Ever since Aristotle's Posterior analytics, syllogistic logic had been a crucial part of philosophical methodology and at times methodology consisted of little else. There are at least two reasons why Aristotle thought syllogistic so important. Firstly, syllogistic was an improvement over Platonic dialectics, because it replaced individual arguments with a group of general schemes for constructing incontrovertible arguments. Secondly, the science most developed at the time, geometry, was easily converted into a syllogistic shape.
From Aristotle, the enthusiasism over syllogistic logic was transferred from one generation to another, and even when the fame of Aristotle dwindled, the syllogistic was still the core of the logic, and the only thing that truly threatened its position in methodology was the relatively young notion of experimental science. Thus, it is no wonder that Wolff is also obliged to give an account of syllogistic in his logic. Because the issue will undoubtedly appear in the future – Hegel at least loves the syllogism as a symbol – I shall expound in the following two blog texts syllogistic logic in more detail. Those who know the syllogistic by heart and those who are bored to death by formal logic can skip ahead.
Before going into syllogisms themselves, I shall say in this text something about their constituents. We have discussed concepts and words in previous texts, but the things between – that is, judgements – are still missing. Now, Wolff – and probably also many other logicians of the time – defines judgements in two manners. Firstly, in judging we supposedly think that a thing has or has not or could or couldn't have some characteristic: the thing is represented by the subject term and its characteristic by the predicate term, which Wolff calls respectively front and back terms (Förder – und Hinterglied). Secondly, the judgement is regarded as a combination of concepts, namely, the subject and the predicate.
The identification of these two definitions is problematic, because on a closer look they define two completely different things. As Husserl noted, thinking a combination of redness and ball or red ball is something else than thinking or considering the possibility or the fact that a ball is red – and as Frege would add, both are different from asserting that a ball is red. It is somewhat disturbing to think that quite a number of people had not noticed these what seem to be obvious platitudes.
A reasonable explanation for this apparent confusion is that Wolff and his fellow logicians had a different paradigm of judgement in mind. While the modern mathematical logic has taught to us to start from sentences like ”Mickey is a mouse”, where an individual is characterised in some manner, the Aristotelian tradition begun from sentences like ”Gold is malleable”. This is a case of a lawlike unification of two universal terms, and because of the lawlikeness, the assertion of their connection appears inevitable.
At least in case of Wolff, the explanation is made even more plausible by two facts. First fact is connected to a difference between universal and particular judgements, which Wolff equates with the difference between necessary or essential and contingent or accidental judgements. The equation itself is interesting, because it tells us something about Wolff's notion of alethic modalities: if all Xs are Ys then an X is essentially an Y, but if the connection between Xs and Ys is accidental, only some Xs can be Ys. Now, Wolff suggests that all the particular judgements can be turned into universal judgements by stating the conditions in which the particular connection of concepts is true: that is, if some Xs are Ys, then all Xs filling suitable conditions are Ys. What is important here is that Wolff clearly accepts that universal/necessary judgements are the norm to which all the other sort of judgements should be transformed.
Secondly, Wolff suggests that we are able to think or judge something through a given sentence only if the concepts combined in the sentence are distinctly known to conform with one another, while we are unable to think the sentence if the concepts are distinctly known to be contradictory; otherwise, we do not know whether we can think it or not. This might in itself sound completely harmless, but Wolff defines the conformity as the necessity of thinking one concept, when you think the other concept. In other words, in a true judgement two concepts must be necessarily or in a lawlike manner connected with one another – an accidental connection of characteristics is then not a true judgement.
A word on the classification of judgements. We have already seen Wolff divide judgements into universal or absolutely valid and particular or contextually valid. In addition, he mentions the division into affirmative (bekräftigende) and negative (verneinende) judgements. These two classifications are actually all that we need in syllogistics. Not only is Wolff then unaware of what Kant called infinite and singular judgements, but he and probably many other logicians fail to think the possibility of dividing judgements according to relation or modalities. Hypothetical and disjunctive judgements appear only in a place where Wolff shows how other deductions can be transformed into syllogistical form, while modalities are discussed in Wolff's ontology. When scholars then say that Kant merely assumed his category system from the logic of his time without any arguments, we might suspect that he actually just assumed the system, which was not based even in logic.