[CASSIRER, Ernst]Newton and Leibniz

8/15/2019 [CASSIRER, Ernst]Newton and Leibniz

1/27

Philosophical Review

Newton and LeibnizAuthor(s): Ernst CassirerSource: The Philosophical Review, Vol. 52, No. 4 (Jul., 1943), pp. 366-391Published by: Duke University Press on behalf of Philosophical ReviewStable URL: http://www.jstor.org/stable/2180670

Accessed: 22/07/2010 01:39

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless

you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you

may use content in the JSTOR archive only for your personal, non-commercial use.

Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at

http://www.jstor.org/action/showPublisher?publisherCode=duke.

Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed

page of such transmission.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

Duke University Press and Philosophical Review are collaborating with JSTOR to digitize, preserve and extend

access to The Philosophical Review.

http://www.jstor.org

http://www.jstor.org/stable/2180670?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/action/showPublisher?publisherCode=dukehttp://www.jstor.org/action/showPublisher?publisherCode=dukehttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/stable/2180670?origin=JSTOR-pdf


2/27

NEWTON AND LEIBNIZ

HE controversy etweenNewton and

Leibniz is one of

the

most mportanthenomena n thehistory f modern hought.

If

we

follow

this

controversy

tep

by step,

f

we studythe

cor-

respondence etween

eibniz and Clarke,

who acted as spokesman

for

Newton, we are

immediately ware that much more was

at

stake than the particular

physical and

metaphysical uestions

which

are explicitly

reatedby the two

adversaries.Newton and

Leibniz

disagreednot merely s to the

solution f these

questions.

They not only had different iews on thenature and properties

of

God,

on the

structure f

the materialuniverse, he concepts

f

space and time, nd the

possibility f an

action at a distance .

However important ll

these questions

may be, they

have here

only

a

mediate and subordinate

significance. hey

are over-

shadowed by

another

problemwhichwas of

vital

nterest or the

future

evelopment

f

scientific

nd philosophic hought.Modern

thought ad reached parting f theways where t had to choose

between two alternatives.

n

the dispute between Newton

and

Leibniz these alternativeswere

clearly

ndicated.

The

two oppos-

ing

theses

were

represented

nd

defended

by

two

powerful

nd

original hinkers ho stood

without rival

n

contemporary

cience

or

philosophy.1

his

is

not, therefore,

mere

scholastic

disputa-

tion.For behind

he

catchwords f

the two schools of

thought

we

feeltheclash and trialof strengthf twogreat ntellectual orces.

Nor is

this simply

controversy

etween

ndividual

hinkers;

t is

rather

collisionbetween

wo

fundamental

hilosophicalmethods.

And it is

this feature

f

the

disputewhich

makes t

important

nd

interestingven

for

the

present-day

eader.

Perusal of the various

papers which

passed between Leibniz

and Clarke

in

the

years

I715

and

17162

does

not suffice or

an

understandingf thefullmeaning ndpurport f thispolemic.At

first

uch a perusal is very disappointing. oth

sides repeat

the

1

The fullauthenticityf the Clarkepapers s provedby the factthatthe

outlines f Clarke's replieshave been found mongNewton'smanuscripts.

2

In the following refer o the Englishedition ublished fterLeibniz'

death:

A

Collection f Papers which Passed Between the

Late

Learned

Mr. Leibniz and

Dr.

Clarke in the Years

17-5

and

T716.

Relatinq to the

Principlesof Natural Philosophy nd Religion.By Samuel Clarke, Lon-

don

717.

366


3/27

GALILEO

AND THE SCIENTIFIC REVOLUTION 367

same arguments

ver and over again

until interaction etween

theirviews seems mpossible. or each

partyobstinately olds

its

ground refusing o enter into his opponent'sviews. Moreover,

from he outsetthe controversy as

obscuredby personal

nvec-

tive. Each side accused the otherof undermining

he foundations

of

natural religion.

The more the discussion

proceeded he more

this tone of arguing

nd reasoning ended

o prevail.Yet this

was

natural and unavoidable. For Samuel

Clarke, who pleaded

for

Newton,was neither scientist

or

a

philosopher. e was

one

of

the best knowntheological ontroversialistsf his time. In his

book

A

Demonstration

f

the

Being

and

Attributes

f

God

he had

undertaken o

demonstratehe existence f God

and all

the

other

fundamental ruths

of the Christian

religion by merely ogical

arguments

nd to answer

ll

the objections

f the free thinkers ,

the sceptics,

he deists,

nd

atheists.3

his book

became

so

famous

that Voltaire could

not

forbear

aying

his respects o its

author.

In his Lettressur les Anglais Voltaire spoke of Clarke as a

veritable

reasoning

machine

(une

vraie machine a raisonne-

ments) 4 And there

were stillotherfactors

ending o obscure

the

point t issue.

The old disputebetweenNewton

and

Leibniz

about

the priority f the

nvention f the

infinitesimalalculus was

not

forgotten. ersonal

ambitions

nd

jealousies, even national

preju-

dices, began

to awake

again.

For

us

this side of the question

has

lost its interest.After the most carefulhistorical nvestigations

this

point eems

now to

be

entirely

leared

p.5

We

know thatboth

Leibniz and Newton,

on

the basis of

independent onsiderations,

had come to the

same results;

we know that

each

method,

he

method

of

fluxions

nd

that of the

differentialnd

integral

al-

culus, has its peculiar

character nd

its

peculiar

merit.

From

the

point of view of the history f

ideas -it has

been rightly

aid-

thereexists no controversyn the annals of sciencemore de-

3The full titleof the

book

s:

A

Demonstration

f

the Being and

Attri-

butesof God, the Obligations

f Natural Religion nd the Truth nd Cer-

tainty f the ChristianRevelation,

More Particularlyn Answer to Mr.

Hobbs,Spinoza and

their ollowers. ondon

705/I706.

4Voltaire, Lettres sur les

Anglais, VII, in Oeuvres,

Paris

i82i,

chez

Lequien,XXVI 33 ff.

6For thehistory f this ontroversy

refer o MoritzCantor,

Vorlesungen

uiber ie Geschichte

er

Mathematik

II

(Leipzig

i898)

274-3i6;

and

to

David Brewster,Memoirs

of the Life, Writings, nd

Discoveriesof Sir

Isaac Newton, dinburgh,855,vol. II, chap.xv, pp. 36-83.


4/27

368 THE

PHILOSOPHICAL

REVIEW [VOL.

LII.

plorable nd less

fertile han

thisdiscussion f the

priority f

the

invention f the

infinitesimal

alculus. It

is remarkable hat

this

famousdisputewhichoriginated nder quite accidental circum-

stances

did not

affect r modify n any

respect he

deas of the

two

adversaries or the

philosophical

tendenciesof

their pupils. It

would

be difficulto show that

single

step of

progresswas made

by

this

controversyver the

new

conceptions f the infinite

nd

the

infinitelymall.

As

a result

of this

conflict he English

school

and the

German

chool of thought

eprived

hemselves or a long

time of all the advantages which theymighthave derivedfrom

united

fforts. he

quarrel

betweenNewtonand

Leibniz,

founded

upon

mere personal

rivalries,

eft the two

philosophical

methods

stationary.

he

detailed

study

of

this quarrel

supplies us

in

the

main

with nteresting

bservations

oncerning he

psychology f

Leibniz, of

Newton, nd of other

minent

cholarsof their ime.

But it gives us very

ittle

nformationboutthe

distinctive eatures

of theLeibnizian and Newtonian ystems.

In

order

to discover

hese

distinctive

eatures

we

must,

ndeed,

try

different

pproach.

We must

endeavor o trace

back the dis-

pute

between

Leibniz and Newton

to its

real

source,

and

to look

behind

he

scenes

of the

great

ntellectual

pectacle resented

ere.

In

this

case we shall find

hat

the deas

propounded

nd

defended

by

these two

adversaries

have

by

no

means

lost

theirvalue

and

interest. hese ideas are stillalive, and, to a certain xtent, hey

are still

n

the

focus

of

modern

hilosophical

nd

scientific

hought

-even though

we

may,

ndeed

we

must,

express

them

n a dif-

ferentmanner.There

was

no real

dissension etweenLeibniz and

Newtonabout

the fundamental

roblem:

he

validity

nd

necessity

of

a mathematical

cience of nature. We

may

call Newton

a

physicist , nd

Leibniz

a

metaphysician ;

ut Leibniz himself

wouldneverhave subscribed o sucha distinction etweenmathe-

matical

nd

metaphysical hought,

or

he admitted o chasm

here.

Whenever

he

mentioned

his

metaphysics

he described

t as

a

metaphysic

f

mathematics .

Ma

Metaphysique ,

e wrote

n

a

letter,

est toute

mathematique .7

e Leon

Bloch,

La Philosophie

de Newton

Paris i908)

II5 f.

7Leibniz,

Letter to de

L'Hospital,

December

27, i694.

See Leibnizens

mathematische

chriften ed.

C. I.

Gerhardt,

alle

I849

ff.)

I

258.


5/27

No. 4.] GALILEO

AND

THE SCIENTIFIC REVOLUTION

369

It would

be a morecorrect tatement f our problem

o saythat

Leibniz defends

deductive deal of scientific

hought

whereas

Newton speaksas the champion f an empirical, merely induc-

tive method.

But even this distinctionwould

be misleading

n

many respects.

Induction

and deduction

are rather vague

terms. hey

have been used

in

various nd widelydivergent

enses.

If we understand

he ideal of induction

n

the sense

of Bacon's

Novum Organum,

r of some more recent

ogicians, s,

for in-

stance, John Stuart Mill, then

we must say

that Newton

never

recommended r defendeda strictly inductive method. The

method ntroduced

y Newton

was of a quite differentype.

What

in Bacon's aphorisms

had only

been dreamed f seemed suddenly

to

have become

a

reality.Newton's first upils

revered

him

not

merely s one

of the greatest

cientists f all time.They

saw in

him the very

ncarnation f

the philosophic

piritbecause he was

the

first

o

understand

what a

philosophy

f

nature

really

s and

means. JohnFriend, an Oxfordprofessor f Chemistry, ho in

his Praelectiones

Chymicae

was

one

of

the first o

try

to apply

the Newtonian

principles

of mechanics

to chemical

problems,

spoke

of Newton

as the

prince

of mathematicians

nd

philo-

sophers .

By

his

excellent

enius ,

he said, he

has

taught

us

a

sure way for

the improvement

f

physics

and has fixed

natural

knowledge

on such weighty

reasons

that

he

has done

more to

illustrate nd to explain it thanall philosophers f all nations.

Friend declared that Newton's

conclusions

n

philosophy

re as

demonstrative

s his

discoveries

are

surprising.9

It

has

been

ignorantly

bjectedby some ,

wrote nother

f

Newton's

disciples,

that the

Newtonian

philosophy,

ike

all

others

before

it,

will

grow old and

out

of date

and

be

succeededby

a

new

system....

But

this

objection

s veryfoolishly

made. For never

philosopher

beforeNewton ever took the method he did. For whilsttheir

systems

re

nothing

ut

hypotheses,

onceits, ictions, onjectures

and

romances

nvented

t

pleasure

nd without

ny

foundation

n

8John

Friend,

n his

remarks

upon

an

account

of

his

Praelectiones

Chymicae,

iven

n the Acta

Eruditorum,

7ii.-See

Philosophical

ransac-

tions, bridged

nd

disposed

under

GeneralHeads,

V

429

sq.

'See the English

edition

f his

Praelectiones

Chymicae.Chymical

ec-

tures:

in which

almost

all the

operations

f

Chymistry

re reduced

to

their rue

principles

nd the

laws of

nature,

ondon 7i2,

Appendix,

74.


6/27


7/27

No. 4.]

GALILEO AND THE

SCIENTIFIC

REVOLUTION

37I

fields

f

physical nquiryNewton

always

insistedupon

this char-

acter

of

his analytical

nduction . As in

Mathematics, o in

NaturalPhilosophy , e said in his Opticks, theinvestigationf

difficult

hingsby the

Method of Analysis,

ught ever to

precede

the

Method of

Composition.... In the two

firstbooks

of these

Opticks,

proceeded

by this

analysis to discover and

prove the

original

differencesf theraysof

light n

respect f refrangibility,

reflexibilitynd

colours....

And these

discoveries eing

proved,

theymay be

assumed n the

method f

composition or

explaining

thephenomena rising from

hem. '14

Newton

did

not

arrive at his

principal heoriesby

simply

ol-

lecting

new facts.

Most of the

empirical videncehe

needed for

constructing is optical

theories r his

theory f gravitationwas

contained

n the workof former

cientists r

contemporaries-in

thework of Galileo and

Kepler,of

Snelliusand Fermat, f Chris-

tian

Huyghens,

nd

of Halley-or

Hooke.

Newton's real

merit

ay

in uniting nd concentratinghedifferentnd dispersed chieve-

ments of

these men.

The most

important nd the most

charac-

teristic

eature

f

his work

was

not

so much

the

discovery

f new

facts as the new

interpretation

f

data

already

available.

The

general

aw

of

gravity

ad

been discussed

ong

before he

publica-

tion

of

Newton's

Principia.

All

the

great

physicists

nd

astro-

nomers

participated

n

this

discussion.They

saw theproblem nd

examined the methodsof its solution.Even Newton's formula

was

not an

entirely

new

discovery.ChristopherWren,

Hooke,

and

Halley,

had

developedtheir theories

f

attraction

n

which,

on the basis of

independent onsiderations,

hey

were led

to

the

conclusionthat the

centripetal

orce

decreased

in

proportion

o

the

squares

of the

distances

eciprocally.

ewton did not

deny

or

underrate he

merits f his

predecessors.

When he

published

his

Principiahe added a special scholium n whichthesemerits re

frankly

cknowledged;

he declared hat

Wren,Hooke, andHalley,

had

independently

educed

the law of

gravity

from the

second

law of

Kepler.'5

Since

the time

of

Kepler

the

hypothesis

f

general

attraction

between

ll

the

celestial

bodies

had, indeed,

been under

considera-

4Newton,

Opticks,

ook III, part

; reprinted romthe fourth dition

(London

I730),

New

York

I93I, p. 404 ff.

15

See Principia, iber I, Propositio V, Corollarium , Scholium.


8/27

372

THE PHILOSOPHICAL

REVIEW [VOL.

LII.

tionby all the

physicists

nd astronomers.

epler

had asserted

hat

not onlydoes theearth ttract he stone,

but the stone

lso

attracts

the earth. And this conceptionplays an important art in his

reform

of

the

Aristotelian

osmology.

Twelve

years before

the

appearance

of

Newton's Principia

Hooke

had submitted

paper

to

the Royal

Society n whichhe

investigated

he nature nd

mag-

nitude

of this attractive

orce.

He declares

that the action

of the

attractive orces

of the celestial

bodies

increases

n proportion o

the

proximity

o theircenters

f the body

on

which

these

forces

act. Now whatthese severaldegreesare , continuedHooke, I

have not yet

experimentally

erified,

ut it is a

notion

which, f

fully prosecuted,

s

it ought

to be, will mightily

ssist

the

as-

tronomers

o

reduce all

the celestial

motionsto

a

certain rule,

which

doubt

will

neverbe done

without t.

He

thatunderstands

the natureof

the

circular

pendulum,

nd of circular

motion,

will

easilyunderstand he

whole

of

thisprinciple,

nd will

know where

tofind irectionsnnatureforthe true tating hereof. his I only

hint

t present o such

as have

ability nd

opportunity

f

prosecut-

ing this

nquiry,

nd

are notwanting f

industry

orobserving nd

calculating,

wishing

heartily

uch may

be found,

having myself

many ther hings

n

hand which would

first omplete,

nd there-

fore

cannot o

well

attend

t.

But

this durst

promise

he

under-

taker

that he will

find ll the great

motionsof the world

to be

influencedy thisprinciple,nd that hetrueunderstandinghere-

of

will

be

the trueperfection

f

astronomy. '

We

may

nfer

from

hese

words that Newton'sdiscovery

ould

not

come

as a surprise

o the astronomers

nd

physicists

f his

own

time.

This

event

was carefully

repared

for,

both

in its

ex-

perimental

nd

in

its

theoretical

spect.

But

the

reallynovel,

and

subsequently

ecisive,

element

onsisted n Newton's systematic

proofof his theory.n thisregardhe was entirely riginal.We

have indeed very

nteresting

iographical

roof

that

Newton saw

his problem

n this ight.

While

preparing

he

first

dition

of

his

Principia

in

I786

he

had

a letter

from

Halley

in

which he was

told

that

Hooke

had

some

pretensions

ith

regard

o the first is-

covery

f the

aw of

gravity.

Newton,

when he heard

of

Hooke's

IG

Hooke,

An Attempt

o

Prove the

Motion

of the

Earth ,Philosophical

Transactions,

o. ioi,

p. I2.-See

Brewster,

emoirs

286 f.


9/27

No. 4.] GALILEO

AND

THE

SCIENTIFIC REVOLUTION 373

claims,became o frightened

t the prospect

f becoming nvolved

in a publiccontroversy

n a question f priority hathe wished to

suppress his third book rather than undergo such an ordeal.

Philosophy ,he wrote

to Halley, is such

an impertinentlyiti-

gious Lady, that a

man had as good be engaged

in lawsuits, s

have to do with her.

I found t so formerly,nd now I am no

sooner

come

near her again, but she gives

me warning. '7

The

fact that thereever was a moment

n

Newton's

ife

in

which

he

seriously esolved o

suppressone of the

most mportant arts

of

his classical work, s one of the greatestparadoxes in Newton's

biography nd in the whole historyof science.

Many

modern

writers

ave

been at a

complete

oss to understand his

fact

which

seemedto be a blot

on

his personal nd scientificharacter. One

cannot

excuse Newton ,

ays one of

his

most recent iographers,

for his

decision

to

suppress

the third book.... What

manner

of

a

man was

Newton

who could thus

contemptuously

ast

off

his

own intellectualhild?There is certainly o parallelto the ncident

in all

history.

id

any

other

man

ever show

a

deeper ealousy

and

vanity

han

Newton,

who

could

let the

personal

criticism

f

an-

other,

nd

a

slight

reflexion n his

own

character, utweigh

he

work

of

his

life

and

the

fruit

f

his

genius? 18

I

think,however,

that we can exculpate Newton from this

charge. It

is

true that

during

his

whole

life he

feared

nothing

morethaninvolvementn public disputes bouthis work.But to

ascribe

this

fact to a sort of

moral weakness,

et alone

to

mere

vanity

r

jealousy,

eems

to

me

a

verypoor psychological xplana-

tion.Vanity nd jealousy

would

have had the opposite ffect; hey

would

rather

have

incited

him

to

such

disputation

han deterred

him from t. There was more than the mere personal factor

n

Newton's

desire

for

peace.

This

desire originated

n his

respect

forhis workand forthegreatness f hisscientificask. f Newton

was ever able

to

bring

himself

o

suppress

the

thirdbook of the

Principia,

he must have been convinced hat

this omissioncould

17

Newton o Halley,June 0, i686.-The

correspondenceetweenNewton

and Halleywas first ublished

n

the Appendix

o

Rigaud's

Historical

Essay

on theFirst Publication f the Principia ,

xford 838. It has sincebeen

reprintedn Brewster'sMemoirs, , Appendix

No. viii,437-456.

'8Louis TrenchardMore, Isaac Newton,

Biography,New York and

London

934, 3II.


10/27


11/27

No. 4.] GALILEO

AND

THE SCIENTIFIC REVOLUTION 375

factual ruth f physics oes not

form n independent

ealmwhich,

in its fundamental

haracter, s

opposed to the truth f logic

and

mathematics. oth realmshave, so to speak, theirown rational,

constitutional

aws. The great

foundation f mathematics ,

ays

Leibniz in the

second paper addressed

to Clarke, is the principle

of contradiction

r identity, hat

is, that a proposition

annot be

true and falseat the same time;

and that herefore

t is what t is,

and

cannot

be what it

is

not.

This one principle

s sufficiento

demonstrate very part of arithmetic

nd geometry, hat is, all

mathematicalrinciples. ut inorder o proceedfrommathematics

to natural philosophy,

another

principle is requisite . . . the prin-

ciple of a sufficienteason,

viz., that nothing

happens without

reason why t

should be so rather han otherwise.

And therefore

Archimedes,when proceeding rom

mathematics

o naturalphilo-

sophy,

n

his

book

De

aequilibrio,

was obliged

to employ par-

ticular case

of the

great principle

f

a sufficient

eason. 20

t is

this principle hat makes physicspossible,because it allows us to

make thegreat

tep

frommathematicso nature, o throw bridge

across the

gap which,

t first

ight,

eems

to

separate

factual ruth

(verites

de fait)

from

necessary

ruth

verites

eternelles).

This

is not,

however,

solution

f

the problem;

t is only

the

statement f the problem.

What does Leibniz

mean

by

his

prin-

ciple

of

sufficient

eason ? We cannotgrasp

his

meaning

o

long

as we take his terms nd his arguments t their facevalue. For

his own description

f his principle, s contained

n his

replies o

Clarke, s

rather

vague.

The

principle

n

question ,

he

says,

is

the

principle

f

the want

of

a sufficient

eason,

n

order to

any

thing's

xisting,

n

order

to

any

event's

happening,

n

order

to

any

truth's

aking

place.

Is this

principle

hatneeds to be

proved '21

Such

argumentation

eems

scarcelyworthy

f

so

great

a

logician

as Leibniz. It was open to all the attackswhichHume laterdi-

rectedagainst

the

objective

validity

f the

principle

f

sufficient

reason.

To discover

he true

and

deeper

sense

of

Leibniz's prin-

ciple

we

must

onsult

he

whole

of

his

logical

work.Leibniz

always

insists that

his

principle

s

pregnant

with the

most

important

consequences.

rom

it

he

expects

real revolution n

philosophic

'

Leibniz

to Clarke,Second

Paper, sect.

, p. 2I.

2

Ibid.,FifthPaper,sect.

25, p. 275.


12/27

376

THE

PHILOSOPHICAL REVIEW

[VOL. LII.

and scientifichinking.

f understood

n its fullest

ense thisprin-

ciple will alter the

whole realm

of metaphysics.

t will make

metaphysics perative nd demonstrative hereasbefore t gen-

erally consisted

only

of emptywords.22 It

must be confessed ,

statesLeibniz,

that

though his greatprinciple

as been

acknow-

ledged,yet t has not

been sufficiently

ade

use of. Which is, in

greatmeasure,

he reason

why he

Prima

Philosophia

has

not been

hitherto o fruitful

nd demonstrative,

s it should have

been. 23

Wherein onsists

he greatness ,

he novelty, he

revolutionary

power thatLeibniz ascribes to theprinciple f sufficienteason?

Leibniz

began with

a description

nd classificationf the

various

types

of

truth.

He

insisted hat ogical

and mathematical

ruth s

necessary ,whereas

empirical ruth

s contingent . ut

he was

not contentwith this

discrimination.

ccording

to Leibniz this

distinction

etween

actual nd necessary ruth, etween he

verites

de fait

and the

veriteseternelles ,

as only a relative,

not an

absolutevalue. It is true that thetwo kindsdo not belongto the

same

class. They cannot be reduced

to a common

denominator.

But that

does not mean that they

re opposed

to one another

r

are mutually

xclusive.However

differenthey

may be, yet they

are interrelated. eibniz

liked to

illustrate his

interrelationy

a

mathematical

xample.

We may

say that factual truth

s incom-

mensurable

with

ogical

and demonstrative

ruth.There

appears

to be no commonmeasure.But it is precisely his conceptof in-

commensurability

hich can lead us

to

the right olution.

f in

geometry

we

speak

of

incommensurableengths

we mean

that

these engths

annot

be expressed

by our

ordinary

rational

num-

bers. They correspond

o surd or

irrational numbers.But

these

irrational

uantities

re

by

no means indeterminate

uan-

tities.

f we cannot

express

them

by

an

ordinary

ractional

um-

ber,we can find n infiniteeriesof rationalnumbersby which

this value is fully

determined.

he

farther

we proceed

in

this

infinite eries of

rational

numbers, he

more

nearly

we

shall

ap-

proximate

he

true value of

the surd

quantity.

t

is

the same

with

empirical

and

rational

truth.24

f course Leibniz

admits

22Ibid.,

ourth

Paper, sect.

5, p. 95.

'

Ibid.,

Fifth

Paper, sect. I,

p.

I73.

2Leibniz stresses

this analogy

in

many

passages.

See especially De

libertate , ouvelles ettres t Opuscules nedits e Leibniz,par Foucherde


13/27

No. 4.] GALILEO AND THE SCIENTIFIC REVOLUTION 377

thatthere re wide areas of human

knowledge n which we have

to be contentwith mere factual truth.All we can do here is to

collect the empiricalevidence withoutbeing able to deduce the

factsfromhigher easonsor principles. ut this s only first nd

preliminarytep. The philosopher nd

the scientistwill never be

satisfied ith his tate f affairs. hey will continue heir nalyses

until hey ome nearer nd nearerto

theirultimate oal-the goal

not merely f collecting, ut also of

understanding,he phenomena

of

nature.Rational or necessary ruth

must be conceived s the

ideal, the limit of empirical ruth. his ideal is not immediately

given, but the search for it is the

essentialtask of science and

philosophy.Rational truth s the

eternalthemeof scientific nd

philosophical nvestigation.n this

sense Leibniz often calls his

principlenot only the principle of

sufficient eason , but the

principium

eddendae

rationis .25

We do not know the reasons

behind ll

things, ut we

must

never

despairof finding nd prov-

ing these reasons. The progressof knowledge s unlimited;nor

does knowledge dmit

of

any

fixed

boundaries.The

maxim

plus

ultra

was

a

favorite

f

Leibniz's.26What

the

principle

f

suffi-

cient reason ,or still better, he

principium eddendaerationis ,

really means and emphasizes

s

that n

the

last

analysis

all em-

pirical truth s

describable

n

terms f

rational ruth nd

reducible

to

the typeof

rational

ruth.27ehind

every

cientific

chievement

we are sure to find newscientificroblem.But this nfinitys in

no

sense opposed

to

a

genuine

rationality.

n

the

contrary,

t

is

the very expression

f

such a

rationality.

t means

that

the

indi-

vidual

steps

taken

n

the advancement

f

our

empirical nowledge

form

convergent,

ot a

divergent,

eries.

By

virtue

of this

con-

vergence,

which

s

ascertained

y

the

principle

f

sufficient

eason,

we

can be

sure

that

there s

a constant

pproximation

owards

truth,hatour empirical nowledge f particularfactswill,more

and more,

be

reduced

to

a

knowledge

of

general

rules and

uni-

versal

principles.

Careil (Paris

I857)

i83; in Philosophische

chrif

en

(ed. Gerhardt)

VII

200.

25

Cf.

Specimen

nventorume admirandis aturae

Generalis rcanis ,

Philosophische

chriften

II

309 Gerhardt.

26

Cf.

GuilelmiPacidii

Plus

Ultra, sive

initia et

specimina

cientiae

generalis ,

bid.

VII 49-51.

2

Cf. Leibniz,LettreaArnauld,July

4,

i686, bid.

I

382.


14/27


15/27

No. 4.] GALILEO

AND THE SCIENTIFIC REVOLUTION 379

three n i659, he wrote his

Specimen demonstrationumoliti-

carum pro eligendo rege Polonorum

novo scribendigenere ad

claram certitudinemxactum .28 his politicalpamphletwas in-

deed writtenn a new style.He

tried o prove more

geometrico ,

by mere arguments n form ,

hat, f all the candidates ompet-

ing for the Polish throne,Stanislaus

Letizinskywas the most

entitled nd themostpromising. y the same method

eibniz tried

to convinceLouis XIV that

t

was much better o attack Egypt

thanto conquerHolland.29

ven

problems

f

Christian ogmatics

were treatedin similar fashion. In

i669

Leibniz publisheda

Defensio trinitatis er nova

reperta ogica ,

in

which

he under-

took to defend

the

Trinitarian

dogma against the objections of

Wissowatius.0

In

like

manner he

attempted

o

refute,by

mere

logical

arguments,

he errors

of Socinus and the adherentsof

Socinian ism.3l

If we

bear

in

mind hesecharacteristic

eatures f

Leibniz's

and

Newton'sphilosophywe can easilyunderstand heirdiscussion f

particular uestions.They

differed

ot

merely

n

theirprinciples,

but also

in

philosophical emperament,

n their

general

frameof

mind.

Leibniz

was

perhaps

the

most

resolute

champion

of ra-

tionalismwho

ever appeared

in

the history f philosophy.

Not

even

Hegel

could outdo

him

in

this

respect.

For Leibniz

there

exists

no separation,

o

chasm,

between

reason and reality .

There is nothingn heaven or on earth,no mystery n religion,

no secret

n

nature,

which

can

defy he power and efforts f rea-

son.

Le

reel ,

he wrote n a

letter, ne

laisse

pas

de

se

gouverner

parfaitement ar l'ideal et l'abstrait; c'est parceque tout se gou-

verne

par

raison et

qu'autrement

l

n'y

auroit

point de

science

ny

regle

ce

qui

ne seroit

pas

conforme vec la nature du souverain

principe. 32

Newton's conception f the task of science was very different.

He

too felt the

pride

of

a

great

scientific enius, but this pride

'

Leibniz,

Opera

omnia, d. Lodov. Dutens,

Genevae 768, Tom.

IV,

3,

522-630.

29

Specimen

demonstrationisoliticae , n Leibniz'

historisch-politische

und

staatswissenschaftlichechriftened. Onno

Klopp,

Hannover

864

ff.)

II

Io~o

f.

30

Opera

omnia ed. Dutens) I io

ff.

'

Ibid.,

Remarques . .

. sur le livre d'un

AntitrinitaireAnglais ,

I 24

ff.

2

Leibniz,Letter to

Varignon, eb.

2,

I702,

in

Mathematische chrif en

(ed. Gerhardt, erlin-Halle,

849

ff.) IV 93 f.


16/27


17/27

No. 4.] GALILEO AND THE SCIENTIFIC REVOLUTION

381

method f fluxions

we may say thatNewton, s a physicist, egan

with study f facts,

whereasLeibniz,

as a logician, egan with

study of forms.Of all the facts of naturemotion s the most

generalone. According

o

Newton'smechanics

here s no

natural

phenomenon hich

s not reducible o motion

nd its general aws.

Hence follows hat

we

shall never find true correspondence

e-

tween

thought

nd reality, etweenmathematics

nd physics,

o

long as we exclude the concept f motion

from he realmof pure

mathematics.t

was, however, recisely his exclusionwhich

con-

stituted ne of the fundamental nd mostcharacteristic eatures

of classical mathematics. lassical mathematics

ad

its

origin

n

Platonic thought.

All the great Greek

mathematicians, rom

Eudoxus and Theaetetusdown to Euclid,

were, directly r

indi-

rectly, upils of Plato.

But from Platonicpointof view it

would

have been a contradiction

n

terms o admit

concept

ike

motion

as a basic principle

f geometry.Geometry

ad been

defined y

Plato as the realmof thea&eo'. The knowledge t which t aims

is knowledge f the

eternal, nd not of that

which s perishing

nd

transient. To introduce

nto pure mathematics he category

f

changewould be to underminets truth nd

certainty.

ut this

was

precisely he step

taken by Newton. He

was not exclusively

r

primarily nterested

n the solutionof abstract

mathematical

ro-

blems. From the outset

f

his scientific

orkhe had

combined

he

studyof algebra or geometry-the tudyof infiniteeries,of the

methods f drawing angents, f the quadrature

f curved

ines-

with

a

study

of natural

phenomena,

f

optical

and

mechanical

questions. Constantly

nd quite naturally

he passed from

one

field

to

the other.

To such a mind

there

could be no

gap,

no

Platonic

severance ,

between he deal worldof mathematics

nd

the

empirical

world of

physics.

n

orderto find he

mathematical

principles f naturalphilosophy Newton had to alter the tradi-

tional

conception

f

mathematics

tself. f mathematics

was

to

fulfill

ts principal ask,

f

it

was destined

o give

us a

theory

f

nature,

it could not overlook

or

minimize nature's principal

phenomenon.

Motion could no longer be regarded as

a mere

physical fact;

it became a

basic

concept, category

of mathe-

matics.

Such

was

the

problem

solved

by

Newton's

theory

of

' Plato,RepublicVII

527a.


18/27

382

THE PHILOSOPHICAL

REVIEW

[VOL. LII.

fluxions.35

physicalconcept,

he concept

of velocity,

was ad-

mitted

o geometry

nd algebra. The increase

and

decrease

of

abstract quantitieswas described n termsof mechanics-as an

increase

or decrease n velocities. n order to determine he

ratios

of the increments

f indeterminateuantities

Newton

described

these

ncrementsy

theterm

moments ; nd to thevelocities

with

which he

quantities ncreasehe

gave the

names motions ,

velo-

citiesof

increase , nd fluxions .

He considered

uantities

ot as

composed

of indivisibles,

ut

as generatedby motion.36

Quan-

titatesmathematicas , e writes, non ut ex partibus uam mini-

mis constantes

ed ut motu continuo

descriptas

hic

considero. 7

This was

not in itself an entirely

ew

conception.

We findthe

same

view

of a generation

f

curved

lines or solids by

con-

tinuous

motions n

Descartes' geometry

r in Kepler's

Stereo-

metriadoliorum .

But

in

these cases the

term motion

s used

in

a mere metaphorical

ense.

It had not yet been

naturalized

n

the realmof mathematics. o legitimatizehis conceptof motion

was one of

the

principal

ims

of

Newton's

heory

f

fluxions.

or

this

purpose

he

had to

change

the whole

hierarchy

f the sciences.

In

his

system

mechanics

s no

longer

subordinated

o

geometry;

it

becomesthe

very

basis

of

geometry.

It

is

the

glory

of

geome-

try ,

ays

Newton

n

the

Preface to

the

Principia,

that

fromfew

principles

brought

from without,

t is

able

to

produce

so

many

things. herefore eometrys foundednmechanical ractice, nd

is nothing

ut that part

of

universal

mechanics

which

accurately

proposes and

demonstrates

he

art

of

measuring. 38

n

Leibniz

we

find

the classical hierarchicorder of scientific

nowledge.

Geometry

nd

arithmeticre subordinated o

logic:

all their

ruths

can

be

derived

from

he mere

principle

f contradiction.

n

me-

chanics

and

physics

t is

necessary

o introduce new

principle,

For the history f the theory f fluxions nd for all technical etails

I must

refer

the

reader to the

monographs

n the subject. See, for

in-

stance,

Ferdinand Rosenberger,

saac Newton

und seine physikalischen

Prinzipien,

Leipzig i895;

and Leon

Bloch, La philosophic

e Newton,

Paris i908.

88For

further

etails ee Brewster,

emoirs I ii ff.

ST

De quadratura

curvarum ,

ntroductio;

n Isaac

Newtoni Opuscula

mathematica

hilosophical

t

philologia

(ed.

Johann Castillioneus,

au-

sanne

nd Geneva 744)

I

203.

a

Principia,

reface

to

first dition,

nglish ranslation

y

Andrew

Motte

in

I729;

reprinted

n the edition

of the

University

f California

Press,

Berkeley, alifornia,

934.


19/27

No. 4.] GALILEO AND THE SCIENTIFIC REVOLUTION 383

the principle f sufficienteason. But even mechanics s simply n

applied arithmetics nd geometry-a studyof geometrical nd

arithmetical elations n concrete. By virtue of Newton's new

orientation f mathematical hought, y the introduction f the

concept of velocity nto pure mathematics, ll this was

com-

pletely hanged.

f

we consider bstract uantities s generated y

continuousmotions, his is not a mere figure f speech. It ex-

presses a real fact, Hae geneses , declared Newton

n

his work

on

the quadratureof curved ines,

in

rerum

natura

ocum

vere

habent t n motucorporum uotidie ernuntur. 39n otherwords,

such

generations

f

quantities

s

are supposed

n the new calculus

are not figments f the human mind, nor are they mere mathe-

matical

conventions. hey

have

a fundamentum

n re

a sup-

port and basis in the natureof things.We do not merely onceive

or

imagine,we see and experience, hesegenerations.

Leibniz's approach to the infinitesimalalculus was quite dif-

ferent.He saw theproblem rom heviewpoint f logic,notfrom

that

of thephysicist.

s a mathematicianeibniz

always

remained

faithful

o the great classical tradition.

He

spoke as

a resolute

Platonist.To

him

mathematics as a branchof logic.

But it

was

logic itselfwhich

n

the philosophy

f

Leibniz

had

assumed

a

new

shape. He by

no

means despised

the

methods f

traditional

ogic,

of Aristotle

nd

the Schoolmen.

He defended

heir

right gainst

the attacks f themoderns.n hisNouveaux Essais sur l'entende-

menthumainhe

praises the

nvention f

the various

forms

f the

syllogism s

one of the

most

beautiful,

nd as one of

the

most

important, chievements f the human mind. It is a species of

universal Mathematics ,he asserted, whose importance s not

sufficientlynown;

and

it

may

be

said

that

an

infallible

rt

is

therein

ontained, rovided

we

know and can use

it,

which

s not

always allowed. 40 he same view is givenin a letter f Leibniz

to

Gabriel

Wagner (i696),

which

was writtenfor the

express

purpose

of

defending

he

Aristotelian

ogic against

its

modern

critics nd

detractors.41n

the other

hand

the

syllogistic

cience

Newton,

De

Quadraturacurvarum ,

ntroductio,

puscula,

ed.

Cas-

tillioni,

204

f.

40Nouveaux

Essais,

Livre IV,

chap. 17, sect. 4.-Eng.

translation

y

A. G. Langley,

econd d., Chicago

and London,

9i6, p. 559.

41

See Philosophischechrif en, d. Gerhardt, II

514

ff.


20/27

384

THE PHILOSOPHICAL

REVIEW

[VOL.

LII.

of Aristotle

did not represent

or Leibniz the

whole extent

of

logic,

but

only a small

portion. n his

Characteristica eneralis

he had found nd studied ypesof arguing nd reasoning ntirely

differentrom hose

contained

n

the

classical logic.

You appear

to apologize

for common logic ,

replies Philalethes

in

the

Nouveaux

Essais, but

I see clearly

hatwhat you bringforward

belongs to

a more sublime ogic, to

which the

common

s only

what the alphabet s to

scholarship. 42

Leibniz had

in view not the

destruction,

ut the perfection, f

classical logic.

He wished

to

analyseall thepossible ypes f deductive easoning nd givethem

adequate symbolic xpression.43

he

new calculus

was but a single

chapter

n

this arger

work. It was

not based on the observation

of

natural

phenomena;

t was

derived

from mathematical on-

cept which

first

ecame

explicit

n

the thought f

Leibniz-in

the

general

conceptof function.

eibniz's analysis brought

his

con-

cept nto focus

so that t

became

one

of the mostpowerful

nstru-

ments f modernmathematics.n this regardwe cannot ookupon

Leibniz and

Newtonas

rivals or adversaries.They

set themselves

differentasks,

nd they

performed hese

asks by different eans.

Newton ttained

his

end by a new orientation f physical

hought;

Leibniz attainedhis by

a new orientation

f logical thought.

Looking at the conflict

n

this ight

we can give

both men their

due. We

can free

their

ontroversy

rom ll

those

accidental

nd

merelypersonalcircumstances hichhave obscured t fromthe

start.

Even one of the most

ntricate

roblems ppears

now

in

a

new perspective.

or a

modern

reader there s perhaps

no

more

interesting

roblem

n

this

controversy

hanthat f space and time.

On this

issue

the

crisis

of

seventeenth-century

hilosophic

nd

scientific

hought uddenly eveloped.

For

Newton

space

and time

were

notonly

real

things,

ut the very

framework f

reality.

hey

belongnotmerely o thematerialworld; they re absoluteattri-

butesof God.

All

this

s asserted

by

Leibniz

to be

radically

wrong.

Time and space

are not

separate

existences;they

possess no sub-

stantial

reality

f

theirown.

They

are

forms or

orders ,

not

things;

they

are not

absolute,

but

merely

relative.Here

Leibniz

4

Nouveaux

Essais, Livre IV,

chap. 7,

sect.7.-Eng.

tr.,p. 566.

For all

details

refer o the excellent

ccount

n Louis Couturat,

a

Logique

de

Leibniz,Paris 1903.


21/27

No. 4.] GALILEO

AND

THE

SCIENTIFIC REVOLUTION

385

envisaged

problemwhichonly

n recent imes

has received lear

and explicit

statement. or

him space and time have no inde-

pendent physicalor metaphysical xistence. Space is the order

whichrenders odies capable

of being situated,

nd by which

hey

have a situation

mongthemselves, hen they

xist together; ime

is thatorder

withrespect o their

uccessivepositions.44In order

to have an idea

of place, and

consequently f

space, it is sufficient

to considerrelations nd the rules of their

hangeswithout

need-

ing to fancy

ny absolutereality ut of the things

whose situation

we consider. 45

I

cannot

nter ntoa systematic

iscussion

f the problem tself.

I wish only to elucidate the

historical ide

of the question.

In

Leibniz's and

Newton's theoriesof space and

time we find

the

same fundamental

pposition

which we were able to observe

n

all

other ields.

his opposition

oes not originate n a meredispute

between

ndividual hinkers

r

in

a conflict etweenphilosophical

schools.Newtonand Leibniz applydifferenttandardsof truth

and they employ

different rames of reference.

Newton

argues

upon

a

principle

hat

at first

ight

eems to admit

of

no

doubt.

f

there s

any truth,

t

must

be found

in

rerum

natura .

All

truth

must be based

on facts. Even mathematical

ruth-the

so-called

ideal truth -forms

no exception o this general

rule.

Newton

had found

a new

type

of mathematics-the

mathematics

f va-

riablequantities.He was convinced hat his form fmathematics,

the doctrine

f

fluxions ,

would

not be

possible

without

sub-

stantial

foundation,

substratum

n

reality.

We cannot

study

he

relations

between

variable

quantities

withoutpresupposing

hat

uniform and continuous

motion which we call duration

or

flux

of time .

f

we

take

away

this

substratum

ll physical hings

and all mathematical

ruth ose their foundation.

Absolute,

true,

and mathematical ime is no mereconcept;it is a fundamental

reality

which

f

itself

nd

from ts

own

natureflows

quably

with-

out

relation

o

anything

xternal.46

eibniz,

too,

is convinced hat

there

must

be

conformity,

f

not

identity,

etween truth

and

reality .

There is no

chasm

between

he

ideal and

the

real

Leibniz,

Third

Paper

to Clarke, ect. 4, p. 57; Fourth

Paper, sect.

1,

p.

113.

4

Leibniz,

ifth

Paper,

sect.

47, p. 199.

See Newton,Principles, ook I, Definition, Scholium.


22/27

386 THE PHILOSOPHICAL

REVIEW [VOL.

LII.

world; they

re

united y

a

preestablished armony .

ut

Leibniz

stresses he oppositepole.

The natureof things nd the nature

of

mind gree. Yet veryoften-Leibniz objects n criticizing ocke-

the consideration f

the

natureof

things

s

nothing

lse

than

the

knowledge f the nature of our mind,and of those innate

deas

which

we have

no

need to

seek

outside. 47 o Newton's realistic

theory

f

space

and

timeLeibniz opposes his own idealistic

heory.

But the term idealism

s not sufficiento give us a clear

char-

acterization f the difference. s a resultof the wide

variety

f

senses nwhich histermhas been used inthe history f idealism,

it has become vague and

misleading.There are almost as many

forms

f

idealism

as

there

re

philosophical

chools

or

systems.

Leibniz's idealism s an

objective ,not a subjective

dealism;

a

mathematical,

ot

a

psychological dealism;

a

Platonic,

not

a

Berkeleyan dealism.

Thus when Leibniz asserted the

ideality

of

space

and time

he

never

meant to cast any doubt upon

the

objective ruth f theseconcepts.He always compares his deality

with

the ideality

f numbers.

Number being

the

very

foundation

of

mathematics,t

is

logically

mmune

to attack.

But Leibniz

objects

to

the interpretationf the objective truth f space and

time contained n

Newton's system.For Leibniz space and time

are relations r

orders,

not absolute existences

r

entities.

pace

is the order of

coexistences ; time the order of

successions .

These things onsist nly n the truth f relations, nd not at all

in

any absolute reality. 48

his truth f relations s dealt

with

n

Leibniz's logic. For him

the theory f space and time

belongs to

logic, not to physics.

These concepts re parts of a

greateruni-

verse,

f

theuniverse f

logical

forms

r,

as Leibniz calls

it,of the

intellectss

ipse .

We

may conclude,

hen, hatthe theories f space and time of

Newton and Leibniz, while diametrically pposed ontologically,

have, nevertheless, point of contact.This becomes

clear when

we

approach

the

problem

from

the

epistemological ngle.

Epis-

temologically he

two theories have a common feature

because

they

have a common

dversary. hey bothresist he thesis

upheld

by

all the

schools

of

English empiricismnd sensationalism.

pace

A7

ouveaux

Essais, I, I,

21

(English

translationy A.

G.

Langley,

.

74).

4

Leibniz,FifthPaper, sect. 47, p.

205.


23/27

No. 4.] GALILEO

AND THE

SCIENTIFIC REVOLUTION 387

and timecannot

be described nd defined n terms

f mere sense-

perception.

With this negative

tatement ewton and Leibniz are

in complete greement. ut evenhere their udgments re based

upon

differenteasons.For Newton

t is clear that pace and time,

as

absolute

entities, re beyond

the reach of immediate ense-

experience.

For Leibniz, on the

otherhand, they

are pure intel-

lectual forms

which nvolve a constructive ower

of the human

mind. The equal

and uniform lux of time signified

or Newton

an ultimate ubstantial eality;

for Leibniz, however,

t amounted

to a necessary ssumption, fundamentalypothesis.f, withour

conventional

historical classifications n mind,

we study the

famous

scholiumof Newton's

Principia,

n

which he insists on

the distinction etween absolute

and relative

motion; we are

at

first onfronted

ith curiousparadox. Newton

beginsby sharply

distinguishingetween he concepts

f the vulgar

and the true

scientificoncepts.Commonpeople

conceive pace,

time, nd

mo-

tion, according o no othernotionsthan the relations hese con-

cepts bear to

sensibleobjects. But from uch

a habit of thinking

certainerrors

and

prejudices

arise which

have to be eradicated

by philosophic

hought.

ecause

the

parts

of absolute

space

can-

not be seen

or

distinguished

rom

ne

anotherby our senses, we

tend

to substitute ense measures for absolute

measures.

This

is

without

nconvenience

or

the

purposes

of

everyday ife,

but it

will not do for philosophy.Here we wish to know the true

nature f things,

nd to

thisend we

must

bstract

rom ur senses

and consider

the

things

themselves s

distinguished

rom

our

measures

of

things

ccording

o the standards

f the senses alone:

in

philosophicis

bstrahendumst

a sensibus. 49

Who

is

speaking

here, we are

tempted o ask. Is it Newton,

the great empiricist,

or

his adversary,

he

intellectualist nd

rationalist

eibniz? As

a matter f factbothNewtonand Leibniz rejectthe standards

of

sensationalism.

he

senses,

taken in

themselves,

annot

yield

us

the

truth.

ut here

again

the two thinkers

ursue

this

principle

in

a twofold

direction.

Newton

is

intent

upon

determining

he

substantial eality

f

space

and

time

s

two

infinite, omogeneous

things,

ndependent

f

any

sensible

object.

Leibniz no

longer

'See

Principia,

Book I,

Definition

,

Scholium.-English

ranslation y

Motte,New Edition,Berkeley, alif., 934,p. 8 ff.


24/27

388

THE PHILOSOPHICAL REVIEW [VOL.

LII.

admitssuch

a reality.According

o

him,

f

we wish

to findthe

ultimate

ource of our ideas

of pure space and pure

timely,

we shall have to inquire intothe nature of our intellect ather

than

nto the nature

of

things.

his difference

s very clearly

x-

pressed

in a passage of the

Nouveaux Essais

sur

l'entendement

humain.

A succession

of perceptions wakes

in

us the idea of

duration,

ut it does not

make it. Our perceptions

ever

have

a

succession ufficiently

onstant nd regular

to correspond

o

that

of time,which

s

a

continuum niform nd

simple, ike a straight

line. Changingperceptions urnishus the occasion for thinking

of

time,

and we measure

it

by

uniform changes.

.

. So

that

knowing he rules

of different

otions,we

can always refer

hem

to the

uniform ntelligible

motions.

.

..

In

this

sense

time

is

the measure of

motion, .e.,

uniformmotion s

the measure

of

non-uniform

otion. 50

We have here the

key to Leibniz's

oppo-

sitionto

all sensationalist

heories

s well as to

his

opposition o

Newton'srealistic heory.

It is

usual, and it appears to

be natural,

o look upon the con-

troversy

between

Newton

and Leibniz as

a

collision

between

scientific

nd metaphysical

hought.But

if we accept

this

inter-

pretation

we are faced with

a grave difficulty.

ow

can we

account for the fact that

our

modern

heories f space

and

time

have adopted the

relativistic

heoryof

Leibniz, whereas they

have veryseverely riticized heNewtonianconcepts f absolute

space

and time? Shall

we

say

that since

the

time of Newton

science

has

developed

from

an

empirical

tate

to

a

more meta-

physical state?

This would of course

be a very strange and

dubious way

of stating

the

problem.

To

regard

Newton as a

mere empiricist

would be just as wrong

as to regard

Leibniz

as

a

mere

metaphysician .

n

the seventeenthenturywe cannot

drawsuch a line of demarcation etweenmetaphysicalnd mathe-

matical,between

theological nd

physical thinking.5'

What both

Newton

and

Leibniz

call

natural

philosophy

s

still embedded

in

the greater

whole

of

metaphysics.

eibniz could not develop

Nouveaux Essais,

Livre

II, chap. 14,

sect.

i6:

English

translation

y

Langley,p. 156.

'

In the case

of Malebranche his has been shown n a

very nteresting

and suggestive rticle by

Paul

Schrecker, Le Parallelisme

theologico-

mathematique

hez Malebranche , evue Philosophique XIII (1938)

87-

124.


25/27


26/27

390

THE PHILOSOPHICAL

REVIEW

[VOL.

LII.

developed

his

special

theory

f

relativity

e

found

it necessary,

first

nd

foremost,

o

analyse

the

meaning

of time.

This

seems

tometobe therealpointof contact etween he viewsof Leibniz

and

those of

modern cience.

In the

eighteenth

entury

he

great scientists

till had

implicit

faith

n Newton's authority.

n I748

Euler wrote his

Reflexions

sur

lespace et

le

temps,55

n

which

he

tried to prove

that

with-

out the

Newtonian

concepts

of an absolute

space

the

law

of

inertia

and,

accordingly,

he

whole

system

of mechanics

would

becomemeaningless.The resultsof Newton's physicswere so

closely

nterwoven

with

his fundamental

oncepts hat

t seemed

impossible

o

give

up

or change

the

latter

without

endangering

the

former.Any

such

attempt-it

was

felt-was

bound

to

end

in complete

cepticism

nd

anarchy.

To

many

great

physicists

Leibniz's

theories

concerning

he

relativity

f

space

and

time

appeared

to

be subversive

houghts.

An

entirely

ew

and

fresh

intellectualmpulsewas required operceive hatthesesubversive

thoughts

ould

be

turned

nto

constructive houghts,

hat a

new

system

f physics

ould

be

builtupon the

ruins

of the

Newtonian

concepts

of

space

and time. Several

men had written ystems

of

philosophy

before

Sir Isaac ,

declared William

Emerson

in

his

commentary

n Newton's

Principia

(I770),

but, for

their

ignorance

of

nature,

none of

them

could stand

the

test.

But his

principlesbeingbuilt upon the unerring oundation f observa-

tions and

experiments,

must

necessarily

tand

good

till the

dis-

solution

of

nature

itself. 56 ven

as late

as the

mid-nineteenth

century

commentators

nd

biographers

of Newton were

still

talking

n a

similar

ein.

To

have

been the chosen age

summoned

to

the

study

of

that

earth,

hese

systems

nd

that

universe,-the

favoured

awgiver

to

worlds

unnumbered,

he

high-priest

n

the

templeof boundless space , exclaimedDavid Brewsterin his

Memoirs

of

the

Life,

Writings,

nd

Discoveries

of

Sir Isaac

Newton,

was

a

privilege

hat could

be

granted

ut to

one mem-

ber of

the

human

family;-and

to have executed

he task

was

an

Histoire de

l'Academie

Royale

des Sciences

et

Belles Lettres

Berlin,

Annee 748.

William

Emerson,

A Short

Comment

n

Sir Isaac

Newton's

Prin-

cipia ,

n

The

Mathematical

rinciples

f

Sir

I.

Newton

(New

Edition,

London

803)

III 86.


27/27

No.

4.]

GALILEO

AND THE

SCIENTIFIC

REVOLUTION

39i

achievement

which

in its

magnitude

an

be

measured only

by

the

infiniten

space,

and

in

the

durationof

its

triumphs

y

the

infinite n time. That Sage-that Lawgiver-that High-priest

was

Newton. 57

No

modern

scientist

would

subscribe

to

this

judgment

without

ritical

reservations.

et

this

apparent

detrac-

tion

takes

nothing

way

from

the

fundamental

merits

of

New-

ton. For

it is

not the

methodof

Newton

but

the

dogmatic

faith

in

his

results,

nd

the

uncritical

se

made of

his

principles,

which

had

to

be

overcome

by the

further

development

f

scientific

thought.As Einsteinsaid in an articlepublishedat the second

centenary f

Newton's

death,58

heoretical

hysics

outgrewNew-

ton's

framework,

which

for

nearly two

centurieshad

provided

fixity

nd

intellectual

uidance for

science.

From

the

dispute

between

Leibniz

and

Newton

and its

pro-

longation

through

he

two

following

enturies

we

may

draw a

general

conclusion. Conflicts

within

the

realm

of

scientific

nd

philosophic hought ppear to be unavoidable.But amidthese n-

cessant

combats t is

comforting

o

see that

the

opposing

powers,

instead

of

being

mutually

estructive,re

of

mutual

ssistance

o,

and

steadily

cooperate

with,

one

another.

f,

as in

the

case

of

Newton and

Leibniz,

the battle

s

fought

etween

wo

thinkers

f

equal

intellectual

tature,

hen

the

struggle

does

not

end

in

the

defeat

or

victory

f

one

party;

it

leads

rather

o a

new

synthesis

of scientific nd philosophic hought.

ERNST

CASSIRER

YALE

UNIVERSITY

57

Brewster,

Memoirs

319.

[CASSIRER, Ernst]Newton and Leibniz

Documents

Transcript of [CASSIRER, Ernst]Newton and Leibniz