Download - [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
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
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
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
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.
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
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.
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
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.
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
6/27
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
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.
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
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.
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
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.
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
10/27
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
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.
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
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
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
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.
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
14/27
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
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.
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
16/27
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
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.
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
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.
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
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.
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
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.
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
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.
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
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.
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
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.
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
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.
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
25/27
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
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.
-
8/15/2019 [CASSIRER, Ernst]Newton and Leibniz
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.