Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

The whole account of the syllogistic art rests on three principles known per se:

The first is: “Whatever things are identical with one third are identical with one another.” The force of discursive proof rests on this. Since reasoning is ordered to inferring a conclusion in which two extremes are joined through the force of some middle term, by which their union is shown, it is necessary that things be united with one another because they are united in some middle term. The opposite holds in like manner when a negative conclusion is inferred, in which one thing is denied and separated from another: one of them must be denied and separated from a third; “for things that are identical with one another, if one of them is distinguished from some third thing, the other too is distinguished and separated from that third.” Therefore, from the denial of one thing with some third thing follows the denial of what is identified with it in relation to that same third thing.

Note that St. Thomas, Summa theologiae I, q. 28, art. 3, ad 1, explains that principle as follows: “Things that are identical with one third are identical with one another, if they are identical with one third in reality and in account.” This does not mean that they are distinguished neither in reality nor in account. Rather, “in reality and in account” must be construed with “with one third,” so that they are identical with one third that is one in reality and in account, that is, not virtually or formally multiple. For in that case something can be identical with one extreme under one formal aspect and with another under a different aspect, and consequently it does not follow that those extremes are identical with one another. Indeed, many paralogisms arise from this, because the middle term is not perfectly and simply one, but multiple, at least virtually or formally. Hence, from the union of such a middle term with the extremes, unless it is under the same formal aspect, no union of the extremes with one another follows. For example, this does not follow: “Whiteness is a relation; whiteness is intense; therefore a relation is intense.” Relation is identified with whiteness in one way, intensity in another, and so they are not identified with one another. Nor does this hold in divine terms: “The Father is the divine essence; the Son is the divine essence; therefore the Son is the Father.” The divine essence in which they are united is, because of its infinite perfection, one most simple reality and virtually multiple; it is modified under different concepts by the Persons, each inadequately.

The second principle is “Dici de omni,” that is: “Whatever is said universally of a subject is said of everything contained under that subject”; for example, if it is affirmed universally of man that he is capable of laughter, it must be affirmed of every individual man.

The third principle is “Dici de nullo,” that is: “Whatever is denied universally of some subject is also denied of everything contained under that subject”; for example, if you deny universally of man that he is a stone, you must deny this of every individual contained under man.

These principles are known per se because the nature of a universal consists in being said of all the things with respect to which it is universal. These principles do not serve an expositional syllogism, which has a singular middle term, but a syllogism with a common middle term. In the latter, reasoning must proceed through the force of some distributed term, because if none is distributed, the argument proceeds from pure particulars, which is a defective form of consequence: particular propositions do not provide a middle term that fully embraces and contains what is to be inferred and united in the conclusion. Once a term is distributed, however, whatever is said or denied of it is also said or denied of what is contained under it through that distribution; thus what was denied or affirmed of the distributed term in the antecedent is rightly concluded of what is contained under it. These two principles therefore serve to establish the necessity of inference, not by reasoning from pure particulars but by distribution.

Hence those syllogisms that are immediately regulated by these two principles are called perfect, because there the application of what is said or denied universally to what is contained under those universals is made evident. Other modes, by contrast, are called imperfect: they are not immediately regulated by these principles, nor is that application made so evident in them; rather, they are regulated mediately, and are therefore reduced to those perfect modes that are regulated immediately and evidently per se by such principles. The four modes of the first figure are regulated immediately by these principles, because in them the middle term is perfectly distributed in the major premise, where it stands universally as subject. When it is then predicated in the minor premise, this very fact makes it evident that what it is predicated of is contained under its universality, and consequently that what was predicated or denied of the middle term, posited universally in the major, also belongs to that thing. This is an immediate manifestation of “Dici de omni” and “Dici de nullo,” because it is shown immediately and per se that something is contained under or denied of a subject taken universally, and that subject is the middle term.¹ See below, question 8, final article.

But for all this to be understood more clearly, and for all the defects of bad consequence and syllogisms to be recognized at the same time, we must treat the goodness and defects of consequences both in general and in particular.