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as a concept of a determinate object.
Kant criticizes the three traditional proofs “ the ontological, cos-
mological, and physico-theological arguments “ for embodying this
transcendental illusion. Although the latter two make a posteriori
arguments, Kant believes they implicitly presuppose the validity
of the a priori ontological argument. This occurs in the assump-
tion that the only possible candidate for the absolutely necessary
being is a being with the highest reality. Although thinkers before
Kant made some of his objections, his evaluation of the ontological
argument is noteworthy for anticipating developments in modern
logic. In arguing that existence is not a real predicate of individuals,
Kant foreshadows Frege™s and Russell™s treatment of the existential
Transcendental illusion III 283
quanti¬er as a second-order predicate or propositional function. Thus
Kant makes a signi¬cant contribution, independent of the critical
philosophy, to the debate over the ontological argument. Despite
rejecting claims to theoretical knowledge of God, Kant maintains
that the idea of God is signi¬cant for practical reason, as a founda-
tion for moral faith, as well as a regulative idea promoting empirical
inquiry.
c h ap t e r 11

Reason and the critical philosophy




As we saw in chapter 10, Kant believes the transcendental ideas of
reason perform two positive functions: ¬rst, the idea of the uncondi-
tioned generates regulative principles for scienti¬c explanations; sec-
ond, the ideal of the ens realissimum provides a basis of moral faith for
practical reason. The last part of the Critique sketches an account of
both functions. Despite the brevity of his account here, Kant claims
that reason is essential to the operations of the understanding. In
spelling out this relation, Kant completes his revolutionary theory
of the intellect. As we saw earlier in the Analytic, in analyzing con-
cepts as predicates of possible judgments, Kant overturned the tradi-
tional view that judging presupposes conceiving. Here he completes
the reversal by showing how judgment presupposes the higher-order
functions of reason.
The ¬nal section of the Critique is the Transcendental Doctrine of
Method. Although this contains four chapters, only the ¬rst two offer
substantive discussions. In chapter I, the Discipline of Pure Reason,
Kant contrasts the methods of philosophy and mathematics. The sig-
ni¬cant aspects here concern his theory of mathematical construction,
and his views on de¬nitions, axioms, and demonstrations. In chap-
ter II, the Canon of Pure Reason, Kant outlines the moral theology
required by practical reason, sketching his conceptions of the good
and the morally ideal world. Here he argues that the moral law requires
us to postulate the existence of God and the immortality of the soul.

1. the a ppend ix: th e re gu l ati ve use of rea s on
Kant explains the positive role of transcendental ideas in an Appendix
to the critique of speculative theology. First, he says, “Everything
284
Reason and the critical philosophy 285
grounded in the nature of our powers must be purposive and con-
sistent with their correct use” (A642/B670). Ideas of reason, then,
must have a positive real function, analogous to their logical use.
This function has two aspects. First, the speculative interest of rea-
son to seek the unconditioned provides the understanding a motive
to inquire into nature. Second, reason supplies methodological prin-
ciples guiding the understanding in creating empirical theories. By
now it is clear that transcendental ideas of reason are regulative only
and not constitutive. Because regulative principles function as imper-
atives rather than assertions, they do not make cognitive claims, but
merely give directions for systematizing empirical knowledge. Despite
their “subjective” character, these ideas have a “necessary regulative
use . . . directing the understanding to a certain goal . . . which,
although it is only an idea (focus imaginarius), . . . serves to obtain
for these concepts the greatest unity alongside the greatest exten-
sion” (A644/B672). Regulative ideas transcend experience and conse-
quently represent only ends to strive for in science, rather than features
of objects. But without them, the understanding could not produce
empirical cognitions, since it would lack a motivation to explain the
phenomena, as well as maxims for proceeding.
At A646/B674 Kant describes reason as the faculty of deriving the
particular from the universal. In logical inferences, the use of reason is
“apodictic,” since the universal is certain and given, and the particular
can be subsumed under it. In its real, explanatory use, by contrast,
reason operates “hypothetically,” by proposing problematic ideas to
¬t the given particulars. Because one can never be certain that the idea
applies to all possible instances, these hypotheses can only approxi-
mate universal rules. In general, the task of reason is to supply unity to
the judgments of the understanding. It does this by “projecting” the
idea of an interconnected whole “ a complete explanation of nature “
as a goal. Kant uses the example of the concept of power: experi-
ence shows that substances have diverse powers. He actually cites the
mental powers, “sensation, consciousness, imagination, memory, wit,
the power to distinguish, pleasure, desire, etc.” (A649/B677). Reason
produces the “logical maxim” to combine these powers under gen-
eral headings, and, ultimately, to seek “a fundamental power” at the
origin of all mental abilities.
But reason supplies more than the stimulus to explain natural
phenomena: in fact the understanding could not function without
Reason and the critical philosophy
286
reason. In a cryptic comment at A647/B675 Kant says, “The hypothet-
ical use of reason is therefore directed at the systematic unity of the
understanding™s cognitions, which, however, is the touchstone of
truth for its rules.” He remarks below that without the law of reason
there would be “no coherent use of the understanding, and, lack-
ing that, no suf¬cient mark of empirical truth; thus in regard to the
latter we simply have to presuppose the systematic unity of nature as
objectively valid and necessary” (A651/B679). Kant™s point is that the
truth values of empirical judgments can be determined only by testing
them for evidence against a system of empirical judgments. In par-
ticular, empirical generalizations can attain the status of laws only by
being subsumed under higher-order laws. Thus empirical cognition
presupposes both the logical (justi¬catory) and the real (explanatory)
functions of reason. Although the ideas of reason are not constitutive,
they are necessary for the understanding to produce cognitive claims.
In addition to motivating the understanding, reason supplies three
methodological principles guiding scienti¬c inquiry, the logical prin-
ciples of genera, species, and the af¬nity or continuity of forms.
Although all three principles were traditionally recognized as presup-
positions of scienti¬c explanation, until Kant no philosopher offered
a systematic justi¬cation.
The ¬rst, logical principle of genera is known as Occam™s razor,
or the law of parsimony. It was expressed in the “scholastic rule that
one should not multiply beginnings (principles) without necessity”
(A652/B680). In other words, the simpler the explanation, the bet-
ter. Scientists apply the principle whenever they seek commonalities
among diverse forms: here Kant adds to his example of mental pow-
ers the attempt to ¬nd common principles for the varieties of salts
and earths. This requires comparing distinct individuals or species
to identify their common characteristics. Rather than representing
merely an aesthetic value, however, the principle has a transcendental
basis. If this law did not obtain, there could be no empirical concepts:
no concept of a genus, nor any other universal concept, indeed no under-
standing at all would obtain . . . The logical principle of genera therefore
presupposes a transcendental one if it is to be applied to nature . . . According
to that principle sameness of kind is necessarily presupposed in the mani-
fold of a possible experience (even though we cannot determine its degree a
priori). (A653“4/B681“2)
Reason and the critical philosophy 287
That is, if we could not presuppose some degree of unity in expe-
rience, concepts of the understanding would have no application.
Thus empirical concept formation presupposes reason™s maxim to
seek unity in the phenomena.
The second principle aims at completeness through speci¬city.
This “law of speci¬cation” balances Occam™s razor by demanding
subspecies for every species. Like the ¬rst law, the second also has a
transcendental ground in the function of the understanding. For the
logical structure of concepts requires that they be not only subsumable
under higher-order concepts, but also subject to partition into lower-
level concepts. These two laws together constitute a tension in reason,
expressing interests both “in the domain (universality) in regard to
genera” and “in content (determinacy) in respect of the manifoldness
of species” (A654/B682).
Finally, Kant derives from these two principles a third, “the law
of the af¬nity of all concepts.” It postulates “a continuous transition
from every species to every other through a graduated increase of vari-
eties” (A657“8/B685“6). That is, the demands for unity and complete-
ness rule out ending the search for both similarities and differences at
any point. Kant says the principle that “there are no different original
and primary genera, which would be, as it were, isolated and separated
from one another” entails that “intervening species are always possi-
ble, whose difference from the ¬rst and second species is smaller than
their difference from each other” (A659“60/B687“8). This idea was
traditionally expressed as the principle that “nature makes no leaps.”
Recognized by Leibniz, it was most fruitfully expressed as the Law
of Least Action by Pierre-Louis Moreau de Maupertuis (1698“1759).
Maupertuis™s version states that whenever changes occur in nature, the
quantity of action is always the smallest possible, where quantity of
action is proportional to the product of a body™s mass and its velocity
and the distance it travels. Kant explains how the law applies to plan-
etary orbits. If we ¬nd that there are variations in the circular orbits of
planets, “we suppose that the movements of the planets that are not
a circle will more or less approximate to its properties, and then we
come upon the ellipse” (A662“3/B690“1). Although Kant does not
say so explicitly, all three principles formally codify his solution to
the Antinomies, namely that the world of appearances is given only
in the empirical regress. For if appearances do not have their nature
Reason and the critical philosophy
288
independently of the regress, then one cannot presuppose limits to
the search for genera or species.
These principles enable the understanding to produce empirical
theories and laws explaining the phenomena. From the Analytic, we
know that from its functions the understanding supplies only a priori
concepts such as substance and causality, which are too abstract to
yield empirical concepts. For example, the First Analogy requires that
all events be thought as changes of substance, but leaves the nature
of substance undetermined. Similarly, although the Second Analogy
guarantees the existence of empirical causal laws, it cannot provide
them. From Kant™s cryptic examples, empirical concept formation
involves comparing individuals (or species) and abstracting from their
differences to identify their similarities. (In effect this is the process
empiricists such as Locke thought gave rise to all concepts.) These
similar features then are represented by empirical concepts, which the
understanding orders in genus“species relations.
In the Critique of the Power of Judgment of 1790 Kant takes a
more systematic approach to empirical explanations. In this work
he emphasizes two uses of judgment, determining and re¬‚ective. As
the First Introduction explains, in determining judgment one applies
a given concept to an individual, thereby making a cognitive claim.
In re¬‚ection one is given an individual, and seeks a concept under
which to subsume it.1 Kant assigns both empirical concept formation
and aesthetic judgment to re¬‚ective judgment. The factor unifying
these two accounts is the transcendental principle of purposiveness, to
which Kant alludes in the Appendix and the Canon of Pure Reason.
The remainder of the Appendix emphasizes the regulative nature
of the principles of reason. In places Kant appears to contradict him-
self, sometimes calling them “objective,” and at other times “subjec-
tive.” As Grier points out, however, a charitable reading can resolve
the dif¬culties.2 There are two related senses in which the principles
are “subjective.” First, Kant consistently maintains that they do not
provide determinate concepts of objects, but only guide the under-
standing in securing such concepts. In that sense they lack objective
validity. And second, because they function as imperatives rather than

1 See Critique of the Power of Judgment, 15.
2 See Kant™s Doctrine of Transcendental Illusion, 268“79, for her discussion of this issue.
Reason and the critical philosophy 289
assertions, they serve as “subjective maxims” for this activity: “I call all
subjective principles that are taken not from the constitution of the
object but from the interest of reason in regard to . . . the cognition
of this object, maxims of reason. Thus there are maxims of specu-
lative reason . . . even though it may seem as if they were objective
principles” (A666/B694). Here Kant explicitly compares the princi-
ples of reason to the “subjective” practical maxims on which agents
act. He attributes the subjectivity of both types of maxims to their
origin in the interests of reason. Despite their “subjectivity” as max-
ims, as Grier points out, the principles are “objective” insofar as they
project an object for the understanding, namely a complete system
of cognition. More telling is Kant™s view that the coherent function
of the understanding presupposes both logical and real functions of
reason. Thus the regulative principles of reason are “indispensably
necessary”: without them there could be no determinate cognition of
objects.
The Appendix ends with remarks “On the ¬nal aim of the natural
dialectic of human reason.” This adds little, primarily emphasizing
the illusion resulting from misusing regulative principles. Of psy-
chological interest is his analysis of two mental failings: “lazy” and
“perverted” reason. Lazy reason occurs when one takes the idea of
God constitutively, thus bypassing the search for natural causes, “so
that instead of seeking them in the universal laws of the mecha-
nism of matter, we appeal right away to the inscrutable decree of the
highest wisdom” (A691/B719). Perverted reason, similarly, takes place
when one reverses the relation between natural phenomena and the
ideal of systematic unity. Here “the concept of such a highest intelli-
gence is determined anthropomorphically, and then one imposes ends
on nature forcibly and dictatorially” (A692/B720). In assuming that
all natural systems are teleological, one effectively destroys the unity
of nature, making it “entirely foreign and contingent in relation to
the nature of things” (A693/B721).
More substantive are Kant™s views of the relation between the ideas
of God and purposive unity in nature. At A686“7/B714“15 he remarks:
“This highest formal unity that alone rests on concepts of reason is
the purposive unity of things, and the speculative interest of reason
makes it necessary to regard every ordinance in the world as if it had
sprouted from the intention of a highest reason.” Such a principle
Reason and the critical philosophy
290
opens up “entirely new prospects for connecting up things in the
world in accordance with teleological laws, and thereby attaining to
the greatest systematic unity among them.” And he returns to the idea
at A694/B722, asserting that “Complete purposive unity is perfection”
and that “The greatest systematic unity . . . is . . . the ground of the
possibility of the greatest use of human reason.” Because this idea
“is legislative for us, . . . it is very natural to assume a corresponding
legislative reason (intellectus archetypus) from which all systematic
unity of nature, as the object of our reason, is to be derived.” As I
indicated above, this notion becomes the basis for Kant™s theory of
re¬‚ective judgment in the third Critique, as well as the key to Kant™s
moral theology.

2. t he doc trine of m e th od : th e di sci pl in e
of re a son
Although “discipline,” positively, means a form of instruction, Kant™s
concern here is with the negative sense, as a corrective: “The com-
pulsion through which the constant propensity to stray from certain
rules is limited and ¬nally eradicated is called discipline” (A709/B737
and note at A710/B738). His discussion of transcendental illusion so
far has concerned the discipline of the “content” of reason. Here he
addresses the discipline of the method of pure reason (A712/B740).
He divides the chapter into four sections, of which the ¬rst is the
most important. Kant™s strategy is to criticize the traditional “ana-
lytic” methods of philosophy by contrasting them with the “synthetic”
method of mathematics. In particular, he argues that dogmatic meta-
physicians are mistaken to think that philosophy can attain synthetic
a priori truths having the immediate certainty of mathematical cogni-
tion. Here he both develops the theory of mathematical construction
and presents a sophisticated theory of de¬nition. The remaining sec-
tions discuss the polemical use of reason, and its use with regard to
hypotheses and proofs, emphasizing Kant™s enlightenment attitude
toward knowledge.
Kant™s main point is that the formal methods of philosophy and
mathematics differ because of the nature of their concepts. Although
both employ a priori concepts, philosophical concepts originate in
the understanding, whereas mathematical concepts derive from pure
Reason and the critical philosophy 291
intuition. In consequence, the objects of mathematics can be con-
structed a priori, unlike the objects of philosophy. Corresponding
to this distinction are differences in the status and evidence of their
principles. On Kant™s view, only mathematics begins with axioms,
produces demonstrations, and can succeed in de¬ning its concepts.
Philosophy can produce neither complete de¬nitions of concepts nor
axiomatic principles. Although Kant™s original distinction between
analytic and synthetic judgments depends on the notion of “concept
containment,” in fact neither pure concepts of the understanding nor
empirical concepts can, strictly speaking, be de¬ned.
Kant begins by characterizing philosophical cognition as ratio-
nal cognition from concepts, and mathematical cognition as “from
the construction of concepts.” To construct a concept is “to exhibit
a priori the intuition corresponding to it.” Although this requires
a non-empirical intuition of an individual object, the construction
must “express in the representation universal validity for all possible
intuitions that belong under the same concept” (A713/B741). Mathe-
matical construction represents in pure intuition an individual object,
which, in spite of its particularity, has universal validity. Although the
construction may take place empirically, for example on paper, it need
not, since ¬gures can be exhibited a priori “through mere imagination,
in pure intuition” (A714/B742). Even when the ¬gure is represented
empirically, features such as the actual lengths of sides or sizes of angles
are irrelevant to the spatial relations being represented. In either case
it proceeds a priori, and thus exhibits synthetic a priori propositions.3
It is tempting to think mathematics and philosophy concern
different objects, the former quantity, the latter quality. This is a
mistake, however, since philosophy deals with magnitudes such as
totality and in¬nity, and mathematics concerns qualitative features
such as “the continuity of extension” (A715/B743). The difference
is not in the object, but in the manner of representing it: “only
the concept of magnitudes can be constructed, i.e., exhibited a pri-
ori in intuition, while qualities cannot be exhibited in anything
but empirical intuition . . . Thus no one can ever derive an intu-
ition corresponding to the concept of reality from anywhere except
3 Friedman agrees with Thompson, Parsons, and Brittan that empirical intuition is required
to establish the real possibility of mathematical concepts. It is not, however, required for pure
mathematics. See Friedman, Kant and the Exact Sciences, 101“2.
Reason and the critical philosophy
292
experience” (A714“15/B742“3). Consider the difference between the
shape and the color of a cone: colors are given only in empirical
intuition, whereas the pure intuition of space affords everything
required to describe the region delineated by a cone. Thus colors
cannot be constructed a priori (although their degree of intensity
can be).
The key is the relation between concepts and their objects. At
A719“20/B747“8 he reminds us that all cognition is ultimately related
to possible intuitions: “for through these alone is an object given.”
Mathematics can construct its concepts a priori because the intuition
of space provides the objects of geometry along with their concepts.4
Philosophical concepts make claims about real properties given only
empirically: “I cannot exhibit the concept of a cause in general in
intuition in any way except in an example given to me by experience,
etc.” (A715/B743). Put technically, the synthetic a priori cognition of
the “thing in general . . . can never yield a priori more than the mere
rule of the synthesis of that which perception may give a posteriori,
but never the intuition of the real object, since this must necessar-
ily be empirical” (A720/B749). So although extensive and intensive
measurements of real properties are constructible in intuition, the
properties themselves are not.
So far we have been treating mathematical construction as if there
were only one kind. In fact Kant distinguishes ostensive constructions
of geometry from symbolic constructions of arithmetic and algebra.
Although the latter also contain synthetic a priori judgments, they
are more abstract, lacking their own object:
But mathematics does not merely construct magnitudes (quanta), as in
geometry, but also mere magnitude (quantitas), as in algebra, where it entirely
abstracts from the constitution of the object that is to be thought . . . In
this case it chooses a certain notation for all construction of magnitudes in
general (numbers), as well as addition, subtraction, extraction of roots, etc.,
and . . . it then exhibits all the procedures through which magnitude is gen-
erated and altered in accordance with certain rules in intuition. (A717/B745)
Friedman explains this clearly.5 First he remarks that, based on Kant™s
theory in the Aesthetic, one would expect time to provide an object

4 Emily Carson emphasizes this point in “Kant on the Method of Mathematics,” 645“51.
5 Kant and the Exact Sciences; see especially 104“14.
Reason and the critical philosophy 293
for arithmetic as space does for geometry. But in fact, numbers are
not temporal “objects,” and arithmetic does not have its own object.
Time comes into play in the science of mechanics: at B49 Kant says,
“our concept of time therefore explains the possibility of as much
synthetic a priori cognition as is presented by the general theory of
motion.” The key is Kant™s distinction between a magnitude as an
object (quanta), and a mere magnitude as a quantity (quantitas).
Friedman says quanta refers to “the particular magnitudes there
happen to be. These are given, in the ¬rst instance, by the axioms
of Euclid™s geometry, which postulate the construction (from the
modern point of view, the existence) of all the relevant spatial mag-
nitudes.”6 In other words, geometry is the science of existing mag-
nitudes given in space. The numerical formulas of arithmetic and
algebra, by contrast, are based on quantity, “the concept of a thing
in general through the determination of magnitude.” Arithmetic and
algebra make no existence assumptions. Rather, their formulas express
“the operations and concepts . . . for manipulating, and thereby cal-
culating the speci¬c magnitude of any magnitudes which happen
to exist.”7 As Kant puts it, symbolic construction “entirely abstracts
from the constitution of the object that is to be thought.” Rather than
presenting the object in intuition, “it chooses a certain notation for all
construction of magnitudes in general (numbers),” and “then exhibits
all the procedures through which magnitude is generated and altered
in accordance with certain rules in intuition” (A717/B745). The for-
mulas of arithmetic and algebra are not principles for constructing
objects, then, but rules for operating with whatever magnitudes are
given in experience.8 As we shall see, Kant also denies these formulas
the character of axioms.
At A718/B746 Kant elaborates two types of spatial (geometrical)
construction. An empirical procedure “would yield only an empir-
ical proposition (through measurement of its angles), which would
contain no universality, let alone necessity.” In the second proce-
dure, “I put together in a pure intuition . . . the manifold that
belongs to the schema of a triangle in general and thus to its concept,
6 7 Kant and the Exact Sciences, 114.
Friedman, Kant and the Exact Sciences, 114.
8 Friedman explains that for Kant, arithmetic is concerned with rational magnitudes, whereas
“algebra is also concerned with irrational or incommensurable magnitudes,” produced by the

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