Cursus Philosophicus Thomisticus, Secunda Pars Artis Logicae

We have often said why Aristotle entitled these books the Posterior Analytics. They are called analytic, that is, resolutory, because they teach how to resolve demonstration and the scientific process into their principles; for this is properly to know, namely, to resolve a thing into its causes and principles. They are called books of posterior resolution because they treat scientific resolution on the side of matter, as distinct from resolution or analysis prioristic, which treats resolution on the side of syllogistic form, the subject of Aristotle’s Prior Analytics and our Summulae. It is therefore clear that the subject matter of these books is demonstration, which is a scientific syllogism, insofar as they consider the material conditions of which demonstration must consist: necessary and per se propositions by which a conclusion is evidently inferred or proved, insofar as the intellect is clearly compelled to assent to the conclusion by the force of such proof and its middle term.

SUMMARY OF THE TEXT OF BOTH BOOKS

Aristotle divides the treatment of posterior resolution into two books. In the first he treats demonstration in itself; in the second, its causes or principles, that is, either its first and highest principles or its middle terms, such as a definition in a question about what a thing is. The first book is divided into 27 chapters,¹ the second into 18, although some editions have 13.²

CONCERNING THE FIRST BOOK³

In book 1 he treats demonstration, which is a syllogism that produces science, through chapter 23. From chapter 23 through 27 he treats its effect, namely science, both in itself and in comparison with opinion and sagacity, which is a certain readiness for finding a middle term or proof.

In chapter 1, then, he treats what is required in advance and must be known before demonstration. He shows that every teaching and learning—that is, comparative knowledge by reasoning—arises from some prior knowledge. He establishes that two things must be known beforehand, whether something is and what it is; and that three things are known beforehand: of the subject, what it is; of the proper attribute, whether it exists; and of the principles by which it is demonstrated, that they are true.

In chapter 2 he defines science, demonstration, and principle, although principles are treated more fully in chapter 8. Science is defined as follows: to know is to cognize the cause on account of which a thing is, and that this is its cause, and that it is impossible for the thing to be otherwise. Here the act of knowing, not the habit, is defined. Demonstration is defined in two ways. First: a demonstration is a syllogism that produces knowing. Second: a demonstration is a syllogism composed of true, first, immediate, prior, better-known premises that are causes of the conclusion. Principle is defined as an immediate proposition, that is, one for which there is no prior proposition or which lacks a middle term by which it might be proved. An immediate proposition or principle is divided into a posit and an axiom. A posit is a proposition that cannot be demonstrated through a middle term; it is the same as an immediate proposition. An axiom is an immediate proposition of the highest certainty, found in every intellect, such as: everything either is or is not. A posit is further divided into a supposition and a definition. A supposition is a self-evident proposition signifying that something is or is not. A definition explains quiddity and functions as a proving middle term; hence it is numbered among principles not as a proposition but as a middle term.

In chapter 3 he rejects two extreme errors about science. The first said: Nothing can be known, because either there is an infinite regress among principles of knowing or the regress stops somewhere. The first is impossible, since an infinite cannot be traversed. The second eliminates science, because the principle at which one stops is not known, lacking a middle term by which it could be known, and so remains unknown. The second error said: Everything is knowable, because the ultimate principle at which one stops is in turn demonstrated by the conclusion, since demonstrations form a circle. The Philosopher resolves both errors, saying against the first group that principles are not demonstrated but are known per se and from their terms; against the second, that there is no circular demonstration, since then a principle would become known through a conclusion that is less known in itself, so that the conclusion would be both better known and less known, prior and not prior, with respect to the principle.

In chapter 4 he first states that demonstration must consist of necessary premises. He explains what is required for a predicate to be necessary: namely, that it be true of all, that is, universally applicable, and per se. Hence he defines what it is for a predicate to be true of all, distinguishes the modes of predication per se, and explains the universal predicate, or what belongs to a thing insofar as it is itself. A predicate true of all belongs neither to some but not others nor sometimes but not at other times; rather, it belongs always and to all. A predicate per se is so either in predicating, in existing, or in causing. In predicating, it is per se in two ways. In the first, the predicate belongs to the quiddity and essence of the subject, as animal belongs to human being. In the second, the subject is included in the account of the predicate, or a proper attribute is predicated of its subject, as “A human being is capable of laughter.” In a third way, something is per se because it exists per se, as a primary substance. In a fourth way, something is said per se because it inheres on account of that thing, that is, it signifies its proper account of causing, as “A physician heals” and “A builder builds”; what does not do so, as “A white thing builds,” is per accidens. Finally, a universal predicate, or what belongs to a thing insofar as it is itself, belongs to all and per se, and is convertible with the subject, as “A human being is rational” or “A human being is capable of laughter.”

In chapter 5 he presents the ways in which one can err or be deceived concerning a universal predicate, or what belongs to a thing insofar as it is itself. He offers a rule for recognizing such a predicate: if the predicate belongs to the subject when everything that does not pertain to the subject’s essence is removed, but the predicate is removed first when the subject itself is removed, then the predicate belongs to the subject insofar as it is itself.

In chapter 6 he proves by several arguments that demonstration consists of necessary and per se premises. He adds that a necessary conclusion can follow from contingent premises, just as truth can follow from falsehood, but it cannot be proved from false premises; only a necessary conclusion follows from necessary premises.

In chapter 7 he proves that demonstration must consist of proper premises, not alien ones, because it consists of premises that are per se; it is not enough to proceed from common premises.

In chapter 8 he continues the same discussion as in chapter 7 and adds that metaphysics is a general science because it treats and teaches principles in the most common way. Note, however, that some editions, such as Cajetan’s text, divide chapter 8 across several chapters through chapter 11, whereas in the Coimbra commentators and others chapter 7 comprises the entire text that in Cajetan extends through chapter 11.

In chapter 9, which others number 8 or 11, he treats common and proper principles. Principles are things that cannot be demonstrated: some cannot be demonstrated absolutely, that is, in any science, and these are axioms; others cannot be demonstrated in some particular science, in which they lack a proving middle term, and these are posits or definitions. Some principles are common, that is, they serve several sciences; others are proper, that is, they serve a determinate science. The most common principles include: It is not true of anything that the same thing can be affirmed and denied of it; of anything it is possible to affirm or deny the same thing.

In chapter 10 he explains how each science has its own questions, how the demonstrator differs from the dialectician, and that the dialectician elicits various middle terms, unlike the demonstrator.

In chapter 11 he distinguishes knowledge or demonstration quia and propter quid, and likewise subalternating and subalternated science. Propter quid science knows through the proximate cause; quia science through a remote cause or an effect.

From chapter 12 through chapter 23, exclusively, he treats matters pertaining to demonstration: for example, that a figure is better suited to demonstration; how an erroneous syllogism is contrary to demonstration; that there is no infinite regress in demonstrations; how mediate propositions can be reduced to immediate ones; and, finally, how universal and particular, affirmative and negative demonstrations are compared with one another.

In chapter 23 he begins to treat the effect of demonstration, namely science. First, he affirms that one science is more certain than another. Second, he says that a science concerned with one genus or subject is one science, while sciences that use different principles are different sciences.

In chapter 26, omitting two other chapters that raise no difficulty, Aristotle compares science with opinion. He says they agree in that they can concern an object that is in some way the same; they differ because science concerns immutable things and opinion mutable things, and because the same person cannot have science and opinion about the same object.

In the final chapter he compares science with sagacity and says that sagacity is a ready conjecture of a middle term, or facility in finding a middle term for proof. Thus it pertains to sagacity to consider middle terms, and to science to consider conclusions.

CONCERNING THE SECOND BOOK⁴

This book treats the causes or principles of demonstration, both on the side of the middle term or definition and on the side of the first indemonstrable principles. He treats the latter, namely first principles, in the final chapter; the middle term of demonstration is treated in the preceding chapters. For anyone seeking a careful explanation of Aristotle’s text, there is a very lucid one by St. Thomas on both books, and a fuller one by Cajetan.

ORDER OF DISCUSSION

We therefore reduce the whole subject of posterior resolution, which treats chiefly of demonstration, to four principal topics or questions. First we shall treat what is required in advance for demonstration, namely, prior knowledge and premises. Second, the very quiddity of demonstration. Third, its effect, namely science, both in itself and in comparison with opinion and faith. Fourth, the unity and distinction of the sciences.