COMMENTARY ON THE
POSTERIOR ANALYTICS OF ARISTOTLE

PREFACE

The purpose of logic is to provide an analytic guide to the discovery of demonstrated truth and all its various approximations throughout the philosophical sciences. In the words of St. Albert the Great, logic “teaches the principles by which one can arrive at the knowledge of things unknown through that which is known” (De Praedicab., tr. I, c. 5, ed. Borgnet 1, 8b). St. Thomas defines logic as an art “directive of the acts of reason themselves so that man may proceed orderly, easily and without error in the very act of reason itself” (Foreword). Logic is thus a construct based on the natural processes of the mind invented for a very specific use, namely, scientific reasoning. Because it is a construct, logic is said to deal with “second intentions,” that is, deliberate constructs of the mind, existing solely in the mind, of ideas based upon the way human beings know reality (“first intentions”), such as predicables, subject, predicate, major premise, minor premise, middle term and conclusion. The analysis and construction of this guide is the scientific, or theoretical, aspect of logic. Under this consideration, logic is itself a science and it is this aspect that modem logicians seem to be interested in. Nevertheless the purpose of this construct is that it be used by thinkers who want to get on with the discovery of truth in the various sciences. In this way the whole of logic is a methodology, solidly established by analysis, to guide the mind in its quest for answers to problems raised in scientific inquiry. The general name given to all of Aristotle’s logical treatises is Organon, the instrument. For this reason Boethius, the 6th century translator of most of Aristotle’s Organon, says that logic is “not so much a science as an instrument of science” (Comm. super Porphyry, ed. 2a, 1, c. 3; see St. Thomas, In Boeth. de Trin., q. 5, a. I ad 2; St. Albert, Post Anal. I, tr. I, c. 1, ed. Borgnet II, 2b).

It must be noted, however, that logic is only a general methodology common to all scientific knowledge (See J.A. Weisheipl, “The Evolution of Scientific Method,” The Logic of Science, ed. V.E. Smith—New York: St. John’s Univ. 1964—59-86). There is over and above this a particular logic peculiar to each field of knowledge. That is to say, the proper method of natural philosophy is not at all identical with that of mathematics, metaphysics or moral philosophy. Logic, or general methodology, must be understood before any of the particular sciences are investigated and organized systematically. This, at least, was the common view accepted by all scholastic thinkers, even though this was not the actual procedure followed in medieval universities (see J.A. Weisheipl, “Classification of the Sciences in Medieval Thought,” Mediaeval Studies, 27 (1965)89).

In studying methodology, or the common logic of all the sciences, Aristotle and those after him followed a logical order which considered problems arising from each step of logical thinking. The scholastics thought they had found this order in the various books of logic. Thus according to St. Thomas (Foreword) the predicables (in the Isagogy of Porphyry) and the categories (in the De praedicamentis of Aristotle) deal with universals that are begotten by the first act of the mind. Propositions, or enunciations (in the Peri hermeneias of Aristotle) deal with constructs of various types of judgement in the second act of the mind. These two areas of logical investigation are prior to the analysis of reasoning itself, the third act of the mind. St. Thomas recognized that there are two types of analysis, or resolution, to be considered: the formal structure of reasoning, which Aristotle discusses in the Prior Analytics, and the material structure of the premises, which can be of three kinds, namely necessary and scientific (considered in the Posterior Analytics), probable and dialectical (considered in the Topics), and erroneous and false (considered in the Sophistici Elenchi). Of all these branches of logic, the most important is the Posterior Analytics, the only logical book commented upon in full by St. Thomas Aquinas. St. Albert clearly states that the Posterior Analytics is the apex, the most perfect and only absolutely desirable (simpliciter desiderabile) study among the logical works of Aristotle (Post. Anal., 1, tr. 1, cap. 1, ed. Borgnet II, 2b). And the Leonine editors of the works of St. Thomas state that “the posterior analytics deal with demonstration and thus are the ultimate goal of the whole science of logic” (Praef. ed. Leon., 1, p. 131).

No one has ever doubted that the Posterior Analytics is an extremely difficult work to understand. Even Themistius, paraphrasing the Greek text, found much to complain about (Paraphrasis in lib. Post., praef.). According to John of Salisbury, after the text was translated into Latin, there was scarcely a master willing to expound it because of its extreme subtlety and obscurity; “there are almost as many stumbling blocks as there are chapters” (Metalogicon IV, c. 6, ed. Webb 171). However, John blames most of this on the bungling mistakes of scribes and he proceeds to give the Latin West the first paraphrase of Aristotle’s difficult work. Part of the difficulty seems to be that this is an early work of Aristotle, for the terminology is not yet fixed and especially in the First Book, Aristotle seems to approach the same point from many directions, giving the reader the impression that many different points are being made. The best guides for understanding Aristotle are St. Thomas Aquinas, St. Albert the Great, Averroes and Robert Grosseteste.

When reading St. Thomas’ commentary one must not only read the text of Aristotle first, but one should have a pencil and sufficient paper to outline the text as understood by St. Thomas. Division of the text was always one of the basic tools of the scholastic method. Therefore it is important to keep in mind this outline in order to understand the point about to be made and to appreciate it in the context of the work as a whole. Clearly Aristotle himself wrote according to a systematic order, and it is up to the reader to appreciate this order.

Since St. Thomas did not know Greek, he had to rely on one of the many Latin translations of the Posterior Analytics available to him. At the time St. Thomas wrote his commentary, around 1270, there were four Latin translations from the Greek and two from the Arabic. Even though it seems that Boethius himself translated the work, the Posterior Analytics had to come into the Latin West anew in the 12th century as part of the logica nova. The common text in the Middle Ages was the version made by James of Venice before 1159; it was the “vulgate text” (Arist. Lat., IV.2) in use during the second half of the 12th century and the earlier part of the 13th century. A very influential version from the Arabic was made by the translator, probably Michael Scott, of the works of Averroes together with the Commentator’s views between 1220 and 1240. St. Thomas was undoubtedly familiar with these two translations, but he most likely relied on the revised version made by William of Moerbeke in the second half of the 13th century (Arist. Lat., IV. 4; cf. De Rubeis, Diss. XXIII, c. 1-2, ed. Leon., 1, cclix-cclxii).

The Posterior Analytics of Aristotle possesses a remarkable unity from beginning to end. The first chapter of Book I is a propaedeutic to the entire work; it poses the fundamental problem concerning the possibility of learning, that is, of demonstrative knowledge. Its point of departure is the problem posed by Plato in the Meno (80 D-86) where Socrates attempts to inquire into the nature of virtue, a subject about which he admittedly does not have full knowledge. Meno, intervenes and objects that all inquiry is impossible, for “a man cannot inquire either about that which he knows, or about that which he does not know; for if he knows, he has no need to inquire; and if not, he cannot, for he does not know the very subject about which he is to inquire.” Either we already know what we seek to learn, and this is not learning, or we do not know what we are seeking, and hence cannot know when we have found it. Plato solves this dilemma by his doctrine of remembering ideas already innate in the mind. The Sophists and nominalists, of the Academy took an opposite view and claimed that all learning is simply an aggregation of individual observations. In other words, the Sophists maintained that there can be no demonstrations, but only the acquisition of a totally new fact. Aristotle took a middle course between these two extremes that would have all knowledge in act or no knowledge in act by his ingenious doctrine of potentiality. Instead of saying that all knowledge is actually in the mind or actually not in the mind, Aristotle insists that all knowledge is potentially in the mind and the business of learning is to draw this potentiality into actuality. Basically it is the same solution Aristotle offers in the Physics to explain the possibility of real change.

In the very question posed for inquiry there is already some knowledge in the mind from which inquiry begins. The all important starting point for inquiry is the question or problem posed. Already we have some idea, if only tentative, of the subject of inquiry, and some knowledge of the predicate; otherwise the question would never have arisen. The purpose of inquiry is to find the definitive medium or middle term that will provide an answer to the question raised. This middle term must be one or all of the physical causes in reality; the mind will not rest until it has found a causal reason for the conclusion. However there are many different kinds of scientific questions that can be raised: whether something exists (an sit), what is it (quid sit), does it have this or that property (quia sit), and why is this so (propter quid). For Aristotle and for St. Thomas only a true, objective, invariable cause can produce demonstrations worthy of the name scientific. This cause or middle term cannot be found outside the area in question, for this would give only a probable view. In other words, if a question is raised concerning the physical world, then only an answer found within natural philosophy will do. One cannot, in this case, appeal to harmony, morals or metaphysics for the right answer. The cause must be found within the context of the question. The answer is not found despite the question or problem, but because of it.

Nothing could be farther from the truth than to think of all demonstrative knowledge as “deductive.” This is only rarely the case. Most scientific inquiry requires the reverse process of analysis or breaking down. Once a middle term, a true medium of demonstration, has been found in whole or in part, the result may be expressed in the form of a syllogism that can be tested according to all the rules described in the Prior Analytics and Sophistici Elenchi. Thus the syllogism is not a means of discovery, but rather a means of exposition of the truth acquired by analysis. In fact the syllogism itself can be expressed in a definition that explicitly states the reason. Aristotle calls such a definition a statement “which differs from the syllogism only in position.”

Although the Posterior Analytics is a scientific work that can be studied and understood in its own right, it cannot be fully understood until one can see this kind of process at work in the various Aristotelian sciences. The scholastics themselves did not grasp the significance of this work until they could see it at work in the other writings of Aristotle. The Physics and Ethics of Aristotle in particular helped to instruct the scholastic in its use. Only then could Albert the Great and St. Thomas apply this methodology to such new branches as theology. St. Thomas’ Summa theologiae is the crowning glory of the use that can be made by applying the methodology to a new realm of knowledge. The very first question of the Summa is a masterpiece of Aristotelian methodology.

Although the present English translation of St. Thomas’ commentary may seem to many to be excessively literal, it has the merit of following the procedure of William of Moerbeke, who rendered, apparently at the request of St. Thomas, a literal translation from the Greek lest any nuance be lost. It is hoped that those who are able will also consult the Latin text in difficult passages.

James A. Weisheipl, O.P.

Pontifical Institute of Mediaeval Studies Toronto, Canada

FOREWORD OF ST. THOMAS AQUINAS

As the Philosopher says in Metaphysics I (980b26), “the human race lives by art and reasonings.” In this statement the Philosopher seems to touch upon that property whereby man differs from the other animals. For the other animals are prompted to their acts by a natural impulse, but man is directed in his actions by a judgment of reason. And this is the reason why there are various arts devoted to the ready and orderly performance of human acts. For an art seems to be nothing more than a definite and fixed procedure established by reason, whereby human acts reach their due end through appropriate means.

Now reason is not only able to direct the acts of the lower powers but is also director of its own act: for what is peculiar to the intellective part of man is its ability to reflect upon itself. For the intellect knows itself. In like manner reason is able to reason about its own act. Therefore just as the art of building or carpentering, through which man is enabled to perform manual acts in an easy and orderly manner, arose from the fact that reason reasoned about manual acts, so in like manner an art is needed to direct the act of reasoning, so that by it a man when performing the act of reasoning might proceed in an orderly and easy manner and without error. And this art is logic, i.e., the science of reason. And it concerns reason not only because it is according to reason, for that is common to all arts, but also because it is concerned with the very act of reasoning as with its proper matter. Therefore it seems to be the art of the arts, because it directs us in the act of reasoning, from which all arts proceed.

Consequently one should view the parts of logic according to the diversity among the acts of reason.

Now there are three acts of the reason, the first two of which belong to reason regarded as an intellect. One action of the intellect is the understanding of indivisible or uncomplex things, and according to this action it conceives what a thing is. And this operation is called by some the informing of the intellect, or representing by means of the intellect. To this

operation of the reason is ordained the doctrine which Aristotle hands down in the book of Predicaments, [i.e., Categories]. The second operation of the intellect is its act of combining or dividing, in which the true or the false are for the first time present. And this act of reason is the subject of the doctrine which Aristotle hands down in the book entitled On Interpretation. But the third act of the reason is concerned with that which is peculiar to reason, namely, to advance from one thing to another in such a way that through that which is known a man comes to a knowledge of the unknown. And this act is considered in the remaining books of logic.

It should be noted that the acts of reason are in a certain sense not unlike the acts of nature: hence so far as it can, art imitates nature. Now in the acts of nature we observe a threefold diversity. For in some of them nature acts from necessity, i.e., in such a way that it cannot fail; in others, nature acts so as to succeed for the most part, although now and then it fails in its act. Hence in this latter case there must be a twofold act: one which succeeds in the majority of cases, as when from seed is generated a perfect animal; the other when nature fails in regard to what is appropriate to it, as when from seed something monstrous is generated owing to a defect in some principle.

These three are found also in the acts of the reason. For there is one process of reason which induces necessity, where it is not possible to fall short of the truth; and by such a process of reasoning the certainty of science is acquired. Again, there is a process of reason in which something true in most cases is concluded but without producing necessity. But the third process of reason is that in which reason fails to reach a truth because some principle which should have been observed in reasoning was defective.

Now the part of logic which is devoted to the first process is called the judicative part, because it leads to judgments possessed of the certitude of science. And because a certain and sure judgment touching effects cannot be obtained except by analyzing them into their first principles, this part is called analytical, i.e., resolvent. Furthermore, the certitude obtained by such an analysis of a judgment is derived either from the mere form of the syllogism—and to this is ordained the book of the Prior Ana1ytics which treats of the syllogism as such—or from the matter along with the form, because the propositions employed are per se and necessary [cf. infra, Lectures 10, 13]—and to this is ordained the book of the Posterior Analytics which is concerned with the demonstrative syllogism.

To the second process of reason another part of logic called investigative is devoted. For investigation is not always accompanied by certitude. Hence in order to have certitude a judgment must be formed, bearing on that which has been investigated. But just as in the works of nature which succeed in the majority of cases certain levels are achieved—because the stronger the power of nature the more rarely does it fail to achieve its effect—so too in that process of reason which is not accompanied by complete certitude certain levels are found accordingly as one approaches more or less to complete certitude. For although science is not obtained by this process of reason, nevertheless belief or opinion is sometimes achieved (on account of the provability of the propositions one starts with), because reason leans completely to one side of a contradiction but with fear concerning the other side. The Topics or dialectics is devoted to this. For the dialectical syllogism which Aristotle treats in the book of Topics proceeds from premises which are provable.

At times, however, belief or opinion is not altogether achieved, but suspicion is, because reason does not lean to one side of a contradiction unreservedly, although it is inclined more to one side than to the other. To this the Rhetoric is devoted. At other times a mere fancy inclines one to one side of a contradiction because of some representation, much as a man turns in disgust from certain food if it is described to him in terms of something disgusting. And to this is ordained the Poetics. For the poet’s task is to lead us to something virtuous by some excellent description. And all these pertain to the philosophy of the reason, for it belongs to reason to pass from one thing to another.

The third process of reasoning is served by that part of logic which is

called sophistry, which Aristotle treats in the book On Sophistical Refutations.

BOOK I

Lecture I
(71al-10)
THE NEED FOR PRE-EXISTENT KNOWLEDGE IN ALL LEARNING

a1. All instruction given— a3. The mathematical sciences— a4. and so are the two— a8. again, the persuasion

Leaving aside the other parts of logic, we shall fix our attention on the judicative part as it is presented in the book of Posterior Analytics which is divided into two parts. In the first he shows the need for the demonstrative syllogism, with which this book is concerned. In the second part he comes to a decision concerning that syllogism (71b8) [Lect. 4).

Now the need for anything directed to an end is caused by that end. But the end of the demonstrative syllogism is the attainment of science. Hence if science could not be achieved by syllogizing or arguing, there would be no need for the demonstrative syllogism. Plato, as a matter of fact, held that science in us is not the result of a syllogism but of an impression upon our minds of ideal forms from which, he said, are also derived the natural forms in natural things, which he supposed were participations of forms separated from matter. From this it followed that natural agents were not the causes of forms in natural things but merely prepared the matter for participating in the separated forms. In like fashion he postulated that science in us is not caused by study and exercise, but only that obstacles are removed and man is brought to recall things which he naturally understands in virtue of an imprint of separated forms.

But Aristotle’s view is opposed to this on two counts. For he maintains that natural forms are made actual by forms present in matter, i.e., by the forms of natural agents. He further maintains that science is made actual in us by other knowledge already existing in us. This means that it is formed in us through a syllogism or some type of argument. For in arguing we proceed from one thing into another.

Therefore, in order to show the need for demonstrative syllogism Aristotle begins by stating that some of our knowledge is acquired from knowledge already existing. Hence he does two things. First, he states his thesis. Secondly, he explains the character of prior knowledge (71a11) [Lect. 2]. Concerning the first he does two things.

First (71a1), he asserts a universal proposition containing his thesis, namely, that the production of knowledge in us is caused from knowledge already existing; hence he says, “Every doctrine and every discipline...” He does not say, “all knowledge,” because not all knowledge depends on previous knowledge, for that would involve an infinite process: but the acquisition of every discipline comes from knowledge already possessed. For the names “doctrine” and “discipline” pertain to the learning process, doctrine being the action exerted by the one who makes us know, and discipline the reception of knowledge from another. Furthermore, “doctrine” and “discipline” are not taken here as pertaining only to the acquisition of scientific knowledge but to the acquiring of any knowledge. That this is so is evidenced by the fact that he explains the proposition even in regard to dialectical and rhetorical disputations, neither of which engenders science. Hence this is another reason why he did not say, “from pre-existent science or intuition,” but “knowledge” universally. However he does add, “intellectual,” in order to preclude knowledge acquired by sense or imagination. For reason alone proceeds from one thing into another.

Then (71a3) he employs induction to prove his thesis; and first of all in regard to those demonstrations in which scientific knowledge is acquired. Of these the best are the mathematical sciences because of their most certain manner of demonstrating. After them come the other arts, because some manner of demonstrating is found in all of them; otherwise they would not be sciences.

Secondly (71a4), he proves the same thing in regard to disputative, i.e., dialectical, arguments, because they employ syllogism and induction, in each of which the process starts from something already known. For in a syllogism the knowledge of some universal conclusion is obtained from other universals already known; in induction, however, a universal is concluded from singulars made known in sense-perception.

Thirdly (71a8), he manifests the same thing in rhetorical arguments, in which persuasion is produced through an enthymeme or example but not through a syllogism or complete induction because of the uncertainty attending the matters discussed, namely, the individual acts of men in which universal propositions cannot be truthfully assumed. Therefore, in place of a syllogism in which there must be something universal, an enthymeme is employed in which it is not necessary to have something universal. Similarly, in place of induction in which a universal is concluded, an example is employed in which one goes from the singular not to the universal but to the singular. Hence it is clear that just as the enthymeme is an abridged syllogism, so an example is an incomplete induction. Therefore, if in the case of the syllogism and induction one proceeds from knowledge already existing, the same must be granted in the case of the enthymeme and example.

Lecture 2
(71a11-23)
EXTENT AND ORDER OF THE PRE-EXISTENT KNOWLEDGE REQUIRED FOR OBTAINING SCIENCE

71a11. The pre-existent knowledge— a16. Recognition of a truth

After showing that every discipline is developed from knowledge already existing, the Philosopher shows what is the extent of this preexisting knowledge. Concerning this he does two things. First, he determines the extent of pre-existing knowledge in regard to the things that must be known in order to attain knowledge of the conclusion, of which scientific knowledge is sought. Secondly, he determines the extent of pre-existing knowledge of the conclusion, of which scientific knowledge is sought through demonstration (71a24) [L.3]. Now two things are included in pre-existing knowledge, namely, the knowledge and the order of the knowledge. First, therefore, he determines the extent of pre-existing knowledge so far as the knowledge itself is concerned. Secondly, so far as the order of the knowledge is concerned (71a16).

In regard to the first it should be noted that the object of which scientific knowledge is sought through demonstration is some conclusion in which a proper attribute is predicated of some subject, which conclusion is inferred from the principles. And because the knowledge of simple things precedes the knowledge of compound things, it is necessary -that the subject and the proper attribute be somehow known before knowledge of the conclusion is obtained. In like manner it is required thatthe principle be known from which the conclusion is inferred, for the conclusion is made known from a knowledge of the principle.

Now the extent of pre-existent knowledge of these three items, i.e., of the principle, of the subject, and of the proper attribute, is limited to knowing two things about them, namely, that each is and what each is. But, as stated in Metaphysics VII, complex things are not defined. For there is no definition of “white man,” much less of an enunciation [proposition]. Hence since a principle is an enunciation, there cannot be preexisting knowledge of what it is but only of the fact that it is true. But in regard to the proper attribute, it is possible to know what it is, because, as is pointed out in the same book, accidents do have some sort of definition. Now the being of a proper attribute and of any accident is being in a subject; and this fact is concluded by the demonstration. Consequently, it is not known beforehand that the proper attribute exists, but only what it is. The subject, too, has a definition; moreover, its being does not depend on the proper attribute—rather its own being is known before one knows the proper attribute to be in it. Consequently, it is necessary to know both what the subject is and that it is, especially since the medium of demonstration is taken from the definition of the subject of the proper attribute.

This, therefore, is why the Philosopher says (71a11) that it is necessary to know beforehand in two ways; because two items are known beforehand concerning things of which we have pre-existing knowledge, namely, that it is and what it is. [Then he goes on to say] that there are some things concerning which it is necessary first to know that they are, such as principles, concerning which he then gives examples, citing as one example the first of all principles, namely, “There is true affirmation or negation about everything.” Again, there are other things, namely, proper attributes, concerning which it is necessary to know what is said to be predicated, i.e., what is signified by their name. And he does not say unqualifiedly, “what it is,” but “what is said to be predicated,” because one cannot properly know of something what it is before it is known that it is. For there are no definitions of non-beings. Hence the question, whether it is, precedes the question, what it is. But “whether a thing is” cannot be shown unless it is known beforehand what is signified by its name. On this account the Philosopher teaches in Metaphysics IV that in disputing against those who deny principles one must begin with the meanings of names. An example of this is “triangle,” concerning which one must know beforehand that its name signifies such and such, namely what is contained in its definition.

But since accidents are referred to their subjects in a definite order, it is not impossible for something which is an accident in relation to one thing to be a subject in relation to something else: for example, a surface is an accident in relation to a bodily substance, but in relation to color it is the first subject. However, that which is a subject in such a way as never to be an accident of anything else is a substance. Hence in those sciences whose subject is a substance, that which is the subject can never be a proper attribute, as in first philosophy and in natural science, which treats of mobile being.

But in those sciences which bear upon accidents, nothing prevents a same thing from being taken as a subject in reference to one proper attribute, and as an attribute in reference to a more basic subject. Nevertheless, this must not develop into an infinite process, for one must arrive at something which is first in that science and which is taken as a subject in such a way that it is never taken as a proper attribute, as is clear in the mathematical sciences, which treat of continuous or discrete quantity. For in these sciences those things are postulated which are first in the genus of quantity; for example, unit and line and surface and the like. Once these are postulated, certain other things are sought through demonstration, such as the equilateral triangle and the square and so on in geometry. In these cases the demonstrations are said to be, as it were, operational, as when it is required to construct an equilateral triangle on a given straight line. But once it has been constructed, certain proper attributes are proved about it; for example, that its angles are equal, or something of that sort. It is clear, therefore, that in the first type of demonstration “triangle” behaves as a proper attribute, and in the second type as a subject. Hence the Philosopher is using “triangle” as a proper attribute and not as a subject when he says by way of example, “We must assume that triangle means so and so” (71a14).

He says, ‘furthermore, that there are certain things about which we must know beforehand both what each is and whether it is. And he uses the example of “one,” which is the principle in every genus of quantity. For although it is somehow an accident in reference to substance, yet in the mathematical sciences, which treat of quantity, it cannot be taken as a proper attribute but only as a subject, since in this genus [quantity] it has nothing prior to it.

The reason for this difference is shown by the fact that the manner in which the aforesaid, namely, principle, proper attribute and subject, are manifested is not the same. For the way in which they are known is not the same: for principles are known through the act of composing and dividing, but subject and proper attribute by the act of apprehending the essence. And this, too, does not belong in similar fashion to a subject and to a proper attribute, since a subject is defined absolutely, for nothing outside its essence is mentioned in its definition; but a proper attribute is defined with dependence on the subject which is mentioned in its definition. Therefore, since they are not known in the same way, it is not surprising if they are not foreknown in the same way.

Then (7a16) he determines the extent of foreknowledge on the part of the order which foreknowing implies. For something is prior to another both in the order of time and in the order of nature. And this twofold order must be considered in regard to pre-existent knowing. For something is known before something else in the sense of being known prior in time. Concerning such things he says that someone could know certain things by knowing them prior to the time when he knows the things to which they are said to be foreknown. But certain others are known at one and the same time, although one is prior by nature to the other. Concerning these he says that one acquires a knowledge of some of these foreknown things at the same time that knowledge of the things to which they are foreknown is acquired. He indicates what these are when he adds that they are the things contained under certain universals of which we have knowledge, i.e., of which it is known that they are contained under such universals.

Then he clarifies this with an example. For since two propositions are needed for inferring a conclusion, namely, a major and a minor; when the major proposition is known, the conclusion is not yet known. Therefore, the major proposition is known before the conclusion not only in nature but in time. Further, if in the minor proposition something is introduced or employed which is contained under the universal proposition which is the major, but it is not evident that it is contained under this universal, then a knowledge of the conclusion is not yet possessed, because the truth of the minor proposition will not yet be certain. But if in the minor proposition a term is taken about which it is clear that it is contained under the universal in the major proposition, the truth of the minor proposition is clear, because that which is taken under the universal shares in the same knowledge, and so the knowledge of the conclusion is had at once. Thus, suppose that someone should begin to demonstrate by stating that every triangle has three angles equal to two right angles. When this is known, the knowledge of the conclusion is not yet known. But when it is later assumed that this figure inscribed in a semicircle is a triangle, he knows at once that it has three angles equal to two right angles. However, if it were not clear that this figure inscribed in the semicircle is a triangle, the conclusion would not be known as soon as the minor was stated; rather, it would be necessary to search for a middle through which to demonstrate that this figure is a triangle.

In giving this example of things which are known at a time prior to the conclusion the Philosopher says that a person obtaining a knowledge of the conclusion through demonstration foreknew this proposition even according to time, namely, that every triangle has three angles equal to two right angles. But inducing this assumption, namely, that this figure in the semicircle is a triangle, he knew the conclusion at the same time, because this induction shares in the evidence of the universal under which it is contained, so that there is no need to search for another middle. He adds, therefore, that “some things are only learnt in this way” (71a23), i.e., learnt in virtue of themselves, so that it is not necessary to learn them through some other middle which is the ultimate reached by analysis in which the mediate is reduced to the immediate. Or it can be read in such a way that the “ultimate,” i.e., the extreme, which is subsumed under the universal middle does not need a further middle to show that it i contained under that universal. And he manifests what those things are which always share the knowledge of their universal, saying that they are the singulars, which are not predicated of any subject, since no middle can be found between singulars and their species.

Lecture 3
(71a24-b9)
PRE-EXISTENT KNOWLEDGE OF THE CONCLUSION

a24. Before he was led on to— a28. If this distinction— a30. for we cannot— b1. yet what they know —b5. On the other hand

Having shown the manner in which certain other things must be known before knowledge of the conclusion is obtained, the Philosopher now wishes to show how we know even the conclusion beforehand, i.e., before knowledge of it is obtained through a syllogism or induction. Concerning this he does two things:

First (71a24), he establishes the truth of the fact, saying that before an induction or syllogism is formed to beget knowledge of a conclusion, that conclusion is somehow known and somehow not known: for, absolutely speaking, it is not known; but in a qualified sense, it is known. Thus, if the conclusion that a triangle has three angles equal to two right angles has to be proved, the one who obtains science of this fact through demonstration already knew it in some way before it was demonstrated; although absolutely speaking, he did not know it. Hence in one sense he already knew it, but in the full sense he did not. And the reason is that, as has been pointed out, the principles of the conclusion must be known beforehand. Now the principles in demonstrative matters are to the conclusion as efficient causes in natural things are to their effects; hence in Physics II the propositions of a syllogism are set in the genus of efficient cause. But an effect, before it is actually produced, pre-exists virtually in its efficient causes but not actually, which is to exist absolutely. In like manner, before it is drawn out of its demonstrative principles, the conclusion is pre-known virtually, although not actually, in its self-evident principles. For that is the way it pre-exists in them. And so it is clear that it is not pre-known in the full sense, but in some sense.

Secondly (71a28), in virtue of this established fact, he settles a doubt which Plato maintained in the book, Meno, which gets its title from the name of his disciple. The doubt is presented in the following manner: A person utterly ignorant of the art of geometry is questioned in an orderly Way concerning the per se known principles from which a geometric conclusion is concluded. By starting with principles that are per se known, to each of which this person ignorant of geometry gives a true answer, Aid leading him thus by questions to the conclusion, he gives the true Answer step by step. From this, therefore, he would have it that even those who seem to be ignorant of certain arts really have a knowledge of them before being instructed in them. And so it follows that either a man learns nothing or he learns what he already knew.

In dealing with this problem he [Aristotle] does four things. First, he suggests that it cannot be settled unless we grant the truth established above, namely, that the conclusion which a person learns through demonstration or induction was already known, not absolutely, but as it was virtually known in its principles concerning which a person ignorant of a science can give true answers. However, according to Plato’s theory the conclusion was pre-known absolutely, so that no one learns afresh but is led to recall by some rational process of deduction. This is similar to Anaxagoras’ position on natural forms, namely, that before they are generated, they already pre-existed in the matter absolutely, whereas Aristotle says that they pre-exist in potency and not absolutely.

Secondly (7100), he shows that the way some have answered Plato’s problem is false, namely, by saying that a conclusion is not in any sense known before it is demonstrated or learned by some method or other. For they might face the following objection based on Plato’s problem: If an unlearned person were asked by someone, “Do you know that every duo (pair) is an even number?” and, if upon answering that he does know this, he were presented with a duo which the person interrogated did not know existed, for example, the duo which is one third of six, the conclusion would be that he knew one third of six to be an even number, a fact which had not been known by him but which he learned through the demonstration proposed to him. And so it seems to follow that he either did not freshly learn this or that he learned what he already knew. To avoid this dilemma, they would answer that the person who was questioned and who answered that he knew every duo to be an equal number did not say that he knew every duo absolutely, but those he knew to be duo’s. Hence, since that duo which was proposed was utterly unknown to him, he did not in any sense know that this duo was an even number. And so it follows that when one knows the principles, the conclusion is not in any sense pre-known, either absolutely or in a qualified sense.

Thirdly (71bl), he refutes this solution in the following way: That is known, concerning which a demonstration is had, or concerning which a demonstration is for the first time received. And this is said on account of those learners who begin to know scientifically. But learners do not obtain a demonstration touching every duo they happen to know but every duo absolutely; and the same applies to every number or every triangle. Therefore, it is not true that he knows something about every number which he knows to be a number, or of every duo which he knows to be a duo, but he knows it about every one absolutely. And that he knows it not only of every number he happens to know is a number, but of every number absolutely, is proved at (71b5) on the ground that the conclusion agrees with the premises in its terms. For the subject and predicate of the conclusion are the major and minor extremes in the premises. But in the premises no proposition concerning number or straight line is stated with the addition, “which you know,” but it is stated of all without qualification. Neither, therefore, is the conclusion of the demonstration asserted with the aforesaid qualification, but it is asserted of all without reservation.

Fourthly (71b5), he presents the true solution of the problem under discussion in terms of the truth already established, saying that there is nothing to prevent a person from somehow knowing and somehow not knowing a fact before he learns it. For it is not a paradox if one somehow already knows what he learns, but it would be, if he already knew it in the same way that he knows it when he has learned it. For learning is, properly speaking, the generation of science in someone. But that which is generated was not, prior to its generation, a being absolutely, but somehow a being and somehow non-being: for it was a being in potency, although actually non-being. And this is what being generated consists in, namely, in being converted from potency to act. In like fashion, that which a person learns was not previously known absolutely, as Plato preferred; but neither was it absolutely unknown, as they maintained whose answer was refuted above. Rather it was known in potency, i.e., virtually, in the pre-known universal principles; however, it was not actually known in the sense of specific knowledge. And this is what learning consists in, namely, in being brought from potential or virtual or universal knowledge to specific and actual knowledge.

Lecture 4
(71b8-72a8)
NATURE OF THE DEMONSTRATIVE SYLLOGISM

b8. We suppose ourselves— b10. when we think that— b12. Now that scientific— b14. Consequently the proper— b16. There may be another— b17. What I now assert— b18. By demonstration I mean— b19. a syllogism, that is— b20. Assuming then that my thesis— b22. Unless these conditions— b23. Syllogism there may indeed— b24. The premises must be true— b27. The premises must be primary— b29. The premises must be the causes

After indicating the need for the demonstrative syllogism, the Philosopher now begins to settle questions concerning the demonstrative syllogism itself. And his treatment is divided into two parts. In the first he determines concerning the demonstrative syllogism. In the second he determines concerning the middle from which the demonstrative syllogism proceeds (89b21) [Book II]. The first is divided into two parts. In the first he determines concerning the demonstrative syllogism in itself. In the second he compares demonstration to demonstration (85a12) [L. 37]. The first is divided into two parts. In the first he determines concerning the demonstrative syllogism. In the second he shows that one does not proceed to infinity in demonstrations (81b10) [L. 31] The first is divided into two parts. In the first he determines concerning the demonstrative syllogism through which we acquire science. In the second he shows how we also acquire ignorance through a syllogism (79b23) [L. 27]. Concerning the first he does three things. First, he determines concerning the demonstrative syllogism by showing what it is. Secondly, he determines concerning the matter of the demonstrative syllogism, pointing out the nature and character of the matter out of which it is formed (73a21) [L. 9]. Thirdly, he determines concerning the form of the syllogism, pointing out the figure in which it is chiefly presented (79a17) [L. 26]. Concerning the first he does three things. First, he shows what the demonstrative syllogism is. Secondly, he clarifies certain terms that appear in the definition of the demonstrative syllogism (72a8) [L. 5]. Thirdly, he excludes certain errors that could arise from his doctrine on the nature of demonstration (755) [L. 7].

In regard to the first it should be noted that in all things which exist for an end, the definition which employs a final cause is both the explanation of the definition which expresses the material cause, and is the middle which proves the latter. For the reason why a house should made of stone and wood is that it is a structure protecting us from the cold and heat. Along these lines, therefore, he gives two definitions demonstration, one of which is expressed in terms of the end of demonstration, which is to know in a scientific manner. And from this one is concluded the other, which is drawn from the matter of a demonstration. Hence he does three things in regard to this. First, he defines what it is to know in a scientific manner. Secondly, he defines demonstration in terms of its end, which is to know in a scientific manner (71b18). Thirdly, from these two definitions he concludes to that definition of demonstration which is expressed in terms of the matter of demonstration (71b19).

Concerning the first he does five things. First (71b8), he determines what the scientific knowing, which he intends to define, bears upon. And in regard to this it should be recognized that we are said to know something in a scientific manner absolutely, when we know it in itself. On the other hand, we are said to know something in a scientific manner qualifiedly, when we know it in something else in which it exists either as a part in a whole (as we are said to know a wall through knowing the house), or as an accident in its subject (as in knowing Coriscus we are said to know who is coming toward us), or as an effect in its cause (as in the example given earlier, we know the conclusion in the principles), or indeed in any fashion similar to these. To know in these ways is to know incidentally, because we are said to know that which is somehow accidental to what is known of itself. However, what the Philosopher intends to define here is scientific knowing in the strict sense and not according to an accident. For this form of knowing is sophistical, since Sophists use a form of argument typified by the following: “I know Coriscus; Coriscus is coming toward me: therefore, I know the person coming toward me.”

Then (71b10) he presents the definition of scientific knowing in the strict sense. Apropos of this it should be noted that to know something scientifically is to know it completely, which means to apprehend its truth perfectly. For the principles of a thing’s being are the same as those of its truth, as is stated in Metaphysics II. Therefore, the scientific knower, if he is to know perfectly, must know the cause of the thing known; hence he says, “when we think that we know the cause” (71b10). But if he were to know the cause by itself, he would not yet know the effect actually—which would be to know it absolutely—but only virtually, which is the same as knowing in a qualified sense and incidentally. Consequently, one who knows scientifically in the full sense must know the application of the cause to the effect; hence he adds, “as the cause of that fact” (71b11). Again, because science is also sure and certain knowledge of a thing, whereas a thing that could be otherwise cannot be known with certainty, it is further required that what is scientifically known could not be otherwise. To repeat: because science is perfect knowledge, lie says, “Men we think that we know the cause”; but because the knowledge through which we know scientifically in the full sense is actual, he adds, “as the cause of that fact.” Finally, because it is certain knowledge, he adds, “and that the fact could not be other than it is (71b11).”

Thirdly (71b12), he explains the definition he laid down, appealing to the fact that both those who know scientifically and those who do not know in that way but believe that they do, take scientific knowing to be as above described. For those who do not know in a scientific manner but believe that they do, are convinced that they know in the manner described, whereas those who know in a scientific manner do know in the manner described. Furthermore, this is the proper way to manifest a definition. For a definition is the notion which a name signifies, as it is stated in Metaphysics IV. But the signification of a name must be based on what is generally meant by those who employ the name. Hence it is stated in Topics II that names must be used as the majority of people use them. Again, careful consideration would indicate that this explanation seems rather to show what the name signifies than to signify something directly. For he does not explain science, concerning which a definition could, properly speaking, be formed, since it is a species of some genus; rather he explains scientific knowing. Hence at the very beginning he said, “We suppose ourselves to possess unqualified scientific knowledge” (71b8) and not that scientific knowledge is such and such.

Fourthly (71b14), he draws a corollary from the definition, namely, that that of which there is unqualified scientific knowledge must be something necessary, i.e., which cannot be otherwise.

Fifthly (71b16), he answers a tacit question, namely, whether there is another way of knowing scientifically in addition to the way described here. And he promises to discuss this later. For it is possible to know scientifically through an effect, as will be explained below (cf. L. 23). Furthermore, there is a sense in which we are said to know scientifically the indemonstrable principles to which no cause is ascribed. But the proper and perfect manner of knowing scientifically is the one we have described.

Then (71b17) he defines the demonstrative syllogism in terms of its end, which is to know in a scientific manner. In regard to this he does three things. First, he asserts that scientific knowing is the end of a demonstrative syllogism or is its effect, since to know scientifically seems to b nothing less than to understand the truth of a conclusion through demonstration.

Secondly (71b18), he defines demonstration in terms of the end, saying that a demonstration is a sciential syllogism, i.e., producing scientific knowledge.

Thirdly (71b18), he explains, “sciential,” saying that a sciential syllogism is one according to which we know scientifically insofar as we understand it, and not in the sense of a syllogism yielding knowledge to be put to use.

Then (71b19) he concludes from the foregoing a definition of the demonstrative syllogism that is based on its matter. Concerning this he does two things. First, he concludes it. Secondly, he clarifies it (71b24).

Concerning the first he does three things. First (71b20), he sets forth the consequent in which the material definition of demonstration is concluded from the premises laid down above. And he says that if scientific knowing is what we have stated it to be, namely, knowing the cause of a thing, etc., then it is necessary that demonstrative science, i.e., science acquired through demonstration, proceed from propositions which are true, first, and immediate, i.e., not demonstrated by some other mid but clear in virtue of themselves (they are called “immediate,” inasmuch as they do not have a middle demonstrating them, but “first,” in relation to other propositions which are proved through them); and which, furthermore, are better known than, prior to, and causes of, the conclusion.

Secondly (71b22), he justifies himself for not adding another element which, it might seem, should be added, namely, that demonstration proceeds from proper principles. But he says that this is understood in virtue of the elements he did state. For since the propositions of a demonstration are causes of the conclusion, they must be its proper principles. For effects require proportionate causes.

Thirdly (71b23), he manifests the necessity of the aforesaid consequence, saying that although a syllogism does not require these conditions in the premises from which it concludes, a demonstration does require them, for otherwise it would not produce science.

Then (71b24) he explains this definition as well as the subsequent statement that unless these conditions are fulfilled in a demonstration it cannot beget science. First, therefore, he shows that a demonstration must proceed from true principles in order to beget science, because there cannot be scientific knowledge of that which does not exist, for example, that the diagonal is symmetrical, i.e., commensurable with the side of the square. For those quantities are said to be incommensurable which lack a common measuring unit. These are quantities whose ratio to one another cannot be expressed in terms of one number to another number. That this is the case with the diagonal of a square and its side is plain from Euclid’s sixteenth proposition. Now what is not true does not exist, for to be and to be true are convertible. Therefore, anything scientifically known must be true. Consequently, the conclusion of a demonstration which does beget scientific knowing must be true, and a fortiori its premises. For the true cannot be known in a scientific way from the false, although something true can follow as a conclusion from something false, as he will show later (cf. Lecture 13).

Secondly (71b27), he shows that the demonstration is composed of first and immediate or indemonstrable principles. For no one can possess scientific knowledge unless he possesses the demonstration of things that can be demonstrated—“and I am speaking per se and not per accidens.” He says this because it would be possible to know some conclusion without having a demonstration of the premises, even were they demonstrable; because one would know it through other principles, and this would be accidental.

Suppose, therefore, that a demonstrator syllogizes from demonstrable, i.e., mediate, premises. Now he either possesses a demonstration of those premises or he does not. If he does not, then he does not know the premises in a scientific way; nor consequently, the conclusion because of the premises. But if he does possess their demonstration, then, since one may not proceed to infinity in demonstrations, principles immediate and indemonstrable must be reached. And so it is required that demonstration proceed from principles that are immediate either straightway or through middles. Hence it is stated in Topics I that demonstration is composed of first and true statements or of statements made credible by these.

Thirdly (71b29), he proves that the propositions of a demonstration are the causes of the conclusion, because we know in a scientific manner when we know the causes. And in virtue of this he shows that they are prior and better known, because every cause is by nature prior and better known than its effect. However, the cause of a demonstrated conclusion must be better known not only with respect to the knowledge of what it is, but also with respect to the knowledge that it is. For in order to demonstrate that there is an eclipse of the sun, it is not enough to know, that the moon is interposed; in addition it is necessary to know that the moon is interposed between the sun and the earth. Again, because prior i and better known are taken in two ways, namely, in reference to us and according to nature, he says that the things from which a demonstration, proceeds are prior and better known absolutely and according to nature, and not in reference to us.

To elucidate this he says that “those things are prior and better known absolutely,” which are farthest from sense, as are universals; but “the prior and better known in reference to us” are nearest to sense, namely, the singulars, which are opposed to universals in the way that the prior and the later are opposite, or in the way that the nearest and the farthest are opposite.

However, it seems that the contrary of this is found in Physics I where it is stated that universals are prior in reference to us and later according to nature. But it should be said that there [in the Posterior Analytics] he is speaking of the order of singular to universal absolutely; and this order must be taken according to the order of sensitive and intellectual knowledge in us. Now in us sensitive knowledge is prior to intellectual, because intellectual knowledge in us proceeds from sense. For this reason the singular is prior and better known in relation to us than the universal. But in Physics I he is not speaking of the order of the universal to the singular absolutely but of the order of the more universal to the less universal, for example of animal to man. In this case the more universal is prior and better known in reference to us. For in every instance of generation, that which is in potency is prior in time but is later according to nature; whereas that which is complete in act is prior by nature but later in time. Now one’s knowledge of a genus is, as it were, potential in comparison to one’s knowledge of the species in which all the essentials of a thing are actually known. Hence, too, in the generation of our science, knowledge of the more common precedes knowledge of the less common.

Again, in the Physics it is stated that it is natural for us to proceed from what is better known to us. Therefore, it seems that a demonstration is composed not of things that are prior absolutely but in reference to But it must be said that here he is speaking according to the fact that what is in the sense is better known in reference to us than what is in the intellect; but there he was speaking according to the fact that what is better known in reference to us is also in the intellect. But demonstrations do not proceed from singulars which are in the sense but only from universals, which are in the intellect.

Or it might be said that in every demonstration one must proceed from things better known to us, provided they are not singulars but universals. For something is made known to us only by that which is more known to us. But sometimes that which is more known in reference to us is also more known absolutely and according to nature, as happens in mathematics where on account of abstraction from matter the demonstrations proceed from formal principles alone. In this case the demonstrations proceed from things which are more known absolutely. But sometimes that which is more known in reference to us is not more known absolutely, as happens in natural sciences where the essences and powers of things are hidden, because they are in matter, but are disclosed to us through the things which appear outwardly. Hence in these sciences the demonstrations are for the most part made through effects which are better known in reference to us but not absolutely. But he is not now speaking of this form of demonstration, but of the first.

Finally, because in his explanation he neglected to point out that demonstration should proceed from proper principles, he hastens to add that this fact is easily ascertainable from what he did say. For from the fact that he stated that demonstration is from things which are first, it follows that it is from proper principles, as he stated above. For “first” and “principle” seem to be the same: for that which is first and highest in each genus is the cause of all the things that are after it, as it is stated in Metaphysics II.

Lecture 5
(72a8-24)
FIRST AND IMMEDIATE PROPOSITIONS

a8. A ‘basic truth’ in a— a9. A proposition is— a10. If a proposition is dialectical— a11. The term ‘enunciation’— a15. I call an immediate— a19. If a thesis assumes

Because the Philosopher had stated above that demonstration is from “first and immediate principles,” but had not yet identified them, he now sets out to identify them. And this is divided into three parts. In the first part he shows what an immediate proposition is. In the second part he shows that such propositions must be better known than the conclusion (72a25) [L. 6]. In the third part he excludes certain errors which arose from the foregoing (72b5) [L. 7]. Concerning the first he does two things. First, he shows what an immediate principle is. Secondly, h divides them (72a15).

With respect to the first he proceeds this way. First (72a8), he recall, what has been said above, namely, that a principle of demonstration I, an immediate proposition, for he had also stated above that a demonstration is composed of things which are first and immediate.

Secondly (ibid.), he defines the immediate proposition and says that a immediate proposition is one which has no other one prior to it. the reason underlying this description is clear from what has been said. For it has been said above that demonstration is composed of things that, are prior. Accordingly, whenever a proposition is mediate, i.e., has a middle through which the predicate is demonstrated of its subject, it is required that there be prior propositions by which this one is demonstrated. For the predicate of a conclusion is present in the middle previously to being present in the subject; in which, however, the middle is present before the predicate is. Therefore, it follows that that proposition which does not have some other one prior to it is immediate.

Thirdly (720), he shows what is the nature of the proposition which is mentioned in the definition of an immediate proposition. Concerning this he does three things:

First, he defines absolutely what a proposition is, saying that it is one or the other part of an enunciation in which one thing is predicated of one thing. For the enunciation has two parts, namely, affirmation and negation. For anyone who syllogizes must propose one or the other of these parts but not both, for this latter procedure is characteristic of one who first raises a question. (Hence it is on this basis that proposition is distinguished from a problem). For just as one and only one thing is concluded in one syllogism, so the proposition which is a principle of the syllogism should be one—and it is one if one thing is stated of one thing. Hence in asserting that it is “one of one,” he distinguishes the proposition from the enunciation which is said to be “of several,” whether sundry things are said of one thing or of one thing sundry.

Secondly (72a10), he lays down the difference between the dialectical and the demonstrative proposition, saying that whereas the demonstrative proposition takes one definite side of a question, the dialectical takes either side indifferently. For since dialectic begins with the probable, it can lead to each side of a contradiction. Hence when it lays down its propositions, it employs both parts of a contradiction and presents them in the form of a question [Is an animal that walks on its feet a man, or not?]. But a demonstrative proposition takes one side definitively, because a demonstrator never has any other alternative but to demonstrate the truth. Hence in forming its propositions he always assumes the true side of a contradiction [An animal which walks on two feet is a man, is it not?]. On this account he does not ask but posits something as known in the demonstration.

Thirdly (72a11), he defines the term, “enunciation,” which appeared in the definition of a proposition, saying that an enunciation embraces both sides of a contradiction, as is clear from what has been said.

Then he shows what contradiction is, saying that contradiction is a form of opposition between whose parts there is of itself no middle. For although between privation and possession and between immediate contraries there is no middle in a given subject, nevertheless, absolutely speaking, there is one; for a stone is neither blind nor seeing, and something white is neither even nor odd. Furthermore, whatever immediacy they have in relation to a definite subject is traced to their participation in contradiction, for privation is negation in a definite subject; and of two things that are immediately contrary, one has some of the marks of privation. But contradiction in the full sense lacks a middle in all cases. And this belongs to it of its very nature and not in virtue of something else. Hence he says that of itself it has no medium.

He then explains what the parts of a contradiction are. For contradiction is an opposition of affirmation and negation; hence one of its parts is affirmation, which asserts something of something, and the other is negation, which denies something of something.

Then (72a15) he divides immediate principle. Concerning this he does two things. First, he divides. Secondly, he subdivides (72a19).

He says therefore first (7205), that there are two types of immediate principles of a syllogism: the first is called a “position” [thesis] and is said to be immediate because one does not demonstrate (neither is it required that the student, i.e., the one being instructed in the demonstrative science, have it, i.e., advert to it or assent to it); the other is called a “dignity” or “maxim,” which anyone who is to be instructed must have in his mind and assent to. That there are such principles is clear from Metaphysics IV, where it is proved that one such is the principle that “affirmation and negation are not simultaneously true,” for no one can believe the contrary of this in his mind ‘ even though he should state it orally. To such principles we give the aforesaid name of “dignity” or “maxim” on account of their certainty in manifesting other things.

To clarify this division it should be noted that any proposition whose predicate is included within the notion of its subject is immediate and known in virtue of itself as it stands. However, in the case of some of these propositions the terms are such that they are understood by everyone, as being and one and those other notions that are characteristic of being precisely as being: for being is the first concept in the intellect. Hence it is necessary that propositions of this kind be held as known in virtue of themselves not only as they stand but also in reference to us. Examples of these are the propositions that “It does not occur that the same thing is and is not” and that “The whole is greater than its part,” and others like these. Hence all the sciences take principles of this kind from metaphysics whose task it is to consider being absolutely and the characteristics of being.

On the other hand, there are some immediate propositions whose terms are not known by everyone. Hence, although their predicate may be included in the very notion of their subject, yet because the definition of the subject is not known to everyone, it is not necessary that such propositions be conceded by everyone. (Thus the proposition, “All right angles are equal,” is in itself a proposition which is immediate and known in virtue of itself, because equality appears in the definition of a right angle. For a right angle is one which a straight line form when it meets another straight line in such a way that the angles on each side are equal). Therefore, such principles are received as being posited or laid down.

There is yet another way, and according to it certain propositions are called “suppositions.” For there are some propositions which can be proved only by the principles of some other science; therefore, they must be supposed in the one science, although they are proved by the principles of the other science. Thus the geometer supposes that he can draw one straight line from one point to another, but the philosopher of nature proves it by showing that there is one straight line between any two points.

Then (72a19) he subdivides a member of the original division, namely, “position,” and says that there is one type of position which takes one side of an enunciation, namely, either affirmation or negation. He refers to this type when he says, “i.e., asserts either the existence or non-existence of a subject.” Such a position is called a “supposition” or “hypothesis,” because it is accepted as having truth. Another type of position is the one which does not signify existence or non-existence: in this way a definition is a position. For the definition of “one” is laid down in arithmetic as a principle, namely, that “one is the quantitatively indivisible.” Nevertheless a definition is not called a supposition, for a supposition, strictly speaking, is a statement which signifies the true or the false. Consequently, he adds that “the definition of ‘one,”’ inasmuch as it signifies neither the true nor the false, “is not the same as ‘to be one,”’ which does signify the true or the false.

Now it might be asked how it is that definition is set down as a member of the subdivision of immediate proposition, if a definition is not a proposition signifying either existence or non-existence. One might answer that in this subdivision he was not subdividing immediate proposition but, immediate principle. Or one might answer that although a definition as such is not an actual proposition, it is one virtually, because once a definition is known, it becomes clear that it is truly predicated of the subject.

Lecture 6
(7245-b4)
KNOWLEDGE OF IMMEDIATE PRINCIPLES

a25. Now since the required— a28. for the cause of an— a33. Now a man cannot believe a36. a man must believe in— attribute’s— a38. he must not only have

After showing what immediate principles are, the Philosopher now determines concerning our knowledge of them. Apropos of this he does two things. First, he shows that immediate principles are better known than the conclusion. Secondly, that the falsity of their contraries ought to be most evident (72a38).

Concerning the first he does three things. First (72a25), he states his proposition and says that because we give our assent to a thing which has been concluded and we know it scientifically precisely because we have a demonstrative syllogism (and this insofar as we know the demonstrative syllogism in a scientific way), it is necessary not only to know the first principles of the conclusion beforehand, but also to know them better than we know the conclusion.

He adds, “either all or some,” because some principles require proof in order to be known; so that before they are proved, they are not better known than the conclusion. Thus the fact that an exterior angle of a triangle is equal to its two opposite interior angles is, until proved, as unknown as the fact that a triangle has three angles equal to two right angles. But there are other principles which, once they are posited, are better known than the conclusion. Or, in another way, there are some conclusions which are most evident; for example, those based on sense perception, as that the sun is eclipsed. Hence the principle through which this is proved is not better known absolutely—the principle being that the moon is between the sun and the earth—although it is better known within the reasoning process that goes from cause to effect. Or, in another way, he says this because he had said above that in the order of time certain principles are known before the conclusion, but others are known along with the conclusion at the same moment of time.

Secondly (72a28), he proves his proposition in two ways: first, with an ostensive argument, thus: That in virtue of which something is so, is itself more so; for example, if we love someone because of someone else, as a master because of his disciple, we love the disciple more. But we know conclusions and give our assent to them because of the principles. Therefore, we know the principles with more conviction and give them stronger assent than the conclusion.

Apropos of this reason it should be noted that a cause is always more noble than its effect. When, therefore, cause and effect have the same name, that name is said principally of the cause rather than of the effect; thus fire is primarily called hot rather than things heated by fire. But sometimes the name of the effect is not attributed to the cause. In that case, although the name the effect has does not belong to the cause, nevertheless, something more noble belongs to it. For example, although the sun does not possess heat, nevertheless, there is in it a certain power which is the principle of heat.

Then (72a33) he proves the same thing with a principle which leads to an impossibility. He reasons thus: Principles are known prior to the conclusion, as has been shown above; consequently, when the principles are known, the conclusion is not yet known. If, therefore, the principles were not more known than the conclusion, it would follow that a man would know things he does not know either as well as or better than the things he does know. But this is impossible. Therefore, it is also impossible that the principles not be better known than the conclusion.

Phrase by phrase this is explained in the following manner: “A man who knows scientifically or even one who knows in a way superior to this, if such there be,” (he says this, having in mind the person who has the intuition of principles, a state he has not yet explained), “cannot give more credence to things he does not know than to things he does know. But this will be the case if one who assents to a conclusion obtained through demonstration did not foreknow,” i.e., did not know the principles better. In Greek it is stated more clearly: “But no one, whether he has scientific knowledge or that form of knowledge which is better than the scientific (if there be such), can believe anything more firmly than the things he knows.”

Thirdly (7206), he clarifies what he had said, saying that his statement to the effect that it is more necessary to believe the principles (either all or some) than the conclusion should be understood as referring to a person who is to acquire a discipline through demonstration. For if the conclusion were more known through some other source, such as sense-perception, nothing would preclude the principles not being better known than the conclusion in that case.

Then (72a38) he shows that it is not only necessary to know the principles more than the demonstrative conclusion, but nothing should be more certain than the fact that the opposites of the principles are false. And this because the scientific knower must not disbelieve the principles, but assent to them most firmly. But anyone who doubts the falseness of one of two opposites cannot assent firmly to the other, because he will always fear that the opposite one might be true.

Lecture 7
(72b5-24)
DISCUSSION OF TWO ERRORS—EXCLUSION OF THE FIRST ONE

b5. Some hold that, owing— b8. The first school— b15. The other party agree— b18. Our own doctrine is that

After determining about the knowledge of the principles of demonstration, the Philosopher now excludes the errors which have arisen from these determinations. Concerning this he does three things. First, he states the errors. Secondly, the reasons they erred (72b8). Thirdly, he removes the roots of these reasons (72b 18).

He says therefore first (72b5), that two contrary errors have arisen from one of the truths established above. For it has been established above that the principles of demonstration must be known and must be even better known. But the first of these is sufficient for our purpose. For some, basing themselves on this first statement, have come to believe that there is no science of anything, whereas others believe that there is science, even to the extent of believing that there is science of everything through demonstration. But neither of these positions is true and neither follows necessarily from their reasons.

Then (72b8) he presents the reasons why they have fallen into these errors. And first of all he presents the reason given by those who say that there is no science, and it is this: The principles of demonstration either proceed to infinity or there is a halt somewhere. But if there is a process to infinity, nothing in that process can be taken as being first, because one cannot exhaust an infinite series and reach what is first. Consequently, it is not possible to know what is first. (They are correct in thus arguing, for the later things cannot be known unless the prior ones are known).

On the other hand, if there is a halt in the principles, then even so, the first things are still not known, if the only way to know scientifically is through demonstration. For first things do not have prior principles through which they are demonstrated. But if the first things are not known, it follows again that the later things are not known in the strict and proper sense, but only on condition that there are principles. For it is not possible for something to be known in virtue of something not known, except on condition that that unknown be a principle. So in either case, whether the principles stop or go on to infinity, it follows that there is no science of anything.

Secondly (72b15), he presents the reasoning of those who say that there is science of everything through demonstration, because to their there is science of everything through demonstration, because to their basic premise-the only way to know scientifically is by demonstration—they added another, namely, that one may demonstrate circularly. From these premises it followed that even if a limit is reached in the series of the principles of demonstration, the first principles are still known through demonstration, because, they said, those principles were demonstrated by previous ones. For a circular demonstration is one which is reciprocal, i.e., something which was first a principle is later a conclusion, and vice versa.

Then (72b18) he cuts away the false bases of these arguments. First, their supposition that the only way to know scientifically is by demonstration. Secondly, their statement that it is legitimate to demonstrate circularly (72b25).

He says therefore first (72b18), that not all scientific knowledge is demonstrative, i.e., obtained through demonstration, but the scientific knowledge of immediate principles is indemonstrable, i.e., not obtained by demonstration. However, it should be noted that Aristotle is here taking science in a wide sense to include any knowledge that is certain, and not in the sense in which science is set off against understanding, according to the dictum that science deals with conclusions and understanding [intuition] with principles.

But that it is necessary for some things to be held as certain without demonstration he proves in the following way: It is necessary that the prior things from which a demonstration proceeds be known in a scientific way. Furthermore, these must be ultimately reduced to something immediate; otherwise one would be forced to admit that there is an actual infinitude of middles between two extremes—in this case between the subject and predicate. Again, one would have to admit that no two extremes could be found between which there would not be an infinitude of middles. But as it is, the middles are such that it is possible to find two things which are immediate. But immediate principles, being prior, must be indemonstrable. Thus it is clear that it is necessary for some things to be scientifically known without demonstration.

Therefore, if someone were to ask how the science of immediate principles is possessed, the answer would be that not only are they known in a scientific manner, but knowledge of them is the source of an science. For one passes from the knowledge of principles to a demonstration of conclusion on which science, properly speaking, bears. But those immediate principles are not made known through an additional middle but through an understanding of their own terms. For as soon as it is known what a whole is and what a part is, it is known that every whole is greater than its part, because in such a proposition, as has been stated above, the predicate is included in the very notion of the subject. And therefore it is reasonable that the knowledge of these principles is the cause of the knowledge of conclusions, because always, that which exists in virtue of itself is the cause of that which exists in virtue of something else.

Lecture 8
(72b-73a20)
THE SECOND ERROR IS EXCLUDED BY SHOWING THAT CIRCULAR DEMONSTRATION IS NOT ACCEPTABLE

b25. Now demonstration must— b33. The advocates of circular— b38. Thus by direct proof— a1. Since then— a6. Moreover, even such

After excluding one false basis by showing that not all science depends on demonstration, the Philosopher now excludes another by showing that it is not possible to demonstrate circularly.

To understand this it should be noted that a demonstration is circular when the conclusion and one of the premises (in converted form) of a syllogism are used to prove the other premise. For example, we might form the following syllogism: