lauantai 1. maaliskuuta 2014

Syllogistic 101 revisited

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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