METAPHYSICS
BOOK XI

LESSON 1

Metaphysics Is the Science of Principles

ARISTOTLE’S TEXT Chapter 1: 1059a 18-1060a 2

899. That wisdom is a science of principles, then, is evident from the first chapters (45-143) of this work, in which problems were raised concerning the statements of other philosophers about the principles of things.

900. But one might raise the question whether wisdom must be understood to be one science or many (181, 190). For if it is one, then the objection might be raised that one science always deals with contraries; but principles are not contraries. And if it is not one but many, what kind of sciences must they be assumed to be (190-197)?

901. Further, one might raise the question whether it is the office of one science or of many to study the principles of demonstration? For if it is the office of one science, why should it be the office of this science rather than of another? And if it is the office of many, what kind of sciences must these be admitted to be (198-201)?

902. Further, there is the question whether it is the office of wisdom to deal with all substances or not (182)? And if not with all, it is difficult to say with what kind it does deal. But if there is one science of all substances, the problem arises how one science can deal with many subjects (202-204).

903. Again, there is the question whether this science is a demonstration of substances alone, or also of accidents (184, 205-207); for if it is a demonstration of accidents, it is not a demonstration of substances. But if there is a different science of accidents, what is the character of each, and which of the two is wisdom? For a demonstrative science of accidents is wisdom; but that which deals with primary things is the science of substances.

904. But the science which we are seeking must not be assumed to be the one which deals with the causes mentioned in the Physics. For it does not deal with the final cause, because such is the good, and this is found in the sphere of practical affairs and in things which are in motion. And it is the first thing which causes motion (for the end is such a nature); but there is no first mover in the realm of immobile things (192).

905. And in general there is the question whether the science which is now being sought is concerned with sensible substances, or whether it is not concerned with these but with certain others (183). For, if it deals with other substances, it must be concerned with either the separate Forms or with the objects of mathematics. Now it is evident that separate Forms do not exist.

906. But nevertheless even if one were to assume that these separate Forms exist, the problem would arise why the same thing should not be true of the other things of which there are Forms as is true of the objects of mathematics. I mean that they place the objects of mathematics between the Forms and sensible things as a kind of third class of entities besides the Forms and the things which exist here. But there is no third man or horse over and above man-in-himself and horse-in-itself and singular men and horses.

907. If, however, the situation is not as they say, with what kind of things must the mathematician be assumed to deal? For he is not concerned with the things which exist here, because none of these are the kind of things which the mathematical sciences study. Nor is the science which we are now seeking concerned with the objects of mathematics; for no one of these is capable of existing separately. Nor does it deal with sensible substances, for these are corruptible (208-219).

9o8. And in general one might raise the question to what science it belongs to consider the problem about the matter of the mathematical sciences (627). It is not the office of the philosophy of nature, for this science is wholly concerned with things which have in themselves a principle of rest and of motion. Nor is it the office of the science which investigates demonstration and scientific knowledge, for it is about this class of things that it makes its investigations. It follows, then, that it pertains to the philosophy which we have proposed to investigate these things.

909. And one might raise the question whether the science which is now being sought must deal with the principles which are called elements by some thinkers (184). But all men suppose these to be present in composite things. And it would seem rather that the science which is now being sought ought to deal with universals, for every intelligible nature and every science is of universals and not of extremes (228), so that in this way they would deal with the primary genera.

910. And these would become being and unity; for these most of all might be thought to contain all existing things and to be principles in the highest degree, because they are first by nature; for when they have been destroyed, everything else is destroyed, since everything is a being and one. But if one supposes them to be genera, then inasmuch as it is necessary for differences to participate in them, and no difference participates in a genus, it would seem that they must not be regarded either as genera or as principles.

911. Further, if what is more simple is more of a principle than what is less simple, and the ultimate members resulting from the subdivision of different genera are more simple than the genera themselves (for these members are indivisible, whereas genera are divided into many different species), it would seem that species are principles to a greater degree than genera. But since species are involved in the destruction of their genera, genera are like principles to a greater degree; for whatever involves something else in its destruction is a principle of that thing (229-234). These and other such points, then, are the ones which cause difficulties.

COMMENTARY

2146. Because the particular sciences disregard certain things which should be investigated, there must be a universal science which examines these things. Now such things seem to be the common attributes which naturally belong to being in general (none of which are treated by the particular sciences since they do not pertain to one science rather than to another but to all in general) and to the separate substances, which lie outside the scope of every particular science. Therefore, in introducing us to such knowledge, Aristotle, after he has investigated these attributes, begins to deal particularly with the separate substances, the knowledge of which constitutes the goal to which the things studied both in this science and in the other sciences are ultimately directed.

Now in order that a clearer understanding of the separate substances may be had, Aristotle first (899:C 2146) makes a summary of the points discussed both in this work and in the Physics’ which are useful for knowing the separate substances. Second (1055:C 2488), he investigates the separate substances in themselves (in the middle of the following book: “Since there are”).

The first part is divided into two. In the first he summarizes the points which act as a preface to the study of substances. In the second (1023:C 2416) he restates the things that pertain to the study of substances (at the beginning of the following book: “The study here”).

He prefaced his study of substances by doing three things. First, he raised the questions given in Book 111, which he now restates under the first point of discussion. Second (924:C 2194), he expressed his views about the things that pertain to the study of this science. These are given in Book IV and are restated here under the second point of discussion (“Since the science”). Third (963:C 2268), he drew his conclusions about imperfect being, i.e., accidental being, motion, and the infinite, about which he had partly established the truth in Books II (152:C 299) and VI (543-59:C 1171-1244) of this work, and partly in Book III of the Physics; and he gives a summary restatement of these under the third point of discussion (“Since the term being”).

The first part is divided into two. First, he raises a question about the study of this science; and second (912:C 2173), about the things established in this science (“Further, there is”).

In regard to the first he does two things. First, he asks in what way the study of this science is concerned with principles and substances. Second (904: C 2156), he asks with what principles and what substances it deals (“But the science”).

In regard to the first he does two things. First, he raises questions about the study of the principles of this science; and second (902:C 2152), about this science’s study of substances (“Further, there is the question”).

In treating the first point (899) he does three things. First, he assumes that the inveselgations of this science are concerned with principles. He says that it is evident from Book I (45-143:C 93-272), in which he argued against the statements that other philosophers have made about the first principles of things, that wisdom is a science of principles. For it was shown in the Prologue to this work that wisdom considers the highest and most universal causes, and that it is the noblest of the sciences.

2147. But one might (900).

Second, he raises a question about the study of the principles by this science which is called wisdom. He says that one can ask whether wisdom, which considers principles, must be one science or many.

2148. However, if we say that it is one, this seems to be inconsistent, because many of the things studied in one science are contraries, since one contrary is the basis for knowing the other, and thus both contraries seem to fall under one art. But since the principles of things are many, they are not contraries, otherwise they could not be combined in one subject. Hence, wisdom, which is concerned with principles, does not seem to be one science. And if it is not one science but many, it is impossible to state what these sciences are.

2149. Now the truth of the matter is that, while wisdom is one science, it considers many principles inasmuch as they are reduced to one genus, because contraries fall under one science since they belong to one genus.

2150. Further, one might (901).

Third, he raises a question about the study which this science makes of the principles of demonstration. He says that it is still a problem whether the study of the principles of demonstration (for example, every whole is greater than one of its parts, and the like) belongs to the study of one science or many. If one claims that such a study belongs to one science, it seems difficult to explain why it belongs to this science rather than to another, since all sciences make common use of these principles. But if one claims that it belongs to many sciences, it seems difficult to give many sitch sciences.

2151. Now the truth of the matter is that there is one science which is chiefly concerned with these principles, and this is the one which investigates the common terms involved in these principles, such as being and non-being, whole and part, and the like; and the other sciences receive such principles from this science.

2152. Further, there is (902).

Then he raises questions about this science's study of substances; and there are two of these. First, he asks whether or not this science considers all substances. If one claims that it does not, it is difficult to indicate what substances it does consider and what not. And if one claims that it considers all substances, the question remains how one and the same science can deal with many substances, since each science treats of one thing.

2153. The truth is that, although this science deals especially with the separate substances, it does treat all substances inasmuch as all belong to one common class of essential being.

2154. Again, there is (903).

Second, he asks whether there is demonstration only with regard to substances or also with regard to accidents; for, if demonstration, properly speaking, were concerned with accidents, there would be no demonstration with regard to substances, since it is the function of demonstration to infer the essential accidents of substances. But if one claims that there is one demon. strative science of substances and an. other of essential accidents, the question remains as to which science each of these is, and whether each is worthy of the name of wisdom. For, on the one hand, it does seem that the science which deals with accidents is wisdom, because demonstration is properly concerned with accidents, and demonstrative science is the most certain. Thus it seems that wisdom, which is a demonstrative science, deals with accidents But, on the other hand, it seems to deal with substances; for since substances are the primary kind of being, it seems that the science which treats of them is the primary science.

2155. Now the truth is that wisdom considers both substances and accidents inasmuch as they have being in common, which constitutes the subject of wisdom; but its demonstrations are concerned chiefly with substances, which are the primary kind of essential beings, and of these it demonstrates the accidents.

2156. But the science (904).

Then he raises more specific questions about the study of this science. First (904:C 2156), he asks about the substances which this science considers; and second (909:C 2166), about the principles which it considers (“And one might”).

In treating the first point he raises four questions. The first (904) has to do with the causes of sensible substances. He says that it does not seem that we should hold that the science which we are seeking is concerned with the four classes of causes discussed in the Physics, because it seems to deal especially with the final cause, which is the most important of all. But this science does not seem to deal with “the final cause,” or goal, because an end or goal has the nature of the good. Now the good relates to operations and to things which are in motion. Hence in the case of immovable things, such as the objects of mathematics, nothing is demonstrated by way of the final cause. It is also evident that the end is what first moves a thing, for it moves the efficient cause. But there does not seem to be a first cause of motion in the case of immovable things.

2157. Now the truth of the matter is that this science considers the classes of causes mentioned, especially the formal and final cause. And furthermore, the end, which is the first cause of motion, is altogether immovable, as will be shown below (1069:C 2526).

2158. And in general (905).

Second, he raises a question about the study of sensible substances. He asks whether this science is concerned with sensible substances or not. For if it is concerned with them, it does not seem to differ from the philosophy of nature. But if it is concerned with other substances, it is difficult to state what these substances are. For it must deal with either “the separate Forms,” i.e., the Ideas, which the Platonists posited, or with the objects of mathematics, which some supposed to exist as an intermediate class of things between the Ideas and sensible substances, for example, surfaces, lines, figures and the like. But it is evident from the previous books that “separate Forms do not exist,” i.e., separate Ideas; and so he immediately raises the question about the objects of mathematics.

2159. Now the true answer to this question is that this science deals with sensible substances inasmuch as they are substances, but not inasmuch as they are sensible and movable; for this latter belongs properly to the philosophy of nature. But the proper study of this science has to do with substances which are neither Ideas nor separate mathematical entities but primary movers, as will be seen below (1055:C 2488).

2160. But nevertheless (906).

Third, he raises a third difficulty as a secondary issue. For, since he had said that there are evidently no separate Forms, he poses the question whether the objects of mathematics are separate. First, he shows that they are not. For if one claims that there are separate Forms and separate mathematical entities over and above sensible substances, why is not the same thing true of all things which have Forms as is true of the objects of mathematics? So that just as the objects of mathematics are assumed “ to be intermediate between the separate Forms and sensible substances as a third class of things over and above the separate Forms and the singular things which exist here (for example, a mathematical line over and above the Form of a line and the perceptible line), in a similar fashion there should be a third man and a third “horse over and above man-in-himself and horse-in-itself” (i.e., the ideal man and the ideal horse, which the Platonists called Ideas) and individual men and horses. But the Platonists did not posit intermediates in such cases as these but only in that of the objects of mathematics.

2161. If, however (907).

Then he argues on the other side of the question; for, if the objects of mathematics are not separate, it is difficult to indicate the things with which the mathematical sciences deal. For they do not seem to deal with sensible things as such, because no lines and circles such as the mathematical sciences investigate are found in sensible things. It seems necessary to hold, then, that there are certain separate lines and circles.

2162. Now the truth of the matter is that the objects of mathematics are not separate from sensible things in being but only in their intelligible structure, as has been shown above in Book VI (537:C 1162) and will be considered below (919:C 2185).

2163. And since he had interjected as a secondary issue this difficulty about the separateness of the objects of mathematics because he had said that forms evidently are not separate, therefore when he says, “Nor is the science which we are now seeking concerned with the objects of mathematics,” he returns to the main question that was raised, namely, with what kind of substances this science deals. And since he had shown that it does not deal with separate Forms (for there are no separate Forms), he now shows by the same reasoning that it does not deal with the objects of mathematics; for neither are they separate in being. And it does not seem to deal with sensible substances, because these are destructible and in motion.

2164. The true answer to this question is the one given above.

2165. And in general one might (908).

Then he gives a fourth difficulty by asking to what science it belongs “to consider the problems about the matter of the mathematical sciences,” i.e., to investigate the things with which the mathematical sciences are concerned. This does not pertain to the philosophy of nature, because it is wholly concerned with those things which have in themselves a principle of rest and of motion and are called natural beings. Therefore he does not examine this problem. Similarly, the investigation of this problem does not seem to belong to that science which is called mathematical, which has as its aim the demonstration and knowledge of mathematical entities; for this kind of science presupposes matter of this sort or a subject of this sort, and some science does investigate this subject. It follows, then, that it is the business of this philosophical science to consider the things of which the mathematical sciences treat.

2166. And one might (909).

Then he asks what kind of principles this science investigates. In regard to this he raises three questions. First, he asks whether this science studies the principles which are called elements by some thinkers. This question seems to refer to the common supposition that principles of this kind are present in, i.e., intrinsic to, the composite, so that in order to know composite things these principles must be known. But from another point of view it seems that this science is concerned with more universal things, because every intelligible nature and every science seems to be “of universals and not of extremes,” i.e., not about the particular things in which the division of common genera terminates. Thus it seems that this science has to do especially with the first genera.

2167. But the truth is that this science deals chiefly with common attributes, yet without making the common factors principles in a Platonic sense. However, it does consider the intrinsic principles of things—matter and form.

2168. And these would (910).

Second, he raises the second problem. For, on the one hand, it seems that unity and being are principles and genera, because these most of all seem to contain all things within their general ambit. And they seem to be principles because they are first by nature; for when they are destroyed, other things are too; for everything is a being and one. Hence, if being and unity are destroyed, everything else is destroyed, but not the other way around.

2169. But, on the other hand, it seems that unity and being are not genera, and therefore they are not principles if genera are principles. For no difference participates actually in a genus, because difference is derived from form and genus from matter; for example, rational is taken from intellective nature, and animal from sensory nature. Now form is not included actually in the essence of matter, but matter is in potentiality to form. And similarly difference does not belong to the nature of a genus, but a genus contains differences potentially. And for this reason a difference does not participate in a genus, because, when I say “rational,” I signify something having reason. Nor does it belong to the intelligibility of rational that it should be animal. Now that is participated in which is included in the intelligibility of the thing which participates; and for this reason it is said that a difference does not participate in a genus. But there cannot be any difference whose intelligibility does not contain unity and being. Hence unity and being cannot have any differences. Thus, they cannot be genera, since every genus has differences.

2170. Now the truth of the matter is that unity and being are not genera but are common to all things analogically.

2171. Further, if what (911).

Then he raises the third question. The problem now is whether genera are principles to a greater degree than species. First, he shows that species are principles to a greater degree than genera; for what is more simple is a principle to a greater degree. But species seem to be more simple, for they are the indivisible things in which the formal division of a genus terminates. But genera are divided into many different species, and therefore species seem to be principles to a greater degree than genera. But in view of the fact that genera constitute species, and not vice versa, genera seem to be principles to a greater degree; for the intelligible structure of a principle is such that, when it is destroyed, other things are destroyed.

2172. Now the truth is that universals are principles, namely, of knowing; and thus genera are principles to a greater degree because they are simpler. The reason why they are divided into more members than species are is that they contain more members potentially. But species contain many members actually. Hence they are divisible to a greater degree by the method of dissolving a composite into its simple constituents.

LESSON 2

Are There Non-Sensible Substances and Principles?

ARISTOTLE’S TEXT Chapter 2: 1060a 3-1060b 3

912. Further, there is the question whether or not we must posit the existence of something besides singular things; and if not, then the science which we are now seeking must deal with these things. But they are infinite in number. And what exists apart from singular things are genera and species; but the science which we are now seeking deals with neither of these. The reason why this is impossible has already been stated (909-911).

913. And in general the problem is whether one must suppose that there is some substance which is separable from sensible substances (i.e., the things which exist here and now), or that the latter are beings and the things with which wisdom deals. For we seem to be looking for another kind of substance, and this constitutes the object of our study: I mean, to know whether there is something which is separable in itself and belongs to no sensible thing.

914. Further, if there is another kind of substance apart from sensible substances, from what kind of sensible substances must it be assumed to be separate? For why should we suppose that it exists apart from men and from horses rather than from other animals or non-living things generally? Yet to devise various eternal substances equal in number to sensible and corruptible ones would seem to be unreasonable.

915. But if the principle we are now seeking is not separable from bodies, what could be more of a principle of things than matter? Yet matter does not exist actually but only potentially; and thus it would seem rather that the specifying principle or form is a more important principle than matter. But the form is corruptible [according to some]; and so in general there is no eternal substance which is separate and exists of itself. But this is absurd; for such a principle and substance seems to exist and is sought by almost all accomplished thinkers as something that exists. For how will there be order in the world if there is not a principle which is eternal, separable and permanent (235-246)?

916. Again, if there is some substance and principle of such a nature as that now being sought, and this one principle belongs to everything and is one and the same for both corruptible and eternal things, the question arises why it is, if this principle is the same for all, that some of the things which come under it should be eternal and some not; for this is absurd. But if all corruptible things have one principle, and eternal things another, we shall face the same problem if the principle of corruptible things is eternal; for if it is eternal, why are not the things which fall under this principle also eternal? But if it is corruptible, it in turn must have some other principle, and this again must have another, and so on to infinity (250-265).

917. But on the other hand, if one were to posit those principles which are thought to be the most unchangeable, namely, being and unity, then, first, if each of these does not signify a particular thing or a substance, how will they be separable and exist of themselves? Yet the eternal and primary principles for which we are looking must be such. But if each of these does signify a particular thing or a substance, all beings will be substances; for being is predicated of all things, and unity is predicated of some. But it is false that all beings are substances.

918. Again, how can the statement of those be true who say that unity is the first principle and a substance, and who generate number as the first thing produced from the unit and matter and say that it is substance? For how are we to understand that the number two and each of the other numbers composed of units is one? For they say nothing about this, nor is it easy to do so.

919. But if someone maintains that lines and what is derived from these (I mean surfaces) are the first principles of things, these are not separable substances but sections and divisions; the former of surfaces, and the latter of bodies (and points are the sections and divisions of lines); and further they are the limits of these same things. And all of these exist in other things, and none are separable.

920. Again, how are we to understand that the unit and the point have substance. For every substance is generated but not the point; for the point amounts to a division (266-283).

921. There is also the problem that, while every science must be about universals and about such and such a universal, a substance is not a universal but is rather a particular and separable thing. Hence, if there is a science of principles, how are we to understand substance to be a principle (288-293) ?

922. Again, the question arises whether or not there is any principle apart from the concrete whole? And by this I mean the matter and what is joined to it. For if not, then everything that is in matter is corruptible. But if there is some principle, it must be the specifying principle or form. Therefore it is difficult to determine in what cases this exists apart and in what not; for in some cases it is evident that the form is not separable, for example, in that of a house (235-247).

923. Again, there is the question whether principles are the same specifically or numerically? For if they are the same numerically, all things will be the same (248-249).

COMMENTARY

2173. Having raised a question about the study of this science, Aristotle now raises a question about the things which are considered in this science. He does this, first (912:C 2173), with regard to substances; and second (916:C 2180), with regard to principles (“Again, if”).

In treating the first issue he raises two questions. First, he asks whether or not it is necessary to posit the existence of something else in reality over and above singular things. Now if one claims that it is not, then it seems to follow that the science which we are now investigating must be concerned with singular things. But this seems to be impossible, because singular things are infinite in number, and the infinite is unknowable. And if one claims that it is necessary to posit the existence of something apart from singular things, they must be genera or species; and then this science would deal with genera and species. First, he explains why this is impossible; for it seems that neither genera nor species are principles, yet this science deals with principles.

2174. The truth of the matter is that in reality there are only singular things, and that anything else exists only in the consideration of the intellect, which abstracts common attributes from particular ones.

2175. And in general (913).

Then he states the second question: whether there is some substance which exists apart from sensible substances existing here and now. This question must be raised here because, if there is nothing apart from sensible substances, only sensible substances are beings. And since wisdom is the science of beings, wisdom must be concerned only with sensible substances, even though we seem in this science to be looking for some other separate reality. It belongs to this science, then, to investigate whether or not there is something apart from sensible substances. And whichever alternative is taken, another question arises.

2176. Further, if there (914).

He therefore poses the question which seems to arise if one claims that there is something separate from sensible substances. The question is whether this separate thing exists apart from all sensible substances or only apart from some. And if only apart from some, it is hard to explain why we should posit a separate substance apart from some sensible substances and not from others. For there does not seem to be any reason why there should be a separate man and a separate horse apart from the men and horses we perceive by the senses, and why this should not be true also of other animals and other non-living things. But if there is some separate substance apart from all sensible substances, it follows that we must posit the existence of certain separate substances which are eternal and equal in number to sensible and corruptible substances. Thus, just as there is a corruptible man, in a similar way there would be an incorruptible man, and the same with horse and ox, and also with other natural bodies. This seems to be absurd.

2177. But if the principle (915).

Then he raises another question which seems to follow if there is no substance separate from sensible substances. This question asks what the first principle is, whether matter or form; for sensible substances are composed of these two principles. For at first glance it seems that nothing can be more of a principle of things than matter, which is the first subject and always continues to exist, as the first philosophers of nature claimed. Yet it would seem that matter cannot be a principle, because it is not an actuality but a potentiality. Hence, since actuality is naturally prior to potentiality, as has been pointed out in Book IX (785:C 1856), the specifying principle or form, which is an actuality, seems to be this principle.

2178. But it seems that form cannot be a principle because a sensible form appears to be corruptible. If a sensible form were the first principle, then, it would seem to follow that there would be no eternal substance, separable and existing of itself. But this is clearly absurd because some such principle, eternal and separate, and some such substance, is sought by [almost all] the famous philosophers. This is reasonable, for there would not be a perpetual order of things in the world if there were no separate and eternal principle which causes things to be perpetual.

2179. The true answer to this question is that there are certain substances which are separate from sensible substances; and these are not the Forms of sensible things, as the Platonists claimed, but the primary movers, as will be shown below (1056:C 2492).

2180. Again, if there (916).

Then he raises the question about principles. First, he asks what kinds of principles there are; second (917:C 2182), what they are (“But on the other hand”); and third (918:C :2184), how they are related to one another (“Again, how can”).

He accordingly asks (916) whether or not, if there is some separate substance and principle such as we are now seeking, it is the principle of all things, corruptible and incorruptible. Now if there is such a principle of all things, the question arises why some of the things which come from the same principle are eternal and some ire not. But if there is one principle for corruptible things and another for incorruptible ones, there remains the question why, if the principle is eternal the things coming from it are not themselves eternal. But if the principle of things is corruptible, and every corruptible thing is capable of being generated, and everything capable of being generated has a principle, it follows that the corruptible principle will have a principle, and that this will have another, and so on to infinity, as has been made clear above in Book II (153:C 301).

2181. The truth of the matter is that the first principle of all things is incorruptible, and that some things are corruptible because of their great distance from that principle. These are the things in which generation and corruption are caused by an intermediate cause which is incorruptible as regards its substance but changeable as regards place.

2182. But on the other hand (917).

Then he asks what the principles of things are. First, he examines the opinions of those men who claimed that the principles are unity and being because these are the most unchangeable. For no matter how a thing varies, it always remains one.

2183. But the opinion of these men gives rise to two questions. The first is whether unity and being signify a particular thing, i.e., a substance; for, if they do not, they cannot be separable and exist of themselves. But we are looking for such principles which are eternal and exist separately. Yet if they do signify a particular thing or substance, it follows that all things are substances, and that nothing is an accident; for being is predicated of any existing thing at all, and unity is predicated of some. Now there are some things which involve multiplicity in their being, and the different ways in which unity is predicated truly of these is clear enough. But it is false that all things are substances; and therefore it seems that unity and being do not signify substance.

2184. Again, how can (918).

The second question or problem which he raises runs as follows: those who maintain that unity, or the unit, is the principle and substance of things say that number is generated as a first product from the unit and matter. And this, i.e., number, they call substance. But evidently this is not true, because, if a number is composed of the unit and matter, it must be something one, just as what is composed of a living principle and matter must be something living. But in what way is the number two or any other number, which is composed of units, one, as the Platonists claimed? This is not easy to explain, inasmuch as it can be said that they neglected to account for this as though it were easy to understand.

2185. But if someone (919).

Second, he examines another opinion about the principles of things. For sonic claimed that “lines and what is derived from them,” namely, surfaces, are principles, because they held that bodies are composed of surfaces, and surfaces of lines. But it is clear that such things are not separate substances which exist of themselves; for such things are sections and divisions: lines being sections and divisions of surfaces, surfaces of bodies, and points of lines. They are also the limits of these things, i.e., points are the limits of lines, and so forth; for a point, which is at the extremity of a line, is the limit of a line. Now what is signified as actually within a line is a section of the line. The same thing is true of, a line in relation to a surface, and of a surface in relation to a body; for it is evident that limits and sections are entities which exist in other things as their subjects. Hence they cannot exist apart. Lines and surfaces, then, are not principles of things.

2186. Again, how are we (920).

Then he introduces another argument. He says that it cannot be understood that the unit and the point have a substance, because substance begins to exist only by way of generation. But when a line is actually divided, the division itself is a point.

2187. The correct answer to these questions is that neither units nor lines nor surfaces are principles.

2188. There is also the problem (921).

After the question about unity and being and dimensions he now raises the question about substances. First, he asks whether substances are principles. The answer seems to be that they are not; for every science is concerned with universals and with “such and such a universal,” i.e., some definite universal subject. Now a substance is not included among universals, but is rather a particular thing which exists of itself. Hence it seems that there is no science of substances. But a science is concerned with principles. Therefore substances are not principles.

2189. The truth is that, although universals do not exist of themselves, it is still necessary to consider universally the natures of things which subsist of themselves. Accordingly, genera and species, which are called second substances, are put in the category of substance; and of these there is scientific knowledge. And certain things which exist of themselves are principles; and these, because they are immaterial, pertain to intelligible knowledge, even though they surpass the comprehension of our intellect.

2190. Again, the question (922).

Second, he asks whether or not there is any “principle apart from the concrete whole,” i.e., the natural whole or composite. He explains that by concrete whole he means matter, or the thing composed of matter. For if there is no principle apart from the composite of matter and form, and those principles which are said to be in matter are corruptible, it follows that nothing is eternal. And if there is some principle apart from the composite, it must be the specifying principle or form. Then the question arises in which cases the form is separate and in which it is not. For it is obvious that in some cases the form is not separate; the form of a house, for example, is not separate from matter. It was for this reason that the Platonists did not posit Ideas or Forms of artificial things, because the forms of such things are actualities which cannot exist of themselves.

2191. The correct answer to this question is that there is some principle apart from matter, and this is not the form of sensible things.

2192. Again, there is (923).

He now asks how the principles of all things are related to one another: whether they are the same numerically or only specifically. For, if they are the same numerically, it follows that all things -are the same numerically. But if they are not the same numerically, this difference will have to be accounted for.

2193. The truth is that, if one is speaking of the extrinsic principles of things, they are the same numerically, since the first principle of all things is an agent and final cause. But the intrinsic principles of things-matter and form-are not the same numerically but only analogically, as will be shown below (1049-54:C 2474-87).

LESSON 3

All Beings Reduced to Being and Unity

ARISTOTLE’S TEXT Chapter 3: 1060b 31-1061b 17

924. Since the science of the philosopher treats of being as being in general and not of some part of it, and the term being is used in many senses and not merely in one, it follows that, if being is used equivocally and not with a common meaning, being does not fall under one science (for such terms do not have a common class). But if the term is used according to one common meaning, being will fall under one science.

925. Therefore the term seems to be used in the way mentioned, like the terms medical and healthy; for each of these is used in many senses. Now the term is used in each of these ways because of some kind of reference. Thus the former is used in reference to the science of medicine; the latter, to health; and still another, to something else; yet in each case the term is referred to the same thing. For both a discussion and a knife are called medical: the one because it comes from the science of medicine, and the other because it is useful to it. The same is true of the term healthy; for one thing is called healthy because it is a sign of health, and another because it produces it. The same is true of other terms. Hence the same thing is true of every instance of being; for each thing is called a being because it is either a modification or a state or a disposition or a motion or something else of this kind which belongs to being as being.

926. And since every being is referred to something one and common, each of the contrarieties may also be referred to the primary differences and contrarieties of being,.whether the primary differences are plurality and unity, likeness and unlikeness, or any others; for these have been considered (304).

927. And it makes no difference whether an existing thing is referred to being or to unity. For even if they are not the same but different, they are nevertheless interchangeable; for what is one is somehow a being, and what is a being is somehow one.

928. Now since it is the office of one and the same science to study all contraries, and one of each pair involves privation (though one might be puzzled how some contraries are predicated privatively, i.e., those which have an intermediate, as just and unjust), in all such cases it is necessary to hold that the privation of the one is not the privation of the whole notion of the other, but only of the last species. For example, if a man is just because of some habitual tendency to obey the laws, the unjust man will not always be deprived of the perfection completely but will fail to obey the laws in some respect; and in this respect privation will belong to him. The same holds true in other cases.

929. Now the mathematician in a sense studies things which are gotten by taking something away; for he speculates by removing from things all sensible qualities, such as heaviness and lightness, hardness and its contrary, and also heat and cold and other sensible contrarieties, and leaves only the quantified and the continuous (some things being such in one, some in two, and some in three dimensions). And he studies the properties of the quantified and the continuous as such and not in any other respect. And of some he considers the relative positions and attributes, and of others the commensurability and incommensurability, and of others the ratios; yet we claim that there is only one science of all these things, namely, geometry. The same holds true of being.

930. For an investigation of the attributes of being as being, and of the contrarieties of being as being, belong to no other science than [first] philosophy; for one would not assign to the philosophy of nature the study of things insofar as they are beings but rather insofar as they participate in motion. For dialectics and sophistry are concerned with the accidents of existing things, but not as beings, nor do they deal with being as being. It follows, then, that it is the philosopher who speculates about the things which we have mentioned, insofar as they are beings.

931. And since every being is referred to some one common meaning, which is used in many senses, and the same applies to contraries (for they are referred to the primary differences and contrarieties of being), and such things can fall under one science, the difficulty which was stated at the beginning of this work (900-904) is solved in this way. I mean the question how there can be one science of things which are many and different in genus.

COMMENTARY

2194. Having raised the foregoing questions, Aristotle now begins to assemble the things that belong to the consideration of this science. This is divided into two parts. In the first (924:C 2194) he indicates the things which this science considers. In the second (956:C 2247) he compares this science with the others (“Every science”).

The first part is divided into two members. First, he shows that it is the office of this science to consider all beings; and second (932:C 2206), that it has to consider the principles of demonstration (“And since the mathematician”).

In considering the first part he does two things. First, he shows that all things are somehow reduced to one. Second (929:C 2202), he shows that the study of this science extends to all things insofar as they are somehow reduced to some one thing (“Now the mathematician”).

In treating the first part he does two things. First, he shows that in view of the goal of our present study it is necessary to ask whether all things are somehow reduced to one. He says that, since the science of philosophy treats being as being in such a way as to consider being in terms of its universal character and not merely in terms of the intelligible character of any particular being, and since the term being is used in many senses and not just in one, if the many senses of being were purely equivocal without any common meaning, not all beings would fall under one science, because they would not in any way be reduced to one common class. And one science must deal with one class of things. But if the many senses of being have one common meaning, all beings can then fall under one science. Hence, in order to answer the question that was raised as to whether this science is one even though it treats many different things, we must consider whether or not all beings are reduced to some one thing.

2195. Therefore the term (925).

Here he shows that all things are reduced to some one thing. In treating this he does two things. First (925:C 2195), he explains his thesis. Second (928:C 2200), he clears up a point that might present a difficulty (“Now since”).

The first is divided into two parts. In the first he shows that all things are reduced to one. In the second (92-7:C 219q), he explains what this one thing is to which all things are reduced (“And it makes no difference”) -

In regard to the first part he does two things. First, he shows that all beings are reduced to one common being; and second (926:C 2198), that all contrarieties are reduced to one contrariety (“And since every”).

He accordingly says, first (925), that the term being is used in the way mentioned above; i.e., it is used of many things according to some common meaning. He makes this clear by means of two examples: the terms medical and healthy.

2196. For both of these terms are used variously, yet in such a way that they are reduced or referred to some one thing. The term medical is used in many ways inasmuch as it is referred in one sense to a medicine and in another to something else. And similarly the term healthy is used in many ways inasmuch as it is referred in one sense to health and in another to something else. Yet in both cases the various senses have reference to the same thing, though in different ways. For example, a discussion is called medical because it comes from the

science of medicine, and a knife is called medical because it is an instrument that is used by the same science. Similarly one thing is called healthy because it is a sign of health, as urine, and another because it causes health, as a medication. The same applies to other terms which are used in a similar way.

2197. It is evident that terms which are used in this way are midway between univocal and equivocal terms. In the case of univocity one term is predicated of different things with absolutely one and the same meaning; for example, the term animal, which is predicated of a horse and of an ox, signifies a living, sensory substance. In the case of equivocity the same term is predicated of various things with an entirely different meaning. This is clear in the case of the term dog, inasmuch as it is predicated both of a constellation and of a certain species of animal. But in the case of those things which are spoken of in the way mentioned previously, the same term is predicated of various things with a meaning that is partly the same and partly different—different regarding the different modes of relation, and the same regarding that to which it is related; for to be a sign of something and to be a cause of something are different, but health is one. Terms of this kind, then, are predicated analogously, because they have a proportion to one thing. The same holds true also of the many ways in which the term being is used; for being in an unqualified sense means what exists of itself, namely, substance; but other things are called beings because they belong to what exists of itself, namely, modifications or states or anything else of this kind. For a quality is called a being, not because it has an act of existence, but because a substance is said to be disposed by it. It is the same with other accidents. This is why he says that they belong to a being (or are of a being). It is evident, then, that the many senses of the term being have a common meaning to which they are reduced.

2198. And since (926).

Next he shows that all contrarieties are reduced to one first contrariety. Since all beings are reduced to one common meaning, and the contrarieties of beings, which are opposite differences, are in themselves a natural consequence of beings, it follows that contrarieties must be reduced to some primary contrariety, whatever it may be, whether it is plurality and unity, likeness and unlikeness, or whatever else are primary differences of beings. And contrarieties of this kind have to be considered in the science which establishes what is true about beings.

2199. And it makes (927).

Then he indicates what this common thing is to which all things are reduced. He says that it makes no difference whether things are reduced to being or to unity; for if it is said that being and unity are not the same conceptually but differ inasmuch as unity adds the note of indivisibility to being, none the less it is evident that they are interchangeable; for everything that is one is somehow a being, and everything that is a being is somehow one; because, just as a substance is a being properly and of itself, so too it is one properly and of itself. The way in which unity is related to being has been explained above in Book IV (301-04:C 548-60) and in Book X (832:C 1974).

2200. Now since (928).

Then he removes a difficulty. He says that, since all contraries are investigated by one science (and the most cogent reason seems to be that in each pair of contraries one contrary is used privatively, and this is known from its opposite term), the difficulty arises how contraries which have an intermediate can be predicated as privations, since in the case of opposites which are privatively opposed there is no intermediate.

2201. The answer to this must be that in the case of such contraries one opposite is not posited as a privation removing all the intelligible notes of the other but as the privation of the last species inasmuch as it detracts from the complete intelligible constitution of the whole species. For instance, if someone is said to be just because he habitually obeys the laws, he will not always be said to be unjust, as if he were deprived of the entire notion of justice, which would be the case if he obeyed the laws in no way—but rather because he fails to obey them in some respects. Hence the privation of justice will be found in him to the extent that he falls short of the perfection of justice. It is for this reason that he can be in an intermediate state, because not everyone who lacks justice is completely deprived of it but only of some part of it. And this intermediate state is one that differs in degree. The same holds true of other contraries. The privation of sight, however, is said to consist in the total lack of sight, and therefore there is no intermediate state between blindness and sight.

2202. Now the mathematician (929).

Here he shows that the investigations of this science extend to all beings insofar as they are reduced to one thing. In treating this he makes a tripartite division. First, he shows by an example from geometry that it is the office of one science to consider all things which are reduced to being. He says that the science of mathematics studies “those things which are gotten by taking something away,” i.e., abstract things. It makes this abstraction, not because it supposes that the things which it considers are separate in reality from sensible things, but because it considers them without considering sensible qualities. For the science of mathematics carries on its investigations by removing from the scope of its study all sensible qualities, such as lightness, heaviness, hardness, softness, heat and cold, and all other sensible qualities, and retains as its object of study only the quantified and the continuous, whether it is continuous in one dimension, as a line, or in two, as a surface, or in three, as a body. And it is primarily interested in the properties of these inasmuch as they are continuous and not in any other respect; for it does not consider the properties of surface inasmuch as it is the surface of wood or of stone. Similarly it considers the relationships between its objects. And in considering figures it also studies their accidents, and how quantities are commensurable or incommensurable, as is clear in Book X of Euclid, “and their ratios,” or proportions, as is clear in Book V of the same work. Yet there is one science of all these things, and this is geometry.

2203. Now what was true for the mathematician is also true for the philosopher who studies being. He passes over a study of all particular beings and considers them only inasmuch as they pertain to being in general. And though these are many, there is nevertheless a single science of all of them inasmuch as all are reduced to one thing, as has been pointed out.

2204. For an investigation (930).

Second, he indicates what science it is that considers the above-mentioned things. He says that the study of the attributes of being as being does not belong to any other science but only to this branch of philosophy. If it did belong to another science, it would mostly seem to belong to the philosophy of nature or to dialectics, which seemingly are the most common of the sciences. Now according to the opinion of the ancient philosophers who did not posit any substances other than sensible ones, it would seem to be the philosophy of nature that is the common science. In this way it would follow that it is the function of the philosophy of nature to consider all substances, and consequently all beings, which are reduced to substance.-But dialectics would seem to be the common science, and also sophistry, because these consider certain accidents of beings, namely, intentions and the notions of genus and species and the like. It follows, then, that it is the philosopher who has to consider the above-mentioned things, inasmuch as they are accidents of being.

2205. And since every (931).

Third, from what has been said, he draws his thesis as his chief conclusion. He says that, since being is used in many senses in reference to some one thing, and since all contrarieties are referred to the first contrariety of being, such things organized in this way can fall under one science, as has been pointed out. Thus he solves the question previously raised: whether there is one science of things which are many and generically different.

LESSON 4

This Science Considers the Principles of Demonstration

ARISTOTLE’S TEXT Chapter 4: 1061b 17-1061b 33

932. And since the mathematician uses the common axioms in a particular way, it must be the office of first philosophy to study principles of this kind. For the axiom or principle that “when equals are subtracted from equals the remainders are equal” is common to all quantities. But mathematics, assuming [principles of this kind], makes a study of some part of the quantified as its proper subject matter, for example, lines or angles or number or some of the other kinds of quantity. Yet it does not consider them inasmuch as they are beings but inasmuch as each is continuous in one, two or three dimensions. Philosophy, however, does not investigate those things which are in some part of matter insofar as each has some attribute, but it considers each of these particular things from the standpoint of being insofar as it is being.

933. Now what applies in the case of the science of mathematics is also true of the philosophy of nature; for the philosophy of nature studies the attributes and principles of beings inasmuch as they are moved, not inasmuch as they are beings. But, as we have said, the primary science considers these attributes and principles insofar as their subjects are beings, and not in any other respect. For this reason it is necessary to hold that this science and the science of mathematics are parts of wisdom (319-23; 900-01).

COMMENTARY

2206. Having shown how the investigations of this science are concerned with beings and with the attributes which belong to being as being, the Philosopher now shows how the investigations of this science are concerned with the first principles of demonstration.

This is divided into two parts. In the first (932:C 2206) he shows that it is the office of this science to consider these first principles of demonstration. In the second (934:C 2211) he draws his conclusions about one principle of demonstration which is prior to the others (“There is a principle”).

In regard to the first he does two things. First (932:C 22o6), he clarifies his thesis by considering the science of mathematics; and second (933:C 2209), by considering the philosophy of nature (“Now what applies”).

In the first part he uses the following argument: all the common axioms which are used by the particular sciences in a way peculiar to themselves and not in their common aspect belong to the consideration of this science. But the first principles of demonstration are used by the science of mathematics and by other particular sciences in a way peculiar to themselves. Therefore an investigation of these principles insofar as they are common belongs to the science which considers being as being.

2207. He accordingly says that, since the mathematician uses “the common axioms in a particular way,” i.e., insofar as they are adapted to his subject matter, it must be the function of first philosophy to consider such principles in their common aspect. For these principles are taken as principles of the sciences insofar as they are adapted to some particular subject matter. He clarifies his statement by an example.

2208. The principle that “when equals are subtracted from equals the remainders are equal” is common to all instances of quantity which admit of equality and inequality. But the science of mathematics presupposes principles of this kind in order to make a special study of that part of quantity which constitutes its proper subject matter; for there is no mathematical science which considers the attributes common to quantity as quantity, because this is the work of first philosophy. The mathematical sciences rather consider those attributes which belong to this or to that quantity; for example, arithmetic considers the attributes that belong to number, and geometry considers those that belong to continuous quantity. Thus the arithmetician uses the above-mentioned principle only inasmuch as it has to do with numbers, and the geometer uses it inasmuch as it has to do with lines and with angles. The geometer, however, does not consider this principle inasmuch as it relates to beings as beings but inasmuch as it relates to being as continuous, whether it is continuous in one dimension, as a line; or in two, as a surface; or in three, as a body. But first philosophy does not study the parts of being inasmuch as each has certain accidents; but when it studies each of these common attributes, it studies being as being.

2209. Now what applies (933).

Then he makes the same thing clear by considering the philosophy of nature. He says that what applies in the case of the science of mathematics is also true of the philosophy of nature; for while the philosophy of nature studies the attributes and principles of beings, it does not consider beings as beings but as mobile. The first science, on the other hand, deals with these inasmuch as they are being, and not in any other respect. Hence, the philosophy of nature and the science of mathematics must be parts of first philosophy, just as any particular science is said to be a part of a universal science.

2210. The reason why common principles of this kind belong to the consideration of first philosophy is this: since all first self-evident propositions are those of which the predicate is included in the definition of the subject, then in order that propositions may be self-evident to all, it is necessary that their subjects and predicates should be known to all. Common notions of this type are those which are conceived by all men, as being and non-being, whole and part, equal and unequal, same and different, and so on. But these belong to the consideration of first philosophy; and therefore common propositions composed of such terms must belong chiefly to the consideration of first philosophy.

LESSON 5

The Principle of Non-Contradiction

ARISTOTLE’S TEXT Chapters 5 & 6: 1061b 34-1062b 19

934. There is a principle in existing things about which it is impossible to make a mistake, but of which one must always do the contrary, I mean acknowledge it as true, namely, that the same thing cannot both be and not be at one and the same time; and the same is also true of other things which are opposed in this way (326-328).

935. And while there is no demonstration in the strict sense of such principles, one may employ an argument ad hominem; for it is impossible to construct a syllogism from a more certain principle than this one. But this would be necessary if there were demonstration of it in the strict sense (329-330).

936. Now anyone who wants to prove to an opponent making statements opposite to one’s own that he is wrong must take some such principle which is the same as this one—that the same thing cannot both be and not be at the same time—but apparently is not the same. For this will be the only method of demonstration that can be used against one who says that opposite statements can be truly made about the same subject.

937. Accordingly, those who are to join in some discussion must understand each other to some extent. And if this does not happen, how will they join in a common discussion? Therefore each of the terms used must be understood and must signify something, and not many things but only one. But if a term does signify many things, it must be made clear to which of these it refers. Hence, one who says that this is and is not, totally denies what he affirms, and thus denies that the term signifies what it signifies. But this is impossible. Hence, if to be this has some meaning, the contradictory cannot be said to be true of the same subject (332-340).

938. Again, if a term signifies something and this is affirmed truly, it must necessarily be so; and what is necessarily so cannot not be. Hence opposite affirmations and negations cannot be true of the same subject (337-338).

939. Again, if the affirmation is in no way truer than the negation, it will not be truer to say that something is a man than to say that it is not a man. And it would also seem that it is either more or not less true to say that a man is not a horse than to say that he is not a man. Hence one will also be right in

saying that the same thing is a horse; for it was assumed that opposite statements are equally true. Therefore it follows that the same thing is a man and a horse, or any other animal (343-345). Hence, while there is no demonstration in the strict sense of these principles, there is still a demonstration ad hominem against one who makes these assumptions.

940. And perhaps if one had questioned Heraclitus himself in this way, he would quickly have forced him to admit that opposite statements can never be true of the same subjects. But he adopted this view without understanding his own statement (328). And in general if what he said is true, not even this statement will be true—I mean that the same thing can both be and not be at one and the same time. For just as when they are separated the affirmation will not be truer than the negation (346), in a similar way when both are combined and taken together as though they were one affirmation, the negation will not be truer than the whole statement regarded as an affirmation.

941. Again, if it is possible to affirm nothing truly, even this statement-that no affirmation is true-will be false (396-397). But if there is a true affirmation, this will refute what is said by those who raise such objections and completely destroy discussion.

Chapter 6

942. The statement made by Protagoras is similar to those mentioned; for he said that man is the measure of all things, meaning simply that whatever appears so to anyone is just as it appears to him. But if this is true, it follows that the same thing is and is not, and is good and evil, and that other statements involving opposites are true; because often a particular thing appears to be good to some and just the opposite to others, and that which appears to each man is the measure.

COMMENTARY

2211. Having shown that a study of the common principles of demonstration belongs chiefly to the consideration of this philosophical science, the Philosopher now deals with the first of these principles (934:C 2212). For just as all beings must be referred to one first being, in a similar fashion all principles of demonstration must be referred to some principle which pertains in a more basic way to the consideration of this philosophical science. This principle is that the same thing cannot both be and not be at the same time. It is the first principle because its terms, being and non-being, are the first to be apprehended by the intellect.

2212. This part is divided into two members. In the first (934:C 2211) he establishes the truth of this principle. In the second (936:C 22T4) he rejects an error (“Now anyone who”).

In reference to the first part he does two things regarding this principle. First, he says that in regard to beings there is a principle of demonstration “about which it is impossible to make a mistake” (i.e., so far as its meaning is concerned), but of which we “must always do the contrary,” namely, acknowledge it as true. This principle is that the same thing cannot both be and not be at one and the same time, granted of course that the other conditions which it is customary to give in the case of a contradiction are fulfilled, namely, in the same respect, in an unqualified sense, and the like. For no one can think that this principle is false, because, if someone were to think that contradictories may be true at the same time, he would then have contrary opinions at the same time; for opinions about contradictories are contrary. For example, the opinion that “Socrates is sitting” is contrary to the opinion that “Socrates is not sitting.”

2213. And while (935).

Second, he says that, while there cannot be demonstration in the strict sense of the above-mentioned principle and other similar ones, one may offer an argument ad hominem in support of it. That it cannot be demonstrated in the strict sense he proves thus: no one can prove this principle by constructing a syllogism from some principle which is better known. But such would be necessary if that principle were to be demonstrated in the strict sense. However, this principle can be demonstrated by using an argument ad hominem against one who admits some other statement, though less known, and denies this one.

2214. Now anyone who (936).

Then he rejects the opinion of those who deny this principle; and this is divided into two parts. First (936:C 2214), he argues against those who deny this principle. Second (943:C 2225), he shows how one can meet this opinion (“Now this difficulty”).

In regard to the first he does two things. First (936:C 2214), he argues against those who unqualifiedly deny this principle. Second (940:C 2221), he turns his attention to certain particular opinions (“And perhaps”).

In regard to the first he does two things. First, he gives the method of arguing against this error. He says that in arguing against an opponent who claims that contradictory propositions may be true, anyone who wants to show that this opinion is false ought to take some such principle which is the same as this one—that the same thing cannot both be and not be at the same time—but apparently is not the same. For, if it were evidently the same, it would not be admitted by an opponent. Yet if it were not the same, he could not prove his thesis, because a principle of this kind cannot be demonstrated from some principle which is better known. Hence, it is only in this way that a demonstration can be made against those who say that contradictories may be true of the same subject, namely, by assuming as a premise what is in fact the same as the conclusion but apparently is not.

2215. Accordingly (937).

Second, he begins to argue dialectically against the above-mentioned error; and in regard to this he gives three arguments, First, he argues as follows: if two men are to join in a discussion in such a way that one may communicate his view to the other in a dispute, each must understand something that the other is saying. For if this were not the case, no statement would be understood by both of them; and thus an argument with an opponent would be pointless.

2216. However, if one of them is to understand what the other is saying, each of the terms used must be understood according to its proper meaning and must therefore signify some one thing and not many things. And if it should signify many, it will be necessary to make clear which of the many things it signifies; otherwise one would not know what the other person means.

2217. Now granted that a term signifies one thing, it is evident that one who says both that this is and that this is not, for example, that Socrates is a man and that he is not a man, denies the one thing which he attributed to Socrates, namely, that he is a man, when he adds that he is not a man; and thus he denies what he first signified. Hence it follows that a word does not signify what it signifies. But this is impossible. Consequently, if a term signifies some definite thing, the contradictory cannot be truly affirmed of the same subject.

2218. Again, if a term (938).

Then he gives the second argument, which runs as follows: if a term signifies some attribute, and the attribute signified by the term is truly affirmed of the same subject of which the term is first predicated, this attribute must belong to the subject of which the term is predicated so long as the proposition is true. For this conditional proposition, “If Socrates is a man, Socrates is a man,” is clearly true. Now every true conditional proposition is a necessary one. Hence, if the consequent is true, the antecedent must be true. But what is, cannot sometimes not be, because to be necessary and to be incapable of not being are equivalent. Therefore so long as the proposition “Socrates is a man” is true, the proposition “Socrates is not a man” cannot be true. Thus it is evident that opposite affirmations and negations cannot be true of the same subject at the same time.

2219. Again, if the affirmation (939).

Then he gives the third argument, which is as follows: if an affirmation is not truer than the negation opposed to it, one who says that Socrates is a man does not speak with greater truth than one who says that Socrates is not a man. But it is evident that one who says that a man is not a horse speaks either with greater or with no less truth than one who says that a man is not a man. Hence, according to this argument, he who says that a man is not a horse will speak with equal or no less truth. But if contradictory opposites are true at the same time, for example, if the proposition “Man is not a horse” is true, and the proposition “Man is a horse” is also true, then it follows that a man is a horse and also any other animal.

2220. But because someone could criticize the foregoing arguments on the grounds that the things assumed in them are less known than the intended conclusion, he therefore answers this by saying that no one of the foregoing arguments is demonstrative in the strict sense, although there can be an argument ad hominem against an opponent who gives this argument, because the things assumed must be admitted to be true even though they are less known, absolutely than what he denies.

2221. And perhaps (940).

Then he rejects the above error by considering certain particular thinkers. He does this, first (940:C 2221), with regard to Heraclitus; and second (942:C 2224), with regard to Protagoras (“The statement”).

Now Heraclitus posited two things: first, that an affirmation and a negation may be true at the same time (and from this it would follow that every proposition, affirmative as well as negative, is true); and second, that there may be an intermediate between affirmation and negation (and from this it would follow that neither an affirmation nor a negation can be true). Consequently every proposition is false.

2222. First (940:C 2222), he raises an argument against Heraclitus’ first position; and second (941:C 2223), against his second position (“Again, if it is possible”).

He accordingly says, first (940), that by giving an argument ad hominem in this way one may easily bring even Heraclitus, who was the author of this statement, to admit that opposite propositions may not be true of the same subject. For he seems to have accepted the opinion that they may be true of the same subject because he did not understand his own statement. And he would be forced to deny his statement in the following way: if what he said is true, namely, that one and the same thing can both be and not be at one and the same time, it follows that this very statement will not be true; for if an affirmation and a negation are taken separately, an affirmation is not truer than a negation; and if an affirmation and a negation are taken together in such a way that one affirmation results from them, the negation will not be less true of the whole statement made up of the affirmation and the negation than of the opposite affirmation. For it is clearly possible for some copulative proposition to be true, just as for some simple proposition; and it is possible to take its negation. And whether the copulative proposition be composed of two affirmative propositions, as when we say “Socrates is sitting and arguing,” or of two negative propositions, as when we say “It is true that Socrates is not a stone or an ass,” or of an affirmative proposition and a negative proposition, as when we say “It is true that Socrates is sitting and not arguing,” nevertheless a copulative proposition is always taken to be true because one affirmative proposition is true. And he who says that it is false takes the negation as applying to the whole copulative proposition. Hence he who says that it is true that man is and is not at the same time, takes this as a kind of affirmation; and that this is not true is the negation of this. Hence, if an affirmation and a negation are true at the same time, it follows that the negation which states that this is not true, i.e., that an affirmation and a negation are true at the same time, is equally true. For if any negation is true at the same time as the affirmation opposed to it, every negation must be true at the same time as the affirmation opposed to it; for the reasoning is the same in all cases.

2223. Again, if it is possible (941).

Then he introduces an argument against the second position of Heraclitus: that no affirmation is true. For if it is possible to affirm that nothing is true, and if one who says that no affirmation is true does affirm something, namely, that it is true that no affirmation is true, then this statement will be false. And if some affirmative statement is true, the opinion of people such as those who oppose all statements will be rejected. And those who adopt this position destroy the whole debate, because if nothing is true, nothing can be conceded on which an argument may be based. And if an affirmation and a negation are true at the same time, it will be impossible to signify anything by a word, as was said above (937:C 2215), and then the argument will cease.

2224. The statement (942).

Here he considers the opinion of Protagoras. He says that the statement made by Protagoras is similar to the one made by Heraclitus and by others who claim that an affirmation and a negation are true at the same time. For Protagoras says that man is the measure of all things, i.e., according to the intellect and the senses, as has been explained in Book IX (753:C 1800), as if the being of a thing depended upon intellectual and sensory apprehension. And one who says that man is the measure of all things merely says that whatever appears so to anyone is true. But if this is maintained, it follows that the same thing both is and is not and is both good and evil at the same time. The same thing is also true of other opposites, because often something seems to be good to some and just the opposite to others, and the way in which things seem or appear is the measure of all things according to the opinion of Protagoras; so that, inasmuch as a thing appears, to that extent it is true.

LESSON 6

Contradictories Cannot Be True at the Same Time

ARISTOTLE’S TEXT Chapter 6: 1062b 20-1063b 35

943. Now this difficulty may be solved by considering the origin of this view.

944. For it seems to have arisen in some cases from the opinion of the philosophers of nature, and in others from the fact that not all men apprehend the same thing in the same way, but something appears pleasant to some and the opposite to others (352).

945. For the view that nothing comes from non-being but everything from being is a doctrine common to nearly all those who have dealt with nature. Thus, since the not-white comes from what is actually white, and not from the not-white, should the not-white have come to be, what becomes not-white will have come to be from what is not not-white. Hence whiteness must come from non being according to them, unless the white and the not-white are the same. But it is not hard to solve this difficulty; for we have stated in our physical treatises in what sense things which come to be come from non-being, and in what sense they come from being (355-356).

946. But it is also foolish to occupy oneself equally with both opinions and with the fanciful statements of those who argue against themselves, because i is evident that one or the other of them must be wrong. This is clear from the facts of sensory perception; for the same thing never appears sweet to some and the opposite to others unless in some the organ of the sense which distinguish the above-mentioned savors has been impaired or injured. And such being the case, some must be taken as the measure and the others not. And I say that th same thing applies in the case of good and evil, of beautiful and ugly, and o other attributes of this kind. For to maintain this view is not different from maintaining that what appears to those who push their finger under their eye an make one object appear to be two must therefore be two because it appears to be so many, and yet that it must be one because to those who do not move their eye the one object appears to be one (369-375).

947. And in general seeing that things here are subject to change and never remain the same, it would be unfitting to base our judgment of the truth on this. For in pursuing the truth one must start with those things which are always the same and never undergo a single change. Such things are those which contain the world; for they do not appear at one time to be such and at another different but they are always the same and admit of no change (365).

948. Further, if there is motion, there is also something that is moved; and everything is moved from something and to something. Therefore that which is moved must be in that from which it is moved, and yet not be in it; and it must be moved to this and come to be in it; but contradictories cannot be true at the same time, as they claim.

949. And if things here are in a state of continuous change and motion as regards quantity, and one were to suppose this even though it is not true, why should they not be permanent as regards quality? For the view that contradictories may be predicated of the same subject seems to be based largely on the assumption that the quantity of bodies does not remain constant; and for this reason they say that the same thing is and is not four cubits long. But a thing’s substance involves quality, and this is of a determinate nature, whereas quantity is of an indeterminate nature (365).

950. Further, when a physician orders them to take some particular food, why do they take it? For why is this particular food bread rather than not bread? Hence it would make no difference whether they ate it or not. But they take the food prescribed as though they know the truth about it and that it is the food prescribed. Yet they should not do this if there is no nature which remains fixed in the sensible world, but everything is always in a state of motion and flux (349).

951. Again, if we are always undergoing change and never remain the same, what wonder is it if to us, as to those who are ill, things never appear the same? For to them also, since they are not in the same condition as when they were well, sensible qualities do not appear to be the same; yet sensible things themselves need not for this reason undergo any change, but they cause different, and not the same, impressions in those who are ill. And perhaps the same thing must happen to those who are well if the above-mentioned change takes place (950). However, if we do not change but always remain the same, there will be something permanent (357-359).

952. Hence, in the case of those who raise the foregoing difficulties as a result of reasoning, it is not easy to meet their arguments unless they assume something and do not demand a reason for it; for every argument and demonstration comes about in this way. For those who admit nothing destroy discussion and reasoning in general, and thus there is no reasoning with such men. But in the case of those who are puzzled by the usual problems, it is easy to meet them and to reject the arguments which cause their difficulty. This becomes clear from what has been said above (943-951).

953. It is evident from these considerations, then, that opposite statements cannot be verified of the same subject at one time (353; 376-377), nor can contrary ones, because every contrariety involves privation. This becomes clear if we reduce the definitions of all contraries to their principle (382). Similarly no intermediate can be predicated of one and the same subject. For if the subject is white, those who say that it is neither white nor black are wrong, for it then follows that it is white and is not white; for the second of the two terms which we have combined is true of it, and this is the contradictory of white (383-391).

954. One cannot be right, then, in holding the views either of Heraclitus (940) or of Anaxagoras; and if this were not so it would follow that contraries would be predicated of the same subject. For when Anaxagoras says that there is a part of everything in everything else, he says that nothing is sweet any more than it is bitter, and so on with any of the other pairs of contraries, since everything is present in everything else, not potentially, but actually and separately.

955. And similarly all statements cannot be true or all false, both because of many other difficulties which might be brought forward on the basis of this position, and because, if all statements are false, anyone who says this will not speak the truth; and if all are true, it will not be false to say that all are false (392).

COMMENTARY

2225. Having argued against those who claim that contradictories may be verified of the same subject at the same time, the Philosopher now shows how these men can be persuaded to abandon this theory. His discussion is divided into two parts. In the first (943:C 2225) he explains his thesis. In the second (953:C 2243) he draws a corollary from what has been said (“It is evident”).

The first part is divided into two members. In the first he explains how it is possible in some cases to deal with the above-mentioned theory. In the second (952:C 2241) he indicates in what cases it can be refuted and in what not (“Hence, in the case”).

In treating the first (943) he does three things. First, he describes the way in which the foregoing theory can be disqualified in some cases. He says that the above-mentioned difficulty which led some people to adopt the position that contradictories may be verified of the same subject at the same time can. be dispelled if one considers its source.

2226. For it seems (944).

Second, he gives two sources of this position. He says that this position seems to have arisen in some cases from the opinion of the philosophers of nature, who claimed that nothing comes to be from non-being, and in others from the fact that not all men make the same judgments about the same things, but something appears pleasant to some and just the opposite to others. For if one were to believe that whatever appears is true, it would follow from this that opposites are true at the same time.

2227. For the view (945).

Third, he shows how the abovementioned position might follow from the two sources just given; and he points out how it may be dealt with. First, he shows how it might follow from the opinion of the philosophers of nature; and second (946:C 2227), from the belief that every appearance is true (“But it is also foolish”).

He accordingly says, first (945), that the doctrine common to nearly all of the thinkers who have dealt with nature is that nothing comes to be from non-being, but everything from being. It is clear that something becomes not-white from what is actually white; but what is not-white does not come from what is not-white. Further, it is also evident that what is not-white comes from what is not not-white. Consequently, it is evident that what is not not-white becomes not-white, just as what is not-black becomes black. It is clear, then, that that from which the not-white comes to be is the white, and it is not not-white. This cannot be understood in the sense that the not-white is entirely non-being, because it would then seem to follow that something comes to be from non-being absolutely. For example, if we were to say that fire comes from what is not-fire, there would be the question how they think that that from which fire comes to be is entirely not-fire. For it would then seem to follow, according to them, that something comes to be from non-being. Hence they claimed that fire lay hidden in that from which fire comes to be, as is evident from the opinion of Anaxagoras, which is given in Book I of the Physics. Similarly, they believed that, if something comes to be not-white from what is not not-white, the not-white must have preexisted in that from which it comes to be, as has been explained. Thus it would follow, according to them, that that from which the not-white comes to be is both white and not-white at the same time, unless it is assumed that something comes to be from non-being.

2228. But this difficulty is not hard to solve, as the Philosopher points out; for it has been explained in Book I of the Physics how a thing comes to be from being and how from nonbeing; for it has been stated that something comes to be from what is a nonbeing in act, though it is incidentally a being in act. But it comes to be properly from matter, which is in potency; for it is accidental to the process of making that the matter from which a thing comes to be should be the subject of form and of privation. Thus it is not necessary that that from which a thing comes to be should be at the same time both a being and a nonbeing in act, but that it should be of itself in potency both to being and to non-being, i.e., both to form and to privation.

2229. But it is also foolish (946).

Then he rejects the foregoing opinion inasmuch as it might be derived from the other source, i.e., from the view that every appearance is judged to be true. First, he rejects this source; and second (947:C 2232), its cause (“And in general”).

He accordingly says, first (946), that, just as it is foolish to think that contradictories may be verified of the same subject at the same time, so too “it is also foolish to occupy oneself with,” i.e., to accept, both of the foregoing opinions of the philosophers who argue against themselves; for it is obvious that one or the other of them must be in error.

2230. This is evident from the facts of sensory perception; for the same thing never appears sweet to some and bitter to others, unless in some the sense organ and the power which discriminates between savors, has been impaired or injured. But since this does happen in some cases, “some must be taken as the measure,” i.e., the judgment of those whose senses are not impaired in this way must be taken as the rule and measure of truth. But this should not be understood to apply to those whose senses are impaired.

2231. And what is evident in the case of sensory perception must also be said to apply in the case of good and evil, of beautiful and ugly, and of all attributes of this kind which are apprehended by the intellect. For if some conceive a thing to be good and others evil, the judgment of those whose intellect has not been impaired by some bad habit or by some bad influence or by some other cause of this kind must be the norm. For if someone were to hold that it is not less fitting to believe the one group rather than the other, this would not differ in any way from saying that things are as they appear “to those who push their finger under their eye,” i.e., who move their eye with their finger, and thereby make one thing appear as two, and say that it must be two because it appears to be so many, and again that it must be one because it appears to be one to those who do not move their eye with their finger. For it is obvious that we must base our judgment about the oneness of things on the judgment which the eye makes when it does not receive some strange impression, and not on the judgment which it makes when it receives such an impression. Now a man judges one visible object to be two because the form of the visible object is made to appear as two to the organ of vision when it is moved; and this double impression reaches the organ of the common sense as though there were two visible objects.

2232. And in general (947).

Then he rejects the basis of the position that every appearance is true. For some held this because they thought that all things are in a state of continuous flux, and that there is nothing fixed and determinate in reality; and thus it would follow that a thing is such only when it is seen.

2233. He therefore presents five arguments against this position. He says, first, that it is altogether unfitting to base our judgment about the whole truth on the fact that these sensible things which are near or close to us are undergoing change and are never permanent. But the truth must be based rather on those things which are always the same and never undergo any change as regards their substance, though they do appear to be subject to local motion. For such things are those “which contain the world,” i.e., the celestial bodies, to which these corruptible bodies are compared as things that have no quantity, as the mathematicians prove. Now the celestial bodies are always the same and do not at one time appear to be such and at another different, for they admit of no change which affects their substance.

2234. Further, if there (948).

Then he gives the second argument against this position. The argument runs thus: if there is motion in these lower bodies, there must be something that is moved, and it must also be moved from something and to something. Hence that which is moved must already be in that from which it is moved and yet not be in it, and this must be moved to something else and be continuously coming to be in it. Thus some definite affirmation, as well as some negation, must be true. And it will not be necessary that a contradiction be true of the same subject, b6cause according to this nothing would be moved. For if the same thing might be at the extreme to which it is moved and not be at it, there would be no reason why a thing which has not yet reached an extreme should be moved thereto, because it would already be there.

2235. And if things (949).

He gives the third argument; and with a view to making this clear it should be borne in mind that, when Heraclitus saw that a thing increased in size according to some definite and very small quantity over a long period of time (for example, a year), he thought that some addition would be made in any part of that time, and that it would be imperceptible because of the very small quantity involved. And because of this he was led to believe that all things, even those which seem to be static, are also being moved continuously by an imperceptible motion, and that after a long time their motion would become apparent to the senses. But his opinion about increase is false; for increase does not take place continuously in such a way that something grows in any part of time, but a body is disposed to increase during some time and then grows, as Aristotle makes quite clear in Book VIII of the Physics.

2236. Hence he says that, if the bodies around us here are in a continuous state of flux and motion as regards quantity, and one wishes to admit this even though it is not true, there is no reason why a thing cannot be unchanging as to its quality. For the opinion that contradictories are true of the same subject at the same time seems to be based largely on the assumption that the quantitative aspect of bodies does not remain constant; and thus some thought that the same thing is and is not four cubits long. But a thing’s substance is defined in terms of some quality, i.e., some form; and quality is of a determinate nature in things, although quantity is of an indeterminate nature because of change, as has been pointed out.

2237. Further, when a physician (950).

Then he gives the fourth argument, which runs thus: if there is nothing fixed in the world as regards being or non-being, why do they take this kind of bread which the physician prescribes and not that? For according to the position given above, why is this bread rather than not-bread? He implies that the answer cannot be in the affirmative any more than in the negative. And thus it would make no difference whether one ate the bread or did not. But we see that they take the bread which the physician prescribes, implying that they form a true judgment about bread itself, and that this kind of bread is really the one which the physician prescribes. Yet this would not be the case if no nature remained fixed in the sensible world but all things are always in a state of motion and flux.

2238. Again, if we (951).

Then he presents the fifth argument: since the above-mentioned position assumes that there is no fixed truth in things because of the continuous change which they undergo, if the truth is identical with appearance it is necessary to say that we men, who make judgments about other things, are either in motion or are not.

2239. For if we are always undergoing change and never remain the same, it is not surprising that things never appear the same to us; and this is the case with those who are ill. For since they have been changed and are not in the same state as when they were well, the sensible qualities which they perceive by way of the senses will not seem the same to them as they did before they became ill. For to those whose sense of taste has been impaired sweet things seem bitter or tasteless; and the same is true of other sensible qualities. Yet sensible qualities themselves are not changed for this reason, but they cause different impressions in those who are ill because their senses are differently disposed. Therefore, if we men, who are continuously undergoing change, make different judgments about other things, this should not be attributed to things but to us.

2240. However, if we are not changing but always remain the same, there will therefore be something permanent in the world and consequently some fixed truth about which we can make positive judgments. For we make judgments not only about other things but also about human nature.

2241. Hence, in the case (952).

Then he indicates who can be disabused of the above opinion and who can not. He says that, if those who adopt the foregoing opinions do so not because of any reasoning, in the sense that they do not assume anything because they are obstinate, and do not inquire into the reasons for the things that they say but stubbornly adhere to the opinions which they hold, it is not easy for them to give up an opinion of this kind. For every argument and every demonstration comes about in this way, namely, by admitting the truth of some statement and investigating the reason for it. But those who admit nothing destroy discussion and every rational argument; and thus no appeal of reason can be addressed to them whereby they can be dislodged from their error.

2242. But if there are any who are perplexed because of certain deficiencies (for example, because they do not understand some things well), it is easy to dispel such an error by removing the difficulties which puzzle them. This is evident from the previous discussion in which he deals with the difficulties that could lead to the above-mentioned opinion.

2243. It is evident (953).

Then he draws three corollaries from what has been said. First, it is evident from the foregoing discussion that opposite statements cannot be verified of the same subject at one and the same time. Consequently it is clear from this that contraries cannot be verified of the same subject at the same time. And this is true because every contrariety involves privation; for one of two contraries is always a priv4on. This becomes evident if one wishes to reduce the definitions of contraries to their first principle; for contained in the notion of black is the privation of white. Since a privation, then, is a kind of negation having a determinate subject, it is evident that, if contraries were true of the same subject, both an affirmation and a negation would have to be true of the same subject at the same time.

2244. Now, it is not only impossible for two contraries to be true of the same subject at the same time, but it is also impossible for an intermediate to be predicated of one and the same subject of which one of two extremes is predicated; for from what has been said in Book X (880-86-.C 2101-10 it is evident that an intermediate between contraries involves the privation of both extremes, whether it is designated by one word or by many or is nameless. Hence an intermediate between white and black, such as red or yellow, contains in its definition the fact that it is neither white nor black. Therefore, if one says that some subject is red when it is really white, he is saying at the same time that it is neither white nor black. Hence he is in error; for it would follow that that subject is both white and not white at the same time; because if it is true that that subject is neither white nor black, the other part of the copulative proposition may be verified of the same subject, and this is the contradictory of being white. Thus it follows that, if an intermediate and an extreme are true of the same subject, contradictories must be true of the same subject.

2245. One cannot (954).

He gives the second corollary. He concludes that, if an affirmation and a negation are not true at the same time, neither the opinion of Heraclitus nor that of Anaxagoras is true. That this is so regarding the opinion of Heraclitus is evident from what has been said. Hence he shows that the same thing applies with respect to the opinion of Anaxagoras. He says that, if Anaxagoras’ opinion is not false, it follows that contraries may be predicated of the same subject, and therefore that contradictories may also be predicated of the same subject. This is shown as follows. Anaxagoras claimed that anything at all comes to be from anything at all, and everything which comes to be comes from something. Hence he was not compelled to maintain that something comes to be from nothing, and thus he claimed that everything is present in everything else. Therefore, since he posited that there is a part of everything in everything else (for example, a part of flesh in bone, and a part of whiteness in blackness, and vice versa), it follows that the whole is no more sweet than bitter. The same holds true of other contrarieties. And this is so if a part of anything is present in any whole not only potentially but actually and separately. And he added this because whatever comes to be from something else must pre-exist in it potentially and not actually. Hence contraries must preexist in the same subject potentially and not actually. This does not mean that contraries exist separately in something, because the potency for contraries is the same. But Anaxagoras did not know how to distinguish between potency and actuality.

2246. And similarly (955).

He gives the third corollary. He concludes from what has been said that both opinions are false, i.e., the opinion of those who said that all statements are true, and the opinion of those who said that all are false. This is evident because of the many difficult and serious conclusions which result from these opinions which have been brought together here and above in Book IV (332402:C 611-748); and especially “because if all statements are false,” he who says that every statement is false makes a statement and thus does not speak the truth. And similarly if all statements are true, he who says that all are false will not say what is false but will speak the truth. And for this reason the position of one who claims that all statements are true is destroyed.

LESSON 7

Metaphysics Differs from All the Other Sciences

ARISTOTLE’S TEXT Chapter 7: 1063b 36-1064b 14

956. Every science seeks certain principles and causes of each of the knowable objects which comes within its scope; for example, medicine and gymnastics do this, and so does each of the other sciences, productive as well as doctrinal. For each of these marks off for itself some class of things and occupies itself with this as with something that is real and a being, though not as being; but there is a certain other science distinct from these which does this.

957. And each of the sciences mentioned somehow assumes the quiddity in some class of things and tries to prove the rest, with greater or lesser certainty. Some derive the quiddity from sensory perception, and some by assuming it from some other science. Hence from such a process of induction it becomes evident that there is no demonstration of the substance and of its quiddity.

958. Now since there is a science of nature, it is evident that it must differ from both the practical and the productive sciences. For in the case of a productive science the source of motion is in the maker and not in the thing made, and it is either the art or some kind of potency. And similarly in the case of a practical science the motion is not in the thing done but rather in the agents. But the science of the philosopher of nature is concerned with things which have a source of motion in themselves. It is evident from these considerations, then, that the philosophy of nature must be neither practical nor productive but speculative; for it must fall in one of these classes.

959. And since it is necessary that each one of the sciences have some knowledge of the quiddity and must use it as a starting point, we must not fail to consider how the philosophy of nature should define things, and how it should consider the intelligible structure of the substance: whether in the same way as the term snub or rather as the term concave. For of these the notion of snub includes the matter of the object, but that of concave is expressed without matter. For snubness comes into being in a nose, and for this reason its intelligible structure includes matter; for snub is a concave nose. It is evident, then, that the intelligible structure of flesh and of eye and of the other parts of the body must always be given along with matter.

960. And since there is a science of being as being and as separable, one must consider whether this science should be held to be the same as the philosophy of nature or rather a science distinct from it. The philosophy of nature deals with things which have a principle of motion in themselves, and mathematics is speculative and is concerned with things which are permanent but are not separable. Therefore there is a science distinct from both of these, which treats of what is separable and immovable; that is to say, if there is some such substance, and I mean one which is separable and immovable, as we shall attempt to prove (1055-76). And if there is some such nature among existing things, this will exist somewhere and will be divine, and it will be the primary and highest principle. It is evident, then, that there are three classes of speculative science: the philosophy of nature, mathematics and theology.

961. The class of speculative sciences, then, is the highest, and of these the last mentioned is highest of all. For it is concerned with the noblest of beings, and each science is said to be higher or lower by reason of its proper object.

962. However, one might raise the question whether the science of being as being is universal or not. For each of the mathematical sciences deals with some one determinate class of things, but a universal science is common to all. If, then, natural substances are the primary beings, the philosophy of nature must be the primary science. But if there is another nature and substance which is separable and immovable, the science which treats of this must be different from and prior to the philosophy of nature, and must be universal because it is prior (902).

COMMENTARY

2247. Having shown with what things this science is concerned, here the Philosopher compares this science with the others. In regard to this he does three things. First (956:C 2247), he indicates what is proper to the particular sciences. Second (958:C 2252), he shows how the particular sciences differ from one another (“Now since”). Third (960:C 2259), he compares this science with the others (“And since there is”).

In treating the first member of this division he does two things, insofar as there are two characteristics which he says pertain to the particular sciences. He accordingly says, first (956), that every particular science seeks certain principles and causes of the proper object of knowledge which comes within its scope. He says certain principles and causes because not every science considers every class of cause.

2248. He gives as an example the science of medicine, whose object is health, and the art of gymnastics, whose object is physical exercise directed to the well-being of the body. The same thing holds true of any of the other sciences, whether they are “productive,” i.e., practical, or “doctrinal,” i.e., theoretical; because each of these particular sciences marks off and takes as its own some determinate class of being inasmuch as it confines itself to that class and deals with it alone. For it is concerned with that class of being as a certain kind of being, though not as being. But to consider this, namely, being as being, belongs to a science which differs from all of the particular sciences.

2249. And each (957).

Second, he gives another characteristic of the particular sciences. He says that each of the above-mentioned particular sciences somehow assumes the quiddity in whatever class of things is considered. Hence it has been stated at the beginning of the Posterior Analytics that it is necessary to assume both the existence and quiddity of the subject. And having assumed this, i.e., the quiddity, which every science uses as a middle term to demonstrate certain things, such as properties and the like, it tries to demonstrate these with greater or lesser certainty; because some sciences have a more certain method of demonstrating, as the mathematical sciences, and others a less certain one, as the natural sciences.

2250. And since he had said that other sciences somehow assume the quiddity, he therefore adds that some sciences derive the quiddity from sensory perception inasmuch as they acquire a knowledge of a thing’s essence from sensible accidents, and that others derive the quiddity by assuming it from other sciences, as particular sciences from universal ones.

2251. Thus it is evident that in the particular sciences there is no demonstration of the substance or the quiddity of a thing. Hence both of the things with which the particular sciences do not concern themselves, i.e., a consideration of the substance or being and its quiddity, pertain to a universal science.

2252. Now since (958).

Then he shows how the particular sciences differ from one another. First (958:C 2252), he shows how the philosophy of nature differs from the productive sciences; and second (959:C 2256), how the mathematical sciences differ from the philosophy of nature (“And since it is necessary”).

He accordingly says, first (958), that, since there is a particular science of nature, it must be different “from the practical,” i.e., from the sciences which govern activity and from those which govern production; for every practical science is either a science of action or a science of production.

2253. In order to understand this difference we must consider a distinction which was made above in Book IX (790:C 1864), namely, that to act and to make differ; for to act is said properly of an operation which remains in the agent and does not pass over into some external matter, for instance, to understand and to perceive and so on. But to make or produce is said of an operation which passes over into some external matter which is changed, for example, to heat and to cut and the like. Hence there is a science of activity by which we are instructed how to perform correctly those operations which are called actions; and moral science is such. But that science by which we make something correctly is a productive science. The art of carpentry and the like belong to this class.

2254. Now the philosophy of nature differs from each of these sciences which govern operations; for the productive sciences do not have a principle of motion in the thing made but in the maker, and this principle is either the art, which is a directive principle, or some potency which is the principle executing the work. Similarly “the practical sciences,” i.e., those governing activity, do not have a principle of motion in that upon which the activity is exercised but rather in the agents.

2255. But those things which belong to the consideration of the philosophy of nature have their principles of motion in themselves, since nature is a principle of motion in the thing in which it exists. It is evident, then, that the philosophy of nature is a science neither of action nor of production but is speculative. For the philosophy of nature must fall into one of these classes, i.e., active, productive or speculative science. Hence, if it is a science neither of action nor of production, it follows that it must be speculative.

2256. And since (959).

Then he shows how the mathematical sciences differ from the philosophy of nature. He says that, since each of the sciences must somehow come to know the quiddity and must use this as a starting point with a view to demonstrating, the sciences must be distinguished on the basis of a different method of defining. Hence in order to understand how the philosophy of nature differs from the other sciences we must not neglect to consider the method which the philosophy of nature uses in defining things, and how the definition should be considered in the philosophy of nature; that is, whether a thing should be defined in the way that snub is or in the way that concave is.

2257. Now the definition of snub includes sensible matter, but that of concave does not; for since snubness is found only in a definite sensible matter, because it is found only in a nose, the intelligible structure of snub must therefore include sensible matter; for snub is defined thus: snub is a concave nose. Sensible matter, however, is not included in the definition of concave or curved. Hence, just as sensible matter is included in the definition of snub, so too it must be included in the definition of flesh and of eye and of the other parts of the body. The same holds true of other natural beings.

2258. The difference between the philosophy of nature and mathematics is taken from this, because the philosophy of nature deals with those things whose definitions include sensible matter, whereas mathematics deals with those things whose definitions do not include sensible matter, although they have being in sensible matter.

2259. And since there is (960).

Then he compares this science with the other particular sciences; and in regard to this he does three things. First (960:C 2259), he compares this science with the different particular sciences in reference to the way in which their objects are separate from matter. Second (961:C 2265), he compares them from the viewpoint of nobility (“The class of speculative sciences”). Third (962:C 2265), he compares them from the viewpoint of universality (“However, one”).

He accordingly says, first (960), that there is a science of being insofar as it is separable; for it is the office of this science not only to establish the truth about being in common (and this is to establish the truth about being as being) but also to establish the truth about things which are separate from matter in being. Hence it is necessary to consider whether this science whose function is to consider these two things is the same as the philosophy of nature or differs from it.

2260. That it differs from the philosophy of nature he makes clear as follows: the philosophy of nature is concerned with things which have a principle of motion in themselves; therefore natural things must have a definite matter, because only that which has matter is moved. But mathematics studies immovable things; for those things whose intelligible structure does not include sensible matter must likewise not have motion in their intelligible structure, since motion is found only in sensible things.

2261. But those things which mathematics considers are not separable from matter and motion in being but only in their intelligible structure. Hence the science which treats that kind of being which is separable from matter and from motion and is immovable in every respect must be one which differs both from mathematics and from the philosophy of nature.

2262. He says here, “if there is some such substance” apart from sensible substances which is immovable in every respect. He says this because the existence of some such substance has not yet been proved, although he intends to prove this.

2263. And if there is some such nature among existing things, i.e., one which is separable and immovable, it is necessary that “such a nature exist somewhere,” i.e., that it be attributed to some substance. And whatever has this nature must be something that is divine and the highest of all; because the simpler and more actual a being is, the nobler it is and the more it is prior and a cause of other things. Thus it is evident that the science which considers separate beings of this kind should be called the divine science and the science of first principles.

2264. From this he again concludes that there are three classes of speculative science: the philosophy of nature, which considers things that are movable and have sensible matter in their definition; mathematics, which considers immovable things that do not have sensible matter in their definition yet exist in sensible matter; and theology, which considers beings that are entirely separate from matter.

2265. The class (961).

Next he compares this science with the others from the viewpoint of nobility. He says that the speculative sciences are the noblest, because of all the sciences the speculative seek knowledge for its own sake, whereas the practical seek knowledge for the sake of some work. And among the speculative sciences there is one that, is highest, namely, theology, since a science which deals with more noble beings is itself more noble; for a science is more noble in proportion to the greater nobility of its object.

2266. However, one might (962).

Then he compares this science with the others from the viewpoint of universality. He says that one might raise the question whether or not the science which deals with separate beings must be held to be a universal science of being as being; and that it must be such he shows by a process of elimination.

2267. For it is evident that the foregoing sciences which deal with operations are not universal sciences, and he therefore omits them. In the case of the speculative sciences it is evident that every mathematical science is concerned with some one determinate class of things. But a universal science deals with all things in common. No mathematical science, then, can be the one which treats all beings in common. Regarding the philosophy of nature it is evident that, if natural substances, which are perceptible and movable, are the primary beings, the philosophy of nature must be the primary science; because the order of the sciences corresponds with that of their subjects, as has been stated already (961:C 2265). But if there is a different nature and substance over and above natural substances, which is separable and immovable, there must be a science which differs from the philosophy of nature and is prior to it. And because it is first, it must be universal; for it is the same science which treats of primary beings and of what is universal, since the primary beings are the principles of the others.

LESSON 8

No Science of Accidental Being

ARISTOTLE’S TEXT Chapter 8: 1064b 15-1065b 4

963. Since the term being in its unqualified sense has many meanings, and one of these is the accidental, it is first necessary to consider this sense of being.

964. Now it is evident that none of the traditional sciences are concerned with the accidental. The science of building does not consider what will happen to the occupants of a house, for example, whether they will dwell there unhappily or in the opposite way; nor is the art of weaving or of shoemaking or of cooking concerned with it. But each of these sciences considers only what is proper to itself, and this is its particular end.

965. Further, no science considers a man insofar as he is a musician or also a grammarian; nor does any science consider the quibble that “when one who is a musician has become a grammarian he will be both at the same time, although he was not so before; but that which is and has not always been, must have come to be; and therefore he must have at the same time become both a musician and a grammarian.” None of the known sciences are concerned with this except sophistry, and thus Plato was not wrong in saying that sophistry is concerned with non-being.

966. That it is impossible to have a science of the accidental will be evident to those who