Critique of Pure Reason (Transcendental Analytic

Immanuel Kant's
Critique
trans. by Norman Kemp Smith
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TRANSCENDENTAL LOGIC
FIRST DIVISION
TRANSCENDENTAL ANALYTIC
TRANSCENDENTAL analytic consists in the dissection of all
our a priori knowledge into the elements that pure understanding
by itself yields. In so doing, the following are the
points of chief concern: (1) that the concepts be pure and
not empirical; (2) that they belong, not to intuition and
sensibility, but to thought and understanding; (3) that
they be fundamental and be carefully distinguished from
those which are derivative or composite; (4) that our table
of concepts be complete, covering the whole field of the pure
understanding. When a science is an aggregate brought into
existence in a merely experimental manner, such completeness
can never be guaranteed by any kind of mere estimate. It is
possible only by means of an idea of the totality of the a priori
knowledge yielded by the understanding; such an idea can
furnish an exact classification of the concepts which compose
that totality, exhibiting their interconnection in a system.
Pure understanding distinguishes itself not merely from all
that is empirical but completely also from all sensibility. It
is a unity self-subsistent, self-sufficient, and not to be increased
by any additions from without. The sum of its knowledge thus
constitutes a system, comprehended and determined by one
idea. The completeness and articulation of this system can at
the same time yield a criterion of the correctness and genuineness
of all its components. This part of transcendental logic
requires, however, for its complete exposition, two books, the
one containing the concepts, the other the principles of pure
understanding.
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TRANSCENDENTAL ANALYTIC
BOOK I
ANALYTIC OF CONCEPTS
By 'analytic of concepts' I do not understand their analysis,
or the procedure usual in philosophical investigations,
that of dissecting the content of such concepts as may present
themselves, and so of rendering them more distinct; but the
hitherto rarely attempted dissection of the faculty of the 
understanding itself, in order to investigate the possibility of 
concepts a priori by looking for them in the understanding alone,
as their birthplace, and by analysing the pure use of this
faculty. This is the proper task of a transcendental philosophy;
anything beyond this belongs to the logical treatment of 
concepts in philosophy in general. We shall therefore follow up
the pure concepts to their first seeds and dispositions in the
human understanding, in which they lie prepared, till at last,
on the occasion of experience, they are developed, and by the
same understanding are exhibited in their purity, freed from
the empirical conditions attaching to them.
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ANALYTIC OF CONCEPTS
CHAPTER I
THE CLUE TO THE DISCOVERY OF ALL PURE
CONCEPTS OF THE UNDERSTANDING
WHEN we call a faculty of knowledge into play, then,
as the occasioning circumstances differ, various concepts
stand forth and make the faculty known, and allow of
their being collected with more or less completeness, in
proportion as observation has been made of them over a longer
time or with greater acuteness. But when the enquiry is
carried on in this mechanical fashion, we can never be sure
whether it has been brought to completion. Further, the 
concepts which we thus discover only as opportunity offers, 
exhibit no order and systematic unity, but are in the end merely
arranged in pairs according to similarities, and in series according
to the amount of their contents, from the simple on to the
more composite -- an arrangement which is anything but 
systematic, although to a certain extent methodically instituted.
Transcendental philosophy, in seeking for its concepts, has
the advantage and also the duty of proceeding according to a
single principle. For these concepts spring, pure and unmixed,
out of the understanding which is an absolute unity; and must
therefore be connected with each other according to one 
concept or idea. Such a connection supplies us with a rule, by
which we are enabled to assign its proper place to each pure
concept of the understanding, and by which we can determine
in an a priori manner their systematic completeness. 
Otherwise we should be dependent in these matters on our own
discretionary judgment or merely on chance.
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THE TRANSCENDENTAL CLUE TO THE DISCOVERY OF
ALL PURE CONCEPTS OF THE UNDERSTANDING
Section I
THE LOGICAL EMPLOYMENT OF THE UNDERSTANDING
The understanding has thus far been explained merely
negatively, as a non-sensible faculty of knowledge. Now since
without sensibility we cannot have any intuition, understanding
cannot be a faculty of intuition. But besides intuition there
is no other mode of knowledge except by means of concepts.
The knowledge yielded by understanding, or at least by the
human understanding, must therefore be by means of concepts,
and so is not intuitive, but discursive. Whereas all intuitions,
as sensible, rest on affections, concepts rest on functions. By
'function' I mean the unity of the act of bringing various 
representations under one common representation. Concepts are
based on the spontaneity of thought, sensible intuitions on the
receptivity of impressions. Now the only use which the 
understanding can make of these concepts is to judge by means of
them. Since no representation, save when it is an intuition,
is in immediate relation to an object, no concept is ever
related to an object immediately, but to some other representation
of it, be that other representation an intuition, or itself
a concept. Judgment is therefore the mediate knowledge of an
object, that is, the representation of a representation of it. In
every judgment there is a concept which holds of many 
representations, and among them of a given representation that is
immediately related to an object. Thus in the judgment, 'all
bodies are divisible', the concept of the divisible applies to
various other concepts, but is here applied in particular to
the concept of body, and this concept again to certain appearances
that present themselves to us. These objects, therefore,
are mediately represented through the concept of divisibility.
Accordingly, all judgments are functions of unity among our
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representations; instead of an immediate representation, a
higher representation, which comprises the immediate 
representation and various others, is used in knowing the object,
and thereby much possible knowledge is collected into one.
Now we can reduce all acts of the understanding to judgments,
and the understanding may therefore be represented
as a faculty of judgment. For, as stated above, the 
understanding is a faculty of thought. Thought is knowledge by
means of concepts. But concepts, as predicates of possible
judgments, relate to some representation of a not yet determined
object. Thus the concept of body means something, for
instance, metal, which can be known by means of that concept.
It is therefore a concept solely in virtue of its 
comprehending other representations, by means of which it can
relate to objects. It is therefore the predicate of a possible
judgment, for instance, 'every metal is a body'. The functions
of the understanding can, therefore, be discovered if we can
give an exhaustive statement of the functions of unity in
judgments. That this can quite easily be done will be shown
in the next section.
THE CLUE TO THE DISCOVERY OF ALL PURE
CONCEPTS OF THE UNDERSTANDING
Section 2
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THE LOGICAL FUNCTION OF THE UNDERSTANDING IN
JUDGMENTS
If we abstract from all content of a judgment, and consider
only the mere form of understanding, we find that the
function of thought in judgment can be brought under four
heads, each of which contains three moments. They may be
conveniently represented in the following table:
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I
Quantity of Judgments
Universal
Particular
Singular II III
Quality Relation
Affirmative Categorical
Negative Hypothetical
Infinite Disjunctive
IV
Modality
Problematic
Assertoric
Apodeictic
As this division appears to depart in some, though not in
any essential respects, from the technical distinctions ordinarily
recognised by logicians, the following observations may
serve to guard against any possible misunderstanding.
1. Logicians are justified in saying that, in the employment
of judgments in syllogisms, singular judgments can
be treated like those that are universal. For, since they
have no extension at all, the predicate cannot relate to part
only of that which is contained in the concept of the subject,
and be excluded from the rest. The predicate is valid of that
concept, without any such exception, just as if it were a
general concept and had an extension to the whole of which
the predicate applied. If, on the other hand, we compare a
singular with a universal judgment, merely as knowledge,
in respect of quantity, the singular stands to the universal as
unity to infinity, and is therefore in itself essentially different
from the universal. If, therefore, we estimate a singular judgment
(judicium singulare), not only according to its own inner
validity, but as knowledge in general, according to its quantity
in comparison with other knowledge, it is certainly different
from general judgments (judicia communia), and in a complete
table of the moments of thought in general deserves a
separate place -- though not, indeed, in a logic limited to the
use of judgments in reference to each other.
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2. In like manner infinite judgments must, in transcendental
logic, be distinguished from those that are affirmative,
although in general logic they are rightly classed with
them, and do not constitute a separate member of the division.
General logic abstracts from all content of the predicate (even
though it be negative); it enquires only whether the predicate
be ascribed to the subject or opposed to it. But transcendental
logic also considers what may be the worth or content of a
logical affirmation that is thus made by means of a merely
negative predicate, and what is thereby achieved in the way
of addition to our total knowledge. If I should say of the soul,
'It is not mortal', by this negative judgment I should at least
have warded off error. Now by the proposition, 'The soul
is non-mortal', I have, so far as the logical form is concerned,
really made an affirmation. I locate the soul in the unlimited
sphere of non-mortal beings. Since the mortal constitutes
one part of the whole extension of possible beings, and the
non-mortal the other, nothing more is said by my proposition
than that the soul is one of the infinite number of things which
remain over when I take away all that is mortal. The infinite
sphere of all that is possible is thereby only so far limited that
the mortal is excluded from it, and that the soul is located
in the remaining part of its extension. But, even allowing
for such exclusion, this extension still remains infinite, and
several more parts of it may be taken away without the concept
of the soul being thereby in the least increased, or 
determined in an affirmative manner. These judgments, though
infinite in respect of their logical extension, are thus, in respect
of the content of their knowledge, limitative only, and cannot
therefore be passed over in a transcendental table of all
moments of thought in judgments, since the function of the
understanding thereby expressed may perhaps be of 
importance in the field of its pure a priori knowledge.
3. All relations of thought in judgments are (a) of the
predicate to the subject, (b) of the ground to its consequence,
(c) of the divided knowledge and of the members of the
division, taken together, to each other. In the first kind of
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judgments we consider only two concepts, in the second
two judgments, in the third several judgments in their relation
to each other. The hypothetical proposition, 'If there is a
perfect justice, the obstinately wicked are punished', really
contains the relation of two propositions, namely, 'There is
a perfect justice', and 'The obstinately wicked are punished'.
Whether both these propositions are in themselves true, here
remains undetermined. It is only the logical sequence which
is thought by this judgment. Finally, the disjunctive judgment
contains a relation of two or more propositions to each other,
a relation not, however, of logical sequence, but of logical
opposition, in so far as the sphere of the one excludes the
sphere of the other, and yet at the same time of community,
in so far as the propositions taken together occupy the whole
sphere of the knowledge in question. The disjunctive judgment
expresses, therefore, a relation of the parts of the sphere
of such knowledge, since the sphere of each part is a 
complement of the sphere of the others, yielding together the
sum-total of the divided knowledge. Take, for instance, the
judgment, 'The world exists either through blind chance,
or through inner necessity, or through an external cause'.
Each of these propositions occupies a part of the sphere of
the possible knowledge concerning the existence of a world in
general; all of them together occupy the whole sphere. To
take the knowledge out of one of these spheres means placing
it in one of the other spheres, and to place it in one sphere
means taking it out of the others. There is, therefore, in a
disjunctive judging a certain community of the known
constitutes, such that they mutually exclude each other,
and yet thereby determine in their totality the true 
knowledge. For, when taken together, they constitute the whole
content of one given knowledge. This is all that need here
be considered, so far as concerns what follows.
4. The modality of judgments is a quite peculiar function.
Its distinguishing characteristic is that it contributes nothing
to the content of the judgment (for, besides quantity, quality,
and relation, there is nothing that constitutes the content of
a judgment), but concerns only the value of the copula in
relation to thought in general. Problematic judgments are
those in which affirmation or negation is taken as merely
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possible (optional). In assertoric judgments affirmation or
negation is viewed as real (true), and in apodeictic judgments
as necessary. Thus the two judgments, the relation of which
constitutes the hypothetical judgment (antecedens et 
consequens), and likewise the judgments the reciprocal relation
of which forms the disjunctive judgment (members of the
division), are one and all problematic only. In the above
example, the proposition, 'There is a perfect justice', is not
stated assertorically, but is thought only as an optional 
judgment, which it is possible to assume; it is only the logical
sequence which is assertoric. Such judgments may therefore
be obviously false, and yet, taken problematically, may be 
conditions of the knowledge of truth. Thus the judgment 'The
world exists by blind chance', has in the disjunctive judgment
only problematic meaning, namely, as a proposition that may
for a moment be assumed. At the same time, like the indication
of a false road among the number of all those roads that
can be taken, it aids in the discovery of the true proposition.
The problematic proposition is therefore that which expresses
only logical (which is not objective) possibility -- a free choice
of admitting such a proposition, and a purely optional
admission of it into the understanding. The assertoric proposition
deals with logical reality or truth. Thus, for instance,
in a hypothetical syllogism the antecedent is in the major
premiss problematic, in the minor assertoric, and what the
syllogism shows is that the consequence follows in accordance
with the laws of the understanding. The apodeictic proposition
thinks the assertoric as determined by these laws of the
understanding, and therefore as affirming a priori; and in
this manner it expresses logical necessity. Since everything
is thus incorporated in the understanding step by step -- 
inasmuch as we first judge something problematically, then
maintain its truth assertorically, and finally affirm it as 
inseparably united with the understanding, that is, as necessary
and apodeictic -- we are justified in regarding these three
functions of modality as so many moments of thought.
 Just as if thought were in the problematic a function of the
understanding; in the assertoric, of the faculty of judgment; in
the apodeictic, of reason. This is a remark which will be explained
in the sequel.
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THE CLUE TO THE DISCOVERY OF ALL PURE
CONCEPTS OF THE UNDERSTANDING
Section 3
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THE PURE CONCEPTS OF THE UNDERSTANDING, OR
CATEGORIES
General logic, as has been repeatedly said, abstracts from
all content of knowledge, and looks to some other source,
whatever that may be, for the representations which it is
to transform into concepts by process of analysis. Transcendental
logic, on the other hand, has lying before it a manifold
of a priori sensibility, presented by transcendental 
aesthetic, as material for the concepts of pure understanding.
In the absence of this material those concepts would be 
without any content, therefore entirely empty. Space and time
contain a manifold of pure a priori intuition, but at the same
time are conditions of the receptivity of our mind -- conditions
under which alone it can receive representations of objects, and
which therefore must also always affect the concept of these
objects. But if this manifold is to be known, the spontaneity
of our thought requires that it be gone through in a certain
way, taken up, and connected. This act I name synthesis.
By synthesis, in its most general sense, I understand the
act of putting different representations together, and of 
grasping what is manifold in them in one [act of] knowledge. Such
a synthesis is pure, if the manifold is not empirical but is given
a priori, as is the manifold in space and time. Before we can
analyse our representations, the representations must themselves
be given, and therefore as regards content no concepts
can first arise by way of analysis. Synthesis of a manifold (be
it given empirically or a priori) is what first gives rise to 
knowledge. This knowledge may, indeed, at first, be crude and 
confused, and therefore in need of analysis. Still the synthesis is
that which gathers the elements for knowledge, and unites
them to [form] a certain content. It is to synthesis, therefore,
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that we must first direct our attention, if we would determine
the first origin of our knowledge.
Synthesis in general, as we shall hereafter see, is the mere
result of the power of imagination, a blind but indispensable
function of the soul, without which we should have no knowledge
whatsoever, but of which we are scarcely ever conscious.
To bring this synthesis to concepts is a function which belongs
to the understanding, and it is through this function of the
understanding that we first obtain knowledge properly so
called.
Pure synthesis, represented in its most general aspect, gives
the pure concept of the understanding. By this pure synthesis
I understand that which rests upon a basis of a priori
synthetic unity. Thus our counting, as is easily seen in the case
of larger numbers, is a synthesis according to concepts, 
because it is executed according to a common ground of unity,
as, for instance, the decade. In terms of this concept, the unity
of the synthesis of the manifold is rendered necessary.
By means of analysis different representations are brought
under one concept -- a procedure treated of in general logic.
What transcendental logic, on the other hand, teaches, is how
we bring to concepts, not representations, but the pure 
synthesis of representations. What must first be given -- with a
view to the a priori knowledge of all objects -- is the manifold
of pure intuition; the second factor involved is the synthesis of
this manifold by means of the imagination. But even this does
not yet yield knowledge. The concepts which give unity to this
pure synthesis, and which consist solely in the representation
of this necessary synthetic unity, furnish the third requisite for
the knowledge of an object; and they rest on the 
understanding. 
The same function which gives unity to the various 
representations in a judgment also gives unity to the mere 
synthesis of various representations in an intuition; and this
unity, in its most general expression, we entitle the pure 
concept of the understanding. The same understanding, through
the same operations by which in concepts, by means of 
analytical unity, it produced the logical form of a judgment,
also introduces a transcendental content into its representations,
by means of the synthetic unity of the manifold in intuition
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in general. On this account we are entitled to call these
representations pure concepts of the understanding, and to
regard them as applying a priori to objects -- a conclusion
which general logic is not in a position to establish.
In this manner there arise precisely the same number of
pure concepts of the understanding which apply a priori to
objects of intuition in general, as, in the preceding table, there
have been found to be logical functions in all possible 
judgments. For these functions specify the understanding 
completely, and yield an exhaustive inventory of its powers. These
concepts we shall, with Aristotle, call categories, for our
primary purpose is the same as his, although widely diverging
from it in manner of execution.
TABLE OF CATEGORIES
I
Of Quantity
Unity
Plurality
Totality
II III
Of Quality Of Relation
Reality Of Inherence and Subsistence
Negation (substantia et accidens)
Limitation Of Causality and Dependence
(cause and effect)
Of Community (reciprocity
between agent and patient)
IV
Of Modality
Possibility -- Impossibility
Existence -- Non-existence
Necessity -- Contingency
This then is the list of all original pure concepts of synthesis
that the understanding contains within itself a priori.
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Indeed, it is because it contains these concepts that it is
called pure understanding; for by them alone can it understand
anything in the manifold of intuition, that is, think an
object of intuition. This division is developed systematically
from a common principle, namely, the faculty of judgment
(which is the same as the faculty of thought). It has not arisen
rhapsodically, as the result of a haphazard search after pure
concepts, the complete enumeration of which as based on
induction only, could never be guaranteed. Nor could we, if
this were our procedure, discover why just these concepts, and
no others, have their seat in the pure understanding. It was
an enterprise worthy of an acute thinker like Aristotle to make
search for these fundamental concepts. But as he did so on no
principle, he merely picked them up as they came his way,
and at first procured ten of them, which he called categories
(predicaments). Afterwards he believed that he had discovered
five others, which he added under the name of post-predicaments.
But his table still remained defective. Besides, there
are to be found in it some modes of pure sensibility (quando,
ubi, situs, also prius, simul), and an empirical concept (motus),
none of which have any place in a table of the concepts that
trace their origin to the understanding. Aristotle's list also
enumerates among the original concepts some derivative concepts
(actio, passio); and of the original concepts some are
entirely lacking.
In this connection, it is to be remarked that the categories,
as the true primary concepts of the pure understanding, have
also their pure derivative concepts. These could not be passed
over in a complete system of transcendental philosophy, but
in a merely critical essay the simple mention of the fact may
suffice.
 I beg permission to entitle these pure but derivative concepts
of the understanding the predicables of the pure understanding
-- to distinguish them from the predicaments [i.e. the
categories]. If we have the original and primitive concepts, it
is easy to add the derivative and subsidiary, and so to give a
complete picture of the family tree of the [concepts of] pure
understanding. Since at present we are concerned not with the
completeness of the system, but only with the principles to be
followed in its construction, I reserve this supplementary work
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for another occasion. It can easily be carried out, with the
aid of the ontological manuals -- for instance, by placing under
the category of causality the predicables of force, action,
passion; under the category of community the predicables
of presence, resistance; under the predicaments of modality
the predicables of coming to be, ceasing to be, change, etc.
The categories, when combined with the modes of pure sensibility,
or with one another, yield a large number of derivative
a priori concepts. To note, and, where possible, to give a 
complete inventory of these concepts, would be a useful and not
unpleasant task, but it is a task from which we can here be
absolved.
In this treatise, I purposely omit the definitions of the 
categories, although I may be in possession of them. I shall 
proceed to analyse these concepts only so far as is necessary in
connection with the doctrine of method which I am propounding.
In a system of pure reason, definitions of the categories
would rightly be demanded, but in this treatise they would
merely divert attention from the main object of the enquiry,
arousing doubts and objections which, without detriment to
what is essential to our purposes, can very well be reserved for
another occasion. Meanwhile, from the little that I have said,
it will be obvious that a complete glossary, with all the requisite
explanations, is not only a possible, but an easy task. The 
divisions are provided; all that is required is to fill them; and a
systematic 'topic', such as that here given, affords sufficient
guidance as to the proper location of each concept, while at
the same time indicating which divisions are still empty.
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This table of categories suggests some nice points, which
may perhaps have important consequences in regard to the
scientific form of all modes of knowledge obtainable by reason.
For that this table is extremely useful in the theoretical part of
philosophy, and indeed is indispensable as supplying the complete
plan of a whole science, so far as that science rests on a -
priori concepts, and as dividing it systematically according to
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determinate principles, is already evident from the fact that
the table contains all the elementary concepts of the understanding
in their completeness, nay, even the form of a system
of them in the human understanding, and accordingly indicates
all the momenta of a projected speculative science, and
even their order, as I have elsewhere shown.
P 116n
* Metaphysical First Principles of Natural Science.
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The first of the considerations suggested by the table is
that while it contains four classes of the concepts of 
understanding, it may, in the first instance, be divided into two
groups; those in the first group being concerned with objects
of intuition, pure as well as empirical, those in the second
group with the existence of these objects, in their relation
either to each other or to the understanding.
The categories in the first group I would entitle the 
mathematical, those in the second group the dynamical. The former
have no correlates; these are to be met with only in the second
group. This distinction must have some ground in the nature
of the understanding.
Secondly, in view of the fact that all a priori division of
concepts must be by dichotomy, it is significant that in each
class the number of the categories is always the same, namely,
three. Further, it may be observed that the third category in
each class always arises from the combination of the second
category with the first.
 Thus allness or totality is just plurality considered as unity;
limitation is simply reality combined with negation; community
is the causality of substances reciprocally determining one
another; lastly, necessity is just the existence which is given
through possibility itself. It must not be supposed, however,
that the third category is therefore merely a derivative, and
not a primary, concept of the pure understanding. For the combination
of the first and second concepts, in order that the third
may be produced, requires a special act of the understanding,
which is not identical with that which is exercised in the
case of the first and the second. Thus the concept of a number
(which belongs to the category of totality) is not always possible
simply upon the presence of concepts of plurality and unity
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(for instance, in the representation of the infinite); nor can I,
by simply combining the concept of a cause and that of a 
substance, at once have understanding of influence, that is, how a
substance can be the cause of something in another substance.
Obviously in these cases, a separate act of the understanding
is demanded; and similarly in the others.
Thirdly, in the case of one category, namely, that of community,
which is found in the third group, its accordance with
the form of a disjunctive judgment -- the form which corresponds
to it in the table of logical functions -- is not as evident
as in the case of the others.
To gain assurance that they do actually accord, we must
observe that in all disjunctive judgments the sphere (that is,
the multiplicity which is contained in any one judgment) is
represented as a whole divided into parts (the subordinate 
concepts), and that since no one of them can be contained under
any other, they are thought as co-ordinated with, not 
subordinated to, each other, and so as determining each other,
not in one direction only, as in a series, but reciprocally, as in
an aggregate -- if one member of the division is posited, all
the rest are excluded, and conversely.
Now in a whole which is made up of things, a similar combination
is being thought; for one thing is not subordinated,
as effect, to another, as cause of its existence, but, simultaneously
and reciprocally, is co-ordinated with it, as cause of the
determination of the other (as, for instance, in a body the
parts of which reciprocally attract and repel each other). This
is a quite different kind of connection from that which is found
in the mere relation of cause to effect (of ground to consequence),
for in the latter relation the consequence does not in
its turn reciprocally determine the ground, and therefore does
not constitute with it a whole -- thus the world, for instance,
does not with its Creator serve to constitute a whole. The
procedure which the understanding follows in representing to
itself the sphere of a divided concept it likewise follows when
it thinks a thing as divisible; and just as, in the former case,
the members of a division exclude each other, and yet are 
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combined in one sphere, so the understanding represents to itself
the parts of the latter as existing (as substances) in such a way
that, while each exists independently of the others, they are
yet combined together in one whole.
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In the transcendental philosophy of the ancients there is
included yet another chapter containing pure concepts of the
understanding which, though not enumerated among the categories,
must, on their view, be ranked as a priori concepts of
objects. This, however, would amount to an increase in the
number of the categories, and is therefore not feasible. They
are propounded in the proposition, so famous among the
Schoolmen, quodlibet ens est unum, verum, bonum. Now,
although the application of this principle has proved very
meagre in consequences, and has indeed yielded only propositions
that are tautological, and therefore in recent times has
retained its place in metaphysics almost by courtesy only, yet,
on the other hand, it represents a view which, however empty
it may seem to be, has maintained itself over this very long
period. It therefore deserves to be investigated in respect of
its origin, and we are justified in conjecturing that it has its
ground in some rule of the understanding which, as often
happens, has only been wrongly interpreted. These supposedly
transcendental predicates of things are, in fact, nothing but
logical requirements and criteria of all knowledge of things in
general, and prescribe for such knowledge the categories of
quantity, namely, unity, plurality, and totality. But these
categories, which, properly regarded, must be taken as material,
belonging to the possibility of the things themselves [empirical
objects], have, in this further application, been used only in
their formal meaning, as being of the nature of logical 
requisites of all knowledge, and yet at the same time have been
incautiously converted from being criteria of thought to be 
properties of things in themselves. In all knowledge of an object
there is unity of concept, which may be entitled qualitative
unity, so far as we think by it only the unity in the combination
of the manifold of our knowledge: as, for example, the unity
of the theme in a play, a speech, or a story. Secondly, there is
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truth, in respect of its consequences. The greater the number
of true consequences that follow from a given concept, the
more criteria are there of its objective reality. This might be
entitled the qualitative plurality of characters, which belong to
a concept as to a common ground (but are not thought in it, as
quantity). Thirdly, and lastly, there is perfection, which consists
in this, that the plurality together leads back to the unity
of the concept, and accords completely with this and with no
other concept. This may be entitled the qualitative completeness
(totality). Hence it is evident that these logical criteria of
the possibility of knowledge in general are the three categories
of quantity, in which the unity in the production of the quantum
has to be taken as homogeneous throughout; and that these
categories are here being transformed so as also to yield 
connection of heterogeneous knowledge in one consciousness, by
means of the quality of the knowledge as the principle of the
connection. Thus the criterion of the possibility of a concept
(not of an object) is the definition of it, in which the unity of
the concept, the truth of all that may be immediately deduced
from it, and finally, the completeness of what has been thus 
deduced from it, yield all that is required for the construction of
the whole concept. Similarly, the criterion of an hypothesis
consists in the intelligibility of the assumed ground of explanation,
that is, in its unity (without any auxiliary hypothesis);
in the truth of the consequences that can be deduced from it
(their accordance with themselves and with experience); and
finally, in the completeness of the ground of explanation of
these consequences, which carry us back to neither more nor
less than was assumed in the hypothesis, and so in an a 
posteriori analytic manner give us back and accord with what
has previously been thought in a synthetic a priori manner.
We have not, therefore, in the concepts of unity, truth, and 
perfection, made any addition to the transcendental table of the
categories, as if it were in any respect imperfect. All that we
have done is to bring the employment of these concepts under
general logical rules, for the agreement of knowledge with
itself -- the question of their relation to objects not being in any
way under discussion.