in the history of art. Let us transfer that argumentation to the sphere of the spiritual culture of the various individuals, and we arrive at one of the elements characteristic of the ideolog­ ical foundations of personalism. According to that doctrine, every new human individual faces, from his very beginnings, the ever-recurre11t task : how can he mould his ego according to models of self-perfecting ? In former times, people were willing to use in this connection the concepts of sanctity, assimilation to the divine ideal, salvation of the so11l, or deserving of eternal felicity. Today, intellectuals feel no longer bound by that complex of concepts and ideas, but the essential idea (which contains certain moral values) may be retained, and is in fact retained by the personalists. This has led to the formation of the educational principles of neohumanism which, weary of the engineer-like, conquistadorial and exploiting attitude of the enthusiasts of progress, turns away from it. It does not look at history from the evolutionary point of view, but is interested solely in the moulding of an individual's spiritual life. In such an interpretation , the attitude towards the achievements of the past is that of imitation, of repeating once more what has been many a time achieved in the past through analogous efforts.

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This concludes a cursory review of those tendencies in the twentieth-century methodology of the humanities which are alien to evolutionism. We have covered diverse trends which share the common trait that they all reveal some form of discordance with evolutionism in its complete form. And such full-fledged evolu­ tionism includes, in our opinion, the following elements : it strives to o ffer genetic explanations of facts, to evaluate the course of events by the criteria of development and progress, to inquire into the most general laws of development, without, how­ ever, rejecting registration of partial regularities and various types of changes in the perfecting of human actions and human products. Each of the c urrents analysed above lacks some of these elements, and their general picture shows that in recent times the European h11manities are not universally interested in the problem of progress. In our opinion, this is to be deplored. It is not our intention to take up cudgels in defence of this or that school which formulates general principles of evolution, but we want to save the problem of progress because we expect from its analysis excellent results in the sphere of the methodology of human skills and abilities, a methodology which investigates empirically verified principles of work well done.

ON THE HISTORY OF THE CONCEPT OF ADEQUATE THEORY*

PETRAZYCKI EXHORTS us to build adequate general theorems. He means sub­ ject-predicate theses able to satisfy the following conditions. Each such thesis ascribes distributively a property to a set of all past, present, future and possible objects, provided that such share a definite property specifically common to them. It ascribes it not only correctly, but also reasonably, in conformity with the methods of correct foundation of connections between properties with respect to a logical or causal nexus. The property so ascribed must also be an attribute exclusively of the elements of the class under discussion, which is the criterion of adequacy. Hence, such and only such a scientific theory is adequate which predicates neither too narrowly nor too broadly, but simply as is required ; this can be guaranteed only in the founding of the connection between the content of the predicate and the specific characteristic of the elements of the class under consideration (qua its elements). Theories which ascribe something to too broad a class of objects are called by Petra.Zycki jumping theories, since their predicates as it were jump into alien spheres, outside their natural boundaries. Such theses are by their very nature false, despite the fact that they may include a correct, though too acquisitive, in­ tention. As examples, we may quote the various sociological theories, for instance the opinion that all social phenomena are reducible to the conquest of social groups by other groups. Those theories which ascribe a property to too narrow a class Petrafycki calls ''limping'', for they suggest the image of something large, based on too narrow a foundation. These, which by reason of their lameness are by no means incorrect, are in his opinion ripe for elimination, since otherwise science would be flooded by such theses as, for instance, the statement that all two-ounce

Let. us consider whether similar ideas l1ad been formulated befor e. Undoubtedly yes. First of all, let us recall what was stated on that matter by Aristotle, which in several points strikingly resembles Petrazycki's recommendations. We refer in this connection to Chapters 4, 5 and 6 of Book One of Posterior Analytics, where the structure of a scientific general sentence is discussed. Numerical generality, consisting in that what is ascribed is in fact an attribute of every, and hence of the first imaginable, copy of a general object, does not suffice for scientific generality (i-o xa{}6Ji.ov). It must, moreover, be an attribute of that to which it is ascribed as such, hence not only xai-a naPi-6�, but also xa{}' av-r6. What is involved here is the necessary nexus between that to which something is ascribed, and that which is ascribed. Further, scientific generality in the stricter sense of the terms includes the condition that that which is ascribed should primarily, as n e w-ro'V, be an attri­ bute of that to which it is ascribed. In other words, there should not be anything more general of which it might also be an attribute. This requires that what is predica­ ted should not only not cover a broader extension (for otherwise it would not be numerically correct), but also should not be referred to a narrower extension than that to which it may be correctly and reasonably referred. It must be ascribed. as it were, as is required - we might say, ''adequately'' (the term is not Aristotelian). As an example of such a general scientific theorem in the stricter sense, we may quote the proved thesis that in every triangle the sum of the inner angles equals two right angles. And only he who knows this theorem knows in a general way that this is a characteristic trait of a triangle. Otherwise, even if he had proved that property separately for any equilateral triangle, any triangle with sides of different lengths, and for any isosceles triangle (and hence general for each of these partial cases, but of course not generally in the stricter sense, but in some pleonastic sense). he still does not know that every triangle has that property (even if the types enume­ rated above exhaust the entire set of triangles), and a fortiori does not know that each triangle has that property as a triangle. Aristotle also agrees with Petrazycki in so far as among the causes of the spreading of inadequate theories he mentions speaking habits : he asserts that sometimes we do not refer the predicate to the proper extension of the subject because there is a lack of a tern1 for precisely that extension. And here are further examples of theorems defective by reason of inade­ quacy : any pair of straight lines on a plane which when intersected by a third straight line yields the corresponding right angles, is a pair of parallel lines ; this is an inade­ quate thesis, which would become adequate if the words ''right angles'' were replaced by ''equal angles''. (The example probably fails since the formulation ''a pair of straight lines on a plane, which when intersected by a third straight line yields equal corresponding angles'' does not differ in extension from a similar for1nulation i n which the word ''equal'' is replaced by "right'', although the formulation ''equal angles'' has a broader extension than the formulation ''right angles".) Should some-

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one prove certain relations between elements of a ratio, relations resulting from the essence of a ratio, not for a ratio in general, but only for ratios of numbers or only for ratios of lines, or only for ratios of solids, or only for ratios of time segments, in each of these cases the thesis would be defective with respect to general­ ity. It is striking that all these examples are taken from the field of mathematics, mostly geometry. This is a difference by comparison with Petrafycki who does not eschew that field, but usually draws 11is examples from experimental disciplines, and out of the two kinds of nexus, which he singles out, he pays much more at­ tention to the causal than to the logical nexus. In Aristotle, rather the converse taking place. He makes a distinction as between the various meanings of the term xaf>· avr6, among whicl1 he mentions something of the nature of efficient nexus and something of the nature of logical relationship. As regards the former, it may be said that an animal died when struck by a blow, whereas we may not, in a state­ ment, connect the fact that a person was walking with the fact that it thundered while he was walking. As regards the latter, something is an attribute of something else as such, if and only if that first something is included in the answer to the question as to what the second something is, or conversely. In the further analysis of generality the former meaning (referring to the efficient nexus) leaves the field, for only the latter meaning (which refers to logical relationship) may come in question in the case of mathematical examples. But puzzling points remain here, for the meaning referring to logical relationship is difficult to apply in detail to the otherwise lucid analyses pertaining to the generality of theorems. Even the first possibility, mentioned in the definition of the second meaning, may prove misleading. For Aristotle it proba­ bly did not mean only such B which, when I ask, what A is, is of a higher order than A , as is the case of the answer : A is such a B which etc. For the line is given by Aris­ totle as an example of something which is included in the answer to the question as to what a triangle is, and yet it would probably not be in the spirit of Aristotle to say that a triangle is such and such a line ; at most, we might say that the triangle is a figure which is formed of lines in a specified way. A still greater difficulty is caused by the second of the two possibilities mentioned in the definition of the second meaning. For instance, evenness (in Greek, ''evenness'' and "that which is even'' have the same for1n : rd ll. e rtoP) is an attribute of number as such, because when answering the question as to what is that which is even, we have to refer to number, for instance, by saying : that which is even is such a number which etc. And yet the statement that every number is even would not be true (and, a fortiori, would not be adequate). To evade those difficulties, we should probably have to assume that Aristotle in his theory of adequacy does not make use of all the possibi­ lities inherent in the meaning, discussed above, of the term xa-D' av-r6, in the same way as he makes no use of its other meanings, which he also mentions. But the issue remains rather puzzling on this point. Petrafycki too, by the way, is enigmatic, for he is very laconic when it comes to the interpretatio n of the logical nexus.