Cursus Philosophicus Thomisticus, Secunda Pars Artis Logicae

Aristotle defines demonstration in two ways: first, with respect to the effect it causes, which is also its end; second, with respect to the matter of which it consists. Thus the first definition is given according to its order of causing, while the second is given insofar as demonstration is caused from its own principles.

The first definition is: “Demonstration is a syllogism that produces knowledge.” 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. The second definition is: “Demonstration is a syllogism consisting of truths that are primary, immediate, prior, better known, and causes of the conclusion.”

With regard to the first definition, observe three expressions: first, the word “syllogism”; second, “produces”; third, “knowledge.”

It is called a syllogism to make clear what form of argumentation demonstration requires, namely the syllogistic form. An enthymeme, unless the proposition it lacks is supplied and it is reduced to the form of a syllogism, does not have a sufficient arrangement to generate knowledge, because in only one premise the middle term is not applied or explained so as actually to connect the extremes. Without this application, there is no evident inference uniting the extremes to one another. Thus, if an enthymeme draws a conclusion, it does so by the power of the syllogism to which it is reduced. Since, however, it is not enough to explain the character of a syllogism on the side of form unless it is also explained on the side of matter—which must carry a necessary connection if it is to serve demonstration—this definition therefore explains such matter by the effect it has, namely generating knowledge, just as the following definition explains it through the intrinsic conditions of which it consists.

The second expression is “produces.” The difficulty here is in what kind of cause demonstration is said to produce knowledge. The brief answer is that we may be speaking either of actual knowledge, or scientific assent, which is knowing itself, or of habitual knowledge, that is, the scientific habit produced by actual knowledge.

If we speak in the first way, it is not the whole demonstration but the premises, suitably arranged and admitted, that are the cause of knowledge. For an integral demonstration, insofar as it includes the premises and the conclusion, includes scientific assent on the side of the conclusion and the cause of that assent on the side of the premises. As was said in the preceding question, art. 3, the premises influence the conclusion both efficiently and formally. They do so efficiently through the assent to the premises, which are formal cognitions or concepts; by these, the intellect in act efficiently works to infer the conclusion. They do so formally through the objects themselves, or the things known, which are represented by these cognitions and specify the cognitive acts of the premises. Since the truths and objects of the principles virtually contain the truths inferred, they also virtually and mediately specify the assent to the conclusion, which explicitly and formally tends toward the truth of the conclusion itself.

If in the second way we speak of the efficient causation of habitual knowledge, it should be said that it is generated by the demonstration itself, not only by reason of the premises but also by the assent to the conclusion. For it is clear that a habit is generated and acquired through acts like those toward which it inclines. The habit of knowledge inclines one to assent to a conclusion from premises; therefore, it is efficiently generated through a similar act. But habits are treated more fully in the Metaphysics and in the books On the Soul; one may also consult 1. 2. q. 51.

The third and final expression is “knowledge,” as in “Demonstration is a syllogism that makes one know.” It is commonly understood as knowledge of the reason why, in conformity with Aristotle’s meaning. For, in defining demonstration, he adds a definition of knowledge of the reason why when he says: “To know is to cognize the cause on account of which a thing is, etc.” Absolutely speaking, however, it is also true that a demonstration of the fact produces knowledge of the fact, and so the definition can readily be adapted to both kinds of demonstration. What knowledge of the reason why and of the fact is, we shall say below in art. 4.

With regard to the second definition of demonstration, note that it is given in terms of the propositions from which a demonstrative syllogism is formed, or ought to be formed, by explaining the conditions required in the premises for a true demonstration to be formed from them.

Demonstration is therefore said to be that which is from truths that are primary, immediate, prior, better known, and causes of the conclusion. Some substitute “proceeds” for the word “is.” They find a special significance in “proceeds,” which denotes discourse. But the Philosopher did not use the verb “proceeds”; he used “is” or “consists.” Both are true: it proceeds with respect to the conclusion inferred, and it consists of the premises and conclusion, because the whole, integral syllogism has them as its parts.

The first three expressions of the definition therefore make clear conditions of the premises that are, as it were, absolute; the remaining three are, as it were, comparative, both with respect to the conclusion and with respect to other propositions.

The first expression is from truths. For although a truth can be concluded from something false by reason of the form and on the supposition that the premises are granted, a truth cannot be proved scientifically from what is false, since proof gives certainty and evidence, which falsity cannot provide for truth.

It is said to be from primary and immediate propositions, that is, from propositions known per se and not demonstrated through another middle term, as St. Thomas explains in 1. Posterior Analytics, lect. 4¹. They are called primary in relation to the propositions proved through them, and immediate because they lack a middle term that demonstrates them, as the holy Doctor says. Thus these two expressions are not superfluous; they explain distinct formal features: that a proposition has not been demonstrated from another, which is to lack a middle term, and that it is apt to demonstrate other propositions, or holds primacy among them, which is to be primary. What a proposition known per se and immediate is, we said in the preceding question, art. 4.

The last three expressions are added to the definition: from propositions prior to, better known than, and causes of the conclusion. Through these expressions the Philosopher explains the premises comparatively, or as applied to the conclusion. In comparing the premises with the conclusion, the middle term by which the premises are connected and make the conclusion clear must be a cause of the conclusion, at least in the order of knowing; consequently, the premises must have priority over the conclusion in the way in which they have causality with respect to it. Finally, they must be better known, because, since they cause the manifestation and knowledge of the conclusion by being principles themselves known, it necessarily follows that they must be better known, for “that on account of which each thing is such is itself more so.”

Some points about these conditions of demonstration, explained by this definition, must briefly be resolved.

FIRST: Must every demonstration consist of premises known per se and without a proving middle term, or is it enough for a demonstration to be resolved into evident premises that have themselves been proved from others and are not immediately known per se?

The answer is that the latter is sufficient. Thus every demonstration will consist of primary and immediate propositions either formally in themselves or virtually, because it deduces formally and per se from such propositions; in this way it is mediately and virtually from primary and immediate propositions. It is enough that a demonstration consist of propositions that can be resolved into propositions known per se. St. Thomas teaches this as well in 1. Posterior Analytics, lect. 4, § He shows². This is clear when, after demonstrating the first or second conclusion in some science, we proceed to a third, fourth, or tenth conclusion, proved through its own premises in such a way that those premises depend on earlier conclusions or on first principles.

SECOND, YOU WILL ASK how it should be understood that demonstration proceeds from the causes of the conclusion. For a demonstration of the fact proceeds from effects or remote causes, while a demonstration of the reason why does not always proceed from causes that are truly causes, as when one attribute in God is proved from another, or the properties of being are proved of being, where no true causality intervenes. Conversely, the first property is caused by the essence, yet is not demonstrated through it, because there is no middle term between the essence and the first property.

The answer is that this definition principally defines demonstration of the reason why, although it can be adapted to demonstration of the fact, as we said, if “causes of the conclusion” is taken to mean causes in the order of knowing and with respect to us, which can also be effects. As for what is added about demonstrations of the reason why, they need not always proceed from a cause that is formally and physically a cause; it is enough that it be virtually or metaphysically a cause, such that one thing is related as the rationale of another, even if it does not cause the other. For example, immutability is the rationale of eternity, and perfection is the rationale of goodness, and so forth.

As for the first property with respect to the essence, the answer is that it is indeed caused by and flows from the essence. But because the essence is the subject of which it must be demonstrated, it cannot be demonstrated of the essence except through the essence itself. Hence, in reality, it lacks a middle term by which it is demonstrated, because that term is identical with the subject. We nevertheless take the definition of the essence as though it were a middle term in the demonstration, distinct not in reality but in reason.

THIRD, IT IS ASKED why the definition says that the premises are better known than the conclusion; this seems to be badly said. First, they are not better known because they are truer, since truth consists in an indivisible point. Second, they are not called better known because they are more certain: the premises are natural causes that influence the conclusion in a natural way. Therefore, they can impart all their certainty to it, especially when the conclusion does not differ in reality from the premises but only in reason. Indeed, if the intellect applies itself more to attending to the knowledge of the conclusion than to the premises, it will communicate greater certainty to the conclusion. Third, in a theological conclusion drawn from one premise of faith and another natural premise, the conclusion is more certain than the natural premise; therefore, a conclusion can surpass one premise in certainty and at times could surpass both. Fourth, the basis for asserting that a principle is better known is not sound. There are two such bases. One is this axiom of Aristotle: “That on account of which each thing is such, etc.” Yet it admits many counterexamples. For it does not work if you say, “A stone is white on account of whiteness, therefore whiteness is whiter”; “blood is shed for health, therefore health is more shed”; or “a man understands through species and habits, therefore the species understand more.” The second basis is that the premises are equivocal causes of the conclusion, while an equivocal cause is nobler than its effect. But one may object to this by citing equivocal instrumental causes, which are not more perfect than their effects: seed is not more perfect than the living thing it produces, nor heat than fire. Yet the premises are instruments of the intellect, which is the principal agent that produces the conclusion.

The answer is that the premises must necessarily be better known, because if they were known equally or less well than the conclusion, the conclusion could in no way be proved through them. The reason is clear: premises are either indemonstrable and known per se from their terms, or demonstrable from other, prior propositions. If they are of the second kind, they are demonstrable before the conclusions deduced from them, and consequently are known earlier, depend on fewer consequences, require fewer middle terms, and are better known as being more independent in truth itself. If they are of the first kind, it is clear that they are better known—as known from their terms—than the conclusions deduced from them, which share in their evidence.

To the first objection, then, it is said that truth is taken in two ways. In one way, from the side of the object it touches, namely being or nonbeing, to which it is adequate. In another way, from the side of the foundation and the mode of grounding such adequation, which in some cases is more or less immutable than in others; thus it grounds the certainty and firmness of truth rather than truth itself. In the first way, truth consists in an indivisible point, although falsity, since it is taken as a departure from the terminus of truth, admits of a range, and one falsity can be greater than another, as St. Thomas teaches in 3. Against the Gentiles, ch. 139. Truth itself touches an indivisible terminus, namely being or nonbeing, not as coming to be but as terminated and already actual, because it touches being or nonbeing as it is in the thing. Falsity, by contrast, departs from being and tends toward its opposite; in this tendency there can be more or less, as with sin. The case is not the same with moral goodness, whose adequation is not to an indivisible rule and to what is already actual, but to conformity with reason, which is the mean of prudence and admits of a range, since it is not bound to determinate rules like an art but varies according to circumstances. Thus speculative truth is regulated according to the thing’s being or nonbeing in itself, while practical truth is regulated according to conformity or nonconformity with reason and prudence. When St. Thomas says in 1. p. q. 17, art. 4 that truth and falsity are contraries, he is speaking of truth and falsity on the side of judgments or acts of the intellect, not on the side of the terminus to which truth is adequate. And in 4. Metaphysics, text 8³, lect. 6 in St. Thomas⁴, the Philosopher did not say that first principles are truest but that they are most certain or firm. In this way, on the side of the foundation—that is, of the firmness and mode of grounding—truth admits of more and less, because the connection of the extremes in “God is” is firmer and more immutable than in “A man is sitting” or “Snow is white.” In this way the premises are also truer than the conclusion, that is, more certain, because the conclusion derives its truth from them.

To the second, the answer is that a wholly univocal natural cause, of the same character as its effect, can communicate all its perfection to the effect, but an equivocal cause cannot, as the premises are to the conclusion. Although the conclusion is sometimes identical with the premises on the side of the thing known as to its entity, and is thus identical in certainty with them, it is nevertheless different in its character as truth. Since one is related as inferred and illuminated and the other as illuminating, the latter must be better known, at least with respect to us. This does not consist in a greater intensity of the intellect, which could contribute to a greater actual adherence on the side of the knower, but not to greater firmness on the side of the thing known—that is, to greater immutability derived from the object.

To the third, the answer is that in theological discourse the conclusion is not more evident than the natural premise, though it may be more certain if the natural premise is considered by itself. If, however, it is considered as elevated and joined to the premise of faith, then the conjunction of the premises is more certain than the conclusion inferred, because it does not express only the natural truth of the premise but its subordination to the supernatural premise, its belonging to that premise in a certain way, and its explaining and applying that premise to draw the inference. The comparison between the conclusion and the premise should not be made with respect to one premise taken alone, but with respect to the premise as it formally is—that is, joined to the other premise—from which the whole and complete basis of inference is drawn. Thus the theological conclusion is more certain than the natural premise as joined to the premise of faith, not considered by itself alone.

To the fourth, the answer is that both bases are sound.

As to the first, the axiom of Aristotle is most true when understood with the proper conditions, which St. Thomas treats in various places: in 1. p. q. 87, art. 2, ad 3; in 1. dist. 12, q. 1, art. 2, ad 2⁵; in 2. Metaphysics, lect. 2⁶; and in 1. Posterior Analytics, lect. 6⁷. In sum, its truth reduces to three conditions. First, cause and effect must be distinct, and the same form must not belong to both. Second, effect and cause must share the same denomination, and one must be said to be such on account of the other—not in just any way, but because the other is also such—so that the denomination of one gives rise to the denomination of the other. Third, the character in which cause and effect share must admit of more and less. The counterexamples given, and similar ones, fail for lack of the second condition because they do not share the same character and denomination. Whiteness is not white, health is not shed, and species do not understand. The argument “The Son breathes the Holy Spirit because of the Father, from whom he receives this, therefore the Father breathes more” fails for lack of the first condition, because both breathe through the same spirative form.⁸ But this will work: “The moon is luminous because the sun is luminous; therefore, the sun is more luminous,” because the moon shines not merely somehow on account of the sun but on account of the sun’s very light. Thus the very character or denomination shared by cause and effect is the cause of something’s being such, as Cajetan aptly notes in his exposition of this chapter 2.

As to the second principle, that the premises are equivocal causes, the answer is that they are truly equivocal causes and are not purely instrumental but principal in their own order, namely in the order of illuminating the conclusion. This is so even though they are moved by the intellective power, with respect to which they are related as an instrument—just as the heavens are called an instrument with respect to an angel, although the heavens, once moved, are an absolute principal cause with respect to lower things. Likewise, every power and virtue of a thing is called its instrument; yet it is not properly an instrument but a form of acting. Otherwise, every habit supervening upon the intellect would have to be called an instrument, which it is not properly called, since it is properly related to the principal agent as a form of acting. A purely instrumental cause presupposes that the principal cause is perfect in act; it actuates and perfects it, but serves and assists it. If, however, it perfects and actuates the cause itself so that it may act, then, even if by determining and completing it, it belongs to the principal cause; but it has a certain likeness to an instrument insofar as it is a power that comes to the principal cause, is subordinated to it, and depends on it. In this way the premises are related to the intellect as a rationale and light that determines its indifference to illuminating and inferring the conclusion.