and a systematic topic like the present； indicates with perfect
precision the proper place to which each conception belongs； while
it readily points out any that have not yet been filled up。
SS 7
Our table of the categories suggests considerations of some
importance； which may perhaps have significant results in regard to
the scientific form of all rational cognitions。 For； that this table
is useful in the theoretical part of philosophy； nay； indispensable
for the sketching of the plete plan of a science； so far as that
science rests upon conceptions a priori； and for dividing it
mathematically； according to fixed principles； is most manifest from
the fact that it contains all the elementary conceptions of the
understanding； nay； even the form of a system of these in the
understanding itself； and consequently indicates all the momenta；
and also the internal arrangement of a projected speculative
science； as I have elsewhere shown。* Here follow some of these
observations。
*In the Metaphysical Principles of Natural Science。
I。 This table； which contains four classes of conceptions of the
understanding； may； in the first instance； be divided into two
classes； the first of which relates to objects of intuition… pure as
well as empirical； the second； to the existence of these objects；
either in relation to one another； or to the understanding。
The former of these classes of categories I would entitle the
mathematical； and the latter the dynamical categories。 The former；
as we see； has no correlates； these are only to be found in the second
class。 This difference must have a ground in the nature of the human
understanding。
II。 The number of the categories in each class is always the same；
namely； three… a fact which also demands some consideration； because
in all other cases division a priori through conceptions is
necessarily dichotomy。 It is to be added； that the third category in
each triad always arises from the bination of the second with the
first。
Thus totality is nothing else but plurality contemplated as unity；
limitation is merely reality conjoined with negation； munity is the
causality of a substance； reciprocally determining； and determined
by other substances； and finally； necessity is nothing but
existence； which is given through the possibility itself。 Let it not
be supposed； however； that the third category is merely a deduced； and
not a primitive conception of the pure understanding。 For the
conjunction of the first and second； in order to produce the third
conception； requires a particular function of the understanding； which
is by no means identical with those which are exercised in the first
and second。 Thus； the conception of a number （which belongs to the
category of totality） is not always possible； where the conceptions of
multitude and unity exist （for example； in the representation of the
infinite）。 Or； if I conjoin the conception of a cause with that of a
substance； it does not follow that the conception of influence； that
is； how one substance can be the cause of something in another
substance； will be understood from that。 Thus it is evident that a
particular act of the understanding is here necessary； and so in the
other instances。
III。 With respect to one category； namely； that of munity；
which is found in the third class； it is not so easy as with the
others to detect its accordance with the form of the disjunctive
judgement which corresponds to it in the table of the logical
functions。
In order to assure ourselves of this accordance； we must observe
that in every disjunctive judgement； the sphere of the judgement （that
is； the plex of all that is contained in it） is represented as a
whole divided into parts； and； since one part cannot be contained in
the other； they are cogitated as co…ordinated with； not subordinated
to each other； so that they do not determine each other
unilaterally； as in a linear series； but reciprocally； as in an
aggregate… （if one member of the division is posited； all the rest are
excluded； and conversely）。
Now a like connection is cogitated in a whole of things； for one
thing is not subordinated； as effect； to another as cause of its
existence； but； on the contrary； is co…ordinated contemporaneously and
reciprocally； as a cause in relation to the determination of the
others （for example； in a body… the parts of which mutually attract
and repel each other）。 And this is an entirely different kind of
connection from that which we find in the mere relation of the cause
to the effect （the principle to the consequence）； for in such a
connection the consequence does not in its turn determine the
principle； and therefore does not constitute； with the latter； a
whole… just as the Creator does not with the world make up a whole。
The process of understanding by which it represents to itself the
sphere of a divided conception； is employed also when we think of a
thing as divisible； and in the same manner as the members of the
division in the former exclude one another； and yet are connected in
one sphere； so the understanding represents to itself the parts of the
latter； as having… each of them… an existence （as substances）；
independently of the others； and yet as united in one whole。
SS 8
In the transcendental philosophy of the ancients there exists one
more leading division； which contains pure conceptions of the
understanding； and which； although not numbered among the
categories； ought； according to them； as conceptions a priori； to be
valid of objects。 But in this case they would augment the number of
the categories； which cannot be。 These are set forth in the
proposition； so renowned among the schoolmen… 〃Quodlibet ens est UNUM；
VERUM； BONUM。〃 Now； though the inferences from this principle were
mere tautological propositions； and though it is allowed only by
courtesy to retain a place in modern metaphysics； yet a thought
which maintained itself for such a length of time； however empty it
seems to be； deserves an investigation of its origin； and justifies
the conjecture that it must be grounded in some law of the
understanding； which； as is often the case； has only been
erroneously interpreted。 These pretended transcendental predicates
are； in fact； nothing but logical requisites and criteria of all
cognition of objects； and they employ； as the basis for this
cognition； the categories of quantity； namely； unity； plurality； and
totality。 But these； which must be taken as material conditions；
that is； as belonging to the possibility of things themselves； they
employed merely in a formal signification； as belonging to the logical
requisites of all cognition； and yet most unguardedly changed these
criteria of thought into properties of objects； as things in
themselves。 Now； in every cognition of an object； there is unity of
conception； which may be called qualitative unity； so far as by this
term we understand only the unity in our connection of the manifold；
for example； unity of the theme in a play； an oration； or a story。
Secondly； there is truth in respect of the deductions from it。 The
more true deductions we have from a given conception； the more
criteria of its objective reality。 This we might call the
qualitative plurality of characteristic marks； which belong to a
conception as to a mon foundation； but are not cogitated as a
quantity in it。 Thirdly； there is perfection… which consists in
this； that the plurality falls back upon the unity of the
conception； and accords pletely with that conception and with no
other。 This we may denominate qualitative pleteness。 Hence it is
evident that these logical criteria of the possibility of cognition
are merely the three categories of quantity modified and transformed
to suit an unauthorized manner of applying them。 That is to say； the
three categories； in which the unity in the production of the
quantum must be homogeneous throughout； are transformed solely with
a view to the connection of heterogeneous parts of cognition in one
act of consciousness； by means of the quality of the cognition；
which is the principle of that connection。 Thus the criterion of the
possibility of a conception （not of its object） is the definition of
it； in which the unity of the conception； the truth of all that may be
immediately deduced from it； and finally； the pleteness of what has
been thus deduced； constitute the requisites for the reproduction of
the whole conception。 Thus also； the criterion or test of an
hypothesis is the intelligibility of the received principle of
explanation； or its unity （without help from any subsidiary
hypothesis）… the truth of our deductions from it （consistency with
each other and with experience）… and lastly； the pleteness of the
principle of the explanation of these deductions； which refer to
neither more nor less than what was admitted in the hypothesis；
restoring analytically and a posteriori； what was cogitated
synthetically and a priori。 By the conceptions； therefore； of unity；
truth； and perfection； we have made no addition to the
transcendental table of the categories； which is plete without
them。 We have