Aristotle, Organon: Analytics (1)

From these logical frameworks, so clearly designed for discussion, Aristotle derived his entire theory of the syllogism. He came to realize that the necessity with which one drew the consequences from theses initially posited was entirely independent of the fact that one was discussing; the professor who expounds, the dialectician who debates, the orator who persuades, whatever the difference in their starting points, employ an equally rigorous line of reasoning: it is the syllogism, that is to say, the method that reveals to thought the union of an attribute with a subject, when this union is not immediately known. It is therefore permissible to study in itself this reasoning “in which, certain things being posited, another necessarily follows from them by the mere fact that the former are posited.”[1] This study is the subject of the Prior Analytics, and it comprises three parts: the genesis of syllogisms (chapters 1 to 26), the means of inventing syllogisms (27-30), and the reduction of all valid reasoning to the syllogism[2].

It was the Platonic division that gave Aristotle the idea of the syllogism; for division is indeed a kind of syllogism; it effectively “unites” an attribute (i.e., mortal) with a subject (i.e., man), once it is admitted that this subject belongs to a genus (i.e., animal), and that this genus is divided into two species, mortal and immortal, the first of which includes man: there are therefore three terms, logically hierarchically ordered, and, thanks to this logical hierarchy, two of them are united by the third. But this is a “weak syllogism,” incapable of concluding necessarily, since it provides no means of discovering in which of the two species, mortal or immortal, man should be placed, and since, moreover, it makes the middle, animal, a broader genus than the mortal attribute[3]. But let us retain the idea of this logical hierarchy, and suppose that there are “three terms which are to one another in such a relation that the last (minor) is in all of the middle, and that the middle is in all of the first (major).”[4] This will result in a “syllogism of extremes.” If A is affirmed of all B (major premise), and B of all (or some) C (minor premise), then A is necessarily affirmed of all (or some) C. Similarly, if A is negated of all B, and B is affirmed of all (or some) C, then A is negated of all (or some) C. Such is the perfect syllogism (first figure), which immediately draws its conclusions from the inspection of the logical hierarchy between A, B, and C. Note also that the hierarchically ordered concepts are not subject, as in the Platonic division, to being taken from the quid pro quo of the subject of the conclusion; they can also be proper nouns and accidents, provided they satisfy the indicated conditions.

Between the three terms, would a logical hierarchy other than the one indicated make the syllogism of extremes possible? Yes, certainly; and it is not necessary for the middle noun to be included in the major premise and to include the minor premise. If, for example, the middle premise is affirmed by the entirety of the major premise and denied by the entirety of the minor premise, it follows that the major premise is denied by the entirety of the minor premise (second figure). This is a syllogism, but an imperfect one, because it does not rely on the immediate inspection of the hierarchy of terms. It will therefore be necessary to demonstrate it, that is, to reduce it to a syllogism of the first figure. This demonstration is carried out by converting the minor premise; being a universal negative (the middle premise is denied by the entirety of the minor premise), it is converted into a universal negative (the minor premise is denied by the entirety of the middle premise), and the syllogism is thus found to belong to the first figure (second mode). This demonstration, which can serve as an example for those of the other three modes, is clearly driven by the desire to find at the heart of every syllogism the same conceptual relationship that places the middle premise between the two extremes.

There is still a syllogism in the case where both the major and minor premises belong to the whole of the middle premise; for one is entitled to conclude that the minor sometimes belongs to the major (third figure). In this case, the hierarchy is the reverse of that of the previous figure, since the middle is more general than both the major and the minor. It will be easy to transform this imperfect syllogism into a perfect one by converting the major premise, which, being a universal affirmative, becomes a particular affirmative, and thus: the middle belongs to a part of the major. The hierarchy of concepts that gave rise to the syllogism is thus restored[5].

In the Platonic division, since the attribute expressed the quiddity of the subject, propositions were always necessary. As soon as one frees oneself from this condition, there is no reason to believe that a syllogism exists only with necessary premises. The propositions can be merely contingent and possible, or they can state a factual truth that is not necessary. These are the three modalities that propositions can present. Hence a new problem: that of determining the modality of the conclusion in each of the three figures, when the modality of the premises is known. Except in the case of the syllogism with necessary premises in the first figure, where it is immediately apparent that the conclusion is necessary, Aristotle demonstrates the modality of the conclusion in all possible cases, using either conversion or reductio ad absurdum[6].

This complicated mechanism of the syllogism is indeed derived from dialectic: the conclusions are, in fact, the problems to be solved. They are posed as questions before the syllogism that must provide an answer. The syllogism often arises from lengthy prior investigations: once the question has been posed—whether a given attribute belongs to a subject or not—one must find the means to resolve it; and this is why two lists must be made, one of all possible subjects of the major premise, and the other of all possible attributes of the minor premise (without, however, going back beyond the proximate genus to include attributes indicating quiddity); it is in the common part of these two lists that the means will necessarily be found[7].

This tentative search for the means stands in complete contrast to the rigid mechanism of the syllogism once it has been found. This contrast becomes strikingly apparent when Aristotle shows how one can deduce truth from falsehood; the truth of the conclusion is in no way a guarantee of the truth of the premises. There is yet another case where deduction is illusory, despite the perfect correctness of the syllogisms; This is the case of circular proof, where one uses as a premise for the conclusion a syllogism that itself had as a premise the conclusion one now wishes to prove[8]. The question, therefore, is now how the premises are justified; the art of syllogistic reasoning certainly allows one to necessarily link the conclusion to the premises; it provides no means of positing premises in cases where these premises are not themselves conclusions of preceding syllogisms.

It is here that the distinction arises between the three arts that all employ the syllogism: apodictic or the art of demonstration, dialectic, and rhetoric. The Posterior Analytics are devoted to apodictic reasoning.