Cursus Philosophicus Thomisticus, Secunda Pars Artis Logicae

Aristotle, refuting two errors of the ancients—one holding that no thing can be known scientifically, the other that everything can be—posited self-evident propositions, which are indemonstrable and not known scientifically, yet are the principles for knowing and illuminating demonstrable conclusions. It is plainly clear that by a direct process of resolution one must arrive at such propositions. For since one thing is demonstrated through another and an infinite regress is impossible, one must arrive at some principle that has no prior principle by which it is demonstrated, yet is the reason and principle for demonstrating other things with which it has a necessary connection. Such a principle is called self-evident, that is, evident from the explanation of its terms alone. Properly speaking, such a principle is not itself scientifically known, but is a principle of knowing. Thus Aristotle contradicts the first error by showing that some things are known scientifically, by arriving at something that is not scientifically known but is self-evident, which is more than merely being known. Consequently, the contrary error is also destroyed: not everything is known scientifically, since one must arrive at a self-evident principle, which is not scientifically known but from which scientific knowledge arises.

Nevertheless, because the ancients replied that first principles are indeed indemonstrable by a direct process through another prior cause, but demonstrable by a circle—that is, through the very conclusion they infer—Aristotle therefore rejects circular demonstration as defective.

A circle in demonstration is a certain progression from principles to conclusions and a return from those conclusions to the principles. Such a process can occur in two ways: in one way, by returning from the same conclusion to the same principles, the same materially, I say, but not formally—that is, when the conclusion is known through another formal middle term than the very principles; or in a second way, this process can proceed from the same conclusion also taken formally, that is, as formally known through the same principles to which the return is made. The first circle is called non-uniform, because one proceeds by a different middle term from principles to conclusions and from conclusions to principles; the second is called uniform, because one proceeds by one and the same middle term from principles to conclusions and from conclusions to principles.

IT MUST THEREFORE BE SAID that Aristotle intends to reject only the formal and uniform circle, not the non-uniform and material one, which is simply not a circle and is not defective.

The first point is proved because, if a formal and uniform circle is admitted, the same will be demonstrated through itself, and the same thing will be said to be more known and less known than itself in the same respect. For if I prove that a human being is capable of laughter because a human being is rational, and then, if it is denied that a human being is rational, I prove this because a human being is capable of laughter, then in the first proof “rational” is better known than “capable of laughter,” and in the second “capable of laughter” is better known than “rational,” since that through which we prove something must be better known than what is proved. Thus the same thing will be formally better known and less known according to the same middle term in the same respect: “rational” with respect to “capable of laughter,” and “capable of laughter” with respect to “rational.”

The second point is proved because a materially taken circle occurs when one returns from a conclusion to an antecedent, the conclusion having been known through another middle term. Then it is not proved through the same thing, but through another, by which that conclusion was made known; and in that different kind or middle term by which it is proved, the conclusion can be better known than the first antecedent from which it was inferred. Although the conclusion is materially one proposition, since it is known through two middle terms, it consequently depends on two antecedents. Thus when we return from it to one antecedent, from which it was proved by virtue of another proof, we do not return formally from the conclusion itself, but from that other antecedent by which it was made evident. Formally and simply, then, there is no circle.

From these points certain objections commonly brought against this view are resolved. For a perfect circle is found among causes, since causes are causes of one another, as is said in 2. Phys. text 30¹ and Metaphysics 5, chapter 2²; therefore it should also be found in demonstrations, since demonstrations are formed through causes.

Again, the Philosopher often uses a circle. For in Posterior Analytics 2, chapter 12³, he teaches that rain can be demonstrated from an abundance of vapors and, conversely, an abundance of vapors from rain. And in On the Heavens 2⁴ he shows that the heavens have anterior and posterior parts because the motion of the heavens begins from one part and not another; that it begins from one part and not another he shows because it has anterior and posterior parts. Similarly, he shows that the stars are immobile in themselves because they are spherical, and conversely that they are spherical because they are immobile. In general, philosophers began to know causes from effects, and afterward knew those same effects from causes.

Finally, a circle can be admitted in dialectical proofs, because proof there is not made through something better known and causative of another. Hence it is the same whether one begins from the conclusion toward the premises or from the premises toward the conclusion. The Philosopher seems to allow this in Posterior Analytics 2, chapter 7⁵, where he allows one definition to be demonstrated through another, from which it is in turn demonstrated, because he says these proofs are dialectical, not demonstrative.

To the first point, the answer is that causes do not form a circle formally, but materially and in different kinds of causation. For there is no circle where the account of dependence is different, and consequently the account of making something known is different. A material cause is made known in one way through a formal cause, a formal cause in another way through a material and efficient cause. And since causes are more than two, a material cause made known through an efficient cause can in turn make a formal cause evident; and a formal cause, made known through a material cause, can in turn make an efficient and final cause evident, and so conversely. This will be treated more fully in 2. Phys.⁶

To the second point, it is said that those demonstrations are not formally circular. For rain, as known through experience, makes known vapors, which are causes of rain; and these, as an efficient cause, demonstrate rain. Literally, however, the Philosopher is not speaking of the same vapors and rain, but of different instances: rain is a cause of vapors, and vapors are a cause not of the same rain, but of another rain.

As for what is adduced from On the Heavens 2, St. Thomas answers there, lecture 7⁷, and again lecture 16⁸, that the Philosopher does not use a formal circle, but a material one, proceeding from the same thing known in another way and in a different kind of cause. For example, if we prove that the heart moves through the motion of a pulsating vein, this pertains to the question whether it exists. But if one asks what the cause of the motion of a pulsating vein is, which pertains to the question what it is, this must be proved through the heart as its cause. This proceeds in a different kind of cause and presupposes another kind of knowledge, for example, experimental knowledge or something similar, concerning what is proved as to whether it exists. Thus, when the Philosopher proves that the stars are spherical because they do not move by themselves, and in turn that they do not move by themselves because they are spherical, this is because he presupposes the first proposition to have been proved through another middle term, as St. Thomas says; the same holds of the other propositions. Likewise, philosophers began to know causes from effects experimentally, as to whether they exist; afterward, however, they proceeded from causes to effects as to why they are so.

To the final objection, the answer is that a formal circle cannot be committed even in probable arguments. For although one does not proceed through an intrinsic cause, one still proceeds from what is more probable to what is less probable. Thus if this unknown point is taken up in the same kind of proof to establish the antecedent, it will be taken as more probable than it; and so it will be more and less probable in the same kind with respect to the same thing, which is as incompatible in probable arguments as in others. If, on the other hand, the probable conclusion appears to be an antecedent in its own right on another basis, then the circle is no longer formal and uniform, as was said of the other proofs. As for the passage of the Philosopher in Posterior Analytics 2, chapter 7, the answer is that it does not prove a formal circle in dialectical proofs, but only compares the proof of one definition through another with a dialectical mode of proof in this respect: a dialectician multiplies middle terms because he proceeds probably, whereas a demonstrator uses only one. The same holds for someone who proves one definition, otherwise known from its terms, by another definition, and conversely.