2-3
BOOK IV
THE SUBJECT OF METAPHYSICS, DEMONSTRATIVELYLesson 1
It is being and its properties
529. In the preceding book the Philosopher proceeded to treat dialectically the things which ought to be considered in this science. Here he begins to proceed demonstratively by establishing the true answer to those questions which have been raised and argued dialectically.
In the preceding book he treated dialectically both the things which pertain to the method of this science, namely, those to which the consideration of this science extends, as well as those which fall under the consideration of this science. And because it is first necessary to know the method of a science before proceeding to consider the things with which it deals, as was explained in Book II (335), this. part is therefore divided into two members. First, he speaks of the things which this science considers; and second (749), of those which fall under its consideration. He does this in Book V ("In one sense the term principle").
The first part is divided into two members. First, he establishes what the subject matter of this science is. Second (534), he proceeds to answer the questions raised in the preceding book about the things which this science considers ("The term being").
In regard to the first he does three things. First, he submits that there is a science whose subject is being. Second (532), he shows that it is not one of the particular sciences ("But this science"); and third (533), he shows that it is the science with which we are now dealing ("Now since").
Now because a science should investigate not only its subject but also the proper accidents of its subject, he therefore says, first, that there is a science which studies being as being, as its subject, and studies also "the attributes which necessarily belong to being," i.e., its proper accidents.
530. He says "as being" because the other sciences, which deal with particular beings, do indeed consider being (for all the subjects of the sciences are beings), yet they do not consider being as being, but as some particular kind of being, for example, number or line or fire or the like.
531. He also says "and the attributes which necessarily belong to being," and not just those which belong to being, in order to show that it is not the business of this science to consider those attributes which belong accidentally to its subject, but only those which belong necessarily to it. For geometry does not consider whether a triangle is of bronze or of wood, but only considers it in an absolute sense according as it has three angles equal to two right angles. Hence a science of this kind, whose subject is being, must not consider all the attributes which belong accidentally to being, because then it would consider the accidents investigated by all sciences; for all accidents belong to some being, but not inasmuch as it is being. For those accidents which are the proper accidents of an inferior thing are related in an accidental way to a superior thing; for example, the proper accidents of man are not the proper accidents of animal.
Now the necessity of this science, which considers being and its proper accidents, is evident from this, that such things should not remain unknown since the knowledge of other things depends on them, just as the knowledge of proper objects depends on that of common objects.
532. Then he shows that this science is not one of the particular sciences, and he uses the following argument. No particular science considers universal being as such, but only some part of it separated. from the others; and about this part it studies the proper accidents. For example, the mathematical sciences study one kind of being, quantitative being. But the common science considers universal being as being, and therefore it is not the same as any of the particular sciences.
533. Here he shows that the science with which we are dealing has being as its subject, and he uses the following argument. Every principle is of itself the principle and cause of some nature. But we are seeking the first principles and utlimate causes of things, as was explained in Book I (57), and therefore these are of themselves the causes of some nature. But this nature can only be the nature of being. This is clear from the fact that all philosophers, in seeking the elements of things inasmuch as they are beings, sought principles of this kind, namely, the first and ultimate ones. Therefore in this science we are seeking the principles of being as being. Hence being is the subject of this science, for any science seeks the proper causes of its subject.
It applies analogically to the different categories.
534. Then he proceeds to answer the questions raised in the preceding book about the things which this science considers, and this is divided into three parts. First, he answers the question whether this science considers substances and accidents together, and whether it considers all substances. Second (548), he answers the question whether it belongs to this science to consider all of the following: one and many, same and different, opposites, contraries, and so forth ("Now although"). Third (588), he answers the question whether it belongs to this science to consider the principles of demonstration ("Moreover, it is necessary").
In regard to the first he does three things. First, he shows that it is the office of this science to consider both substances and accidents. Second (546), he shows that this science is chiefly concerned with substances ("But in every respect"). Third (547), he shows that it pertains to this science to consider all substances ("Now of every").
In regard to the first part he uses this kind of argument: those things which have one term predicated of them in common, not univocally but analogously, belong to the consideration of one science. But the term being is thus predicated of all beings. Therefore all beings, i.e., both substances and accidents, belong to the consideration of one science which considers being as being.
535. Now in this argument he gives, first (535), the minor premise; second (544), the major premise ("Therefore, just as"); and third (545), the conclusion ("It is evident, then").
He accordingly says, first, that the term being, or what is, has several meanings. But it must be noted that a term is predicated of different things in various senses. Sometimes it is predicated of them according to a meaning which is entirely the same, and then it is said to be predicated of them univocally, as animal is predicated of a horse and of an ox. Sometimes it is predicated of them according to meanings which are entirely different, and then it is said to be predicated of them equivocally, as dog is predicated of a star and of an animal. And sometimes it is predicated of them according to meanings which are partly different and partly not (different inasmuch as they imply different relationships, and the same inasmuch as these different relationships are referred to one and the same thing), and then it is said "to be predicated analogously," i.e., proportionally, according as each one by its own relationship is referred to that one same thing.
536. It must also be noted that the one thing to which the different relationships are referred in the case of analogical things is numerically one and not just one in meaning, which is the kind of oneness designated by a univocal term. Hence he says that, although the term being has several senses, still it is not predicated equivocally but in reference to one thing; not to one thing which is one merely in meaning, but to one which is one as a single definite nature. This is evident in the examples given in the text.
537. First, he gives the example of many things being related to one thing as an end. This is clear in the case of the term healthy or healthful. For the term healthy is not predicated univocally of food, medicine, urine and an animal; because the concept healthy as applied to food means something that preserves health; and as applied to medicine it means something that causes health; and as applied to urine it means something that is a sign of health; and as applied to an animal it means something that is the recipient or subject of health. Hence every use of the term healthy refers to one and the same health; for it is the same health which the animal receives, which urine is a sign of, which medicine causes, and which food preserves.
538. Second, he gives the example of many things being related to one thing as an efficient principle. For one thing is called medical because it possesses the art of medicine, as the skilled physician. Another is called medical because it is naturally disposed to have the art of medicine, as men who are so disposed that they may acquire the art of medicine easily (and according to this some men can engage in medical activities as a result of a peculiar natural constitution). And another is called medical or medicinal because it is necessary for healing, as the instruments which physicians use can be called medical. The same thing is also true of the things called medicines, which physicians use in restoring health. Other terms which resemble these in having many senses can be taken in a similar way.
539. And just as the above-mentioned terms have many senses, so also does the term being. Yet every being is called such in relation to one first thing, and this first thing is not an end or an efficient cause, as is the case in the foregoing examples, but a subject.
For some things are called beings, or are said to be, because they have being of themselves, as substances, which are called beings in the primary and proper sense. Others are called beings because they are affections or properties of substances, as the proper accidents of any substance. Others are called beings because they are processes toward substance, as generation and motion. And others are called beings because they are corruptions of substances; for corruption is the process toward non-being just as generation is the process toward substance. And since corruption terminates in privation just as generation terminates in form, the very privations of substantial forms are fittingly called beings. Again, certain qualities or certain accidents are called beings because they are productive or generative principles of substances or of those things which are related to substance according to one of the foregoing relationships or any other relationship.
And similarly the negations of those things which are related to substances, or even substance itself, are also called beings. Hence we say that non-being is non-being. But this would not be possible unless a negation possessed being in some way.
540. But it must be noted that the above-mentioned modes of being can be reduced to four.
(1) For one of them, which is the most imperfect, i.e., negation and privation, exists only in the mind. We say that these exist in the mind because the mind busies itself with them as kinds of being while it affirms or denies something about them. In what respect negation and privation differ will be treated below (564).
541. (2) There is another mode of being inasmuch as generation and corruption are called beings, and this mode by reason of its imperfection comes close to the one given above. For generation and corruption have some admixture of privation and negation, because motion is an imperfect kind of actuality, as is stated in the Physics, Book III.
542. (3) The third mode of being admits of no admixture of non-being, yet it is still an imperfect kind of being, because it does not exist of itself but in something else, for example, qualities and quantities and the properties of substances.
543. (4) The fourth mode of being is the one which is most perfect, namely, what has being in reality without any admixture of privation, and has firm and solid being inasmuch as it exists of itself. This is the mode of being which substances have. Now all the others are reduced to this as the primary and principal mode of being; for qualities and quantities are said to be inasmuch as they exist in substances; and motions and generations are said to be inasmuch as they are processes tending toward substance or toward some of the foregoing; and negations and privations are said to be inasmuch as they remove some part of the preceding three.
544. Here he gives the major premise of the first argument. He says that it is the office of one science to study not only those things which are referred "to one thing," i.e., to one common notion, but also those which are referred to one nature according to different relationships. And the reason for this is that the thing to which they are referred is one; just as it is clear that one science, medicine, considers all health-giving things. The same thing holds true of other things which are spoken of in the same way.
545. Then he draws his intended conclusion. This is evident of itself.
546. Then he shows that this science, even though it considers all beings, is chiefly concerned with substances. He uses the following argument. Every science which deals with many things that are referred to one primary thing is properly and principally concerned with that primary thing on which other things depend for their being and from which they derive their name; and this is true in every case. But substance is the primary kind of being. Hence the philosopher who considers all beings ought to consider primarily and chiefly the principles and causes of substances. Therefore his consideration extends primarily and chiefly to substances.
547. Then he shows by the following argument that it is the business of the first philosopher to consider all substances. There is one sense and one science of all things belonging to one class; for example, sight is concerned with all colors, and grammar with all words. Therefore, if all beings somehow belong to one class, all species of being must belong to the consideration of one science which is a general science, and different species of being must belong to the different species of that science. He says this because it is not necessary for one science to consider all the species of one genus according to the special notes of every single species, but only inasmuch as they agree generically. But according to their specific notes the different species of one genus belong to the special sciences, as happens in the present case. For inasmuch as all substances are beings or substances, they belong to the consideration of this science; but inasmuch as they are a particular kind of substance, as a lion or an ox, they belong to the special sciences.
Lesson 2
Metaphysics also treats of "being-one".
548. Here he proceeds to show that the study of common attributes such as one and many and same and different belongs to the consideration of one and the same science; and in regard to this he does two things. First, he shows that this is true of each attribute taken separately by arguing from proper or specific principles. Second (570), he shows that this is true of all attributes taken together by arguing from common principles.
In regard to the first he does two things. First, he shows that the philosopher ought to investigate all these attributes. Second (568), he tells us how to investigate them.
In regard to the first he does two things. First, he shows that it is the office of this science to consider unity and its species. Second (564), he shows that it is the office of one and the same science to consider all opposites.
In regard to the first he does two things. First, he shows that it is the office of this science to consider unity. Second (561), he shows that it also,belongs to it to examine the species of unity.
He therefore says, first, that being and unity are the same and are a single nature. He says this because some things are numerically the same which are not a single nature but different natures, for example, Socrates, this white thing, and this musician. Now the terms one and being do not signify different natures but a single nature. But things can be one in two ways: (1) for some things are one which are associated as interchangeable things, like principle and cause; and (2) some are interchangeable not only in the sense that they are one and the same numerically [or in subject] but also in the sense that they are one and the same conceptually, like garment and clothing.
549. Now the terms one and being signify one nature according to different concepts, and therefore they are like the terms principle and cause, and not like the terms tunic and garment, which are wholly synonymous. -Yet it makes no difference to his thesis if we consider them to be used in the same sense, as those things which are one both numerically and conceptually. In fact this will "rather support our undertaking," i.e., it will serve his purpose better; for he intends to prove that unity and being belong to the same study, and that the species of the one correspond to those of the other. The proof of this would be clearer if unity and being were the same both numerically and conceptually rather than just numerically and not conceptually.
550. He proves that they are the same numerically by using two arguments. He gives the first where he says, "For one man," and it runs as follows. Any two things which when added to some third thing cause no difference are wholly the same. But when one and being are added to man or to anything at all, they cause no difference. Therefore they are wholly the same. The truth of the minor premise is evident; for it is the same thing to say "man" and "one man." And similarly it is the same thing to say "human being" and "the thing that is man;" and nothing different is expressed when in speaking we repeat the terms, saying, "This is a human being, a man, and one man." He proves this as follows.
551. It is the same thing for man and the thing that is man to be generated and corrupted. This is evident from the fact that generation is a process toward being, and corruption a change from being to non-being. Hence a man is never generated without a human being being generated, nor is a man ever corrupted without a human being being corrupted; and those things which are generated and corrupted together are themselves one and the same.
552. And just as it has been said that being and man are not separated either in generation or in corruption, so too this is evident of what is one; for when a man is generated, one man is generated, and when a man is corrupted, one man is also corrupted. It is clear, then, that the apposition of these [i.e., of one or being to man] expresses the same thing, and that just because the term one or being is added to man it is not to be understood that some nature is added to man. And from this it is clearly apparent that unity does not differ from being, because any two things which are identical with some third thing are identical with each other.
553. It is also evident from the foregoing argument that unity and being are the same numerically but differ conceptually; for if this were not the case they would be wholly synonymous, and then it would be nonsense to say, "a human being," and "one man." For it must be borne in mind that the term man is derived from the quiddity or the nature of man, and the term thing from the quiddity only; but the term being is derived from the act of being, and the term one from order or lack of division; for what is one is an undivided being. Now what has an essence, and a quiddity by reason of that essence, and what is undivided in itself, are the same. Hence these three-thing, being, and one- signify absolutely the same thing but according to different concepts.
554. Then he gives the second argument, which has to do with sameness or identity of subject. This argument is as follows. Any two attributes which are predicated essentially and not accidentally of the substance of each thing are the same in subject, or numerically. But unity and being are such that they are predicated essentially and not accidentally of the substance of each thing; for the substance of a thing is one in itself and not accidentally. Therefore the terms being and one signify the same thing in subject.
555. That the terms being and one are predicated essentially and not accidentally of the substance of each thing can be proved as follows. If being and one were predicated of the substance of each thing by reason of something added to it [i.e., accidentally], being would have to be predicated also of the thing added, because anything at all is one and a being. But then there would be the question whether being is predicated of this thing (the one added) either essentially or by reason of some other thing that is added to it in turn. And if the latter were the case, then the same question would arise once again regarding the last thing added, and so on to infinity. But this is impossible. Hence the first position must be held, namely, that a thing's substance is one and a being of itself and not by reason of something added to it.
556. But it must be noted that Avicenna felt differently about this; for he said that the terms being and one do not signify a thing's substance but something added to it. He said this of being because, in the case of anything that derives its existence from something else, the existence of such a thing must differ from its substance or essence. But the term being signifies existence itself. Hence it seems that being, or existence is something added to a thing's essence.
557. He spoke in the same way of one, because he thought that the one which is interchangeable with being and the one which is the principle of number are the same. And the one which is the principle of number must signify a reality added to the substance, otherwise number, since it is composed of ones, would not be a species of quantity, which is an accident added to substance. He said that this kind of one is interchangeable with being, not in the sense that it signifies the very substance of a thing or being, but in the sense that it signifies an accident belonging to every being, just as the ability to laugh belongs to every man.
558. But in regard to the first point he does not seem to be right; for even though a thing's existence is (+) other than its essence, it should not be understood to be something added to its essence after the manner of an (~) accident, but (+) something established, as it were, by the principles of the essence. Hence the term being, which is applied to a thing by reason of its very existence, designates the same thing as the term which is applied to it by reason of its essence. [Existence is later clarified as the act of essence.]
559. Nor does it seem to be true that the one or unity which is interchangeable with being and that which is the principle of number are the same; for nothing that pertains to some special class of being seems to be characteristic of all beings. Hence the unity which is limited to a special class of being-discrete quantity-does not seem to be interchangeable with universal being. For, if unity is a proper and essential accident of being, it must be caused by the principles of being as being, just as any proper accident is caused by the principles of its subject. But it is not reasonable that something having a particular mode of being should be adequately accounted for by the common principles of being as being. It cannot be true, then, that something which belongs to a definite genus and species is an accident of every being.
560. Therefore the kind of unity which is the principle of number differs from that which is interchangeable with being; for the unity which is interchangeable with being signifies being itself, adding to it the notion of undividedness, which, since it is a negation or a privation, does not posit any reality added to being. Thus unity differs from being in no way numerically but only conceptually; for a negation or a privation is not a real being but a being of reason, as has been stated (540).
However, the kind of unity which is the principle of number adds to substance the note of a measure, which is a special property of quantity and is found first in the unit. And it is described as the privation or negation of division which pertains to continuous quantity; for number is produced by dividing the continuous. Hence number belongs to mathematical science, whose subject cannot exist apart from sensible matter but can be considered apart from sensible matter. But this would not be so if the kind of unity which is the principle of number were separate from matter in being and existed among the immaterial substances, as is true of the kind of unity which is interchangeable with being.
561. Then he concludes that it is the business of the philosopher to consider the parts of unity, just as it is to consider the parts of being. First, he proves this; and second (563), he shows that there are different parts of philosophy corresponding to the different parts of being and unity.
He says, first, that since being and unity signify the same thing, and the species of things that are the same are themselves the same, there must be as many species of being as there are of unity, and they must correspond to each other. For just as the parts of being are substance, quantity, quality, and so on, in a similar way the parts of unity are sameness, equality and likeness. For things are the same when they are one in substance, equal when they are one in quantity, and like when they are one in quality. And the other parts of unity could be taken from the other parts of being, if they were given names. And just as it is the office of one science, philosophy, to consider all parts of being, in a similar way it is the office of this same science to consider all parts of unity, i.e., sameness, likeness and so forth. And to this "starting point," i.e., unity, "almost" all contraries may be referred.
562. He adds this qualification because in some cases this point is not so evident. Yet it must be true; for since one member of every pair of contraries involves privation, they must be referred back to certain primary privatives, among which unity is the most basic.
And plurality, which stems from unity, is the cause of otherness, difference and contrariety, as will be stated below. He says that this has been treated "in our selection," or extract, "of contraries," i.e., a treatise which is the part selected to deal with contraries, namely, Book X (2000-21) of this work.
563. Here he shows that the parts of philosophy are distinguished in reference to the parts of being and unity. He says that there are as many parts of philosophy as there are parts of substance, of which being and unity chiefly are predicated, and of which it is the principal intention or aim of this science to treat.
And because the parts of substance are related to each other in a certain order, for immaterial substance is naturally prior to sensible substance, then among the parts of philosophy there must be a first part. (1) Now that part which is concerned with sensible substance is first in the order of instruction, because any branch of learning must start with things which are better known to us. He treats of this part in Books VII (1300) and VIII of this work. (2) But that part which has to do with immaterial substance is prior both in dignity and in the aim of this science. This part is treated in Book XII (2488) of this work.
Yet whatever parts are first must be continuous with the others, because all parts have unity and being as their genus. Hence all parts of this science are united in the study of being and unity, although they are about different parts of substance. Thus it is one science inasmuch as the foregoing parts are things which correspond to "these,"i.e., to unity and being, as common attributes of substance. In this respect the philosopher resembles the mathematician; for mathematical science has different parts, one of which is primary, as arithmetic, another secondary, as geometry, and others following these in order, as optics, astronomy and music.
Lesson 3
It also considers "one-many", "negation-privation" etc.
564. Here he shows that it is the office of this science to consider opposites; and in regard to this he does two things. First, he shows that it is the office of this science to consider privation and negation; and second (567), to consider contraries ("But plurality").
He accordingly says (306) that, since it pertains to one science to consider opposites (for example, it belongs to medicine to consider health and sickness, and to grammar to consider agreement and disagreement), and since plurality is the opposite of unity, the study of privation and negation must belong to that science which deals with unity and plurality. For the consideration "of both" involves unity; that is, the study of unity, whose concept entails negation and privation, depends on both of these. For, as has been said above (553), what is one is an undivided being, and division relates to plurality, which is the opposite of unity. Hence the study of negation and privation belongs to that science whose business it is to consider unity.
565. Now there are two kinds of negation: (1) simple negation, by which one thing is said absolutely not to be present in something else, and (2) negation in a genus, by which something is denied of something else, not absolutely, but within the limits of some determinate genus. For example, not everything that does not have sight is said absolutely to be blind, but something within the genus of an animal which is naturally fitted to have sight.
And this difference is present in unity over and above "what is implied in negation"; i.e., it is something by which it differs from negation, because negation expresses only the absence of something, namely, what it removes, without stating a determinate subject. (1) Hence simple negation can be verified both of a non-being, which is not naturally fitted to have something affirmed of it, and of a being which is naturally fitted to have something affirmed of it and does not. For unseeing can be predicated both of a chimera and of a stone and of a man. (2) But in the case of privation there is a determinate nature or substance of which the privation is predicated; for not everything that does not have sight can be said to be blind, but only that which is naturally fitted to have sight. Thus since the negation which is included in the concept of unity is a negation in a subject (otherwise a non-being could be called one), it is evident that unity differs from simple negation and rather resembles the nature of privation, as is stated below in Book X (2069) of this work.
566. But it must be noted that, although unity includes an implied privation, it must not be said to include (~) the privation of plurality; for, since a privation is subsequent in nature to the thing of which it is the privation, it would follow that unity would be subsequent in nature to plurality. And it would also follow that plurality would be given in the definition of unity; for a privation can be defined only by its opposite. For example, if someone were to ask what blindness is, we would answer that it is the privation of sight. Hence, since unity is given in the definition of plurality (for plurality is an aggregate of units), it would follow that there would be circularity in definitions. (+) Hence it must be said that unity includes the privation of division, although not (~) the kind of division that belongs to quantity; for this kind of division is limited to one particular class of being and cannot be included in the definition of unity. (+) But the unity which is interchangeable with being implies the privation of formal division, which comes about through opposites, and whose primary root is the opposition between affirmation and negation. For those things are divided from each other which are of such a kind that one is not the other. Therefore being itself is understood first, and then non-being, and then division, and then the kind of unity which is the privation of division, and then plurality, whose concept includes the notion of division just as the concept of unity includes the notion of undividedness. However, some of the things that have been distinguished in the foregoing way can be said to include the notion of plurality only if the notion of unity is first attributed to each of the things distinguished.
567. Here he shows that it is the business of the philosopher to consider contraries, or opposites; for plurality is the opposite of unity, as has been said (564), and it is the office of one science to consider opposites. Hence, since this science considers unity, sameness, likeness and equality, it must also consider their opposites, plurality, otherness or diversity, unlikeness and inequality, and all other attributes which are reduced to these or even to unity and plurality. And contrariety is one of these; for contrariety is a kind of difference, namely, of things differing in the same genus. But difference is a kind of otherness or diversity, as is said in Book X (2017). Therefore contrariety belongs to the consideration of this science.
568. Then he deals with the method by which the philosopher ought to establish these things. He says that, since all of the above-mentioned opposites are derived from unity, and the term one is used in many senses, all of the terms designating these must also be used in many senses, i.e., same, other, and so on. Yet even though all of these are used in many senses, it is still the work of one science, philosophy, to know the things signified by each of these terms. For if some term is used in many senses, it does not therefore follow that it belongs to another or different science. For if the different things signified are not referred to "with one meaning," or according to one concept, i.e., univocally, or are not referred to one thing in different ways, as in the case of analogous things, then it follows that it is the office of another, i.e., of a different, science, to consider them; or at least it is the office of one science accidentally, just as astronomy considers a star in the heavens, i.e., the dog star, and natural science considers a dog-fish and a dog. But all of these are referred to one starting point. For things signified by the term one, even though diverse, are referred back to a primary thing signified as one; and we must also speak in the same way of the terms same, other, contrary, and others of this kind.
Regarding each of these terms, then, the philosopher should do two things. (1) First, he should distinguish the many senses in which each may be used; and (2) second, he should determine regarding "each of the predicates," i.e., each of the names predicated of many things, to what primary thing it is referred. For example, he should state what the first thing signified by the term same or other is, and how all the rest are referred to it; one inasmuch as it possesses it, another inasmuch as it produces it, or in other ways of this kind.
569. He draws his conclusion from what has been said, namely, that it belongs to this science to reason about those common predicates and about substance; and this was one of the problems investigated in the questions treated dialectically in Book III (393).
Lesson 4
General reasons for that (difference between metaphysics and dialectics or sophistry).
570. Here he uses arguments based on common principles to prove what the philosopher ought to consider regarding all of the foregoing attributes. First, he proves his thesis; and second (587), he introduces his intended conclusion ("It is evident").
In regard to the first part he does two things. First, he proves his thesis; and second (586), he draws a corollary from what has been said ("And for this reason").
He gives three arguments to prove his thesis. The second (572) begins where he says, "An indication of this"; and the third (578), at "Further, one corresponding."
The first argument is as follows. All questions that can be raised must be answered by some science. But questions are raised about the common attributes mentioned above, for example, that raised about sameness and otherness: whether Socrates and Socrates sitting are the same; and that raised about contraries: whether one thing has one contrary, and how many meanings the term contrary has. Hence these questions must be answered by some science which considers sameness and contrariety and the other attributes mentioned above.
571. That this is the job of the philosopher and of no one else he proves thus: that science whose office is to consider being as being is the one which must consider the first properties of being. But all of the above-mentioned attributes are proper accidents of unity and being as such. For number as number has properties, such as excess, equality, commensurability, and so on, some of which belong to a number taken absolutely, as even and odd, and some to one number in relation to another, as equality. And even substance has proper attributes, "as the resistant," or body, and others of this kind. And in a similar way being as being has certain properties, which are the common attributes mentioned above; and therefore the study of them belongs to the philosopher. Hence those dealing with philosophy have not erred in their treatment of these things "by being unphilosophical," i.e., by considering them in a way that does not pertain to the investigations of philosophy, but because in treating them they pay no attention to substance, as though they were completely unmindful of it despite the fact that it is the first thing which the philosopher ought to consider.
572. Then he gives a second argument to prove the same point. This argument employs an example and runs thus: dialecticians and sophists assume the same guise as the philosopher inasmuch as they resemble him in some respect. But the dialectician and sophist dispute about the above-mentioned attributes. Therefore the philosopher should also consider them. In support of his first premise he shows how dialectics and sophistry resemble philosophy and how they differ from it.
573. Dialectics resembles philosophy in that it is also the office of the dialectician to consider all things. But this could not be the case unless he considered all things insofar as they agree in some one respect; because each science has one subject, and each art has one matter on which it operates. Therefore, since all things agree only in being, evidently the subject matter of dialectics is being and those attributes which belong to being; and this is what the philosopher also investigates. And sophistry likewise resembles philosophy; for sophistry has "the semblance of wisdom," or is apparent wisdom, without being wisdom. Now anything that takes on the appearance of something else must resemble it in some way. Therefore the philosopher, the dialectician and the sophist must consider the same thing.
574. Yet they differ from each other. The philosopher differs from the dialectician in power, because the consideration of the philosopher is more efficacious than that of the dialectician. For the philosopher proceeds demonstratively in dealing with the common attributes mentioned above, and thus it is proper to him to have scientific knowledge of these attributes. And he actually knows them with certitude, for certain or scientific knowledge is the effect of demonstration. The dialectician, however, proceeds to treat all of the above-mentioned common attributes from probable premises, and thus he does not acquire scientific knowledge of them but a kind of opinion. The reason for this difference is that there are two kinds of beings: beings of reason and real beings. The expression being of reason is applied properly to those notions which reason derives from the objects it considers, for example, the notions of genus, species and the like, which are not found in reality but are a natural result of the consideration of reason. And this kind of being, i.e., being of reason, constitutes the proper subject of logic. But intellectual conceptions of this kind are equal in extension to real beings, because all real beings fall under the consideration of reason. Hence the subject of logic extends to all things to which the expression real being is applied. His conclusion is, then, that the subject of logic is equal in extension to the subject of philosophy, which is real being.
Now the philosopher proceeds from the principles of this kind of being to prove the things that have to be considered about the common accidents of this kind of being. But the dialectician proceeds to consider them from the conceptions of reason, which are extrinsic to reality. Hence it is said that dialectics is in search of knowledge, because in searching it is proper to proceed from extrinsic principles.
575. But the philosopher differs from the sophist "in the choice," i.e., in the selection or willing, or in the desire, of a way of life. For the philosopher and sophist direct their life and actions to different things. The philosopher directs his to knowing the truth, whereas the sophist directs his so as to appear to know what he does not.
576. Now although it is said that philosophy is scientific knowledge, and that dialectics and sophistry are not, this still does not do away with the possibility of dialectics and sophistry being sciences. For dialectics can be considered both from the viewpoint of theory and from that of practice. (1) From the viewpoint of theory it studies these conceptions and establishes the method by which one proceeds from them to demonstrate with probability the conclusions of the particular sciences; and it does this demonstratively, and to this extent it is a science. (2) But from the viewpoint of practice it makes use of the above method so as to reach certain probable conclusions in the particular sciences; and in this respect it falls short of the scientific method.
The same must be said of sophistry, because from the viewpoint of theory it treats by means of necessary and demonstrative arguments the method of arguing to apparent truth. From the viewpoint of practice, however, it falls short of the process of true argumentation.
577. But that part of logic which is said to be demonstrative is concerned only with theory, and the practical application of it belongs to philosophy and to the other particular sciences, which are concerned with real beings. This is because the practical aspect of the demonstrative part of logic consists in using the principles of things, from which proceeds demonstration (which properly belongs to the sciences that deal with real beings), and not in using the conceptions of logic.
Thus it appears that some parts of logic are at the same time scientific, theoretical, and practical, as exploratory dialectics and sophistry; and one is concerned with theory and not practice, namely, demonstrative logic.
Lesson 5
This science considers the first principles of demonstration.
588. Here he answers another question raised in Book III (387): whether it belongs to this science to consider the first principles of demonstration. This is divided into two parts. In the first he shows that it belongs to this science to make a general study of all these principles; and in the second (596) he shows that it also belongs to it to make a special study of the first of these principles ("And it is fitting").
In regard to the first he does three things. First, he raises the question whether it belongs to one or to different sciences to consider substance and the principles which are called axioms in the mathematical sciences. He assigns these principles more to the mathematical sciences because such sciences have more certain demonstrations and use these self-evident principles in a more manifest way inasmuch as they refer all of their demonstrations to them.
589. Second, he answers this question by saying that a single science investigates both of the foregoing things, and that this is the philosophy with which we are now concerned.
590. Third, he proves his proposed answer, and in regard to this he does two things. First, he proves it. Second (595), he introduces his main conclusion ("It is evident").
Now he proves his proposed answer in two ways. He does this, first, by an argument; and second (592), by an example ("Hence no one").
The argument is as follows: whatever principles pertain to all beings, and not just to one class of beings distinct from the others, belong to the consideration of the philosopher. But the above-mentioned principles are of this kind. Therefore they belong to the consideration of the philosopher. He proves the minor premise as follows. Those principles which all sciences use pertain to being as being. But first principles are principles of this kind. Therefore they pertain to being as being.
591. The reason which he gives for saying that all sciences use these principles is that the subject genus of each science has being predicated of it. Now the particular sciences do not use the foregoing principles insofar as they are common principles, i.e., as extending to all beings, but insofar as they have need of them; that is, insofar as they extend to the things contained in the class of beings which constitutes the subject of a particular science about which it makes demonstrations. For example, the philosophy of nature uses them insofar as they extend to changeable beings and no further.
592. Then he proves what he had said by using an example. First, he introduces the proof; and second (593), he rejects a false notion held by some men ("However, some").
He accordingly says, first, that no one whose chief intention is to hand down scientific knowledge of some particular being has attempted to say anything about the truth or falsity of first principles. Neither the geometer nor the arithmetician does this even though they make the greatest use of these principles, as was said above (588). Hence it is evident that the investigation of these principles belongs to this science.
593. Here he rejects the false notion held by some men, and in regard to this he does two things. First, he rejects the false notion of those who occupied themselves with these principles even though they did not concern them. Second, (594), he rejects the false notion of those who wanted to deal with these principles in a different way than they should be dealt with.
He accordingly says, first, that even though none of the particular sciences ought to deal with the above-mentioned principles, nevertheless some of the natural philosophers have dealt with them; and they did so not without reason. For the ancients did not think that there was any substance besides the changeable corporeal substance with which the philosophy of nature is concerned. Hence they believed that they alone established the truth about the whole of nature and therefore about being, and thus about first principles, which must be considered along with being. But this is false, because there is still a science which is superior to the science of nature. For nature itself, i.e., natural being, which has its own principle of motion, constitutes in itself one class of universal being.
But not every being is of this kind, because it has been proved in the Physics, Book VIII, that an unchangeable being exists. Now this unchangeable being is superior to and nobler than changeable being, with which the philosophy of nature is concerned. And since the consideration of common being belongs to that science which studies the primary kind of being, then the consideration of common being belongs to a different science than the philosophy of nature. And the consideration of common principles of this kind will also belong to this science. For the philosophy of nature is a part of philosophy but not the first part, which considers common being and those attributes which belong to being as being.
594. Then he rejects the other false notion, which concerns the way in which such principles should be treated. For some men investigated these principles with the aim of demonstrating them. And whatever they said about the truth of these principles, i.e., how they must be accepted as true by force of demonstration, or how the truth found in all these principles must be reached, they did through ignorance of, or lack of skill in, "analytics," which is that part of logic in which the art of demonstration is treated. For "they must know these principles in order to attain scientific knowledge"; i.e., every science acquired by demonstration depends on these principles.
But "those who are learning," i.e., the pupils who are being instructed in some science, must not seek these principles as something to be demonstrated. Or, according to another text, "those who have scientific knowledge must attain science from these principles"; i.e., those who attain knowledge by demonstration must come to know common principles of this kind and not ask that they be demonstrated to them.
595. He draws the conclusion primarily intended, namely, that it will be the function of the philosopher to consider every substance as such and also the first syllogistic principles. In order to make this clear it must be noted that self-evident propositions are those which are known as soon as their terms are known, as is stated in Book I of the Posterior Analytics. This occurs in the case of those propositions in which the predicate is given in the definition of the subject, or is the same as the subject. But it happens that one kind of proposition, even though it is self-evident in itself, is still not self-evident to all, i.e., to those who are ignorant of the definition of both the subject and the predicate. Hence Boethius says in De Hebdomadibus that there are some propositions which are self-evident to the learned but not to all. Now those are self-evident to all whose terms are comprehended by all. And common principles are of this kind, because our knowledge proceeds from common principles to proper ones, as is said in Book I of the Physics. Hence those propositions which are composed of such common terms as whole and part (for example, every whole is greater than one of its parts) and of such terms as equal and unequal (for example, things equal to one and the same thing are equal to each other), constitute the first principles of demonstration. And the same is true of similar terms. Now since common terms of this kind belong to the consideration of the philosopher, then it follows that these principles also fall within his scope. But the philosopher does not establish the truth of these principles (~) by way of demonstration, but (+) by considering the meaning of their terms. For example, he considers what a whole is and what a part is; and the same applies to the rest. And when the meaning of these terms becomes known, it follows that the truth of the above-mentioned principles becomes evident.
Lesson 6
This science considers particularly the very first principle, that of contradiction.
596. He shows here that it is the first philosopher who is chiefly concerned with the first principle of demonstration; and in regard to this he does two things. First, he shows that it is the business of the first philosopher to consider this principle; and second (611), he begins to examine this principle.
In regard to the first he does three things.. First, he shows that it is the office of this science to consider the first principle of demonstration. Second (597), he indicates what this principle is. Third (606), he rejects certain errors regarding this same principle.
In regard to the first point he uses the following argument. In every class of things that man is best informed who knows the most certain principles, because the certitude of knowing depends on the certitude of principles. But the first philosopher is best informed and most certain in his knowledge; for this was one of the conditions of wisdom, as was made clear in the prologue of this work (35), namely, that he who knows the causes of things has the most certain knowledge. Hence the philosopher ought to consider the most certain and firmest principles of beings, which he considers as the subject-genus proper to himself.
597. Then he shows what the firmest or most certain principle is; and in regard to this he does two things. First, he states the conditions for the most certain principle; and then (600) he shows how they fit a single principle ("And let us").
He accordingly gives, first, the three conditions for the firmest principle. (1) The first is that no one can make a mistake or be in error regarding it. And this is evident because, since men make mistakes only about those things which they do not know, then that principle about which no one can be mistaken must be the one which is best known.
598. (2) The second condition is that it must "not be hypothetical," i.e., it must not be held as a supposition, as those things which are maintained through some kind of common agreement. Hence another translation reads "And they should not hold a subordinate place," i.e., those principles which are most certain should not be made dependent on anything else. And this is true, because whatever is necessary for understanding anything at all about being "is not hypothetical," i.e., it is not a supposition but must be self-evident. And this is true because whatever is necessary for understanding anything at all must be known by anyone who knows other things.
599. (3) The third condition is that it is not acquired (~) by demonstration or by any similar method, but (+) it comes in a sense by nature to the one having it inasmuch as it is naturally known and not acquired. For first principles become known through the natural light of the agent intellect, and they are not acquired by any process of reasoning but by having their terms become known. This comes about by reason of the fact that memory is derived from sensible things, experience from memory, and knowledge of those terms from experience. And when they are known, common propositions of this kind, which are the principles of the arts and sciences, become known.
Hence it is evident that the most certain or firmest principle should be such that there can be no error regarding it; that it is not hypothetical; and that it comes naturally to the one having it.
600. Then he indicates the principle to which the above definition applies. He says that it applies to this principle, as the one which is firmest: it is impossible for the same attribute both to belong and not belong to the same subject at the same time. And it is necessary to add "in the same respect"; and any other qualifications that have to be given regarding this principle "to meet dialectical difficulties" must be laid down, since without these qualifications there would seem to be a contradiction when there is none.
601. That this principle must meet the conditions given above he shows as follows: (1) It is impossible for anyone to think, or hold as an opinion, that the same thing both is and is not at the same time, although some believe that Heraclitus was of this opinion. But while it is true that Heraclitus spoke in this way, he could not think that this is true; for it is not necessary that everything that a person says he should mentally an opinion.
602. But if one were to say that it is possible for someone to think that the same thing both is and is not at the same time, this absurd consequence follows: contraries could belong to the same subject at the same time. And "let us suppose that the same things are established," or shown, here as in the usual proposition established in our logical treatises. For it was shown at the end of the Peri hermineas I that contrary opinions are not those which have to do with contraries but those which have to do with contradictories, properly speaking. For when one person thinks that Socrates is white and another thinks that he is black, these are not contrary opinions in the primary and proper sense; but contrary opinions are had when one person thinks that Socrates is white and another thinks that he is not white.
603. Therefore, if someone were to think that two contradictories are true at the same time by thinking that the same thing both is and is not at the same time, he will have contrary opinions at the same time; and thus contraries will belong to the same thing at the same time. But this is impossible. It is impossible, then, for anyone to be mistaken in his own mind about these things and to think that the same thing both is and is not at the same time. And it is for this reason that all demonstrations reduce their propositions to this proposition as the ultimate opinion common to all; for this proposition is by nature the starting point and axiom of all axioms.
604. (2 & 3) The other two conditions are therefore evident, because, insofar as those making demonstrations reduce all their arguments to this principle as the ultimate one by referring them to it, evidently this principle is not based on an assumption. Indeed, insofar as it is by nature a starting point, it clearly comes unsought to the one having it and is not acquired by his own efforts.
605. Now for the purpose of making this evident it must be noted that, since the intellect has two operations, one by which it knows quiddities, which is called the understanding of indivisibles, and another by which it combines and separates, there is something first in both operations. In the first operation the first thing that the intellect conceives is being, and in this operation nothing else can be conceived unless being is understood.
And because this principle-it is impossible for a thing both to be and not be at the same time-depends on the understanding of being (just as the principle, every whole is greater than one of its parts, depends on the understanding of whole and part), then this principle is by nature also the first in the second operation of the intellect, i.e., in the act of combining and separating. And no one can understand anything by this intellectual operation unless this principle is understood. For just as a whole and its parts are understood only by understanding being, in a similar way the principle that every whole is greater than one of its parts is understood only if the firmest principle is understood.
606. Then he shows how some men erred regarding this principle; and in regard to this he does two things. First, he touches on the error of those who rejected the foregoing principle; and second (607) he deals with those who wished to demonstrate it ("But some").
He accordingly says that some men as was stated above about Heraclitus (601), said that the same thing can both be and not be at the same time, and that it is possible to hold this opinion; and many of the philosophers of nature adopt this position, as will be made clear below (665). For our part, however, we now take as evident that the principle in question is true, i.e., the principle that the same thing cannot both be and not be; but from its truth we show that it is most certain. For from the fact that a thing cannot both be and not be it follows that contraries cannot belong to the same subject, as will be said below (663). And from the fact that contraries cannot belong to a subject at the same time it follows that a man cannot have contrary opinions and, consequently, that he cannot think that contradictories are true, as has been shown (603).
607. Then he mentions the error of certain men who wished to demonstrate the above-mentioned principle; and in regard to this he does two things. First, he shows that it cannot be demonstrated in the strict sense; and second (608), that it can be demonstrated in a way ("But even").
Thus he says, first , that certain men deem it fitting, i.e., they wish, to demonstrate this principle; and they do this "through want of education," i.e., through lack of learning or instruction. For there is want of education when a man does not know what to seek demonstration for and what not to; for not all things can be demonstrated. For if all things were demonstrable, then, since a thing is not demonstrated through itself but through something else, demonstrations would either be circular (although this cannot be true, because then the same thing would be both better known and less well known, as is clear in Book I of the Posterior Analytics, or they would have to proceed to infinity. But if there were an infinite regress in demonstrations, demonstration would be impossible, because the conclusion of any demonstration is made certain by reducing it to the first principle of demonstration. But this would not be the case if demonstration proceeded to infinity in an upward direction. It is clear, then, that not all things are demonstrable. And if some things are not demonstrable, these men cannot say that any principle is more indemonstrable than the above-mentioned one.
608. Here he shows that the above-mentioned principle can be demonstrated in a certain respect. He says that it may be demonstrated by disproof. In Greek the word is ἐλεγκτικῶς, which is better translated as by refutation, for an ἔλεγκος is a syllogism that establishes the contradictory of a proposition, and so is introduced to refute some false position. And on these grounds it can be shown that it is impossible for the same thing both to be and not be.
But this kind of argument can be employed only if the one who denies that principle because of difficulties "says something," i.e., if he signifies something by a word. But if he says nothing, it is ridiculous to look for a reason against one who does not make use of reason in speaking; for in this dispute anyone who signifies nothing will be like a plant, for even brute animals signify something by such signs.