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.

A demonstrable proposition has two conditions: first, that it concerns necessary matter; second, that it is proved and illuminated by some middle term. By reason of necessity it is opposed to opinion; by reason of the middle term it is opposed to a proposition known through itself, that is, one lacking a middle term. Thus, to distinguish demonstrable from non-demonstrable propositions, these two matters must be explained: namely, how a proposition requires necessary matter, and which propositions are known through themselves.

Concerning the first point, it is certain according to Aristotle, in this first book, chapters 6 and 7¹, that demonstration must proceed from necessary and per se principles.

There are, nevertheless, SOME MODERN AUTHORS who think that a true demonstration can also concern contingent matter, as Vázquez indicates in his commentary on the First Part, disputation 4, chapter 7, and Cabero here, disputation 2, doubt 3; they require only that the acts be certain and evident. Hence, in an imperfect demonstration, such as one from an effect, there could be knowledge of contingents. For this syllogism—“Every animal becomes warm while it runs; Peter runs and is an animal; therefore, he becomes warm”—is neither probable nor erroneous; therefore it is demonstrative.

This can be confirmed in physics, which is a true science and yet deals with many contingents, such as the fact that there is heat in summer and cold in winter, and so on, which could occur otherwise. Finally, it is confirmed in theology, which has many contingents as conclusions, deduced from two propositions of faith or at least one natural proposition, and yet is a science that is absolutely certain and infallible. Likewise, divine faith itself concerns and believes many contingents on the part of its material object, and yet it is infallible.

If it is said that faith has this character by reason of the divine testimony on which it formally rests, not by reason of its material object, we will say the same about science: by reason of its formal character and act it will be certain and infallible, yet it will not have anything necessary as its material object.

BUT THESE POINTS DO NOT OBSTRUCT our assertion, although some ancient philosophers, moved in part by the second argument, denied that true science exists; among them were the Academics, and Heraclitus and Cratylus held the same view. Plato partly agreed with them, thinking that there is no science of corruptible things. Yet, so that he would not deny science altogether, he posited separate Ideas of which there could be science, as we reported above from St. Thomas, q. 3, art. 2. That science must concern a necessary object is clear from this: scientific assent must be certain and firm concerning the conclusions inferred; otherwise it would not be science but opinion, nor would it be an intellectual virtue, since it would be imperfect and weak. A virtue, however, must be a disposition of what is perfect. But a certain and firm assent cannot be had if the connection is not necessary but contingent, since assent must be firm in truth, which is conformity to being or non-being. If, then, someone says with certainty and firmness that something is or is not, while in reality it is contingent, it can change in reality; and then either the assent changes or it does not. If it changes, such science no longer remains, but its opposite does. If it does not change, it is falsified, because reality is otherwise than the assent. Therefore it is incompatible with science for a firm and certain assent to concern a contingent object.

To the first argument, then, the reply is that neither in a priori nor in a posteriori science can there be a certain and evident act concerning contingent matter. In the syllogism given, it is clear that it is not demonstrative but probable, because the minor premise—“Peter is an animal and runs”—is not certain in the part “and runs,” but contingent; and so it infers a probable conclusion. In natural philosophy, however, there are demonstrations about things that could occur otherwise, though not according to a contingent connection, but a necessary one. For example, that there are rains in winter is contingent with respect to the event, yet it is an infallible and necessary connection that at that time rains are natural and generally due; and this is wholly necessary.

To the confirmation, the reply is that theology does not rely on the connections or truths of things as they are in themselves, but on them insofar as they are subject to virtual revelation and a higher light. Although things in themselves have contingent connections, with respect to God and insofar as they are subject to his knowledge they add an infallible connection. Our theology is subalternated to divine science and presupposes that its principles are known there evidently; consequently, there they are considered according to infallible and immutable connections. Hence, formally speaking, theology does not concern contingent connections but rather infallible ones presupposed—that is, insofar as it presupposes that they are evidently proved in divine science—even though they are contingent with respect to their proximate causes, as St. Thomas teaches in Summa theologiae I, q. 14, art. 13, which is usually explained at greater length there. It is proper to a subalternated science to have its evidence and certainty presupposed in the higher, subalternating science, as we shall say in the next question, where we will also discuss theology's subalternation.

As to what is added about faith, the reply is likewise that faith does not derive its infallibility from things themselves but from divine testimony, as is usually taught in Summa theologiae II–II, q. 1. To the further objection, the reply is that there is a difference between faith and science, because science is received from things themselves and uses one truth to illuminate another. Therefore, if the truth is not firm and immutable, its illumination will not be firm and certain either. Thus, from the contingency of the object and the non-necessary connection, one rightly infers a contingent and fallible formal character. Faith, however, does not derive its formal character from the connection of things, but from divine testimony, which is extrinsic to the things themselves but most certain and infallible in itself; therefore it can concern contingent things without doing so contingently.

FROM THESE POINTS IT FOLLOWS what other conditions belong to demonstration on the part of the object demonstrated: namely, that it concern universals and what is perpetual, and proceed from proper principles. It must concern what is perpetual, not positively in existing, but objectively, by grounding a truth that does not depend on a mutable connection. It must also concern universals, because science concerns necessities; a necessary connection is found only between essential predicates, and between a subject and its properties. Essential predicates belong to the definition of a thing; but a definition is not given of singulars as singulars, but of the thing's essence itself, which is common and belongs to the species. A proper property, however, flows from the principles of the essence, not from the principles of individuation; thus the connection of proper properties is not with singulars as singulars. Finally, demonstration must proceed from proper principles and not extraneous ones, because it must proceed from things necessarily and per se connected. But it is incompatible for something to be per se connected with another and yet extraneous to it, since nothing is more proper than that on which something per se depends and with which it has a per se, that is, intrinsic, connection. Even if demonstrations in mathematics sometimes proceed according to extrinsic relations, a proportion or adaptation of one thing to another that is wholly intrinsic is presupposed there; thus, by reason of the relation included, they do not proceed wholly from extrinsic principles, although that relation is not an effect or cause but a proportion. And what is demonstrated by supernatural light, although extrinsic, is nevertheless derived from God, in whom there are immutable and infallible connections with things, however contingent they may be. Therefore that manifestation is ultimately resolved into something intrinsic, at least on the part of the relation that all creatures have to the first cause and its ordering.

Concerning the second point to be explained in this article, namely, which propositions lack a middle term and are called known through themselves, two matters seem to require explanation. First, must propositions known through themselves lack every a priori and intrinsic middle term, or also an extrinsic and a posteriori one? Likewise, although they lack a middle term in one science, can they nevertheless be proved by another, for example, by metaphysics or another higher science? Second, specifically concerning propositions in which a first property is predicated of a subject, are they absolutely indemonstrable?

To the first difficulty the reply is that, absolutely speaking, it suffices for a proposition known through itself to lack an intrinsic middle term; it need not also lack an extrinsic middle term, whether through effects, through an extrinsic cause (efficient or exemplary), or through a reduction to impossibility. The reason is that, by the very fact that something is united to another immediately through itself, it has within itself a sufficient principle for the connection of the extremes to be known immediately once the terms are known and understood, since they are united and connected immediately. Thus their conjunction can become known without any middle term other than the terms themselves. Whatever is known, from the explanation of the terms alone, to be connected with another is the object of a proposition known through itself—that is, a proposition whose connection is knowable from the explanation of the terms. Therefore, an extrinsic middle term does not prevent a proposition from being known through itself, since it is knowable from its own principles and intrinsically, by knowing the terms alone; thus it is called per se known in itself. Only accidentally and with respect to us can it be called not per se known, if the terms themselves are not commonly known to us. By “terms” we do not mean words and concepts, but the things signified by them, insofar as the connection of the extremes becomes known through their simple explanation, without proof. I say “simple explanation” because of angelic cognition, which by a simple intuition penetrates both principles and conclusions; but this is so because, by its eminence, that simple mode is equivalent to our scientific mode of knowing through discourse and proof. For a proposition to be known through itself, however, it must become known through a simple explanation of the terms, without any middle term for proving or inferring it, either formally or virtually.

From this it is inferred that all propositions containing a definition or an essential predicate are absolutely indemonstrable, even if they are not first principles containing the most common predicates. For, by the very fact that something is immediately connected with another and belongs to its concept, once the terms alone are explained, the connection of the extremes is knowable in itself, without any other circuit of reasoning or proving middle term.

It is inferred, secondly, that there is no incompatibility in propositions known through themselves being proved by an extrinsic middle term or by a reduction to impossibility; for this does not oppose the immediate and intrinsic connection of the predicates. For this reason metaphysics explains and defends all the other principles, not ostensively, but by reducing them to impossibility and to that highest principle: “Everything either is or is not.”

You will say: A reduction to impossibility is equivalent to an ostensive demonstration of the truth, because a reduction to impossibility shows the falsity of the opposite proposition and therefore the truth of its own principle. For whoever asserts the falsity or impossibility of one side asserts the truth of its opposite, since the same thing cannot be affirmed and denied.

The reply is that a reduction to impossibility proceeds only from the supposition that some conclusion is denied and some premise granted; thus, from the opposite of the denied conclusion, it infers the opposite of what was granted. But this does not show the truth of the conclusion itself determinately and in itself. Rather, it shows that if the truth of the inferred proposition is denied, one must grant two contradictories among the granted premises. It does not demonstrate how or from what the proposition has its truth.

It is inferred, thirdly, that when we take as premises or principles something proved by another science through intrinsic proof—as occurs in a subalternated science with respect to its subalternating science—those are not principles absolutely, but conclusions demonstrated by another science. This is not absolutely to lack an intrinsic and a priori middle term, but for that middle term not to be reached by this lower science, just as in the same science one demonstrated conclusion can be taken as a principle for demonstrating another conclusion. How a subalternated science uses principles proved by its subalternating science will be discussed in the next question. Thus Aristotle is understood when he teaches that some principles are absolutely indemonstrable, while others are indemonstrable in a qualified sense. Those are absolutely indemonstrable that lack an intrinsic middle term; those are indemonstrable in a qualified sense that are not demonstrated by a lower science but by a higher one. Nevertheless, it is also possible for propositions absolutely indemonstrable to be proved through some extrinsic middle term. Hence it happens that in the sciences their subjects are sometimes demonstrated a posteriori, through extrinsic causes, or from another science to which they are subalternated. Therefore, it belongs to a science only to presuppose of its subject what it is—which is to lack an intrinsic middle term pertaining to its quiddity—not an extrinsic middle term that does not pertain to what it is.

You will say: What if a middle term demonstrating a proposition known through itself a posteriori and its knowledge from the terms occur at the same time? How will the intellect stand?

The reply is that these two kinds of knowledge can coexist in the intellect, because they proceed through different middle terms, just as one object could be known through different sciences. They cannot, however, belong to the same act, because one act is of only one species and, consequently, of one middle term and one specifying principle. But it is not one specifying principle to know something from a simple explanation of the terms and to know it a posteriori through an effect. For even propter quid knowledge and quia knowledge differ in species, as we shall say in article 4. Nor can one species contain within itself lower differences unless it belongs to a higher order, which does not appear to be the case here.

Concerning the second difficulty, note only that a first property flowing from a subject can be compared either with the subject itself, really and in itself, or with its definition, through which it is explained to us. If it is compared with the subject in itself, it lacks a real middle term, because no middle term is given between it and the subject; but it does not lack a middle term distinct by reason, namely, the definition, which is distinguished by reason from the subject and through which the property is proved of the subject. For example, it is proved of a human being that he is teachable because he is a rational animal. If, however, the property is compared with the definition itself, to which it is immediately connected, it renders the proposition indemonstrable, that is, devoid of a middle term. Nor does it matter that the property flows from the essence and so can be known through the essence itself. It has this immediately, that is, without an additional real middle term, and thus it lacks a middle term, although it has a subject from which it flows. The middle term that is the definition is not really distinct from the defined thing, which means that the middle term is not distinct from the subject.

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.

In the preceding question, article 1, we said that the question whether something exists concerns only existence or possibility—that is, whether some thing is given—yet not the cause or root on account of which it is given. The same procedure is to be followed in assigning the difference between demonstration quia and demonstration propter quid. For they differ chiefly in this: demonstration quia intends only to show evidently that something is true, that is, that it really obtains, without treating how it is true or the cause on account of which it obtains; demonstration propter quid investigates this cause.

The Philosopher distinguishes these demonstrations in Posterior Analytics, chapter 11 (otherwise 10)¹, both with respect to different sciences and with respect to one and the same science, for they can be found in either case. They occur in different sciences because many sciences do not know the cause and root of some thing, but know evidently only that such a thing exists, whether those sciences are disparate from one another or one is subordinate to another: knowing the why belongs to the subalternating science, and knowing the that to the subalternated science. We shall explain this more conveniently in the next question, when treating how subalternating and subalternated sciences differ. In one and the same science the Philosopher distinguishes these demonstrations by their different modes of proceeding; for, as St. Thomas observes in Posterior Analytics, lecture 23², a demonstration must proceed from true and immediate causes. Hence a demonstration can fall short of being propter quid either because it proceeds from effects rather than causes, or because it proceeds from remote rather than immediate and proximate causes, which are not the determinate root of this truth. For example, if someone proves that a stone does not breathe because it is not an animal, he gives a remote cause, since some animals do not breathe; hence this chiefly serves for negative demonstrations.

From this one may incidentally gather that some people, with insufficient care, confuse demonstration propter quid with demonstration a priori, and demonstration quia with demonstration a posteriori. This is not so: although every demonstration propter quid is a priori, the converse does not hold; and although every demonstration a posteriori is quia, the converse does not hold. For demonstration quia consists only in showing a truth, but not its proper and immediate root. That a truth obtains can sometimes be shown through something posterior, namely an effect; sometimes through something prior, namely a remote cause; and sometimes through something concomitant. Thus not every demonstration quia is only a posteriori, that is, from an effect; sometimes it proceeds through something prior, namely a remote cause. But every demonstration propter quid is always a priori, because it is always through a cause, and a proximate and immediate one.

Two things, then, remain to be explained here: First, whether this division is adequate; second, what sort it is, whether a division of a genus into species or of an analogue into its analogates.

As to the first, it should be said that this division is adequate; this is the common view, although the Commentator is commonly credited, at the beginning of the Physics, with adding another member of demonstration, which he called demonstration simpliciter, namely one that demonstrates not only the why but also that the thing exists. Others say that demonstration from a sign is neither propter quid nor quia.

NEVERTHELESS, OUR ASSERTION IS PROVED as follows: this division is given through members immediately opposed, one of which entails the contradictory negation of the other. For demonstration quia is that which presents some truth without showing its proper and particular root, whether this is done through a remote cause, an effect, or something else with which that truth has a per se connection, although it does not arise from it. Demonstration propter quid, however, is that which shows some truth according to its own proper cause and root, known as such. For an immediate, proximate cause is the contradictory opposite of a remote cause. Therefore these demonstrations differ by immediate opposition and thus adequately exhaust what is divided. This does not happen with demonstration a priori and a posteriori, because a demonstration can be made through something that is neither prior nor posterior, but concomitant, something simultaneous with another; for example, correlatives are simultaneous, and one is demonstrated through the other, as when, if there is a father, there is a son, and yet they do not stand as prior and posterior. Likewise, in mathematics demonstrations frequently occur that are founded on some proportion or correspondence between lines or other figures, without the notion of cause or effect intervening. To this also belong demonstrations drawn from acts of cognition or seeing, as when you say, “The stone is seen by me; therefore the stone exists”; and yet the stone’s being seen is neither the cause nor the effect of the stone’s existence. Whether demonstration propter quid and demonstration quia can be divided into other members, as the Commentator seems to hold in the cited place, we shall say in the solution of the last argument.

But you may ask what we mean by a remote cause and a proximate cause. The answer is that, as understood from Master Soto in Posterior Analytics I, question 5, and Cajetan on chapter 12 of Posterior Analytics I, a remote cause is one that is not convertible with its effect; for a remote cause influences its effect only remotely, and so exceeds it. When it is convertible with its effect, formally speaking and per se, it is called a proximate cause.

That a cause is not formally and proximately convertible with its effect can be considered in three ways. First, although it is convertible with the effect, it is not so immediately, but something must intervene between cause and effect, as essence considered with respect to the third and fourth properties, which it causes through the first or second. Second, by the opposite extreme, a cause is called remote when it is not convertible with its effect, nor does it entail the effect or follow from it, although it sometimes produces such an effect. For example, one might say that someone has a fever because he has an agitated pulse: sometimes an agitated pulse occurs without fever, as in someone running; sometimes, conversely, fever occurs without an agitated pulse, as in someone dying. Third, a cause is called remote when it is not adequately convertible with its effect, yet is a sufficient cause for inferring the effect’s negation, though not for positively positing the effect. Thus “It is not an animal; therefore it does not breathe” is valid, whereas “It is an animal; therefore it breathes” is not; and so the term “animal” is called a remote cause of breathing. To this belongs the example the Philosopher gives here of the man who, asked whether there were flute players in Scythia, replied that there were not even vines—a truly very remote cause.³

As for the character of this division, whether it is univocal or analogical, THE WHOLE DIFFICULTY comes down to whether both demonstrations cause knowledge simpliciter, or only demonstration propter quid. For the definition given above seems to belong to the latter alone: to know is to cognize the cause on account of which a thing is, and that this is its cause. Therefore the demonstration that does not cognize the cause on account of which a thing is does not simply produce knowledge, and so it agrees analogically with demonstration propter quid in the notion of scientific demonstration. On the other hand, demonstration quia and propter quid seem to agree univocally, since demonstration quia has certainty and evidence concerning its object; therefore it is opposed to opinion in the same way as knowledge propter quid. Opinion is uncertain and lacking evidence. Therefore it has the substance and essence of knowledge, since it has the substance and essence of evidence and certainty, which oppose and destroy opinion; thus it belongs to knowledge.

Nevertheless, one should say that demonstration or knowledge quia intrinsically and substantially has the nature of demonstration, insofar as it has certainty and evidence; thus it is absolutely a univocal demonstration according to the formal mode of proceeding certainly and evidently. But it participates imperfectly in the nature of knowledge, because it does not deal with a perfectly scientific object, which is quiddity and what follows upon quiddity; rather, it deals with the very question whether something exists, without attaining the root and cause of the truth on account of which it exists.

That it makes a true and proper demonstration on the side of certainty and evidence is deduced from St. Thomas, Summa theologiae I, q. 2, a. 2, where he proves that there can be a demonstration that God exists, although we proceed through effects, which are better known to us. The reason is clear. For demonstration quia rests on a necessary connection between effect and cause, or between a remote cause and an effect, as when through necessary connection it is proved that everything that comes to be comes to be from another, and that there is no infinite regress. Likewise, in negative demonstrations the negation of a remote cause rightly entails the negation of the effect, although the effect does not follow from the cause’s positive presence alone. Thus “It is not an animal; therefore it does not breathe” is valid, but not positively, “It is an animal; therefore it breathes.” Demonstration quia, then, is certain and evident.

But that on the side of the object it attains it is not perfect knowledge is proved because it does not attain the what, but only whether the thing exists. Yet the question whether it exists is presupposed to knowledge; hence no science can supply principles for proving whether its subject exists, but must presuppose these from elsewhere. Therefore demonstration quia necessarily proceeds from things external to the object, although not external to the connection with the conclusion demonstrated. Yet science that is properly and perfectly science does not proceed from things external, as the Philosopher proves in Posterior Analytics I, chapter 7⁴. Therefore demonstration quia deals only with preambles to science, not with the proper object of science, which is the what. Hence knowledge quia can belong and be reduced to the same knowledge propter quid. Although it proceeds from extraneous principles and in this respect seems to be of a different species, it is of a different species only imperfectly, like an embryo of knowledge serving the principal science in a ministerial way. For it deals with preambles and presuppositions to science, namely the question whether a thing exists, which will be explained better in the solution to the last argument. How it belongs to a subalternated science to know the that, and to a subalternating science to know the why, will be explained in the next question. This resolves the reasons for doubt raised at the beginning of this little question.

THE ARGUMENTS ARE SOLVED.

Against the first conclusion one argues, because on the one hand more demonstrations than propter quid and quia seem to be given, and on the other hand fewer. More seem to be given. First, there can be the demonstration that the Commentator in Physics I calls demonstration simpliciter, namely one that demonstrates both that the thing exists and why it exists, which is at once demonstration propter quid and quia. Again, demonstration through a sign demonstrates neither through a cause nor through an effect adequate to the thing; therefore it is a third kind of demonstration. Again, demonstration leading to the impossible, and likewise negative demonstration in which some negation is taken as the middle term, proceed neither through a cause nor through an effect, since neither negation nor impossibility is the cause or effect of the thing demonstrated. Finally, demonstration in which something is inferred to belong to an inferior from some superior predicate is neither quia nor propter quid, as in this syllogism: “Every animal is a substance; every human being is an animal; therefore every human being is a substance,” where the term “animal” is neither cause nor effect with respect to substance.

To the first example Cajetan replies in Posterior Analytics I, chapter 13, that the Commentator’s demonstration is not intermediate between demonstration quia and propter quid, but subdivides demonstration propter quid, as if to say: one demonstration is propter quid only, and another demonstrates both propter quid and at the same time that the thing exists. It seems truer, however, that demonstration propter quid always includes demonstration quia virtually and eminently. For one who demonstrates the cause of a truth, all the more demonstrates that such a truth obtains; but not conversely, for one who demonstrates that a truth obtains does not thereby also demonstrate the cause on account of which it obtains.

To the second example it is said that demonstration through a sign of itself proves only that the thing exists, and does not show its cause and root, whether the sign is an effect, a remote cause, or something concomitant; hence it belongs to demonstration quia.

To the third one replies that the demonstration of which the Philosopher treats here can be said to be only an ostensive demonstration; nevertheless, even demonstration by reduction to the impossible is reduced to demonstration propter quid or quia. For if it leads to the impossible through the causes of that impossibility, it is propter quid; but one that leads to the impossible from effects is demonstration quia. Thus, if you say, “If a horse reasons, it follows that it is rational,” the reasoning proceeds through effects. But if you say, “If a stone is alive, it follows that it moves itself,” it is propter quid. As for negative demonstration, we say that a negative can also in its own way be the cause of a negation, as “It is not an animal; therefore it is not rational” is valid. Thus, when the proper and immediate cause for denying something is brought forward, the demonstration is propter quid.

To the fourth it is said that this is demonstration quia: it proves only that such a truth obtains, without adducing its proximate and adequate cause, but rather an identical and remote one; for “animal” is not the proper and sole cause of something’s being a substance. However, when one proceeds from universal to singular, as in “Every human being is capable of laughter; therefore Peter is,” either this is not a proper demonstration but an exposition of the parts contained in the universal, or, if it is a demonstration, it is propter quid, for it presents the cause on account of which Peter is capable of laughter.

The second argument is: Demonstration quia, however certainly and evidently it proceeds, does not quiet the intellect, but leaves it still suspended until it knows the cause and root of the truth. But it is proper to knowledge to quiet the intellect; hence St. Thomas says in Posterior Analytics I, lecture 18⁵ that to know from proper principles alone is truly to know. And in lecture 23⁶ he says that demonstration propter quid is demonstration simpliciter. Therefore demonstration quia is not simply and univocally demonstration.

It is confirmed because demonstration quia is not composed of premises that are necessary without qualification; therefore it is not demonstration without qualification.

The antecedent is proved: the premises are either a remote cause or an effect. A remote cause does not have a necessary connection with its effect, as being an animal with being capable of breathing. Effects, too, are either supposed known through a cause or through experience. If through a cause, that demonstration will be propter quid; if through experience, its cognition is fallible and consequently does not ground a necessary demonstration.

The answer is that knowledge quia is imperfect knowledge and not knowledge simpliciter on the side of its object, because in that object it attains not the what but whether it exists. But with respect to what it does attain, it perfectly quiets the intellect, namely with respect to whether it exists, although it leaves the intellect unconvinced and unquiet with respect to what it is, since that does not pertain to it. In this respect that demonstration is imperfect, because it does not attain the notion of quiddity. Nor does St. Thomas mean more in those places where he attributes the nature of demonstration simpliciter only to demonstration propter quid: that is, if it is considered on the side of the perfectly scientific object, which is quiddity, for this it does not attain without qualification. But if it is considered according to the mode of attaining scientifically, that is, certainly and evidently, then demonstration quia too is demonstration simpliciter.

To the confirmation one replies that a remote cause serves chiefly for negative demonstration when it is not convertible with its effect, as “It is not an animal; therefore it does not breathe” is valid, but not positively, “It is an animal; therefore it breathes.” If, however, the remote cause is convertible with its effect, as when a mediated proper property is inferred from some essence, then one may also validly proceed positively from a mediated or remote cause. Nor can it be said that, in negative demonstration, the negation of a remote cause makes the demonstration propter quid, as when one demonstrates that a stone does not breathe because it is not an animal. This, I say, cannot be said, because although that negation sufficiently establishes the negation of breathing, since it does not deny the proper and immediate cause of breathing, it does not present the negation through its proper and immediate cause. For the proper reason for a negation is known through the immediate opposing form.

As for what is added about effects, they are per se known when they are known through certain and indubitable experience, or at least made evident inductively, because every science has its origin in induction; for example, when we show from effects that there is a first cause, it is indubitable that some effects exist.

The final argument is: Demonstration quia and propter quid proceed from different principles and under a different light, one from effects and the other from causes. Therefore they ought to generate habits different in species, because a scientific habit differs according to diversity of principles and light. Demonstration quia is therefore not reduced to knowledge propter quid, since it is not reduced to its principles.

THE ANSWER IS that if demonstration quia and propter quid proceed in different sciences, whether placed in a subalternating relation or disparate, then it is clear that they also belong to different habits. But if both demonstrations proceed in the same science—insofar as demonstration quia touches the question whether the object exists, and demonstration propter quid the question what it is, as, conversely, in theology God’s existence is proved by demonstration quia—then some say that, although demonstration quia and propter quid proceed from different principles and so are different in species, they nevertheless generate the same assent in species and consequently the same habit, just as heat produced by fire and by the sun is of the same species. So says Master Soto, Posterior Analytics I, question 5. Others, such as Master Cabero, say those assents are different in species.

But it seems to me that this can be resolved more clearly from Cajetan’s view in Summa theologiae I, q. 2, a. 3, where he says that, since no science proves from its own proper principles that its subject exists, but does so from extraneous principles appropriated to it, when those extraneous principles are better known to us, theology proves that God exists not from its own principles simply, but from principles proper to it ministerially, namely those known by natural light that serve theology. Hence we say that although demonstration quia, when it occurs in the same science in which one proceeds propter quid, proceeds from extrinsic principles and consequently principles distinct from those of demonstration propter quid, nevertheless, because they are appropriated to the object of that science and dispose one toward it—since they concern whether it exists and prepare one to understand its quiddity and demonstrate properties of it—demonstration quia is said to be reduced to demonstration propter quid. For although it proceeds from different principles, they are nevertheless appropriated to the object of demonstration propter quid, disposing and preparing for it through a demonstration of the thing with respect to whether it exists. And although the assents are different in species if these demonstrations are considered in themselves and separately, as it were in their entity, insofar as they are coordinated and one is appropriately ordered to the other, preparing for it, demonstration quia belongs reductively to the same species of knowledge as demonstration *propter quid—not absolutely, but appropriately and reductively, or dispositively—just as dispositions toward a substantial form, although entitatively, are of a distinct genus.