When I for the first time spoke of
Wolff's theory of judgements I was perplexed by the question where did Kant actually get his
twelve-part classification of judgments, on which his scheme of
categories is supposedly based. Wolff's more extensive treatment of
the topic of judgements in his Latin logic is still far from Kant's
neat classification, but is at least a step towards it.
It is easy to start from what has not
changed: there's still no account of modalities as a logical
question. There's also no division of judgements according to
relation in the Kantian sense. Wolff does distinguish categorical
from hypothetical judgements, former thought to be true in all
circumstances, latter, on the other hand, only under some express
circumstances (note that the ”if-then”-clause is not viewed as an
operation for forming new judgements, but as an expression of the
conditionality of the consequent, which is the true judgement in this
case). Yet, this is a division and not trivision, like with Kant.
Furthermore, both categorical and hypothetical judgements are
apparently classified as simple propositions and distinguished from
the class of complex propositions, which then contains disjunctions as one member,
but in addition, e.g. conjunctions.
It is the divisions of quality and
quantity that are almost in the shape that we will later find with
Kant, and Wolff even uses the terms quality and quantity to indicate
the special characteristics of these divisions. Thus, in addition to affirmative and negative judgements, Wolff does
speak of infinite judgements, which are affirmative in their form,
although they have some indication of negativity in them, that is, hidden
in the predicate (e.g. ”this creature is immortal”, which seems
affirmative at first sight, but contains the negative prefix ”im-”
and therefore negates the proposition ”this creature is mortal”).
Still, Wolff appears not to take the
affirmative, negative and infinite judgements to form a trivision of
judgements of equal stature. Instead, he calls infinite judgements a
species of negative judgements, which appears to suggest that it is
more a question of first dividing all judgements into affirmative and
negative, and then negative judgements into properly negative and
infinite judgements. Wolff thus first asks whether the judgement
contains some indication of negativity and then distinguishes case
where the indicator is explicit ”not” attached to copula from a
case where a more implicit indicator of negativity is attached to
predicate.
Kant's trivision of judgements
according to their quantity in universal, particular and singular
judgements is also seen in Wolff's Latin logic. An interesting point
is that Wolff does not classify singular judgements with universal
judgements, although their behavior as describing one set of things
(with only thing) would make it possible. Instead, Wolff supposes
that all singular terms are implicitly part of some species and then
singular judgements could be regarded as just explicit forms of some particular judgements.
In addition to these three judgement
types Wolff also mentions an undetermined judgement, in which it is
not indicated whether it is universal or particular. In some cases
such indeterminate judgements would be universal – if I say
”triangles are figures”, I certainly mean all the triangles. Then
again, if a guardsman had yelled ”Turks are at our doors” during
the siege of Vienna, he wouldn't have meant that every single Turk
was there, but only some of them.
In addition to undetermined judgements,
Wolff also notes that some apparently universal judgements are actually
singular. He means cases like ”all the soldiers form an army”:
clearly none of the individual soldiers forms an army by himself, but
only the whole group of them. Wolff is thus referring to cases where
we speak of a collection of things as a single individual: later on
this intuition was developed in more detail with set theory.
Despite all this variety, Wolff is
quick to point out that we can actually do with a simpler
classification: infinite judgements can be viewed as affirmative or
negative, singular judgements as particular and indefinite judgements
as either universal or singular. The main reason for this tidying up
is undoubtedly the use of judgement forms in classification of
syllogisms. Another reason lies in the neat application known as
square of opposition:
The basic idea of the square is to
represent some important relations between different statements that
differ only by their form (in Kantian terms, their quality and
quantity), but share the content or concern same concepts. Thus,
universal affirmative judgements and particular negative judgements
are contradictories, and same goes for universal negative judgements
and particular affirmative judgements. Contradictories, then, are
such pairs of judgements, only one of which can be true and one of
which also must be true: for instance, ”all spies are Finnish”
and ”some spies are not Finnish” cannot both be true, but one of
them must surely be true.
Universal affirmative judgements and
universal negative judgements are contraries, that is, only one of
them can be true, although it is possible that neither is true, in
the case that both particular affirmative and particular negative
judgements are true (e.g. if some roses are red and some are not,
then neither are all roses red nor all roses not red). The latter two
judgement types are called subcontraries, that is, both of them
cannot be false, although both of them could also be true. Finally,
particular affirmative or negative judgements are subalterns of
corresponding universal judgements, which means that a universal
judgement implies the corresponding particular judgement (if all
humans are rational, then certainly some particular humans, like Inuits, are
also rational).
We have to make the reservation that
the square of opposition might fail, if we allow concepts that do not
refer to any real objects, such as round squares. All round squares
are clearly round, but as squares, none of them are round: both of
the judgements can be true, because there are no round squares. It is
then a matter of whether we prefer the beauty of the square of
opposition over the possible use of such empty terms: both of them
cannot be accepted.
Note that the judgements I have been
speaking of are in Wolffian logic combinations of concepts, that is, something within
consciousness. Just like mental concepts can correspond to
linguistic, communicable, words, similarly mental judgements can
correspond to linguistic, communicable propositions or combinations
of words. Wolff does note that the correspondence might not be
perfect – something that Aristotle already noted. What we say,
might actually refer to different thoughts in different contexts, for
instance, when we say ”it was a fluke”, we might refer to a fish
or to a stroke of luck: this phenomenon in case of single words we
would call homonymy. Similarly, we could use different expressions to
convey the very same thought, which in case of single words we would
call synonymy.
So much for judgements, next time we
once more enter the proper syllogistic.
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