Problematical
Assertorical
Apodeictical
As this division appears to differ in some； though not essential
points； from the usual technique of logicians； the following
observations； for the prevention of otherwise possible
misunderstanding； will not be without their use。
1。 Logicians say； with justice； that in the use of judgements in
syllogisms； singular judgements may be treated like universal ones。
For； precisely because a singular judgement has no extent at all；
its predicate cannot refer to a part of that which is contained in the
conception of the subject and be excluded from the rest。 The predicate
is valid for the whole conception just as if it were a general
conception； and had extent； to the whole of which the predicate
applied。 On the other hand； let us pare a singular with a general
judgement； merely as a cognition； in regard to quantity。 The
singular judgement relates to the general one； as unity to infinity；
and is therefore in itself essentially different。 Thus； if we estimate
a singular judgement （judicium singulare） not merely according to
its intrinsic validity as a judgement； but also as a cognition
generally； according to its quantity in parison with that of
other cognitions； it is then entirely different from a general
judgement （judicium mune）； and in a plete table of the momenta
of thought deserves a separate place… though； indeed； this would not
be necessary in a logic limited merely to the consideration of the use
of judgements in reference to each other。
2。 In like manner； in transcendental logic； infinite must be
distinguished from affirmative judgements； although in general logic
they are rightly enough classed under affirmative。 General logic
abstracts all content of the predicate （though it be negative）； and
only considers whether the said predicate be affirmed or denied of the
subject。 But transcendental logic considers also the worth or
content of this logical affirmation… an affirmation by means of a
merely negative predicate； and inquires how much the sum total of
our cognition gains by this affirmation。 For example； if I say of
the soul； 〃It is not mortal〃… by this negative judgement I should at
least ward off error。 Now； by the proposition； 〃The soul is not
mortal；〃 I have； in respect of the logical form； really affirmed；
inasmuch as I thereby place the soul in the unlimited sphere of
immortal beings。 Now； because of the whole sphere of possible
existences； the mortal occupies one part； and the immortal the
other； neither more nor less is affirmed by the proposition than
that the soul is one among the infinite multitude of things which
remain over； when I take away the whole mortal part。 But by this
proceeding we acplish only this much； that the infinite sphere of
all possible existences is in so far limited that the mortal is
excluded from it； and the soul is placed in the remaining part of
the extent of this sphere。 But this part remains； notwithstanding this
exception； infinite； and more and more parts may be taken away from
the whole sphere； without in the slightest degree thereby augmenting
or affirmatively determining our conception of the soul。 These
judgements； therefore； infinite in respect of their logical extent；
are； in respect of the content of their cognition； merely
limitative； and are consequently entitled to a place in our
transcendental table of all the momenta of thought in judgements；
because the function of the understanding exercised by them may
perhaps be of importance in the field of its pure a priori cognition。
3。 All relations of thought in judgements are those （a） of the
predicate to the subject； （b） of the principle to its consequence； （c）
of the divided cognition and all the members of the division to each
other。 In the first of these three classes； we consider only two
conceptions； in the second； two judgements； in the third； several
judgements in relation to each other。 The hypothetical proposition；
〃If perfect justice exists； the obstinately wicked are punished；〃
contains properly the relation to each other of two propositions；
namely； 〃Perfect justice exists；〃 and 〃The obstinately wicked are
punished。〃 Whether these propositions are in themselves true is a
question not here decided。 Nothing is cogitated by means of this
judgement except a certain consequence。 Finally； the disjunctive
judgement contains a relation of two or more propositions to each
other… a relation not of consequence； but of logical opposition； in so
far as the sphere of the one proposition excludes that of the other。
But it contains at the same time a relation of munity； in so far as
all the propositions taken together fill up the sphere of the
cognition。 The disjunctive judgement contains； therefore； the relation
of the parts of the whole sphere of a cognition； since the sphere of
each part is a plemental part of the sphere of the other； each
contributing to form the sum total of the divided cognition。 Take； for
example； the proposition； 〃The world exists either through blind
chance； or through internal necessity； or through an external
cause。〃 Each of these propositions embraces a part of the sphere of
our possible cognition as to the existence of a world； all of them
taken together； the whole sphere。 To take the cognition out of one
of these spheres； is equivalent to placing it in one of the others；
and； on the other hand； to place it in one sphere is equivalent to
taking it out of the rest。 There is； therefore； in a disjunctive
judgement a certain munity of cognitions； which consists in this；
that they mutually exclude each other； yet thereby determine； as a
whole； the true cognition； inasmuch as； taken together； they make up
the plete content of a particular given cognition。 And this is
all that I find necessary； for the sake of what follows； to remark
in this place。
4。 The modality of judgements is a quite peculiar function； with
this distinguishing characteristic； that it contributes nothing to the
content of a judgement （for besides quantity； quality； and relation；
there is nothing more that constitutes the content of a judgement）；
but concerns itself only with the value of the copula in relation to
thought in general。 Problematical judgements are those in which the
affirmation or negation is accepted as merely possible （ad libitum）。
In the assertorical； we regard the proposition as real （true）； in
the apodeictical； we look on it as necessary。* Thus the two judgements
（antecedens et consequens）； the relation of which constitutes a
hypothetical judgement； likewise those （the members of the division）
in whose reciprocity the disjunctive consists； are only problematical。
In the example above given the proposition； 〃There exists perfect
justice；〃 is not stated assertorically； but as an ad libitum
judgement； which someone may choose to adopt； and the consequence
alone is assertorical。 Hence such judgements may be obviously false；
and yet； taken problematically； be conditions of our cognition of
the truth。 Thus the proposition； 〃The world exists only by blind
chance；〃 is in the disjunctive judgement of problematical import only：
that is to say； one may accept it for the moment； and it helps us
（like the indication of the wrong road among all the roads that one
can take） to find out the true proposition。 The problematical
proposition is； therefore； that which expresses only logical
possibility （which is not objective）； that is； it expresses a free
choice to admit the validity of such a proposition… a merely arbitrary
reception of it into the understanding。 The assertorical speaks of
logical reality or truth； as； for example； in a hypothetical
syllogism； the antecedens presents itself in a problematical form in
the major； in an assertorical form in the minor； and it shows that the
proposition is in harmony with the laws of the understanding。 The
apodeictical proposition cogitates the assertorical as determined by
these very laws of the understanding； consequently as affirming a
priori； and in this manner it expresses logical necessity。 Now because
all is here gradually incorporated with the understanding… inasmuch as
in the first place we judge problematically； then accept
assertorically our judgement as true； lastly； affirm it as inseparably
united with the understanding； that is； as necessary and apodeictical…
we may safely reckon these three functions of modality as so many
momenta of thought。
*Just as if thought were in the first instance a function of the
understanding； in the second； of judgement； in the third； of reason。 A
remark which will be explained in the sequel。
SECTION III。 Of the Pure Conceptions of the Understanding； or
Categories。 SS 6
General logic； as has been repeatedly said； makes abstraction of all
content of cognition； and expects to receive representations from some
other quarter； in order； by means of analysis； to convert them into
conceptions。 On the contrary； transcendental logic has lying before it
the manifold content of a priori sensibility； which transcendental
aesthetic presents to it in order to give mat