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objects for us.
Kant™s argument in the Third Analogy rests on a similar appeal to the
threefold source of our representation of objective time determinations:
(1) the discursive source (our logical forms of judgment); (2) the intuitive
source (space and time as the pure forms of our sensible intuition); and
(3) the a priori syntheses of imagination that bring it about that appear-
ances are combined in such ways that they can be reflected under
concepts according to the logical forms of our judgments. I will not
attempt here to rehearse Kant™s argument in all its complexity. I will
recall only enough to help me answer Friedman™s principled objection to
my interpretation.

Friedman maintains that because of the Aristotelian view of nature I
supposedly attribute to Kant, I make it incomprehensible why it should
be an a priori law of nature that substances are in relations of universal
interaction. Only on Newton™s concept of gravitational force, Friedman
urges, is it the case that every action must have an equal and opposite
reaction. No such necessity exists on an Aristotelian view of substance.14
Now, I have suggested above that Kant™s argument in the First Analogy
of Experience accounts both for the pull of Aristotelianism in our ordin-
ary perception and for the progress from what we might call this ˜˜mani-
fest image™™ to the Newtonian ˜˜scientific image™™ of the world.15 In other
words, in my understanding of Kant™s argument, the mental capacities at
work in generating the Aristotelian image of the world also explain why
it was both possible and necessary that this image be eventually super-
seded by a Newtonian (mathematical) worldview. The same is true of
Kant™s argument in the Third Analogy. Here what we need to under-
stand is why Kant thinks that the same capacities that generate the
representation of objective simultaneity among the objects of our ordin-
ary perceptual world also provide us with the a priori knowledge that
they exist in relations of universal reciprocal action.
As I understand it, Kant™s argument is along the following lines: we
experience individual material things as existing simultaneously in space
only if we combine (synthesize) our perceptions of things present to our
senses with our representations (in imagination) of things not present to
our senses, in such a way that they can be reflected under concepts
combined in reciprocal hypothetical judgments, such as: ˜˜If A is present
to my senses at time t at point p1 relative to my own body, then B (which

See Friedman, ˜˜Logical forms,™™ p. 209:
On the Aristotelian conception of the community of substances in space, there is no
particular need for reciprocal interaction. The sun influences changing objects of the
earth, for example, but since the sun undergoes no actual change itself, neither the
earth nor objects upon it influence the sun in turn. In Kant™s Newtonian conception,
by contrast, every action must have an equal and opposite reaction, and so the earth
does necessarily influence the sun in turn “ through its own (relatively small)
gravitational force.
See above, p. 54. What I mean is that in my reading, Kant accounts both for the fact that the
world appears to us as a world of only relatively permanent, qualitatively determined
things, subject to generation and corruption (this is what I call the ˜˜pull of Aristotelianism
in our ordinary perceptual world™™), and for the fact that ultimately, the unity of the time-
determinations of appearances depends on our recognizing the existence of one sub-
stance, matter, whose states change according to universal mathematical laws (the
Newtonian view of nature).

is not present to my senses) is also present at this same time t, at point p2
relative to my own body; and conversely, if B is present to my senses at
time t at point p2 relative to my own body, then A (which is not present to
my senses) is also present at this same time t, at point p1 relative to my
own body.™™ This is of course far from a representation of causal interac-
tion. However, if we generalize these statements to the reciprocal con-
ditioning of all things with respect to their places and changes of place,
states and changes of states, in one space and one time (in which our own
body is also situated), then we obtain the idea that all material substances,
insofar as they are perceived (experienced) as existing simultaneously,
stand in relations of universal reciprocal determination such that each
and every substance™s being at a certain place, in a given state, at a
given time, is a determining ground for each and every other sub-
stance™s being in a given place, in a given state, at that same time.
This (as yet indeterminate) notion of reciprocal determination of
position and state, when instantiated to the empirical concept of
material substance as something movable in space, is presupposed
in Newton™s Third Law of Motion. And as Friedman has shown, the
latter, when instantiated to the Keplerian regularities in the motions
of celestial bodies, leads to Newton™s formulation of the empirical law
of universal gravitation.16
If this explanation is correct, then Kant holds that although it is
only with Newton™s mathematical science of nature (prepared by
Kepler, Copernicus, Galileo, Descartes, and others) that a determi-
nate notion of universal interaction is formulated and expressed in a
mathematical law, an implicit, indeterminate notion of the reciprocal
determination of things and their states has to be at work in each and
every one of our experiences of the objective simultaneity of things
(where ˜˜experience™™ does not mean mere sense perception, but the
synthesis of perceptions by means of which they are related to inde-
pendently existing objects that they are taken to be the perception
of). This indeterminate notion is a far cry from Newton™s law of the
equality of action and reaction of moving forces (the Third Law of
Motion in the Principia) and even further from the mathematical law
of universal gravitation. But Kant™s point is that in order to formulate
these laws we need to have an a priori principle stating that all

See Michael Friedman, ˜˜Causal laws and the foundations of natural science,™™ in Paul Guyer
(ed.), The Cambridge Companion to Kant (Cambridge: Cambridge University Press, 1992),
pp. 161“99.

appearances stand in universal reciprocal determination. For “ as
Kant argues in the Metaphysical Foundations of Natural Science “ this
principle is presupposed in Newton™s third law,17 which is itself pre-
supposed in Newton™s proof of the inverse square law. The justifica-
tion of this principle is provided by the argument of the Third
Analogy: we would have no experience of identifiable and re-identifiable
objects existing simultaneously in space unless we presupposed the
universal reciprocal determination of their positions and states; now,
according to the Transcendental Deduction of the Categories, the
conditions of possibility of experience are the conditions of possibility
of the object of experience; so, there would be no objects of experi-
ence simultaneously existing in space unless they were in universal
reciprocal determination of their positions and states.
Because they are thus individuated in one space and one time by way
of the universal mutual determination of their positions and states,
appearances can be known under concepts according to a universal
subordination of genera and species for which the discursive form is
the form of disjunctive judgment. This, I argue, is the explanation for
the correspondence, in the Metaphysical Deduction of the Categories,
between the logical form of disjunctive judgment and the category of
community (universal interaction): the category of community is the
concept guiding the syntheses of appearances so that they can be
reflected under concepts according to the logical form of disjunctive
judgment. Now, Friedman objects that he simply does not see how only a
Newtonian conception of interaction makes possible concept formation
generating a universal subordination of genera and species.18 But that is
not what I say. Certainly an Aristotelian view of nature does represent it
according to universal subordinations of genera and species. Indeed
Kant explicitly acknowledges the Aristotelian ancestry of this discursive
form of systematicity.19 What I maintain is that according to Kant, since
material things are individuated in space and recognized as existing at
the same time only by way of the presupposition, which eventually
becomes the determinate knowledge, of their universal reciprocal
action, the concepts of natural kinds under which they are recognized
and combined according to the form of disjunctive judgment “ which is

Immanuel Kant, Metaphysical Foundations of Natural Science, trans. Michael Friedman
(Cambridge: Cambridge University Press, 2004), AAiv, p. 544.
See Friedman, ˜˜Logical forms,™™ p. 210.
See Critique of the Power of Judgment, First Introduction, AAxx, pp. 214“15.

the form according to which our concepts of natural kinds are coordi-
nated and subordinated to one another “ these concepts of natural kinds
are concepts of relational properties: forces. This is confirmed by the
appendix to the Transcendental Dialectic, where Kant insists that the
highest goal of natural science is to order all its concepts of force under
that of ˜˜one and the same moving force™™ (A663/B681).

Like Friedman, I insist that according to Kant, Newtonian science rests
on the presupposition of the universal validity of the causal principle.
But precisely for this reason, I maintain that Newtonian science is of no
use at all to prove the causal principle: this would be circular. So what we
need to know is: how does Kant prove its validity with respect to all
appearances, namely all objects that appear to our senses? Here again
the answer I propose rests on my analysis of Kant™s account of the ways in
which figurative synthesis generates our representation of the objective
ordering of appearances in time. In this case, I argue that according to
Kant, we would not even experience a succession as an objective succes-
sion unless this succession appeared to ˜˜presuppose something upon
which it follows according to a rule™™ (A189). Because this is a necessary
presupposition of any experience of objective succession, experiencing
such a succession is also looking for the ˜˜something upon which it
follows, according to a rule.™™ That is to say, experiencing a succession
as objective is also looking for the event or state of affairs that might be
known as an instantiation of the antecedent of a hypothetical rule whose
consequent is instantiated by the given objective succession. What the
antecedent is, we can find out only empirically. But the principle accord-
ing to which there is such an antecedent is an a priori law, and thus
absolutely necessary. And the connection we have found empirically, if
true (namely, if we have correctly identified the relevant connection in
relation to the unity of experience) is a necessary connection.
I nowhere state, nor do I for a moment entertain, the view attributed
to me by Michael Friedman that Kant defends a strictly inductive
method for discovering causal connections. On the contrary, I argue
that for Kant what makes it possible for us to progress from the mere
hypothetical judgment ˜˜if the sun shines on the stone, the stone gets
warm™™ to the causal judgment, ˜˜the sun warms the stone,™™ is that we have
already presupposed the a priori validity of the causal principle. And
what makes such a presupposition legitimate is the argument I just

recalled: no objective succession would be experienced unless its per-
ception had been obtained (˜˜synthesized™™) in accordance with the causal
principle (namely under the presupposition that ˜˜something precedes,
upon which it follows according to a rule™™). This being granted, it
remains that in Kant™s own words, the sensible mark by which we
recognize the existence of a causal connection is the constant conjunc-
tion of similar events or states of affairs: in the chapter on the
Schematism of the Pure Concepts of the Understanding, Kant defines
the schema of cause as ˜˜the real which, whenever posited, something else
always follows. It consists therefore in the succession of the manifold,
insofar as it is subject to a rule™™ (A144/B183).
In the Second Analogy, after expounding his argument for the claim
that presupposing the truth of the causal principle is an a priori condi-
tion of all experience, Kant considers a possible objection to this view. It
might seem, he says, that this claim contradicts the observations we all
make, according to which it is only by witnessing repeated similar
sequences of events that we come up with a rule for these sequences,
and thus form a concept of causal connection: thus the concept would
appear to be empirical after all. Kant™s reply is that it is here as with all
other a priori representations: we draw them out of experience, as clear
concepts, only because we have put them there in the first place (see
Now, Friedman objects to my citing this passage in support of my
claim that for Kant, particular causal connections are known only from
experience. According to Friedman, in referring to the ˜˜common obser-
vation™™ according to which our knowledge of particular causal rules is
acquired empirically, Kant is not expressing his own view. Rather, he is
giving voice to a view he expressly opposes. But I think Friedman™s
interpretation is not supported by the text. He may be misled by
Kemp Smith™s translation, which says:
This [i.e. the statement that the truth of the causal principle is an a priori
presupposition of all experience] may seem to contradict all that has
hitherto been taught in regard to the procedure of our understanding.
The accepted view is that only through the perception and comparison of
events repeatedly following in a uniform manner upon preceding appear-
ances are we enabled to discover a rule according to which, etc. . . .

But the text really says:
This may seem to contradict all the remarks [Bermerkungen] that have
always been made about the way our understanding proceeds; according

to those remarks, only through the perception and comparison of events
repeatedly following in a uniform manner . . . are we enabled to discover
a rule, etc. . . . (A195“6/B240“1, my translation)20

Later in the same paragraph, Kant continues:

The case is the same here as with other pure a priori representations (e.g.
space and time) that we can extract as clear concepts from experience
only because we have put them into experience, and experience is hence
brought about through them. (ibid.)

What Kant is opposing, then, is the view that just as particular causal
connections are known empirically, so is the universal causal principle
itself. In other words, he opposes the inference from the empirical char-
acter of our knowledge of particular causal connections to the empirical
character of our knowledge of the causal principle itself. The same point is
made even more explicitly in the Transcendental Methodology:

If wax that was previously firm melts, I can cognize a priori that some-
thing must have preceded (e.g. the heat of the sun) on which this has
followed in accordance with constant law, though without experience, to
be sure, I could determinately cognize neither the cause from the effect
nor the effect from the cause a priori and without instruction from
experience. [Hume] therefore falsely inferred from the contingency of
our determination in accordance with the law the contingency of the law
itself . . . (A766/B794)

Friedman charges that in stressing as I do the empirical character of
our knowledge of particular causal connections, I make Kant a propo-
nent of a Baconian inductivist method in natural science. It is true that I
relate Kant™s analysis of the transition from judgments of perception to
judgments of experience, in the Prolegomena, to the striking reference
Kant makes to Bacon in the B Preface of the Critique of Pure Reason.
There Kant credits Bacon with having ˜˜partly occasioned, and partly
further stimulated, since one was already on its track, [a] discovery
[which] can . . . be explained by a sudden revolution in the way of

At the time of my discussion with Friedman, the Guyer and Wood translation had only
recently appeared, and Kemp Smith™s was still the most familiar. The translation I give
here is the one I offered at the time, against Kemp Smith™s. For all other citations I return
to Guyer and Wood™s translation, unless otherwise indicated. On the particular point at
hand, Guyer and Wood concur with me in not attributing to Kant Kemp Smith™s mislead-
ing disclaimer: ˜˜The accepted view is that . . . ™™

thinking™™ (Bxii).21 The ˜˜discovery™™ Kant refers to is that ˜˜in order to
know something securely a priori, [one] had to ascribe to the thing
nothing except what followed necessarily from what [one] had put into
it in accordance with one™s concept.™™ After thus crediting Bacon, Kant
adds: ˜˜Here I will consider natural science only insofar as it is grounded
on empirical principles™™ (this is in contrast to geometry and its construc-
tions according to a priori concepts, for which he cited earlier the
example of Thales). He then cites as examples of the ˜˜revolution in
the manner of thinking™™ in natural science, Galileo™s experiments
with the inclined plane, Torricelli™s experiments with atmospheric
pressure, and even (less felicitously) Stahl™s experiments in transform-
ing metal into calcar. The point appears to be, then, that even Bacon,
the inspirer of a strictly empirical method in natural science, really
participates in the ˜˜revolution in the way of thinking™™ characteristic of
modern science, for even he taught his contemporaries that ˜˜reason
must approach nature with its principles in one hand, according to
which alone the agreement among appearances can count as laws,
and, in the other hand, the experiments thought out in accordance
with these principles™™ (Bxiii). In KCJ I suggest that here Kant may
have in mind Bacon™s explanation of the method of ˜˜crucial experi-
ments,™™ which he admittedly interprets in strangely aprioristic
terms.22 If my reading is correct, Kant™s reference to Bacon is
meant to show that although all natural science (and therefore
Newtonian science itself) is empirical science, it would be impossible
unless it could rely on strictly a priori principles.
To sum up: the reason I do not take myself to attribute to Kant the
defense of a strictly inductivist method in natural science is twofold.
First, for Kant as I understand him, although all knowledge of any
particular empirical connection is empirical, it rests on a presupposition
that is not empirical, but a priori: that of the universal validity of the
causal principle. Second, even though the schema of causality, and so the
empirical feature of objects of experience by which we will be alerted to
the presence of a causal connection, is, as it was for Hume, the repetition
of generically identical sequences of events or states of affairs (˜˜the real
upon which, whenever it is posited, something else always follows™™
[A144/B183]), nevertheless what makes possible the universalization of

Cf. KCJ, p. 176.
See KCJ, pp. 176“7, nn. 22 and 23.

such observed correlations into causal connections is the use of mathe-
matical concepts and methods to formulate universal laws of nature.23

Concluding remarks
In his concluding remarks, Friedman quotes Cassirer™s charge (in his
1910 book, Substanzbegriff und Funktionsbegriff)24 according to which the
Aristotelian theory of concepts and concept formation is responsible for
the errors both of rational metaphysics and of traditional empiricism,
and is in fundamental tension with the modern mathematical science of
nature. According to Friedman, my book brought to unprecedented
light the fact that precisely this tension between Aristotelianism and
Newtonianism is at the core of Kant™s critical philosophy. For I am
supposed to have shown that in his metaphysical deduction of the
categories, Kant adopts an Aristotelian view of concepts, judgments,
and concept formation. But in the System of Principles of the Critique
of Pure Reason and in the Metaphysical Foundations of Natural Science he is a
clear proponent of Newtonianism and the mathematical method in
natural science. Because I have not perceived the tension my own
analyses thus revealed, I have not asked the question Friedman now
asks: does Kant have the resources to resolve it?
But does Kant defend an Aristotelian theory of concepts and concept
formation, in the metaphysical deduction of the categories? I do not
think he does. Indeed one of the grounding theses of my book is that
although the forms of Kant™s ˜˜general pure logic™™ are essentially
Aristotelian, the use he argues we make of them in cognition is a radical
break from the Aristotelian view of concept formation shared by his
predecessors in the German Schulphilosophie, for two reasons: (1) because
for him the form of judgment is prior to its matter (concepts and objects),
so that even the most strictly empirical concepts are formed under the
guidance of the acts of judging and their forms; and (2) because before
any such acts of empirical concept formation, synthesis, that is, combina-
tion in imagination of manifolds in space and time, must have occurred.
In insisting on these two aspects of Kant™s anti-abstractionist view of
concept formation, I am in agreement with Cassirer, whose main target,

On this point, see also ch. 6 in this volume, especially pp. 172“7.
Ernst Cassirer, Substanzbegriff und Funktionsbegriff. Untersuchungen u die Grundfragen der
Erkenntniskritik (Berlin 1910, repr. Darmstadt: Wissenschaftliche Buchgesellschaft, 1969).
Transl. W. C. Swabey and M. C. Swabey, Substance and Function (New York: Dover, 1953).
References to the text are given in the German edition.

when he attacks the modern, psychologistic version of Aristotelian
abstractionism, is quite explicitly Mill, not Kant.25
What Cassirer does challenge in Kant is the view that understanding
the nature of mathematical concepts is understanding the ways in which
they are grounded in pure acts of the mind. To this view and to the role
Kant assigns to the pure intuition of time in generating concepts of
number, Cassirer opposes Frege™s and Dedekind™s logicist program of
a purely logical derivation of arithmetical concepts and laws. Only this
program and the modern quantificational logic of relations that makes it
possible, says Cassirer, can reliably overcome the old Aristotelian view of
concepts and the ontological primacy of substance over relations.26 This
leaves us, it seems to me, with a question slightly different from the one
Friedman reproaches me for not having formulated. Friedman™s ques-
tion is: ˜˜Does Kant™s epistemology have the resources to resolve the
tension between Aristotelianism and Newtonianism in Kant™s natural
philosophy?™™ To this question I have argued that the answer is, yes,
Kant does have the resources: the pure forms of intuition as the pure
forms of manifoldness, distinct from and complementary to the forms of
discursive concepts and concept formation. But the next question is: if
these resources offer the means to understand the move from
Aristotelianism to Newtonianism, do they also offer the means to under-
stand the nineteenth- and twentieth-century superseding of Newtonian
natural science, with its reliance on Euclidean space and strictly deter-
ministic causal laws? Interestingly, Kant™s theory of space and time as
pure forms of intuition, which bears the brunt of Kant™s account for the
move from Aristotelianism to modern mathematical natural science, is
also what primarily needs to be revisited in order to come to terms with
later developments in mathematics, their relation to logic, and their
application in natural science. I suggest that a re-examination of Kant™s
theory of space and time should not neglect either of its aspects: neither
Kant™s view of the role of spatiotemporal intuition in representing the
middle-sized objects of our ordinary perceptual experience, nor the role
of spatiotemporal intuition in grounding our scientific worldview.
Under both aspects such a re-examination was beyond the scope and
ambition of my book.


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