THE METAPHYSICAL DEDUCTION OF THE CATEGORIES
The aim of the _Aesthetic_ is to answer the first question of the
_Critique_ propounded in the Introduction, viz. 'How is pure
mathematics possible?'[1] The aim of the _Analytic_ is to answer the
second question, viz. 'How is pure natural science possible?' It has
previously[2] been implied that the two questions are only verbally of
the same kind. Since Kant thinks of the judgements of mathematics as
self-evident, and therefore as admitting of no reasonable doubt[3],
he takes their truth for granted. Hence the question, 'How is pure
mathematics possible?' means 'Granted the truth of mathematical
judgements, what inference can we draw concerning the nature of the
reality to which they relate?'; and the inference is to proceed from
the truth of the judgements to the nature of the reality to which
they relate. Kant, however, considers that the principles underlying
natural science, of which the law of causality is the most prominent,
are not self-evident, and consequently need proof.[4] Hence, the
question, 'How is pure natural science possible?' means 'What
justifies the assertion that the presuppositions of natural science
are true?' and the inference is to proceed from the nature of the
objects of natural science to the truth of the _a priori_ judgements
which relate to them.
[1] B. 20, M. 13.
[2] pp. 23-5.
[3] Cf. p. 24, note 1.
[4] Cf. p. 24, notes 2 and 3.
Again, as Kant rightly sees, the vindication of the presuppositions
of natural science, to be complete, requires the discovery upon a
definite principle of _all_ these presuppositions. The clue to this
discovery he finds in the view that, just as the perceptions of space
and time originate in the sensibility, so the _a priori_ conceptions
and laws which underlie natural science originate in the
understanding; for, on this view, the discovery of all the conceptions
and laws which originate in the understanding will be at the same time
the discovery of all the presuppositions of natural science.
Kant therefore in the _Analytic_ has a twofold problem to solve.
He has firstly to discover the conceptions and laws which belong to
the understanding as such, and secondly to vindicate their application
to individual things. Moreover, although it is obvious that the
conceptions and the laws of the understanding must be closely
related,[5] he reserves them for separate treatment.
[5] E. g. the conception of 'cause and effect', and the law
that 'all changes take place according to the law of the
connexion between cause and effect'.
The _Analytic_ is accordingly subdivided into the _Analytic of
Conceptions_ and the _Analytic of Principles_. The _Analytic of
Conceptions_, again, is divided into the _Metaphysical Deduction of
the Categories_, the aim of which is to discover the conceptions
of the understanding, and the _Transcendental Deduction of the
Categories_, the aim of which is to vindicate their validity,
i. e. their applicability to individual things.
It should further be noticed that, according to Kant, it is the
connexion of the _a priori_ conceptions and laws underlying natural
science with the _understanding_ which constitutes the main difficulty
of the vindication of their validity, and renders necessary an answer
of a different kind to that which would have been possible, if the
validity of mathematical judgements had been in question.
"We have been able above, with little trouble, to make comprehensible
how the conceptions of space and time, although _a priori_ knowledge,
must necessarily relate to objects and render possible a synthetic
knowledge of them independently of all experience. For since an object
can appear to us, i. e. be an object of empirical perception, only by
means of such pure forms of sensibility, space and time are pure
perceptions, which contain _a priori_ the condition of the possibility
of objects as phenomena, and the synthesis in space and time has
objective validity."
"On the other hand, the categories of the understanding do not
represent the conditions under which objects are given in perception;
consequently, objects can certainly appear to us without their
necessarily being related to functions of the understanding, and
therefore without the understanding containing _a priori_ the
conditions of these objects. Hence a difficulty appears here, which
we did not meet in the field of sensibility, viz. how _subjective
conditions of thought_ can have _objective validity_, i. e. can
furnish conditions of the possibility of all knowledge of objects;
for phenomena can certainly be given us in perception without the
functions of the understanding. Let us take, for example, the
conception of cause, which indicates a peculiar kind of synthesis in
which on A something entirely different B is placed[6] according to a
law. It is not _a priori_ clear why phenomena should contain something
of this kind ... and it is consequently doubtful _a priori_, whether
such a conception is not wholly empty, and without any corresponding
object among phenomena. For that objects of sensuous perception must
conform to the formal conditions of the sensibility which lie _a
priori_ in the mind is clear, since otherwise they would not be
objects for us; but that they must also conform to the conditions
which the understanding requires for the synthetical unity of thought
is a conclusion the cogency of which it is not so easy to see. For
phenomena might quite well be so constituted that the understanding
did not find them in conformity with the conditions of its unity, and
everything might lie in such confusion that, e. g. in the succession
of phenomena, nothing might present itself which would offer a rule of
synthesis, and so correspond to the conception of cause and effect, so
that this conception would be quite empty, null, and meaningless.
Phenomena would none the less present objects to our perception, for
perception does not in any way require the functions of thinking."[7]
[6] _Gesetzt._
[7] B. 121-3, M. 75-6.
This passage, if read in connexion with that immediately preceding
it,[8] may be paraphrased as follows: 'The argument of the _Aesthetic_
assumes the validity of mathematical judgements, which as such relate
to space and time, and thence it deduces the phenomenal character of
space and time, and of what is contained therein. At the same time the
possibility of questioning the validity of the law of causality, and
of similar principles, may lead us to question even the validity of
mathematical judgements. In the case of mathematical judgements,
however, in consequence of their relation to perception, an answer is
readily forthcoming. We need only reverse the original argument and
appeal directly to the phenomenal character of space and time and of
what is contained in them. Objects in space and time, being
appearances, must conform to the laws according to which we have
appearances; and since space and time are only ways in which we
perceive, or have appearances, mathematical laws, which constitute the
general nature of space and time, are the laws according to which we
have appearances. Mathematical laws, then, constitute the general
structure of appearances, and, as such, enter into the very being
of objects in space and time. But the case is otherwise with the
conceptions and principles underlying natural science. For the law of
causality, for instance, is a law not of our perceiving but of our
thinking nature, and consequently it is not presupposed in the
presentation to us of objects in space and time. Objects in space
and time, being appearances, need conform only to the laws of our
perceiving nature. We have therefore to explain the possibility of
saying that a law of our thinking nature must be valid for objects
which, as conditioned merely by our perceiving nature, are independent
of the laws of our thinking; for phenomena might be so constituted as
not to correspond to the necessities of our thought.'
[8] B. 120-1, M. 73-4.
No doubt Kant's _solution_ of this problem in the _Analytic_ involves
an emphatic denial of the central feature of this statement of it,
viz. that phenomena may be given in perception without any help from
the activity of the understanding.[9] Hence it may be urged that this
passage merely expresses a temporary aberration on Kant's part, and
should therefore be ignored. Nevertheless, in spite of this
inconsistency, the view that phenomena may be given in perception
without help from the activity of the understanding forms the basis
of the difference of treatment which Kant thinks necessary for the
vindication of the judgements underlying natural science and for that
of the judgements of mathematics.
[9] Cf. B. 137-8, M. 85, and B. 160 note, M. 98 note.
We may now consider how Kant 'discovers' the categories or conceptions
which belong to the understanding as such.[10] His method is sound in
principle. He begins with an account of the understanding in general.
He then determines its essential differentiations. Finally, he argues
that each of these differentiations involves a special conception,
and that therefore these conceptions taken together constitute an
exhaustive list of the conceptions which belong to the understanding.
[10] B. 91-105, M. 56-63.
His account of the understanding is expressed thus: "The understanding
was explained above only negatively, as a non-sensuous faculty of
knowledge. Now, independently of sensibility, we cannot have any
perception; consequently, the understanding is no faculty of
perception. But besides perception there is no other kind of
knowledge, except through conceptions. Consequently, the knowledge of
every understanding, or at least of every human understanding, is a
knowledge through conceptions,--not perceptive, but discursive. All
perceptions, as sensuous, depend on affections; conceptions,
therefore, upon functions. By the word function, I understand the
unity of the act of arranging different representations under one
common representation. Conceptions, then, are based on the spontaneity
of thinking, as sensuous perceptions are on the receptivity of
impressions. Now the understanding cannot make any other use of these
conceptions than to judge by means of them. Since no representation,
except only the perception, refers immediately to the object, a
conception is never referred immediately to an object, but to some
other representation thereof, be that a perception or itself a
conception. A judgement, therefore, is the mediate knowledge of an
object, consequently the representation of a representation of it. In
every judgement there is a conception which is valid for many
representations, and among these also comprehends a given
representation, this last being then immediately referred to the
object. For example, in the judgement 'All bodies are divisible', our
conception of the divisible refers to various other conceptions; among
these, however, it is herein particularly referred to the conception
of body, and this conception of body is referred to certain phenomena
which present themselves to us. These objects, therefore, are
mediately represented by the conception of divisibility. Accordingly,
all judgements are functions of unity in our representations, since,
instead of an immediate, a higher representation, which comprehends
this and several others, is used for the knowledge of the object, and
thereby many possible items of knowledge are collected into one. But
we can reduce all acts of the understanding to judgements, so that the
_understanding_ in general can be represented as a _faculty of
judging_."[11]
[11] B. 92-4, M. 56-7.
It is not worth while to go into all the difficulties of this confused
and artificial passage. Three points are clear upon the surface. In
the first place, the account of the understanding now given differs
from that given earlier in the _Critique_[12] in that, instead of
merely distinguishing, it separates the sensibility and the
understanding, and treats them as contributing, not two inseparable
factors involved in all knowledge, but two kinds of knowledge. In the
second place, the guise of argument is very thin, and while Kant
ostensibly _proves_, he really only _asserts_ that the understanding
is the faculty of judgement. In the third place, in describing
judgement Kant is hampered by trying to oppose it as the mediate
knowledge of an object to perception as the immediate knowledge of an
object. A perception is said to relate immediately to an object; in
contrast with this, a conception is said to relate immediately only to
another conception or to a perception, and mediately to an object
through relation to a perception, either directly or through another
conception. Hence a judgement, as being the use of a conception, viz.
the predicate of the judgement, is said to be the mediate knowledge of
an object. But if this distinction be examined, it will be found that
two kinds of immediate relation are involved, and that the account of
perception is not really compatible with that of judgement. When a
perception is said to relate immediately to an object, the relation in
question is that between a sensation or appearance produced by an
object acting upon or affecting the sensibility and the object which
produces it. But when a conception is said to relate immediately to
another conception or to a perception, the relation in question is
that of universal and particular, i. e. that of genus and species or
of universal and individual. For the conception is said to be 'valid
for' (i. e. to 'apply to') and to 'comprehend' the conception or
perception to which it is immediately related; and again, when a
conception is said to relate mediately to an object, the relation
meant is its 'application' to the object, even though in this case
the application is indirect. Now if a perception to which a
conception is related--either directly or indirectly through another
conception--were an appearance produced by an object, the conception
could never be related to the object in the sense required, viz. that
it applies to it; for an appearance does not _apply to_ but is
_produced_ by the object. Consequently, when Kant is considering a
conception, and therefore also when he is considering a judgement,
which is the use of a conception, he is really thinking of the
perception to which it is related as an _object of_ perception, i. e.
as a perceived individual, and he has ceased to think of a perception
as an appearance produced by an object.[13] Hence in considering
Kant's account of a conception and of judgement, we should ignore his
account of perception, and therefore also his statement that judgement
is the mediate knowledge of an object.
[12] B. 74-6, M. 45-6.
[13] Kant, in _illustrating_ the nature of a judgement,
evades the difficulty occasioned by his account of
perception, by illustrating a 'perception' by the 'conception
of body', and 'objects' by 'certain phenomena'. He thereby
covertly substitutes the relation of universal and individual
for the relation of an appearance and the object which causes
it.
If we do so, we see that Kant's account of judgement simply amounts to
this: 'Judgement is the use of a conception or 'universal'; the use of
a conception or universal consists in bringing under it corresponding
individuals or species. Consequently, judgement is a function
producing unity. If, for instance, we judge 'All bodies are
divisible', we thereby unify 'bodies' with other kinds of divisible
things by bringing them under the conception of divisibility; and if
we judge 'This body is divisible' we thereby unify this divisible
body with others by bringing it and them under the conception of
divisibility.'[14] Again, since 'the understanding in general can be
represented as a _faculty of judging_', it follows that the activity
of the understanding consists in introducing unity into our
representations, by bringing individuals or species--both these being
representations--under the corresponding universal or conception.[15]
[14] It is not Kant's general account of judgement given in
this passage, but the account of perception incompatible with
it, which leads him to confine his illustrations to universal
judgements.
[15] We may note three minor points. (1) Kant's definition of
function as 'the unity of the act of arranging [i. e. the act
which produces unity by arranging] different representations
under a common representation' has no justification in its
immediate context, and is occasioned solely by the
forthcoming description of judgement. (2) Kant has no right
to distinguish the activity which _originates_ conceptions,
or upon which they depend, from the activity which _uses_
conceptions, viz. judgement. For the act of arranging diverse
representations under a common representation which
originates conceptions is the act of judgement as Kant
describes it. (3) It is wholly artificial to speak of
judgement as 'the representation of a representation of an
object'.
Having explained the nature of the understanding, Kant proceeds to
take the next step. His aim being to connect the understanding with
the categories, and the categories being a plurality, he has to show
that the activity of judgement can be differentiated into several
kinds, each of which must subsequently be shown to involve a special
category. Hence, solely in view of the desired conclusion, and in
spite of the fact that he has described the activity of judgement as
if it were always of the same kind, he passes in effect from the
singular to the plural and asserts that 'all the functions of the
understanding can be discovered, when we can completely exhibit the
functions of unity in judgements'. After this preliminary transition,
he proceeds to assert that, if we abstract in general from all content
of a judgement and fix our attention upon the mere form of the
understanding, we find that the function of thinking in a judgement
can be brought under four heads, each of which contains three
subdivisions. These, which are borrowed with slight modifications from
Formal Logic, are expressed as follows.[16]
I. _Quantity._
Universal
Particular
Singular.
II. _Quality._
Affirmative
Negative
Infinite.
III. _Relation._
Categorical
Hypothetical
Disjunctive.
IV. _Modality._
Problematic
Assertoric
Apodeictic.
These distinctions, since they concern only the form of judgements,
belong, according to Kant, to the activity of judgement as such, and
in fact constitute its essential differentiations.
[16] B. 95, M. 58.
Now, before we consider whether this is really the case, we should
ask what answer Kant's account of judgement would lead us to expect
to the question 'What are all the functions of unity in judgement?'
The question must mean 'What are the kinds of unity produced by
judgement?' To this question three alternative answers are prima facie
possible. (1) There is only one kind of unity, that of a group of
particulars unified through relation to the corresponding universal.
The special unity produced will differ for different judgements, since
it will depend upon the special universal involved. The kind or form
of unity, however, will always be the same, viz. that of particulars
related through the corresponding universal. For instance, 'plants'
and 'trees' are unified respectively by the judgements 'This body is a
plant' and 'This body is a tree'; for 'this body' is in the one case
related to other 'plants' and in the other case to other 'trees'. And
though the unity produced is different in each case, the kind of unity
is the same; for plants and trees are, as members of a kind, unities
of a special kind distinct from unities of another kind, such as the
parts of a spatial or numerical whole. (2) There are as many kinds of
unity as there are universals. Every group of particulars forms a
unity of a special kind through relation to the corresponding
universal. (3) There are as many kinds of unity as there are highest
universals or _summa genera_. These _summa genera_ are the most
general sources of unity through which individuals are related in
groups, directly or indirectly. The kinds of unity are therefore in
principle the Aristotelian categories, i. e. the highest forms of
being under which all individuals fall.
Nevertheless, it is easy to see that the second and third answers
should be rejected in favour of the first. For though, according to
Kant, a judgement unifies particulars by bringing them under a
universal, the special universal involved in a given judgement belongs
not to the judgement as such, but to the particulars unified. What
belongs to the judgement as such is simply the fact that the
particulars are brought under a universal. In other words, the
judgement as such determines the kind of unity but not the particular
unity. The judgements 'Gold is a metal' and 'Trees are green',
considered merely as judgements and not as the particular judgements
which they are, involve the same kind of unity, viz. that of
particulars as particulars of a universal; for the distinction between
'metal' and 'green' is a distinction not of kinds of unity but of
unities. Moreover, to anticipate the discussion of Kant's final
conclusion, the moral is that Kant's account of judgement should have
led him to recognize that judgement involves the reality, not of any
special universals or--in Kant's language--conceptions, but of
universality or conception as such. In other words, on his view of
judgement the activity of the understanding implies simply that there
_are_ universals or conceptions; it does not imply the existence of
special conceptions which essentially belong to the understanding,
e. g. that of 'cause' or 'plurality'.[17]
[17] To this failure in Kant's argument is due the difficulty
in following his transition from 'function' to 'functions' of
judgements. The judgement, as Kant describes it, always does
one and the same thing; it unifies particulars by bringing
them under a universal. This activity does not admit of
differentiation.
If we now turn to the list of the activities of thought in judgement,
borrowed from Formal Logic, we shall see that it is not in any way
connected with Kant's account of judgement.[18] For if the kinds of
judgement distinguished by Formal Logic are to be regarded as
different ways of unifying, the plurality unified must be allowed to
be not a special kind of group of particulars, but the two conceptions
which constitute the terms of the judgement[19]; and the unity
produced must be allowed to be in no case a special form of the unity
of particulars related through the corresponding universal. Thus the
particular judgement 'Some coroners are doctors' must be said to unify
the conceptions of 'coroner' and of 'doctor', and presumably by means
of the conception of 'plurality'. Again, the hypothetical judgement
'If it rains, the ground will be wet' must be said to unify the
judgements 'It rains' and 'The ground will be wet', and presumably by
means of the conception of 'reason and consequence'. In neither case
can the act of unification be considered a special form of the act of
recognizing particulars as particulars of the corresponding universal.
The fact is that the distinctions drawn by Formal Logic are based on a
view of judgement which is different from, and even incompatible with,
Kant's, and they arise from the attempt to solve a different problem.
The problem before Kant in describing judgement is to distinguish the
understanding from the sensibility, i. e. thought from perception.
Hence he regards judgement as the act of unifying a manifold given in
perception, directly, or indirectly by means of a conception. But this
is not the problem with which Formal Logic is occupied. Formal Logic
assumes judgement to be an act which relates material given to it in
the shape of 'conceptions' or 'judgements' by analysis of this
material, and seeks to discover the various modes of relation thereby
effected. The work of judgement, however, cannot consist _both_ in
relating particulars through a conception _and_ in relating two
conceptions or judgements.
[18] Moreover, the forms of judgement clearly lack the
systematic character which Kant claims for them. Even if it
be allowed that the subdivisions within the four main heads
of quantity, quality, relation, and modality are based upon
single principles of division, it cannot be said that the
four heads themselves originate from a common principle.
[19] In the case of the third division, the plurality unified
will be two prior judgements.
It may be urged that this criticism only affects Kant's argument, but
not his conclusion. Possibly, it may be said, the list of types of
judgement borrowed from Formal Logic really expresses the essential
differentiations of judgement, and, in that case, Kant's only mistake
is that he bases them upon a false or at least inappropriate account
of judgement.[20] Moreover, since this list furnishes Kant with the
'clue' to the categories, provided that it expresses the essential
differentiations of judgement, the particular account of judgement
upon which it is based is a matter of indifference.
[20] It may be noted that the account cannot be merely
inappropriate to the general problem, if it be _incompatible_
with that assumed by Formal Logic.
This contention leads us to consider the last stage of Kant's
argument, in which he deduces the categories in detail from his list
of the forms of judgement. For it is clear that unless the forms of
judgement severally involve the categories, it will not matter whether
these forms are or are not the essential differentiations of
judgement.
Kant's mode of connecting the categories in detail with the forms of
judgement discovered by Formal Logic is at least as surprising as his
mode of connecting the latter with the nature of judgement in general.
Since the twelve distinctions within the form of judgement are to
serve as a clue to the conceptions which belong to the understanding,
we naturally expect that each distinction will be found directly to
involve a special conception or category, and that therefore, to
discover the categories, we need only look for the special conception
involved in each form of judgement.[21] Again, since the plurality
unified in a judgement of each form is the two conceptions or
judgements which form the matter of the judgement, we should expect
the conception involved in each form of judgement to be merely the
type of relationship established between these conceptions or
judgements. This expectation is confirmed by a cursory glance at the
table of categories.[22]
I. _Of Quantity._
Unity
Plurality
Totality.
II. _Of Quality._
Reality
Negation
Limitation.
III. _Of Relation._
Inherence and Subsistence (_Substantia et Accidens_)
Causality and Dependence (_Cause and Effect_)
Community (_Reciprocity between the agent and patient._)
IV. _Of Modality._
Possibility--Impossibility
Existence--Non-existence
Necessity--Contingence.
If we compare the first division of these categories with the first
division of judgements we naturally think that Kant conceived
singular, particular, and universal judgements to unify their terms
by means of the conceptions of 'one', of 'some', and of 'all'
respectively; and we form corresponding, though less confident,
expectations in the case of the other divisions.
[21] This expectation is confirmed by Kant's view that
judgement introduces unity into a plurality by means of a
conception. This view leads us to expect that different forms
of judgement--if there be any--will be distinguished by the
different conceptions through which they unify the plurality;
for it will naturally be the different conceptions involved
which are responsible for the different kinds of unity
effected.
[22] B. 106, M. 64.
Kant, however, makes no attempt to show that each form of judgement
distinguished by Formal Logic involves a special conception. In fact,
his view is that the activities of thought studied by Formal Logic do
not originate or use any special conceptions at all. For his actual
deduction of the categories[23] is occupied in showing that although
thought, when exercised under the conditions under which it is studied
by Formal Logic, does not originate and use conceptions of its own, it
is able under certain other conditions to originate and use such
conceptions, i. e. categories.[24] Hence if we attend only to the
professed procedure of the deduction, we are compelled to admit that
the deduction not only excludes any use of the 'clue' to the
categories, supposed to be furnished by Formal Logic, but even fails
to deduce them at all. For it does not even nominally attempt to
discover the categories in detail, but reverts to the prior task of
showing merely that there are categories. Doubtless Kant thinks that
the forms of judgement formulated by Formal Logic in some way
_suggest_ the conceptions which become operative in thought under
these other conditions. Nevertheless, it is impossible to see how
these forms of judgement can suggest these conceptions, unless they
actually presuppose them.
It is clear, however, that the professed link[25] between the forms of
judgement and the categories does not represent the actual process by
which Kant reached his list of categories; for he could never have
reached any list of categories by an argument which was merely
directed to show that there are categories. Moreover, an inspection of
the list shows that he actually reached it partly by noticing the
conceptions which the forms of judgement seemed to presuppose, and
partly by bearing in mind the general conceptions underlying physics
which it was his ultimate aim to vindicate. Since this is the case,
and since the categories can only be connected with the forms of
judgement by showing that they are presupposed in them, the proper
question to be considered from the point of view of the metaphysical
deduction is simply whether the forms of judgement really presuppose
the categories.[26]
[23] B. 102-5, M. 62-3.
[24] Cf. p. 166.
[25] B. 102-5, M. 62-3.
[26] As we shall see later, the real importance of the
passage in which Kant professes to effect the transition from
the forms of judgement to the categories (B. 102-5, M. 62-3)
lies in its introduction of a new and important line of
thought, on which the transcendental deduction turns.
Consideration of it is therefore deferred to the next
chapter.
If, however, we examine the forms of judgement distinguished by Formal
Logic, we find that they do not presuppose the categories. To see
this, it is only necessary to examine the four main divisions of
judgement _seriatim_.
The first division of judgements is said to be a division in respect
of quantity into singular, particular, and universal. So stated, the
division is numerical. It is a division of judgements according as
they make an assertion about one, more than one, or all the members of
a kind. Each species may be said to presuppose (1) the conception of
quantity, and (2) a conception peculiar to itself: the first
presupposing the conception of one member of a kind, the second that
of more than one but less than all members of a kind, the third that
of all members of a kind. Moreover, a judgement of each kind may
perhaps be said to relate the predicate conception to the subject
conception by means of one of these three conceptions.
The fundamental division, however, into which universal and singular
judgements enter is not numerical at all, and ignores particular
judgements altogether. It is that between such judgements as
'Three-sided figures, as such, are three-angled' and 'This man is
tall'. The essential distinction is that in the universal judgement
the predicate term is apprehended to belong to the subject through
our insight that it is necessitated by the nature of the subject term,
while in the singular judgement our apprehension that the predicate
term belongs to the subject is based upon the perception or experience
of the coexistence of predicate and subject terms in a common subject.
In other words, it is the distinction between an _a priori_ judgement
and a judgement of perception.[27] The merely numerically universal
judgement, and the merely numerically particular judgement[28] are
simply aggregates of singular judgements, and therefore are
indistinguishable in principle from the singular judgement. If then we
ask what conceptions are really presupposed by the kinds of judgement
which Kant seeks to distinguish in the first division, we can only
reply that the universal judgement presupposes the conception of a
connected or systematic whole of attributes, and that the singular
judgement presupposes the conception of the coexistence of two
attributes in a common subject. Neither kind of judgement presupposes
the conception of quantity or the conceptions of unity, plurality, and
totality.
[27] I owe this view of the distinction to Professor Cook
Wilson's lectures on logic.
[28] 'Some coroners are doctors' of course in some contexts
means, 'it is possible for a coroner to be a doctor,' and is
therefore not numerical; but understood in this sense it is
merely a weakened form of the universal judgement in which
the connexion apprehended between subject and predicate terms
is incomplete.
The second division of judgements is said to be a division in respect
of quality into affirmative, negative, and infinite, i. e. into
species which may be illustrated by the judgements, 'A college is a
place of education,' 'A college is not a hotel,' and 'A college is a
not-hotel'. The conceptions involved are said to be those of reality,
of negation, and of limitation respectively. The conception of
limitation may be ignored, since the infinite judgement said to
presuppose it is a fiction. On the other hand, the conceptions of
reality and negation, even if their existence be conceded, cannot be
allowed to be the conceptions presupposed. For when we affirm or deny,
we affirm or deny of something not mere being, but being of a
particular kind. The conceptions presupposed are rather those of
identity and difference. It is only because differences fall within an
identity that we can affirm, and it is only because within an identity
there are differences that we can deny.
The third division of judgements is said to be in respect of relation
into categorical, hypothetical, and disjunctive judgements. Here,
again, the conclusion which Kant desires is clearly impossible. The
categorical judgement may be said to presuppose the conception of
subject and attribute, but not that of substance and accident. The
hypothetical judgement may be conceded to presuppose the conception of
reason and consequence, but it certainly does not presuppose the
conception of cause and effect.[29] Lastly, while the disjunctive
judgement may be said to presuppose the conception of mutually
exclusive species of a genus, it certainly does not presuppose the
conception of reciprocal action between physical things.
[29] No doubt, as the schematism of the categories shows,
Kant does not think that the hypothetical judgement
_directly_ involves the conception of cause and effect, i. e.
of the relation of necessary succession between the various
states of physical things. The point is, however, that the
hypothetical judgement does not involve it at all.
The fourth division of judgement is said to be in respect of modality
into assertoric, problematic, and apodeictic, the conceptions
involved being respectively those of possibility and impossibility, of
actuality and non-actuality, and of necessity and contingence. Now,
from the point of view of Kant's argument, these conceptions, like
those which he holds to be involved in the other divisions of
judgement, must be considered to relate to reality and not to our
attitude towards it. Considered in this way, they resolve themselves
into the conceptions of--
(1) the impossible (impossibility);
(2) the possible but not actual (possibility, nonexistence);
(3) the actual but not necessary (existence, contingence);
(4) the necessary (necessity).
But since it must, in the end, be conceded that all fact is necessary,
it is impossible to admit the reality of the conception of the
possible but not actual, and of the actual but not necessary. There
remain, therefore, only the conceptions of the necessary and of the
impossible. In fact, however, the distinctions between the assertoric,
the problematic, and the apodeictical judgement relate to our attitude
to reality and not to reality, and therefore involve no different
conceptions relating to reality. It must, therefore, be admitted
that the 'metaphysical' deduction of the categories breaks down
doubly. Judgement, as Kant describes it, does not involve the
forms of judgement borrowed from Formal Logic as its essential
differentiations; and these forms of judgement do not involve the
categories.