Debunking science

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171

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B36

09887

$ B

YD

30

266

.

T

.

E

BELI

-

NUMBER FORTY FOUR

WASHINGTON

Edited

by

UNIVERSITY

OF

eseor

Debunking Science

Glenn

Hughes

CHAPBOOKS

Price 650

UNIVERSITY OF WASHINGTON CHAPBOOKS No. 1. A Short View of Menckenism - In Menckenese By JOSEPH B. HARRISON

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Modern

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OVER

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A

of

WILMOT ELLI Japan Book Translations GLENN HUGHES AND YOZAN IWASAKI New England Twelve Woodcuts ERNEST THORNE THOMPSON With Jaques Foreword Bertha Eugene The Art Neill JosEPH SHIPLEY By ALLEN ROGERSBENHAM Clio and Mr Croce Victoria Twelve Woodcuts Viola PATTERSON With Foreword Frederick Morgan Padelford Perry Percursor The Story Takano Nagahide By HERBERT GOWEN Monsieur De Baleac Entertains Visitor PIERRE LOVING The Crisis Film John GOULD FLETCHER Language and Style Notes HULME Read Herbert Edited Fifteen Poets

on

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No . . . .

22 .

No No No

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No

.2524 . . 23

21 . 20 . . 19

No No No

18 .

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17

No

Ta

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14

No No

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No

16 15

12 13 . .

.

.

No

Dramatic Censorship BARRETT CLARK

By

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An .

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H

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10 11

No .

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Note

Our Own Diogenes

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With

VERNON Louis PARRINGTON Lawrence Indiscretion RICHARD ALDINGTON Interpretation Lillian Gish EDWARDWAGENKNECHT England and Ireland Twelve Woodcuts Richard BENNETT With Foreword Zona Gale Japan Three Women Poets Modern Book Translations GLENN HUGHES AND YOzan IWASAKI The Haunted Biographer Dialogues Dead GAMALIEL BRADFORD The Journal Japanese loheleth Kenko Musings the Fourteenth Century HERBERT GOWEN Christopher Morley Multi Uno BABETTE HUGHES Remy Gourmont Modern Man Letters RICHARD ALDINGTON Hio The Great Learning Newly Rendered into the American Language Ezra POUND Hawaii Twelve Woodcuts AMBROSE PATTERSON Bovarysm Philosophy The Art Jules Gaultier

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No. 2. The Painter Looks at Nature By WALTER F. ISAACI No . 3. Four and Twenty Block -Prints for Four and Twenty Rhymes Old Nursery Rhymes Illustrated by Students at the Univer sity of Washington , under Direction

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No. 26. William Congreve , A Conversation Between Swift and Gay

By BONAMY DOBREL By Louis ADAMIC By EDWARDWAGEN KNICHT By C. HARTLEY GRATTAN Australian Literature By BENJAMIN D CASSERES The Superman in America Vernon Louis Parrington : American Scholar By Joseph B. HARRISON By GEORGE WILLIAMSON No . 32. The Talent of T. S. Eliot No . 33. Historic Philadelphia : Twelve Woodcuts HARLES R. GARDNER By V . F. CALVERTON No. 34. The New Ground of Criticism By Sophus Keith WINTHER No. 35. The Realistic War Novel No . 36. Speak the Speech: Reflections on Good English and the Reformers By BARRETT H. CLARK By HERBERT REAN No. 37. Julien Benda and the Nero Humanism By PHILIPPE SOUPAULT No. 38. The American Influence in France By EDWARD GODFREY Cox No . 39. Naming Day in the Garden of Eden No . 40 . Some Ultra -Modern French Poets : A Book of Translations . By BARETTE HUGH ES No . 41 . Logger - Talk : Some Notes on the Jargon of the Pacific By Guy WILLIAMS Northwest Woods By Virgil GEDDES No. 42. Beyond Tragedy : Footnotes on the Drama By PRESCOTT CHAPLIN No . 43 . Mexicans : Twelve Woodcuts With a Foreword by RUPERT HUGHES

No . 27 . No . 28. No. 29. No . 30. No . 31.

Robinson Jeffers : A Portrait Utopia Americana

By E. T. BELL

No . 44 . Debunking Science

IN PREPARATION No . 45 . Sigrid Undset : A Nordic Moralist

: By Victor

VINDE

VISITAR na i din

najcent

DESTIKING

SCIENCH

Debunking Science by E

. T . BELL

OP CoricBUY comeBD . Com

1930 UNIVERSITY

OF WASHINGTON Seattle

Book STORE

Copyright

,

1930

, by Glenn

Printed in the United

HUGHES

States of America

Pici . 74376.9

QIMI

B36

DEBUNKING

192

SCIENCE

DEBUNKING

SCIENCE

I

SHORTLY before his death the Field Marshal Earl Haig , who nothing

if

and who warned men

of England

to

not sanely never was

late

was

conservative an

alarmist ,

the schoolboys and young guard against what

be on their

of science . He referred

he termed the superstition

manias of our time for making pseudo -religion out of science and a pseudo

to the epidemic a

. He might, with greater inclusiveness , have warned the

out of religion

science

brevity and equal boys not to be a lot of credulous young dupes. Whatever the cause , the world is growing impa tient with believes

in

advertised

.

in

to

lay

the lighthearted ungulli thirty today those under the great war justified only that the war suddenly

fool. Some

to

This

of

bility

a

is

called

as a virtue . Whoever now impossible the is not canonized but is

credulity

all the world

that science had begun

DEBUN KING SCIENCE to grow

up

, an

unpleasant fact which before 1918

negligible handful of pro fessionals and a score or two of defeated generals. gas attacks , soundly Unanswerable methodical Zeppelin night crusades over swarming cities and was familiar to only

brilliant

men ,

submarine

women and

a

against

subtleties

children ,

shipsful

demonstrated

of

instan

the whole inert mass of civilized that the Greek and Hebrew cultures ,

taneously

to

humanity

belles lettres and vague philosophies hold up but a badly cracked glass through which to view life as it is and not as it may have been . The belated

world

demonstrations spectacular

tunately is

hope for

were so still half blind .

of the war unfor

that the bewildered

But there is abundant

all .

convinced

Those who knew better than to be by fireworks and forensics, are now to

be converted themselves headedness

to and

.

Haig ' s in

spite

Jarred

“ superstition ”

in spite

of

of their superficial hard

from

their

extremes

of pre

war indifference to science , the public thinkers , the incorrigible mystics and the popular philosophizers

after science as the inerrant star which to light our stumbling race to reward ever lasting joy and festivity after gorgeous debauch

,

a

is

of

its

now blunder

DE BUNKING SCIENCE glandularly prolonged

dividends without cap

.

and dissipation without drawbacks

credit the popu Haig realized many

.

science

elevating

of

,

of

,

a

at

,

To

.

of

to

the temperament the beholder put another object art one superb the decade just past the next century shining wise and generous will raise

,

its

in

the most precious and the most

all

of

monument

a

,

be

it

if

figure

of

,

followers science from religion toughminded new which the

tenderminded

of

be

according

to

,

slackest lipservice

afar hint irreverently label the superstition Against this picture depressing may

the spiritual

of

.

,

the elder

the

.

Already

seers

Indeed

we are as

be

inestimable

even

, if

larized

gained

,

science

is

to

lucre

prophets promise humanity

dazzled

grossly material

or

all

not

The wealth

to

these

by

which is

,

fied three score and

ital

of

ten

centuries beyond the sancti

dur .

a

if

a

of

, of as

a

In

in

the synthetic metals treasuries graceful pose eager flight the figure young girl running her head turned half back glimpse over her shoulder she would catch able

the third decade

it

,

of

,

of

of

to

of

,

of

the invisible competitor she had outdistanced antiquarians the Twenty First will suggest Century that all human kind was the flapper the Twentieth who first

DEBUNKING SCIENCE

10

taught

a

worldwide generation

to the past , merely because

it

exactly what respect is

not the

present

,

is

proper .

They may even surmise that , this Atalanta like Eve, ate her apples before she started the race . The conjecture of the antiquar

due and

ians

will become a

certainty

when

, having

satisfied

themselves that the runner is indeed young , lithe and feminine , they observe that she is thumbing

her nose .

And any of them who feel impelled to warn the young generation of their day against whatever errors may then be in fashion , will con clude that it might save time and drop a hint to the girls .

to

ignore

the boys

The young men and women of today have debunked so many of our inherited frauds and superstitions that it seems not unreasonable to hope that they and their children will succeed in debunk ing the rest . That all debunkers must add new boshes of their own to supply the vacua by the annihilation of the old , is probably

nature. This perhaps present superstition of disconcertingly regions, hole .

science

is

produced suddenly

Nevertheless ,

in

the

science a

created a law

of

true origin of the : having somewhat vacuum

in

certain

expanded and filled the spite

of the preposterous

DE BUN KING SCIENCE bulk

of

of today ,

the neobunk

continually

solidity

C decreasing

11

we may look

for

a

the newer bunks,

in

the densest of them is immediately seen through for the pure gas which it is . Of all the debunking this generation must do,

until

that

even

necessary

relatively

is the most urgent .

science

in

large fraction

, as

To keep the

whole

free

,

all

common agreement

of

we have .

sound as anything

of the

of

shadow

A

is, by

today

science

conscious

estimates

Others

.

can

.

The see

admit

it

in

.

the niche their

All

be

,

and they

to

. of

branch and root the

,

to

out

debunking

will

squatting

probably

would

their own interest

well meaning professional popular -

bunk which

idol

rip

,

critical moods

them

and ousted fetish

,

a

fatter

some discredited

to

of

science

only

aid

spare the time

have

others again as

minds

of

be

?

Perhaps some their guild willing but unable may

of

not the scientists

should

set

,

Why

scientific

younger men

,

false

peculiarly the task and women who will learn the facts is

reliability

to

science

in

by

in

livings

of

imposture , and to eliminate as quickly as possible from the minds of those who do not make their

,

by

,

of

izers and prophets science zealously aided unscrupulous quacks have sown broadcast over the

DE BUN KING SCIENCE . Until , how

.

is

too

tradition

are

.

fathers knew which the young

do

a

post

the

for their joyous task debunk comprehensive ignorance The

ing First things which their

,

the qualifications

of of

flapper generation ?

the work which

.

any

,

,

if

What

slothful

too

undertake

to

logged

are

or do

-

The children must

parents

their

unlikely

will crystalize into altru

that scientific self interest istic action

disbelieving

,

the mystic seven

is

that twice three

for

whole fair field of modern science ever , some martyr is barbecued

it

12

not know and consequently will not have unlearn are happily almost uncountable Sec equal lethargic importance ond their indif

,

, of

issues which men still under sixty

to

ference

is

, of

.

,

to

today

con

,

of

of

it

to

be

to

,

by is

of

.

significant out

to

sider somehow all the muddled and irrelevant past And third com plete the sacred number the curt refusal the spell young hypnotized any the name only middle however great may seem those vaguely

of

in

With

the

.

,

.

to

their the future this triple key hands the young are already generations ahead their elders age

,

ill -

In

only one serious respect does younger appear prepared although generation even this

DE BUNKING SCIENCE defect may

Their

the end be their

in

sentiment

than passive indifference . them

from

osmosis very

gulled

. More than

least that

the debunking

To

will is

debunk

from

the post - flapper

from

look for

a

is

desirable

.

The

quickly where

science

most needed

.

expecting

This alone will not save by a sort of spiritual

indifference

respect

.

tradition is no warmer

toward

being

greatest strength

is an

aggressive dis

keen , refreshing generation

skepticism

is as futile as

a roué slowly mortifying sharp edge of an active doubt The

passion from

boredom

.

might well debunk science , shrive it of the last shred of superstition , in half a generation . Unfor and

being incompat

skepticism

on

.

if

—

then

particularly

apparently irremediable

indifference

and

will

and toward We are thrown

consequent

of

never

This appalling

any enthusiastic

and here the rock the middle generation needs his overshadowing cathedral is

living

.

,

science

back

die

skepticism

its

is

dearth

they

,

of

up

all

wake

till

ible , hundreds of millions now

boredom

,

boredom

in

,

tunately

debunker

yet too

subtle and too

to

sacrosanct

to

are

as

of

.

of

on

found the darkest pes simism The unwarranted creeds and crass super being injected into the clean body stitions science which

the

and the young have

by

be

.

it

little

the roaders who regret that purified cutting wind

-

middle

Those

of

to

of -

,

is

ruption

.

at large to be safe subjects decomposition indifference Active cor salutary skepticism indicated initiate the cor painless

by

believing world

for

DE BUNKING SCIENCE

14

as

a

at

,

is

a

so

science must doubt may reflect that skepticism least They may wind even find some comfort

clean

of

keep the winds

to

,

to

by

.

;

,

sanitation

light

destroy are ruthlessly exposing

seem

and submitting

science

in

rotten

of

is

what

Many who

they hope

the reek

it

,

of in

charred flesh fact creating

tainted

been

to

turies this one has never

by

in

all

of

.

in

the the many winds which have blown across human affairs the past twenty cen

memory that

doubt

the

for

the debunk philosophic to

the classic

.

be

for less irrational opponents only disgruntled and selfish humanist ignored

no

in

.

of

is

beauty hold that there science and life that science has induced the kind in

of

is

of

science

bunk that

in

the propagation cellar

lighted

of

,

,

the

no

,

Of these

science

for

traffic

The valuers

.

mushrooms sense may

any

to

is

values damp poorly

,

what

a

theory

of

,

if

With the values ers will have little

, of

.

ever clean

joy

Their

DEBUN KING SCIENCE

15

of joint, and with such there is no argument . Nor is it profitable to wrangle with others who shout that the horrors of war , and whine that the miseries of peace are due more noses are merely out

largely

to

than to their own stupidity

science

incompetence

.

They with

the rest

will

best and worst that science can give.

and

share the

The best

what concerns the debunkers . That best is a tive disbelief in those things which have shown than

to

be

false,

and no more assertive

temperately

a

suspended

a

been

disbelief

judgment

toward

those things for which there is much evidence they are not false

is

posi

that

.

To make superstition in the name of science impossible is the principal objective of those who Superstition

they define as

more than

to

,

science lead

does also the significant but

now

own known

be nonsense

these few

simple

principles

mind the ,

With

in

.

to

things once held

techniques

perpetuation

to

,

superstition

Belief what

read into the conclu given unequivocally

of

science

the recognized

not superstition is

Attempts

as

by

sions

evidence

be

it

may

of

ever

be .

of

the lack

is

the best evidence available .

in

all

science

belief against

of to

.

would debunk

DE BUNKING SCIENCE

16

debunkers are ready

.

to attack their enemy

Science

thus far , they declare , in spite of the manifest evils that have come with it , has been too decent a thing by the superstition mongers . And

to be prostituted

as

a

tactics , they

matter of sound

propose

the enemy in detail , beginning

. Ironically

weakest position

,

destroy

to

his fort.

their assault on

enough , the one

be the position most exposed to attack like

steel and

distance are revealed

.

concrete

closer inspection

on

from

a

foundations that looked

as

out to

Its

ress that has stood for centuries in the uncritical mind as the symbol of impregnable strength , turns

.

crumbling sand

at

is

in

to go

can

retains

,

how

those things

.

,

with

regards with rea it

,

and exactly

own methods

of

its

By by

what

it

,

suspicion

entitled

far

the earliest

science has abandoned sonable

science

possible moment what things

no

know

interested

it

The public

is

plenty will remain

be

To

.

competent

debunked

.

must

to

,

,

That accomplished

science

subject

that be

be

the most

public

in

a

,

of

,

,

”

a

its

of

acknowledge worthy

all professionals to

majority

of

in

be "

to

anthromorphic ideal science course understood but merely the corps those particular subject whom workers substantial

satisfy

DEBUNKING SCIENCE all but

the aspirations of who have

a

17

those congenital believers

genius for being duped

.

II Where may we made

to be

in

expect

beginning

reasonable

a

this project of debunking

science ?

Happily it is not necessary to guess . A perfectly definite beginning has already been made , most appropriately , in that science which used to be

from

.

then

right with our hopeful

credited

the eternal verities

once

,

For

,

say

us

. Not

a

not

dated

that the modern crit

1908 be

began

is the

of

race

-

about

let

back

to in

far

ical movement the world war

,

to go

sharp

queen

is

the too

of them all . So historic mark that it may be precisely styled

science

a

,

be

it

,

that

alleged

scien has

or

one other the numerous popularizations current acknowledged men who are leaders

by

of

a

is

?

that these men touch major part fundamental doubt which may affect the reasoning which they and their fellows science

The answer

of

presented

no in

by

excellently

asked

the magnitude

of

escaped analysis

of

disturbance

may

in

tific

possible

it

How

is

.

youth

DEBUN KING SCIENCE

18

soar above facts a hard saying . three thousand

to

It

mystical possibilities cannot be

words .

But

inspect the relevant works O named

in

opinion

on

There men

,

as

is

two or

in

of

a

few

of

the men

able to form

his own

this point at least asl .:

is a

as to

proved

This

anyone who cares to

will be

the sequel ,

justified

.

sharp disagreement

what well

among competent

and what cannot be irreconcilable divergence of

can be proved as an

opinion

as to what is sense and what is nonsense . point This is the major one that will be made :

the dispute

is

between those men

of

science

who of

all are most competent, in the common opinion of experts, to judge the issue . In the particular field concerned , the only one relevant here , the men cited are as competent they disagree

as

is

Einstein

in

.

Notice the word

" nonsense ” above

inability , among

.

his.

And

It was

their

other things , to define this word by other than Russell s epigram , “ a meaningless

'

noise ,” that brought to grief the heroic attempt of

Russell and Whitehead to put mathematical rea soning on

a firm

basis

.

More than may appear on the surface is con cealed beneath the controversy . It involves the

DE BUNKING SCIENCE

whatever that asserts gen any particular personal This not

for

you

say

general

a

by

on

not pas

us

-

il

you

dit

do

qui dit généralité

(

this

object that which

. ne

Et

!

quote Hadamard

science

if

?

And

infinite

say

's

.

“

:

Has not

general

is

science

stated

right with the

its

point

clearly

who believe that all

those

world

been

To

of of

.

The fact has

a

.

opinion leader

is

to

any system

in

erality

The same

conclusions

.

for any of

generality

applies

claims to attain

in so far as science

science

its

whole of

19

Let say about this gen hear what the other side has erality without which modern mathematics but insignificant shadow may itself whatever This

conservative

be

of up

—

to

be

be

saved

from

the

past

Not

Queen

of

Gauss declared

all

,

.

mathematics

twenty years will probably occupy one generation

Mathematics Sciences

,

of

the

of

whatever

cleaning

.

enough

task

is

be

wreckage

to

and

The

salvaging

,

.

they arrive

physics and

sciences The latter may left physics the foundations when can

in

the experts

the realm

.

the less exact

in

generality

of

the rôle

of

of

an

is

to

”

from

a

)

?

infinité

the

scientists who use mathematics

,

in

,

in

their work particularly those more specula tive flights which fascinate the credulous would

DE BUNKING SCIENCE To more

seem

an

of

relatively invariable results

tacitly assumed

inductions from

laws

nature

not the actual machinery

the

believe

,

to

will

in

deeper

.

them

experiments

the spirit

mathematical reason

Hence

.

is

freely used

gifted with the

individual

, , of of

"

passages from

,

In to

all

nearly

persist

,

even the most conservative

to

greater durability than

”

significance and probably

in

giving

ing

cautious workers the

that

if

experiments

of

handful of

eyes

of

agree with Gauss .

are

20

the prized

those

gener

,

is

indestructible bedrock

all human of

the

facts

of

.

,

its

of

pernicious corollaries with all irre fragibly established For are not experimental ality

and are not the conclusions mathe matical reasoning necessarily true provided the hypotheses true The desired conclusion does

on

is

.

Yet

a

work for

it

a

the most

to

likely

such

as

two

at

generation

reputable scientist use any sense other than

be in

nature

”

"

laws

guesses which may or

of

that

of

Nor would

.

not follow the phrase

?

be

,

,

experience

Aimsy

.

is

No

-

foundations these that more than one being reared pseudo religion

. of

in

for

satisfactory justification has ever been given connecting any way the consequences reasoning mathematical with the physical world

DE BUN KING SCIENCE It

has

yet even

not

implied

problem

posed , or whether ertheless

,

whether the

is what mathematicians call necessarily

it

is nonsense

well

. Nev

hunger of the uncritical

the consuming

mind for what

decided

been

21

imagines

or finality prevailing it shadows in the famine of substance . Even if it be granted that the problem of physical inference is not as mean

impels

it

to be certainty

of

sourer than

equally destructive the tools used

on

a

,

rhombus there remains doubt concerning the nature

is

assertion that yellow

of

ingless as

an

the

to feast upon

on

,

one side the problem and that side the impor tant one for those who breed superstition

.

science

,

of

all mental

in

. . ” . . ( . of in

lies chiefly results

treasures

for that

the human

the

what intellect

,

its

pure

charm

:

, " .

in

avers

certainty

of

he

)

absolute beyond

The

,

of

,

Wonderland who anything but uncritical mathematics

of

by

the author Alice his strictly logical work was “

,

was confessed

is

that

The older credulity which high average user the mathe

.

still

is

of

reasoning

system

matics

self consistent

-

mathematical analysis

a

cast

serious doubt has competent judges upon the valid as

been

of

ity

not

by

Until comparatively recently

DE BUNKING SCIENCE

22

for.

us only

of something ! More light , more light ! . . . . . 'And if our fate be death , give light and let us die !' This is the cry craves

Let

be sure

per that , through all the ages , is going up from plexed Humanity , and Science has little else to meet the demands of pure mathe may minor dissent

its

of

more

is

that most the statements moving testimony are false The one thing that has become increasingly clear

Dodgson

all

the past twenty

years

of

no

:

in

is

this present certainty whatever regarding there the major conclusions modern pure mathe others

is at

above

.

's

in

absolute

today but

certainty

A

little concerned with important objection

intellect

be

,

a

,

as

an

.”

matics this rejoined that instructed

it

conclusions

is

the

.

than

really

To

,

votaries

will

of

offer , that

that those

it

,

is

mathematics

.

in

,

or

provable

is

judge disagree violently what not proved

to as

what

only

know

to

not merely

We

is

competent

themselves to

among

as

who

.

-

are

be

to

self consistent

prospect that proved

will

exists today

be

there any immediate

pure mathematics

as

nor

is

,

matics

.

is

of

to

so

in

of

dispute And some the fundamental matters SA IS mo are deceptively simple that common sense would are unhesitatingly assent their truth where the against them expert opinion weight

DE BU

N

are two

There

KING SCIENCE

23

diametrically opposed

schools .

Each denies the contentions is

able ,

to

certain

a

extent ,

of the other , and each to destroy the conclu

by the other. The questions on disagreement which there is are not trivialities ; they are the very roots of the whole vast tree of modern mathematics . The consequent uncer sions

reached

tainty

affects

every

conclusion

not only mathematics itself , but by

reached

mathematical

also

meth be y

or

others the doctrine

of

of

,

those

x

follow

used

mysterious

whether they plus whom

to

to by

as

is

subconsciously

symbolism

is

the tricks

as

in

to

all

ods, whether those methods be applied by experts

the

at

,

that science

least

tainted with mathematical reason o

'

will

-

the world

a

light

is

possible

of

is

seem

it

as

far a

so

in

,

ing

would as

It

.

Egyptian trinity

For what the normal human being pro desires his reachings out after the infinite vided the act him significant and not obviously superrational something nonsensical least

.

to

at

to

—

of is

is

-

in

-

the wisp

the

in

rationality "

of

it

a

who crave dash their aspirations will not find

in

sophisticates

.

of

being beyond every casual attack the extent thinking upon the mere rudiments Those rarer absolute

24

DEBUN KING SCIENCE

certainties

”

of

clusion

of pure mathematics , or deduced

science

by an

in

any

con

of

application

mathematics to idealized results of experiment , for the " absolute certainties ” one and all have

.

Here, of

course ,

for

vanished

is the day of glory which the mystagogues and the obscurantists have been

to

,

the

”

“

will

has broken down

Dante and

Thir

un world which has grown wish them Godspeed

.

science

Science

a

”

;

accustomed

And

!

Century to

teenth

"

.

pining since Darwin they will exult back

III generation

ago there was apparently

A

but one recognized doubter mathematicians Leo Today any professional mathe pold Kronecker

.

,

among

matician who has acquainted himself with the work is

, to

by fix

trusting

is

it

a

at of

the past twenty years will admit that there least bitter disagreement and that the very thing which firmly before essential

As

, .

both

.

there are equally authoritative men

in

,

as

be

as

mathematical reared structure quicksand analysis may stable about already mentioned there are two schools and any

DEBUNKING SCIENCE

25

The essential thing to be established is the fol lowing . Is the body of modern mathematics self

In other words, can it be proved that precise application of the rules of the

consistent? a

rigidly

mathematical game diction ,

such

will not

as “ A

this point , among

is

B

lead to

a

flat contra

is not B ” ? On as vital , mathe present hope of recon

and

A

others almost

maticians are split beyond ciliation . One school holds that with sufficient tinkering proof of self -consistency is minor a attainable although not yet in sight. To give the adherents of

this

James'

William

view

label

and

term

the tender

them

fits

minded .

name, let us recall

a

for the tenderminded mathematicians are repeating detail the history spheres their kind other Their opponents the toughminded believe that the disputed funda designation

,

,

.

in

of

in

,

The

The present

they

error

controversy

be

to

defy the tender their reasoning

likened

.

and

mathe

by

certain

of

discover

in

,

nonsense

have shown

conclusion

of

one major

is

to

matics minded

is

that more than

They further claim

an

useful

.

sary

or

in

to

-

,

mentals are necessarily self inconsistent and that any event they have ceased either neces

DEBUN KING SCIENCE

the toughminded

of

any one

to

the innumerable

physical

of the past two centuries over

physical theory maturity and

, they old

be

A

,

its

theories now discarded . point out, has youth

its

disputes

its

26

The analogy obvious and need not pressed beyond the death and burial the decrepit theory When senescent physical theory fails

two hundredth gland repose

and

Centuries

Twentieth

infin

the without of

elaborated

the

the great mathematicians

,

by

ite

toughminded suggest that the theory Nineteenth

The

.

seek

of

to

allowed

is

,

transplantation

it

the hundredth

or

a

.

to

respond

to

of

,

.

is

age

it

,

is

unnecessarily prolonged and must not

complicated

If

the tough overlooked that

of

,

m

minded are right

century

.

half

the past

be

for

it

an

in

manner

is

as

actually used mathematical analysis impossible has been committing suicide today

which

keep them

from

enough

worrying about their

the types

flagrant

of

to

The clearest examples dictions which certain

of

'.

their own neighbors

to

ment the mathematicians have troubles

of

.

of

,

of

with the mathematical theory the infinite goes out also all generality including that the sup physical science posed laws But for the mo

contra

mathematical

DE BUNKING SCIENCE reasoning however , seen

a

from

technical .

are rather

lead

Fortunately ,

fair picture of some of them can be a verbal example due to Weyl . The of Weyl 's contradiction is paper by the late F . P . Ramsey .

following

statement

transcribed

from

a

“ Some adjectives have meanings which predicates of the adjective word itself ; thus word ‘short is short , but the word ' long ' is long . Let us call adjectives whose meanings

of

it,

of

is

it

and com

,

a

we have

it

if

a

.

So

predicate

.

is

a

its

meaning heterological

of

its

it

is

,

heterological therefore

are

Now is 'heterological heterologi meaning predicate is , not heterological not But not

is

,

it

it

is

that

If

not

others

.

heterological cal ?

, like 'short ', autological ;

them

is

predicates

are

the

their

own

resolved

complete

the

as

stuff

Weyl

's

science

on

as of

Many have

silly

satisfaction

.

to

.

a

to

found no better than this contradiction

Almost

superstition

too

not

?

it

,

Foolish

attempt

is

.”

plete contradiction

these

of

is

true the disputed mathematical analysis

.

tions

of

the same

.

's

is

-

one

of

successful logi cian mathematicians can convince another that his Precisely solution correct and his rival wrong

Unfortunately not

technical founda

of philosophy will recall

's

Established

,

such

and

of

in

fought like

has

each

a

.

There

Church

Berkeley attacked

little more than

that

said

interests

vested

one

such

,

It

is

.

been

lusty devils when

were assailed achieved

no

many of

have been regiment

is

there

Science

the differential

called

has

sore head and

a

what now integral calculus

doctrine

a

between

.

fuxions

acri

Bishop Berkeley and

Newton over the latter

—

of

the followers

of

monious controversy

its

Amateurs

and

the

DEBUN KING SCIENCE

28

and

gen

a

in

course

to

any fairly intelligent reader today with

a

.

to

be

.

of

to

of

.

he

ridicule The things was admit were cornerstones the math Today only very ematical dogma his time college sophomore dull could converted the faith which Berkeley unsuccessfully attacked And erous anointment

too obtuse

of in

of

it

and

reaches

some

of

get

at

.

farther back than Newton

To

,

it

on

,

the

Our own judg the past fifty years

the disputed work goes much deeper similar but

ment

is

the Eighteenth

the

.

masterpieces

of

Nineteenth

the sense the second half Century simply does not exist

of

Proof

in

.

of

is

calculus behind him amazed learn what passed great the mathematicians for proof among the Eighteenth Century

the

DEBUN KING SCIENCE

29

trouble it seems that we shall have

to

emend

Aristotle . With Berkeley and the doubts of the Eighteenth Century comfortably ignored , the leading mathe

maticians of the first half of the Nineteenth , using sharper tools with greater caution , proceeded to exploit the legacy

of Newton and

to

create

new

theories of their own . This was a tre mendous activity , much of it critical . But the old ere not dispelled . doubts were Then came came Karl period of

Weierstrass , usually ranked as the greatest of analysts , who incidentally undertook to show that the puzzles about the " infinitely small ” and the great ” could be obviated . His work “ infinitely

, Georg Cantor

inspired

two

others

Dedekind

,

attempt

to

and Richard put the infinite itself on

to

sound basis . Without ysis is meaningless .

such

a

Cantor , it attacks

of

is

reported

something

,

, mathematical anal

was subject

akin

to

madness

to

recurrent

. His

best

work , the modern doctrine of the infinite , was done succeeding these in the extraordinary lucidity

'

attacks .

Cantor s disciples

celestial

splendors

won

for

us , ”

as

still believe that he

(“ the Paradise

Hilbert

puts

it )

which

saw

Cantor

on his frequent

39

DEBUXKING SCIENCE

absences

from

may

be

the

worth

in

sense .

world of

, it is

For what it

interesting to among experts

this connection

that Cantor is not alone the mathematical infinite who have exhibited wo . mental aberrations, including paranoia observe

on

Contemporaneously with Cantor and Dedekind , great mathematician , Kronecker , began a third working , but destructively , on the same problem . Kronecker was the first of the finitists . He was eminently sane . Unlike Berkeley , as a mathema tician he was the equal in technical skill of any of his opponents .

With

ness he declared

that

should

lack

shown

entity

.

be

was addressed

an

as

,

be

a

to

reasonable demand which

he

for any mathematical supposed proved

it

to

demand that

so

C

se existence whose

is

actual construction apparently

to

his

was

a

.

as

would do it. ous theories any ing

his contemporaries , his successors Among objections the marvel his rivals was new one irritat

of of

the nonsense

faction

if he himself

and time to destroy what he considered

It

strength

toughminded

characteristic

This

exasperated

the that for forty

Suppose

,

explanation

.

two

of

word

or

a

at

.

it

or

completely more they ignored particular point The issue here perhaps needs

years

for exam

DE BUNKING SCIENCE ple , that

of

set

31

physical problem has been reduced which defy explicit solution

a

to a

by

equations

command , and suppose further problem is such that an explicit

the means at our that the original solution

is

of no particular

interest

, but that

it

is

know whether it does have a solution though we may not be able to find one . The even mathematician frequently meets the conditions by

also

stated that

actually an

injus

greater

infinity

many

method attained

mathe

this the finitists object that could

do

To

method

has done what

suggest

mathematician

this

in

even

and

a

not

to

,

one

;

is

no

.

matical operations

him

a

,

should

whereby the solution could provided we could perform

asked

somewhere

—

be a

do

. He

to

able

is

he

instances

it

, .

he

merits

tice than

Not

to

him

for constructing the solution was asked of

exist

in

does

but is unable to exhibit

of

solution

a —

a

that

( but where ? )

,

proving

to

be

important

what

turn the other side retorts is

it

.

,

utterly incredible

a

very ancient

Plato And what may seem any toughminded individual

.

least

echo

, of

hear as

we

an

of mathematics

to

old

at

,

creed

this retort as

In

side the domain

,

is

that the objection irrelevant that not math anthropomorphic ematical but and therefore out

DEBUNKING SCIENCE

32 it

is

fact that many of

a

the leading mathema

ticians today believe that mathematical theorems are discovered in the following sense : they have existed in the ideal universe of mathematical truths since the beginning of time, or before , and the

an

is

It

proof

dictum

construction

proves

pre

proof

was

,

No

and

,

is

,

“

.

his disturbing

worthless

.

to

establish

cisely nothing

On this point there

”

exhibit the thing whose existence

ports

to

which

is

of

ob fails the proof pur Kronecker

existence

existence

no

that

”

jected

"

all arguments an

To

.

.

of

to

its

passage through life eternity human mind in recognizes merely comes upon and these eternal images the everlasting truth interest ing theory

not

.

yet agreement

is

to

of or of

in

In

as

mathematical reasoning classic logic fre excluded quent appeal the law made

for

on

.

is

point out about twenty excluded middle may

flat contradictions when

applied

an

or

tions consisting

of

uncountable

collec infinite num to

lead

to

's

L

. E . J.

to

Brouwer years ago that Aristotle

It

.

of

:

a

is

it

proposition false either true middle Kronecker overlooked the bearing this his LS OW campaign own destruction was reserved

are

precisely

physical

those

science

that space and time are

of

there

.

permeates

also

assumed

up

is

it

33

.

theory

Their

For

Such collections modern mathematics

.

of

things

interest

in

of

ber

DE BUNKING SCIENCE

a

of

In

is

.

sets

;

countable

be

for

's .

with

passing

should

it

his

.

the drama

if

,

infinite set

an

was not convinced that

asser

necessarily

is

concerning

anywhere

of

the infinite

that

where the hero

in

,

by

He stated

integration

he

mathematics

,

of

the theory

an

pendently

true

false

. his contemporaries

from

the

With the begin

the contradictions were

no

of

theories ning this century

.

of

Kronecker had anticipated paradoxes

so

or

middle This all Aristotle framed

after

experience

others

break

that Brouwer criticism was made inde Lebesgue who revolutionized also

mentioned

tion

possible

excluded

,

knew

no

from

of

he

the law

a

.

or

the law

rather unreasonable

is

down

listen when they hear

of

refuse

of to

of ,

continuous and hence not made countable points Logicians number instants sometimes

's

,

appeared

,

mental Principia Mathematica

In

.

of

to

numerous that even the tenderest minded could longer shut their eyes them 1910 when the first volume Whitehead and Russell monu many

DEBOXKING SCIENCE rejoiced .

The

,

resolved

assumption

There

it has

is

paradoxes

had

brilliantly

been

at the expense , however , of a new , the notorious " axiom of reducibility .”

no need

what that

to describe

. By

been abandoned

the first important work

a

axiom

curious freak

of Brouwer

on

of

the

was ; irony

foun

appeared

dations of mathematics about the time that Principia went to press . If not killed before it was born , Principia was at least mutilated by the earlier work of Brouwer in 1908

Russell

's

supposed

resolution of the paradoxes

by the majority

of mathema the first the new axiom excited sus It was too far - fetched . Finally , in the

was never accepted ticians . picion

.

From

.

second edition

inability ,

, the authors

stated clearly

their own

with the help of the disputed axiom , to validate the cardinal assumption of all mathe even

matical analysis (the Dedekind section ) . Roughly it amounts to this : mathematical ysis as

it

works today must make

numbers ( such

as the square

use

anal

of irrational

root of two ) ; the

in which such numbers exist is hazy . reputed Their mathematical existence implies the

sense of any

disputed remain

.

theories

of the infinite .

Without

a

satisfactory

The paradoxes theory of irra

DEBUNKING SCIENCE

35

Galileo

.

,

to

wrong he

as

,

If

a

to

of

is

it

of ,

.

.

compass the infinite merely Kronecker was not destructive give impossible satisfactory maintained by describing square account the root two with

our attempts

does

it

remarked

that something

follow

is

,

.

seem

as

But

axis

to

It

turn on would

its

tional numbers , among other things , Achilles does not catch up with the tortoise , and the earth cannot

a

a

as

Half

a

it

imagination

.

of

,

if

, . as

flights

restrict their

of

,

of

he

of

In

in

?

try

it

infinite sequences numbers why way out proposed his own theory Analysts have the difficulty rule disliked his proposal adopted would considerably terms

cen

of

no

in

,

.

it

be

may hence less repugnant lack any something spectacular At rate one mething more

tury

I

,

's

infi

concealed

of

is

of

is rid

.

to

but one the generality mathematical

.

seems

hidden be

exist

.

to

ceases

,

also

which

be

, ”

of

To To

..it

The

neath what Kronecker called indeterminates

out which his theory

it

this

to

technically

,

More

disguises it

protean

any

“

it

the notion

believe that

modern objection superficially gets

open

of

in

theory too nite which

opinion

solled called

he

as

personal is

express

detac algebraic magnitudes

a

theory

of

in

morcon seriously yet has succeeded seriously defacing Kronecker

with

DEBUNKING SCIENCE

36

During the last five years the dean of living has

mathematicians , David Hilbert , a man whose tire less genius for nearly fifty years enriched

, of

declares

“

,

one

”

.

us

No

the Paradise

from

shall

Cantor won

which

for

."

us

chase

“

skeptics

minded

he

-

of

,

of

with dozens beautiful things has put his supreme life effort into the defense tough modern mathematics against the attacks mathematics

regarded

is a

is

It

.

as

by

's

to

contribution the defense epochmaking his disciples

Theory

of

Hilbert

cent enough rules must

be

,

to

to

prove that the math Demonstration which aims game played according ematical certain inno

.

-

in

is

consistency

,

work the problem

begin

bequeathes its

emphatic terms

of

the generation

to

In

just about

.

eventual efficacy

for

enthusiasm

tenderminded faith he

rather

a

and

to

his theory

its

Hilbert himself professes

needed

in

it

. of

of

,

self consistent Thus proof consistency far the has not arrived that part mathematics where most urgently

scientific

recommending

-

of

where

appears

to

Hilbert

it

placed

by

tion

is

is

of

.

a

as

promising tool demonstrating that modern This problem reasoning as mathematical free self contradic his own theory

DE BUNKING SCIENCE ,

belong

ahead

of all others confronting

37

the science

Familiar with theoretical physics , and

of our age.

at the application of pure mathematics to the mathematics of physical problems , Hilbert undoubtedly grasps the implications of this prob

an adept

specialist

one - sided

as no

lem

can

.

we may

So

agree that the problem has at last been formulated by one whose achievements entitle his opinions to

all who work

respect from

,

And there ,

.

in science

a

on

finger

par

,

Wittgenstein

by

is

the issue

understood

The problem

it .

solve

; is

.

Hilbert

of

,

Principia

,

but failed

to

and after him

middle

position are those who

,

formulated Hilbert these retort the question under discussion

irrelevant

,

sort

of

a

.

is

problem

In

to as

naïve

have misunderstood the nature

,

Russell the

rather

those

Demonstration

by

said

to

,

but another

of

who believe that the Theory

rather unkind

once

it

.

Both have been offered The first LOT has been given more than

but

, .

least two possible answers

is

this there are

at

To

.

theory and who cannot ticular flaw

his

his

put

unfortunately agreement appears to cease . In his forthright way Hilbert declares that he will abandon on the threshold anyone who disputes

like

DEBUNKING SCIENCE

38

Lusin

,

state

Hilbert is

if

that

they

have

understood what

saying , then his assumptions

as objectionable

reducibility .

as Russell

's

are at least

discredited

of

axiom

Lusin further remarks that the mod

ern mind may be a little satiated with paradises in general and with Cantor ' s in particular . This is a

delightfully frank remark from one who himself hath drunk the milk of paradise .

,

by

so

put

it .

blun

asserted that Kronecker had

of

Hilbert

subtle on

that more than one interpretation may Briefly

.

is

the matter

be is

,

although

-

have been

Van der Waerden

theory which false This done two page article a

to

of

in

consequence appears

his

Sw The second type of retort is to answer Hilbert's challenge and show him definitely one inevitable

.

'

to s

is

priori true

.

à

is

positions which

least part category

of

at a

Demonstration

in

of

to

's

prove

put

that Hilbert equivalent

fact identical with

the disputed

that one Hilbert theory aims This would appear Theory

in

and

to

of

,

begging the question

is

of

to

Van der Waerden seems show purported refutation Kronecker

assuming

as

,

a

of

,

in

,

in

to

his objections the theory existence proofs not logically but far more crudely one might blunder adding column numbers dered

with

the the

DE BUNKING SCIENCE efforts of beginners A

equals

B

Where

: let

A

in

Geometry :

equal

To prove that therefore A equals B .

;

B

do we stand ?

then

39

The one fact estab

lished by the controversies of the past fifty years competent men , recognized by is this : equally

mathematical experts the world over

legiti

as their

mate leaders by virtue of superior intelligence , are in complete disagreement over the foundations of reasoning

.

Certainty

has

at present of might recognize

which

form

As mathematical

we

.

there is no hope

and

any

in

vanished return

,

its

mathematical

modern

reasoning

permeates

,

say

,

of

of

lead

to

,

processes flat con

follow that scientific

foundations

which

to

seem

on

would

are risky

rear

the revision

of

can

of

safely trust

mathematics

finding out has begun

—

exactly how much

science

by

debunking we

of

.

creeds

The work

in

a

,

it

,

new

use

their own strict domain

tradictions analogies

lavish to

,

in

which

by

gained

have been

to

the

on

of

of

as

of

current physical the nature the universe many dazzling details nothing and mystic generalizations physical the science speculations

those

who call

, ,

in

.

themselves finitists and intuitionists The first tentative raids are already evident other sciences

DE BUNKING SCIENCE .

notably physics

To some the outcome in mathe and utterly destruc

matics will

CI seem

devastating

of all

faith

in

tive

anything .

These are as

all

40

as were those who pinned

mis

,

is

,

”

in

to

it

order

ten

in

science

necessary to

”

Is

it ?

in

fable

their

you work

appreciate

the bitter old

,

?

, and

;

,

false masks

a

in

discredited

lie

. . ."

old and

the clothes

truth

1

hopes

youth

repulsive

whiles

wrinkled

and

vesture that beguiles

false

a

is

all

of

in

dress

as

also

because

an

modes

of

, of

Stripped naked False dreams

as

a

cold rage seizes one

show

unbidden

careless ears

into

at

discords

's

To

Because

mute despair

new

decrepit harridan tricked

young

girl

.

And wail life

a

“

break the seals

of

?

point

Why

out

a

believe the whole its

“

believe of

't

if

don

do

Why

,

derminded friends

by

The toughminded are often asked you

injunction

.

it

as

to

is

good that which sound today was when first uttered

an

as

“

,

of

of

.

in

to

their the yet belief witchcraft Never has the excision error destroyed anything that were not better out the way and Prove all things hold fast taken

14 RETURN

TO DESK

DAY USE FROM

WHICH BORROWED

LOAN DEPT . This book is due on the last date stamped below , or on the date to which renewed . Renewed books are subject to immediate recall .

91 PM

-2

66

14

General Library University California Berkeley

of

)

(

-

LD 21A 60m G4427810 476B

25

OCT

-7 ', 66

. .

CIR

23 1978

REC

NOV

ID

°78

RECO

NON

NOV -211966 -