METAPHYSICS
BOOK V

LESSON I

Five Senses of the Term "Principle." The Common Definition of Principle

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403. In one sense the term principle [beginning or starting point] means that from which someone first moves something; for example, in the case of a line or a journey, if the motion is from here, this is the principle, but if the motion is in the opposite direction, this is something different. In another sense principle means that from which a thing best comes into being, as the starting point of instruction; for sometimes it is not from what is first or from the starting point of the thing that one must begin, but from that from which one learns most readily. Again, principle means that first inherent thing from which something is brought into being, as the keel of a ship and the foundation of a house, and as some suppose the heart to be the principle in animals, and others the brain, and others anything else of the sort. In another sense it means that non-inherent first thing from which something comes into being; and that from which motion and change naturally first begins, as a child comes from its father and mother, and a fight from abusive language. In another sense principle means that according to whose will movable things are moved and changeable things are changed; in states, for example, princely, magistral, imperial, or tyrannical power are all principles. And so also are the arts, especially the architectonic arts, called principles. And that from which a thing can first be known is also called a principle of that thing, as the postulates of demonstrations. And causes are also spoken of in the same number of senses, for all causes are principles.

404. Therefore, it is common to all principles to be the first thing from which a thing either is, comes to be, or is known. And of these some are intrinsic and others extrinsic. And for this reason nature is a principle, and so also is an element, and mind, purpose, substance, and the final cause; for good and evil are the principles both of the knowledge and motion of many things.

COMMENTARY

Principle

751. Now it should be noted that, although a principle and a cause are the same in subject, they nevertheless differ in meaning; for the term principle implies an order or sequence, whereas the term cause implies some influence on the being of the thing caused. Now an order of priority and posteriority is found in different things; but according to what is first known by us order is found in local motion, because that kind of motion is more evident to the senses. Further, order is found in three classes of things, one of which is naturally associated with the other, i.e., continuous quantity, motion and time. For insofar as there is priority and posteriority in continuous quantity, there is priority and posteriority in motion; and insofar as there is priority and posteriority in motion, there is priority and posteriority in time, as is stated in Book IV of the Physics. Therefore, because a principle is said to be what is first in any order, and the order which is considered according to priority and posteriority in continuous quantity is first known by us (and things are named by us insofar as they are known to us), for this reason the term principle, properly considered, designates what is first in a continuous quantity over which motion passes. Hence he says that a principle is said to be “that from which someone first moves something,” i.e., any part of a continuous quantity from which local motion begins. Or, according to another reading, “Some part of a thing from which motion will first begin”; i.e., some part of a thing from which it first begins to be moved; for example in the case of a line and in that of any kind of journey the principle is the point from which motion begins. But the opposite or contrary point is “something different or other,” i.e., the end or terminus. It should also be noted that a principle of motion and a principle of time belong to this class for the reason just given.

752. But because motion does not always begin from the starting point of a continuous quantity but from that part from which the motion of each thing begins most readily, he therefore gives a second meaning of principle, saying that we speak of a principle of motion in another way “as that from which a thing best comes into being,” i.e., the point from which each thing begins to be moved most easily. He makes this clear by an example; for in the disciplines one does not always begin to learn from something that is a beginning in an absolute sense and by nature, but from that from which one “is able to learn” most readily, i.e., from those things which are better known to us, even though they are sometimes more remote by their nature.

753. Now this sense of principle differs from the first. For in the first sense a principle of motion gets its name from the starting point of a continuous quantity, whereas here the principle of continuous quantity gets its name from the starting point of motion. Hence in the case of those motions which are over circular continuous quantities and have no starting point, the principle is also considered to be the point from which the movable body is best or most fittingly moved according to its nature. For example, in the case of the first thing moved [the first sphere] the starting point is in the east. The same thing is true in the case of our own movements; for a man does not always start to move from the beginning of a road but sometimes from the middle or from any terminus at all from which it is convenient for him to start moving.

754. Now from the order considered in local motion we come to know the order in other motions. And for this reason we have the senses of principle based upon the principle of generation or coming to be of things. But this is taken in two ways; for it is either “inherent,” i.e., intrinsic, or “non-inherent,” i.e., extrinsic.

755. In the first way, then, a principle means that part of a thing which is first generated and from which the generation of the thing begins; for example, in the case of a ship the first thing to come into being is the base or keel, which is in a certain sense the foundation on which the whole superstructure of the ship is raised. And, similarly, in the case of a house the first thing that comes into being is the foundation. And in the case of an animal the first thing that comes into being, according to some, is the heart, and according to others, the brain or some such member of the body. For an animal is distinguished from a non-animal by reason of sensation and motion. Now the principle of motion appears to be in the heart, and sensory operations are most evident in the brain. Hence those who considered an animal from the viewpoint of motion held that the heart is the principle in the generation of an animal. But those who considered an animal only from the viewpoint of the senses held that the brain is this principle; yet the first principle of sensation is also in the heart even though the operations of the senses are completed in the brain. And those who considered an animal from the viewpoint of operation, or according to some of its activities, held that the organ which is naturally disposed for that operation, as the liver or some other such part is the first part which is generated in an animal. But according to the view of the Philosopher the first part is the heart because all of the soul’s powers are diffused throughout the body by means of the heart.

756. In the second way, a principle means that from which a thing’s process of generation begins but which is outside the thing. This is made clear in the case of three classes of things. The first is that of natural beings, in which the principle of generation is said to be the first thing from which motion naturally begins in those things which come about through motion (as those which come about through alteration or through some similar kind of motion; for example, a man is said to become large or white); or that from which a complete change begins (as in the case of those things which are not a result of motion but come into being through mutation alone). This is evident in the case of substantial generation; for example, a child comes from its father and mother, who are its principles, and a fight from abusive language, which stirs the souls of men to quarrel.

757. The second class in which this is made clear is that of human acts, whether ethical or political, in which that by whose will or intention others are moved or changed is called a principle. Thus those who hold civil, imperial, or even tyrannical power in states are said to have the principal places; for it is by their will that all things come to pass or are put into motion in states. Those men are said to have civil power who are put in command of particular offices in states, as judges and persons of this kind. Those are said to have imperial power who govern everyone without exception, as kings. And those hold tyrannical power who through violence and disregard for law keep royal power within their grip for their own benefit.

758. He gives as the third class things made by art; for the arts too in a similar way are called principles of artificial things, because the motion necessary for producing an artifact begins from an art. And of these arts the architectonic, which “derive their name” from the word principle, i.e., those called principal arts, are said to be principles in the highest degree. For by architectonic arts we mean those which govern subordinate arts, as the art of the navigator governs the art of ship-building, and the military art governs the art of horsemanship.

759. Again, in likeness to the order considered in external motions a certain order may also be observed in our apprehensions of things, and especially insofar as our act of understanding, by proceeding from principles to conclusions, bears a certain resemblance to motion. Therefore in another way that is said to be a principle from which a thing first becomes known; for example, we say that “postulates,” i.e., axioms and assumptions, are principles of demonstrations.

760. Causes are also said to be principles in these ways, “for all causes are principles.” For the motion that terminates in a thing’s being begins from some cause, although it is not designated a cause and a principle from the same point of view, as was pointed out above (750).

761. Therefore, it is (404).

Then he reduces all of the abovementioned senses of principle to one that is common. He says that all of the foregoing senses have something in common inasmuch as that is said to be a principle which comes first (1) either with reference to a thing’s being (as the first part of a thing is said to be a principle) or (2) with reference to its coming to be (as the first mover is said to be a principle) or with reference to the knowing of it.

762. But while all principles agree in the respect just mentioned, they nevertheless differ, because some are intrinsic and others extrinsic, as is clear from the above. Hence nature and element, which are intrinsic, can be principles-nature as that from which motion begins, and element as the first part in a thing's generation. "And mind," i.e., intellect, and "purpose," i.e., a man's intention, are said to be principles as extrinsic ones. Again, "a thing's substance," i.e., its form, which is its principle of being, is called an intrinsic principle, since a thing has being by its form. Again, according to what has been said, that for the sake of which something comes to be is said to be one of its principles. For the good, which has the character of an end in the case of pursuing, and evil in that of shunning, are principles of the knowledge and motion of many things; that is, all those which are done for the sake of some end. For in the realm of nature, in that of moral acts, and in that of artifacts, demonstrations make special use of the final cause.

LESSON 2

The Four Classes of Causes. Several Causes of the Same Effect. Causes May Be Causes of Each Other. Contraries Have the Same Cause

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405. In one sense the term cause means that from which, as something intrinsic, a thing comes to be, as the bronze of a statue and the silver of a goblet, and the genera of these. In another sense it means the form and pattern of a thing, i.e., the intelligible expression of the quiddity and its genera (for example, the ratio of 2: 1 and number in general are the cause of an octave chord) and the parts which are included in the intelligible expression. Again, that from which the first beginning of change or of rest comes is a cause; for example, an adviser is a cause, and a father is the cause of a child, and in general a maker is a cause of the thing made, and a changer a cause of the thing changed. Further, a thing is a cause inasmuch as it is an end, i.e., that for the sake of which something is done; for example, health is the cause of walking. For if we are asked why someone took a walk, we answer, "in order to be healthy"; and in saying this we think we have given the cause. And whatever occurs on the way to the end under the motion of something else is also a cause. For example, reducing, purging, drugs and instruments are causes of health; for all of these exist for the sake of the end, although they differ from each other inasmuch as some are instruments and others are processes. These, then, are nearly all the ways in which causes are spoken of.

406. And since there are several senses in which causes are spoken of, it turns out that there are many causes of the same thing, and not in an accidental way. For example, both the maker of a statue and the bronze are causes of a statue not in any other respect but insofar as it is a statue. However, they are not causes in the same way, but the one as matter and the other as the source of motion.

407. And there are things which are causes of each other. Pain, for example, is a cause of health, and health is a cause of pain, although not in the same way, but one as an end and the other as a source of motion.

408. Further, the same thing is sometimes the cause of contraries; for that which when present is the cause of some particular thing, this when absent we sometimes blame for the contrary. Thus the cause of the loss of a ship is the absence of the pilot whose presence is the cause of the ship's safety. And both of these—the absence and the presence—are moving causes.

COMMENTARY

The four causes

763. Here the Philosopher distinguishes the various senses in which the term cause is used; and in regard to this he does two things. First, he enumerates the classes of causes. Second (783), he gives the modes of causes (“Now the modes”).

In regard to the first part he does two things. First, he enumerates the various classes of causes. Second (777), he reduces them to four (“All the causes”).

In regard to the first part he does two things. First, he enumerates the different classes of causes. Second (773), he clarifies certain things about the classes of causes (“And since”).

He accordingly says, first, that in one sense the term cause means that from which a thing comes to be and is “something intrinsic,” i.e., something which exists within the thing. This is said to distinguish it from a privation and also from a contrary; for a thing is said to come from a privation or from a contrary as from something which is not intrinsic; for example, white is said to come from black or from not-white. But a statue comes from bronze and a goblet from silver as from something which is intrinsic; for the nature bronze is not destroyed when a statue comes into being, nor is the nature silver destroyed when a goblet comes into being. Therefore the bronze of a statue and the silver of a goblet are causes in the sense of matter. He adds “and the genera of these,” because if matter is the species of anything it is also its genus. For example, if the matter of a statue is bronze, its matter will also be metal, compound and body. The same holds true of other things.

764. In another sense cause means the form and pattern of a thing, i.e., its exemplar. This is the formal cause, which is related to a thing in two ways. (1) In one way it stands as the intrinsic form of a thing, and in this respect it is called the formal principle of a thing. (2) In another way it stands as something which is extrinsic to a thing but is that in likeness to which it is made, and in this respect an exemplar is also called a thing’s form. It is in this sense that Plato held the Ideas to be forms. Moreover, because it is from its form that each thing derives its nature, whether of its genus or of its species, and the nature of its genus or of its species is what is signified by the definition, which expresses its quiddity, the form of a thing is therefore the intelligible expression of its quiddity, i.e., the formula by which its quiddity is known. For even though certain material parts are given in the definition, still it is from a thing’s form that the principal part of the definition comes. The reason why the form is a cause, then, is that it completes the intelligible expression of a thing’s quiddity. And just as the genus of a particular matter is also matter, in a similar way the genera of forms are the forms of things; for example, the form of the octave chord is the ratio of 2:1. For when two notes stand to each other in the ratio of 2:1, the interval between them is one octave. Hence twoness is its form; for the ratio of 2:1 derives its meaning from twoness. And because number is the genus of twoness, we may therefore say in a general way that number is also the form of the octave, inasmuch as we may say that the octave chord involves the ratio of one number to another. And not only is the whole definition related to the thing defined as its form, but so also are the parts of the definition, i.e., those which are given directly in the definition. For just as two-footed animal capable of walking is the form of man, so also are animal, capable of walking and two-footed. But sometimes matter is given indirectly in the definition, as when the soul is said to be the actuality of a physical organic body having life potentially.

765. In a third sense cause means that from which the first beginning of change or of rest comes, i.e., a moving or efficient cause. He says “of change or of rest,” because motion and rest which are natural are traced back to the same cause, and the same is true of motion and of rest which are a result of force. For that cause by which something is moved to a place is the same as that by which it is made to rest there. “An adviser” is an example of this kind of cause, for it is as a result of an adviser that motion begins in the one who acts upon his advice for the sake of safeguarding something. And in a similar way “a father is the cause of a child.” In these two examples Aristotle touches upon the, two principles of motion from which all things come to be, namely, purpose in the case of an adviser, and nature in the case of a father. And in general every maker is a cause of the thing made and every changer a cause of the thing changed.

766. Moreover, it should be noted that according to Avicenna, there are four modes of efficient cause, namely, perfective, dispositive, auxiliary and advisory.

An efficient cause is said to be perfective inasmuch as it causes the final perfection of a thing, as the one who induces a substantial form in natural things or artificial forms in things made by art, as a builder induces the form of a house.

767. An efficient cause is said to be dispositive if it does not induce the final form that perfects a thing but only prepares the matter for that form, as one who hews timbers and stones is said to build a house. This cause is not properly said to be the efficient cause of a house, because what he produces is only potentially a house. But he will be more properly an efficient cause if he induces the ultimate disposition on which the form necessarily follows; for example, man generates man without causing his intellect, which comes from an extrinsic cause.

768. And an efficient cause is said to be auxiliary insofar as it contributes to the principal effect. Yet it differs from the principal efficient cause in that the principal efficient cause acts for its own end, whereas an auxiliary cause acts for an end which is not its own. For example, one who assists a king in war acts for the king’s end. And this is the way in which a secondary cause is disposed for a primary cause. For in the case of all efficient causes which are directly subordinated to each other, a secondary cause acts because of the end of a primary cause; for example, the military art acts because of the end of the political art.

769. And an advisory cause differs from a principal efficient cause inasmuch as it specifies the end and form of the activity. This is the way in which the first agent acting by intellect is related to every secondary agent, whether it be natural or intellectual. For in every case a first intellectual agent gives to a secondary agent its end and its form of activity; for example, the naval architect gives these to the shipwright, and the first intelligence does the same thing for everything in the natural world.

770. Further, to this genus of cause is reduced everything that makes anything to be in any manner whatsoever, not only as regards substantial being, but also as regards accidental being, which occurs in every kind of motion. Hence he says not only that the maker is the cause of the thing made, but also that the changer is the cause of the thing changed.

771. In a fourth sense cause means a thing’s end, i.e., that for the sake of which something is done, as health is the cause of walking. And since it is less evident that the end is a cause in view of the fact that it comes into being last of all (which is also the reason why this cause was overlooked by the earlier philosophers, as was pointed out in Book I (1771), he therefore gives a special proof that an end is a cause. For to ask why or for what reason is to ask about a cause, because when we are asked why or for what reason someone walks, we reply properly by answering that he does so in order to be healthy. And when we answer in this way we think that we are stating the cause. Hence it is evident that the end is a cause. Moreover, not only the ultimate reason for which an agent acts is said to be an end with respect to those things which precede it, but everything that is intermediate between the first agent and the ultimate end is also said to be an end with respect to the preceding agents. And similarly those things are said to be causes from which motion arises in subsequent things. For example, between the art of medicine, which is the first efficient cause in this order, and health, which is the ultimate end, there are these intermediates: reducing, which is the most proximate cause of health in those who have a superfluity of humors; purging, by means of which reducing is brought about; “drugs,” i.e., laxative medicine, by means of which purging is accomplished; and “instruments,” i.e., the instruments by which medicine or drugs are prepared and administered. And all such things exist for the sake of the end, although one of them is the end of another. For reducing is the end of purging, and purging is the end of purgatives. However, these intermediates differ from each other in that (1) some are instruments, i.e., the instruments by means of which medicine is prepared and administered (and the administered medicine itself is something which nature employs as an instrument); and (2) some—purging and reducing—are processes, i.e., operations or activities.

772. He concludes, then, that “these are the ways in which causes are spoken of (405),” i.e., the four ways; and he adds “nearly all” because of the modes of causes which he gives below. Or he also adds this because the same classes of causes are not found for the same reason in all things.

773. And since (406).

Then he indicates certain points which follow from the things said above about the causes, and there are four of these. The first is that, since the term cause is used in many senses, there may be several causes of one thing not accidentally but properly. For the fact that there are many causes of one thing accidentally presents no difficulty, because many things may be accidents of something that is the proper cause of some effect, and all of these can be said to be accidental causes of that effect. But that there are several proper causes of one thing becomes evident from the fact that causes are spoken of in various ways. For the maker of a statue is a proper cause and not an accidental cause of a statue, and so also is the bronze, but not in the same way. For it is impossible that there should be many proper causes of the same thing within the same genus and in the same order, although there can be many causes providing that (1) one is proximate and another remote; or (2) that neither of them is of itself a sufficient cause, but both together. An example would be many men rowing a boat. Now in the case in point these two things are causes of a statue in different ways: the bronze as matter, and the artist as efficient cause.

774. And there are (407).
Then he sets down the second fact that may be drawn from the foregoing discussion. He says that it may also happen that any two things may be the cause of each other, although this is impossible in the same class of cause. But it is evident that this may happen when causes are spoken of in different senses. For example, the pain resulting from a wound is a cause of health as an efficient cause or source of motion, whereas health is the cause of pain as an end. For it is impossible, that a thing should be both a cause and something caused. Another text states this better, saying that “exercise is the cause of physical fitness,” i.e., of the good disposition caused by moderate exercise, which promotes digestion and uses up superfluous humors.

775. Now it must be borne in mind that, although four causes are given above, two of these are related to one another, and so also are the other two. (1) The efficient cause is related to the final cause, and (2) the material cause is related to the formal cause. The efficient cause is related to the final cause because the efficient cause is the starting point of motion and the final cause is its terminus. There is a similar relationship between matter and form. For form gives being, and matter receives it. Hence the efficient cause is the cause of the final cause, and the final cause is the cause of the efficient cause. The efficient cause is the cause of the final cause inasmuch as it makes the final cause be, because by causing motion the efficient cause brings about the final cause. But the final cause is the cause of the efficient cause, not in the sense that it makes it be, but inasmuch as it is the reason for the causality of the efficient cause. For an efficient cause is a cause inasmuch as it acts, and it acts only because of the final cause. Hence the efficient cause derives its causality from the final cause. And form and matter are mutual causes of being: form is a cause of matter inasmuch as it gives actual being to matter, and matter is a cause of form inasmuch as it supports form in being. And I say that both of these together are causes of being either in an unqualified sense or with some qualification. For substantial form gives being absolutely to matter, whereas accidental form, inasmuch as it is a form, gives being in a qualified sense. And matter sometimes does not support a form in being in an unqualified sense but according as it is the form of this particular thing and has being in this particular thing. This is what happens in the case of the human body in relation to the rational soul.

776. Further, the same thing (408).

Then he gives the third conclusion that may be drawn from the foregoing discussion. He says that the same thing can be the cause of contraries. This would also seem to be difficult or impossible if it were related to both in the same way. But it is the cause of each in a different way. For that which when present is the cause of some particular thing, this when absent “we blame,” i.e., we hold it responsible, “for the contrary.” For example, it is evident that by his presence the pilot is the cause of a ship’s safety, and we say that his absence is the cause of the ship’s loss. And lest someone might think that this is to be attributed to different classes of causes, just as the preceding two were, he therefore adds that both of these may be reduced to the same class of cause—the moving cause. For the opposite of a cause is the cause of an opposite effect in the same line of causality as that in which the original cause was the cause of its effect.

LESSON 3

All Causes Reduced to Four Classes

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409. All the causes mentioned fall under one of the four classes which are most evident. For the elements of syllables, the matter of things made by art, fire and earth and all such elements of bodies, the parts of a whole, and the premises of a conclusion, are all causes in the sense of that from which things are made. But of these some are causes as a subject, for example, parts, and others as the essence, for example, the whole, the composition and the species, whereas the seed, the physician, the adviser, and in general every agent, are all sources of change or of rest. But the others are causes as the end and the good of other things. For that for the sake of which other things come to be is the greatest good and the end of other things. And it makes no difference whether we say that it is a good or an apparent good. These, then, are the causes, and this the number of their classes.

410. Now the modes of causes are many in number, but these become fewer when summarized. For causes are spoken of in many senses; and of those which belong to the same class, some are prior and some subsequent. For example, both the physician and one possessing an art are causes of health, and both the ratio of 2:1 and number are causes of the octave chord; and always those classes which contain singulars. Further, a thing may be a cause in the sense of an accident, and the classes which contain these; for example, in one sense the cause of a statue is Polyclitus and in another a sculptor, because it is accidental that a sculptor should be Polyclitus. And the universals which contain accidents are causes; for example, man is the cause of a statue, and even generally animal, because Polyclitus is a man and an animal. And of accidental causes some are more remote and some more proximate than others. Thus what is white and what is musical might be said to be the causes of a statue, and not just Polyclitus or man. Again, in addition to all of these, i.e., both proper causes and accidental causes, some are said to be causes potentially and some actually, as a builder and one who is building. And the distinctions which have been made will apply in like manner to the effects of these causes, for example, to this statue, or to a statue, or to an image generally, or to this bronze, or to bronze, or to matter in general. And the same applies to accidental effects. Again, both proper and accidental causes may be spoken of together, so that the cause of a statue may be referred to as neither Polyclitus nor a sculptor but the sculptor Polyclitus. But while all these varieties of causes are six in number, each is spoken of in two ways; for causes are either singular or generic; either proper or accidental, or generically accidental; or they are spoken of in combination or singly; and again they are either active or potential causes. But they differ in this respect, that active causes, i.e. singular causes, exist or cease to exist simultaneously with their effects, as this particular one who is healing with this particular person who is being healed, and as this particular builder with this particular thing which is being built. But this is not always true of potential causes; for the builder and the thing built do not cease to exist at the same time.

COMMENTARY

Four modes of causes

777. Here the philosopher reduces all causes to the classes of causes mentioned above (409), saying that all those things which are called causes fall into one of the four classes mentioned above. For “elements,” i.e., letters, are said to be the causes of syllables; and the matter of artificial things is said to be their cause; and fire and earth and all simple bodies of this kind are said to be the causes of compounds. And parts are said to be the causes of a whole, and “premises,” i.e., propositions previously set down from which conclusions are drawn, are said to be the causes of the conclusion. And in all of these cases cause has a single formal aspect according as cause means that from which a thing is produced, and this is the formal aspect of material cause.

778. Now it must be noted that propositions are said to constitute the matter of a conclusion, not inasmuch as they exist under such a form, or according to their force (for in this way they would rather have the formal aspect of an efficient cause), but with reference to the terms of which they are composed. For a conclusion is constituted of the terms contained in the premises, i.e., of the major and minor terms.

779. And of those things of which something is composed, some are like a subject, for example, parts and the other things mentioned above, whereas some are like the essence, for example, the whole, the composition and the species, which have the character of a form whereby a thing’s essence is made complete. For it must be borne in mind that (1) sometimes one thing is the matter of something else in an unqualified sense (for example, silver of a goblet), and then the form corresponding to such a matter can be called the species. (2) But sometimes many things taken together constitute the matter of a thing; and this may occur in three ways. (a) For sometimes things are united merely by their arrangement, as the men in an army or the houses in a city; and then the whole has the role of a form which is designated by the term army or city. (b) And sometimes things are united not just by arrangement alone but by contact and a bond, as is evident in the parts of a house; and then their composition has the role of a form. (c) And sometimes the alteration of the component parts is added to the above, as occurs in the case of a compound; and then the compound state itself is the form, and this is still a kind of composition. And a thing’s essence is derived from any one of these three—the composition’ species, or whole—as becomes clear when an army, a house, or a goblet is defined. Thus we have two classes of cause.

780. But the seed, the physician and the adviser, and in general every agent, are called causes for a different reason, namely, because they are the sources of motion and rest. Hence this is now a different class of cause because of a different formal aspect of causality. He puts seed in this class of cause because he is of the opinion that the seed has active power, whereas a woman’s menstrual fluid has the role of the matter of the offspring.

781. There is a fourth formal aspect of causality inasmuch as some things are said to be causes in the sense of the end and good of other things. For that for the sake of which something else comes to be is the greatest good “and the end” of other things, i.e., it is naturally disposed to be their end. But because someone could raise the objection that an end is not always a good since certain agents sometimes inordinately set up an evil as their end, he therefore replies that it makes no difference to his thesis whether we speak of what is good without qualification or of an apparent good. For one who acts does so, properly speaking, because of a good, for this is what he has in mind. And one acts for the sake of an evil accidentally inasmuch as he happens to think that it is good. For no one acts for the sake of something with evil in view.

782. Moreover, it must be noted that, even though the end is the last thing to come into being in some cases, it is always prior in causality. Hence it is called the “cause of causes”, because it is the cause of the causality of all causes. For it is the cause of efficient causality, as has already been pointed out (775); and the efficient cause is the cause of the causality of both the matter and the form, because by its motion it causes matter to be receptive of form and makes form exist in matter. Therefore the final cause is also the cause of the causality of both the matter and the form. Hence in those cases in which something is done for an end (as occurs in the realm of natural things, in that of moral matters, and in that of art), the most forceful demonstrations are derived from the final cause. Therefore he concludes that the foregoing are causes, and that causes are distinguished into this number of classes.

783. Now the modes (410).

Then he distinguishes between the modes of causes. And causes are distinguished into classes and into modes. For the division of causes into classes is based on different formal aspects of causality, and is therefore equivalently a division based on essential differences, which constitute species. But the division of causes into modes is based on the different relationships between causes and things caused, and therefore pertains to those causes which have the same formal aspect of causality. An example of this is the division of causes into proper and accidental causes, and into remote and proximate causes. Therefore this division is equivalently a division based on accidental differences, which do not constitute different species.

784. He accordingly says that there are many modes of causes, but that these are found to be fewer in number when “summarized,” i.e., when brought together under one head. For even though proper causes and accidental causes are two modes, they are still reduced to one head insofar as both may be considered from the same point of view. The same thing is true of the other different modes. For many different modes of causes are spoken of, not only with reference to the different species of causes, but also with reference to causes of the same species, namely, those which are reduced to one class of cause.

785. (1) For one cause is said to be prior and another subsequent; and causes are prior or subsequent in two ways: (1) In one way, when there are many distinct causes which are related to each other, one of which is primary and remote, and another secondary and proximate (as in the case of efficient causes man generates man as a proximate and subsequent cause, but the sun as a prior and remote cause); and the same thing can be considered in the case of the other classes of causes. (2) In another way, when the cause is numerically one and the same, but is considered according to the sequence which reason sets up between the universal and the particular; for the universal is naturally prior and the particular subsequent.

786. But he omits the first way and considers the second. For in the second way the effect is the immediate result of both causes, i.e., of both the prior and subsequent cause; but this cannot happen in the first way. Hence he says that the cause of health is both the physician and one possessing an art, who belong to the class of efficient cause: one possessing an art as a universal and prior cause, and the physician as a particular, or special, and subsequent cause. The same thing is true of the formal cause, since this cause may also be considered in two ways; for example, for an octave chord “double,” or the ratio of 2:1, or the number two, is a formal cause as one that is special and subsequent, whereas number, or the ratio of one number to another or to the unit, is like a universal and prior cause. And in this way too “always those classes which contain singulars,” i.e., universals, are said to be prior causes.

787. (2) Causes are distinguished in another way inasmuch as one thing is said to be a proper cause and another an accidental cause. For just as proper causes are divided into universal and particular, or into prior and subsequent, so also are accidental causes. Therefore, not only accidental causes themselves are called such, but so also are the classes which contain these. For example, a sculptor is the proper cause of a statue, and Polyclitus is an accidental cause inasmuch as he happens to be a sculptor. And just as Polyclitus is an accidental cause of a statue, in a similar way all universals “which contain accidents,” i.e., accidental causes, are said to be accidental causes, for example, man and animal, which contain under themselves Polyclitus, who is a man and an animal.

788. And just as some proper causes are proximate and some remote, as was pointed out above, so also is this the case with accidental causes. For Polyclitus is a more proximate cause of a statue than what is white or what is musical. For an accidental mode of predication is more remote when an accident is predicated of an accident than when an accident is predicated of a subject. For one accident is predicated of another only because both are predicated of a subject. Hence when something pertaining to one accident is predicated of another, as when something pertaining to a builder is predicated of a musician, this mode of predication is more remote than one in which something is predicated of the subject of an accident, as when something pertaining to a builder is predicated of Polyclitus.

789. Now it must be borne in mind that one thing can be said to be the accidental cause of something else in two ways: (1) in one way, from the viewpoint of the cause; because whatever is accidental to a cause is itself called an accidental cause, for example, when we say that something white is the cause of a house. (2) In another way, from the viewpoint of the effect, i.e., inasmuch as one thing is said to be an accidental cause of something else because it is accidental to the proper effect. This can happen in three ways:

The first is that the thing has a necessary connection with the effect. Thus that which removes an obstacle is said to be a mover accidentally. This is the case whether that accident is a contrary, as when bile prevents coolness (and thus scammony is said to produce coolness accidentally, not because it causes coolness, but because it removes the obstacle preventing coolness, i.e., bile, which is its contrary); or even if it is not a contrary, as when a pillar hinders the movement of a stone which rests upon it, so that one who removes the pillar is said to move the stone accidentally.

In a second way, something is accidental to the proper effect when the accident is connected with the effect neither necessarily nor in the majority of cases but seldom, as the discovery of a treasure is connected with digging in the soil. It is in this way that fortune and chance are said to be accidental causes.

In a third way things are accidental to the effect when they have no connection except perhaps in the mind, as when someone says that he is the cause of an earthquake because an earthquake took place when he entered the house.

790. [Cross-division of all] And besides the distinction of all things into causes in themselves or proper causes and accidental causes, there is a third division of causes inasmuch as some things are causes potentially and some actually, i.e., actively. For example, the cause of building is a builder in a state of potency (for this designates his habit or office), or one who is actually building.

791. And the same distinctions which apply to causes can apply to the effects of which these causes are the causes. For effects, whether particular or universal, can be divided into prior and subsequent, as a sculptor may be called the cause of this statue, which is subsequent; or of a statue, which is more universal and prior; or of an image, which is still more universal. And similarly something is the formal cause of this particular bronze; or of bronze, which is more universal; or of matter, which is still more universal. The same things can be said of accidental effects, i.e., of things produced by accident. For a sculptor who is the cause of a statue is also the cause of the heaviness, whiteness or redness which are in it as accidents from the matter and are not caused by this agent.

792. (3) Again, he gives a fourth division of causes, namely, the division into simple causes and composite causes. A cause is said to be simple (a) when, for example, in the case of a statue, the proper cause alone is considered, as a sculptor, or when an accidental cause alone is considered, as Polyclitus. But a cause is said to be composite when both are taken together, for example, when we say that the cause of a statue is the sculptor Polyclitus.

793. (b) There is moreover another way in which causes are said to be composite, i.e., when several causes act together to produce one effect, for example, when many men act together in order to row a boat, or when many stones combine in order to constitute the matter of a house. But he omits the latter way because no one of these things taken in itself is the cause, but a part of the cause.

794. And having given these different modes of causes, he brings out their number, saying that these modes of causes are six in number, and that each of these have two alternatives so that twelve result. For these six modes are (1-2) either singular or generic (or, as he called them above, prior and subsequent); (3-4) either proper or accidental (to which the genus of the accident is also reduced, for the genus to which an accident belongs is an accidental cause); and again, (5-6) either composite or simple. Now these six modes are further divided by potency and actuality and thus are twelve in number. Now the reason why all these modes must be divided by potency and actuality is that potency and actuality distinguish the connection between cause and effect. For active causes are at one and the same time particulars and cease to exist along with their effects; for example, this act of healing ceases with this act of recovering health, and this act of building with this thing being built; for a thing cannot be actually being built unless something is actually building. But potential causes do not always cease to exist when their effects cease; for example, a house and a builder do not cease to exist at one and the same time. In some cases, however, it does happen that when the activity of the efficient cause ceases the substance of the effect ceases. This occurs in the case of those things whose being consists in coming to be, or whose cause is not only the cause of their coming to be but also of their being. For example, when the sun’s illumination is removed from the atmosphere, light ceases to be. He says “singular causes” because acts belong to singular things, as was stated in Book I of this work (21).

LESSON 4

The Proper Meaning of Element; Elements in Words, Natural Bodies, and Demonstrations. Transferred Usages of "Element" and Their Common Basis

ARISTOTLE'S TEXT Chapter 3: 1014a 25-1014b 15

411. The inherent principle of which a thing is first composed and which is not divisible into another species is called an element. For example, the elements of a word are the parts of which a word is composed and into which it is ultimately divided and which are not further divided into other words specifically different from them. But if they are divided, their parts are alike, as the parts of water are water; but this is not true of the syllable. Similarly, people who speak of the elements of bodies mean the component parts into which bodies are ultimately divided and which are not divided into other bodies specifically different. And whether such parts are one or many, they call them elements. And similarly the parts of diagrams are called elements, and in general the parts of demonstrations; for the primary demonstrations which are contained in many other demonstrations are called the elements of demonstrations; and such are the primary syllogisms which are composed of three terms and proceed through one middle term.

412. People also use the term element in a transferred sense of anything which is one and small and useful for many purposes; and for this reason anything which is small and simple and indivisible is called an element. Hence it follows that the most universal things are elements, because each of them, being one and simple, is found in many things, either in all or in most of them. And to some the unit and the point seem to be principles. Therefore, since what are called genera are universal and indivisible (for their formal character is one), some men call the genera elements, and these more than a difference, since a genus is more universal. For where the difference is present the genus also follows, but the difference is not always present where the genus is. And in all these cases it is common for the element of each thing to be the primary component of each thing.

COMMENTARY

Element

795. Here he distinguishes the different senses of the term element, and in regard to this lie does two things. First, he gives the different senses in which the term element is used. Second (807), he indicates what all of them have in common (“And in all these”).

In regard to the first he does two things. First, he explains how the term element is used in its proper sense; and second (802), how it is used in transferred senses (“People also use”).

First, he gives a sort of description of an element, and from this one can gather the four notes contained in its definition. The first is that an element is a cause in the sense of that from which a thing comes to be; and from this it is clear that an element is placed in the class of material cause.

796. The second is that an element is the principle from which something first comes to be. For copper is that from which a statue comes to be, but it is still not an element because it has some matter from which it comes to be.

797. The third is that an element is inherent or intrinsic; and for this reason. it differs from everything of a transitory nature from which a thing comes to be, whether it be a privation or a contrary or the matter subject to contrariety and privation, which is transitory; for example, when we say that a musical man comes from a nonmusical man, or that the musical comes from the non-musical. For elements must remain in the things of which they are the elements.

798. The fourth is that an element has a species which is not divisible into different species; and thus an element differs from first matter, which has no species, and also from every sort of matter which is capable of being divided into different species, as blood and things of this kind.

Hence he says, as the first note, that an element is that of which a thing is composed; as the second, that it is that of which a thing is “first” composed; as the third, that it is “an inherent principle”; and as the fourth, that it is “not divisible into another species.”

799. He illustrates this definition of element in four cases in which we use the term element. For we say that letters are the elements of a word because every word is composed of them, and of them primarily. This is evident from the fact that all words are divided into letters as ultimate things; for what is last in the process of dissolution must be first in the process of composition. But letters are not further divided into other words which are specifically different. Yet if they should be divided in any way, the parts in which the division results would be “alike,” i.e., specifically the same, just as all parts of water are water. Now letters are divided according to the amount of time required to pronounce them, inasmuch as a long letter is said to require two periods of time, and a short letter one. But while the parts into which letters are so divided do not differ as the species of words do, this is not the case with a syllable; for its parts are specifically different, since the sounds which a vowel and a consonant make, of which a syllable is composed, are specifically different.

800. He gives as a second example natural bodies, certain of which we also call the elements of certain others. For those things into which all compounds are ultimately dissolved are called their elements; and therefore they are the things of which bodies of this kind are composed. But those bodies which are called elements are not divisible into other bodies which are specifically different, but into like parts, as any part of water is water. And all those who held for one such body into which every body is dissolved and which is itself incapable of being further divided , said that there is one element. Some said that it is water, some air, and some fire. But those who posited many such bodies also said there are many elements. Now it should be borne in mind that when it is set down in the definition of an element that an element is not divisible into different species, this should not be understood of the parts into which a thing is divided in a quantitative division (for wood would then be an element, since any part of wood is wood), but in a division made by alteration, as compounds are dissolved into simple bodies.

801. As a third example he gives the order of demonstrations, in which we also employ the word element; for example, we speak of Euclid’s Book of Elements. And he says that, in a way similar and close to those mentioned, those things which “are parts of diagrams,” i.e., the constituents of geometrical figures, are called elements. This can be said not only of the demonstrations in geometry but universally of all demonstrations. For those demonstrations which have only three terms are called the elements of other demonstrations, because the others are composed of them and resolved into them. This is shown as follows: a second demonstration takes as its starting point the conclusion of a first demonstration, whose terms are understood to contain the middle term which was the starting point of the first demonstration. Thus the second demonstration will proceed from four terms the first from three only, the third from five, and the fourth from six; so that each demonstration adds one term. Thus it is clear that first demonstrations are included in subsequent ones, as when this first demonstration—every B is A, every C is B, therefore every C is A—is included in this demonstration—every C is A, every D is C, therefore every D is A; and this again is included in the demonstration whose conclusion is that every E is A, so that for this final conclusion there seems to be one syllogism composed of several syllogisms having several middle terms. This may be expressed thus: every B is A, every C is B, every D is C, every E is D, therefore every E is A. Hence a first demonstration, which has one middle term and only three terms, is simple and not reducible to another demonstration, whereas all other demonstrations are reducible to it. Hence first syllogisms, which come from three terms by way of one middle term, are called elements.

802. People also use (412).

Here he shows how the term element is used in a transferred sense. He says that some men, on the basis of the foregoing notion or meaning of element, have used the term in a transferred sense to signify anything that is one and small and useful for many purposes. For from the fact that an element is indivisible they understood that it is one; and from the fact that it is first they understood that it is simple; and from the fact that other things are composed of elements they understood that an element is useful for many purposes. Hence they set up this definition of an element in order that they might say that everything which is smallest in quantity and simple (inasmuch as it is not composed of other things) and incapable of division into different species, is an element.

803. But when they had set up this definition of element, it turned out that by using it in a transferred sense they had invented two senses of element. First, they called the most universal things elements; for a universal is one in definition and is simple (because its definition is not composed of different parts) and is found in many things, and thus is useful for many purposes, whether it be found in all things, as unity and being are, or in most things, as the other genera. And by the same reasoning it came about, second, that they called points and units principles or elements because each of them is one simple thing and useful for many purposes.

804. But in this respect they fell short of the true notion of a principle, because universals are not the matter of which particular things are composed but predicate their very substance. And similarly points are not the matter of a line, for a line is not composed of points.

805. Now with this transferred notion of element established, the solution to a question disputed in Book III (431-36) becomes clear, i.e., whether a genus or a species is more an element, and whether a genus or a difference is more an element; for it clearly follows that genera are elements to a greater degree because genera are more universal and indivisible. For there is no concept or definition of them which must be composed of genera and differences, but it is species which are properly defined. And if a genus is defined, it is not defined insofar as it is a genus but insofar as it is a species. Hence a species is divided into different parts and thus does not have the character of an element. But a genus is not divisible into different parts, and therefore they said that genera are elements more than species. Another translation reads, “For their formal character is one,” that is, indivisible, because even though genera do not have a definition, still what is signified by the term genus is a simple conception of the intellect which can be called a definition.

806. And just as a genus is more an element than a species is because it is simpler, in a similar way it is more an element than a difference is, even though a difference is simple, because a genus is more universal. This is clear from the fact that anything which has a difference has a genus, since essential differences do not transcend a genus; but not everything which has a genus necessarily has a difference.

807. Last of all he says that all of the foregoing senses of element have this note in common, that an element is the primary component of each being, as has been stated.

LESSON 5

Five Senses of the Term Nature

ARISTOTLE'S TEXT Chapter 4: 1014b 15-1015a 20

413. Nature means, in one sense, the generation of things that are born, as if one were to pronounce the letter u [in fusij] long. And in another sense it means the immanent principle from which anything generated is first produced. Again, it means the source of the primary motion in any beings which are by nature, and it is in each inasmuch as it is such. Now all those things are said to be born which increase through something else by touching and by existing together, or by being naturally joined, as in the case of embryos. But being born together differs from touching, for in the latter case there need be nothing but contact. But in things which are naturally joined together there is some one same thing in both, instead of contact, which causes them to be one, and which makes them to be one in quantity and continuity but not in quality. Again, nature means the primary thing of which a natural being is composed or from which it comes to be, when it is unformed and immutable by its own power; for example, the bronze of a statue or of bronze articles is said to be their nature, and the wood of wooden things, and the same applies in the case of other things. For each thing comes from these though its primary matter is preserved. For it is also in this sense that men speak of the elements of natural beings as their nature; some calling it fire, others earth, others water, others air, and others something similar to these, whereas others call all of them nature. In still another sense nature means the substance of things which are by nature, as those who say that nature is the primary composition of a thing, as Empedocles says, "Of nothing that exists is there nature, but only the mixing and separating-out of what has been mixed. Nature is but the name men give to these. For this reason we do not say that things which are or come to be by nature have a nature, even when that from which they can be or come to be is already present, so long as they do not have their form or species. Hence that which is composed of both of these exists by nature, as animals and their parts.

414. Again, nature is the primary matter of a thing, and this in two senses: either what is primary with respect to this particular thing, or primary in general; for example, the primary matter of bronze articles is bronze, but in general it is perhaps water, if everything capable of being liquefied is water. And nature is also a thing's form or substance, i.e., the terminus of the process of generation. But metaphorically speaking every substance in general is called nature because of form or species, for the nature of a thing is also a kind of substance.

415. Hence, from what has been said, in its primary and proper sense nature is the substance of those things which have within themselves as such the source of their motion. For matter is called nature because it is receptive of this. And processes of generation and growth are called nature because they are motions proceeding from it. And nature is the source of motion in those things which are by nature, and it is something present in them either potentially or in complete actuality.

COMMENTARY

Nature

808. Here he gives the different meanings of the term nature. And even though an investigation of the term nature appears not to belong to first philosophy but rather to the philosophy of nature, he nevertheless gives the different meanings of this term here, because according to one of its common meanings nature is predicated of every substance, as he will make clear. Hence it falls under the consideration of first philosophy just as universal substance does.

In regard to the first he does two things. First (808), he distinguishes the different senses in which the term nature is used. Second (824), he reduces all of these to one primary notion (“Hence, from what”).

In regard to the first he does two things. First, he gives five principal senses in which the term, nature is used. Second (821), he gives two additional senses connected with the last two of these (“Again, nature”).

(1) He accordingly says, first, that in one sense nature means the process of generation of things that are generated, or, according to another text which states this in a better way, “of things that are born.” For not everything that is generated can be said to be born but only living things, for example, plants and animals and their parts. The generation of non-living things cannot be called nature, properly speaking, according to the common use of the term, but only the generation of living things inasmuch as nature may mean the nativity or birth of a thing... Yet even from this text it can be understood that the term nature means the generation of living things by a certain lengthening or extension of usage.

809. Again, from the fact that nature was first used to designate the birth of a thing there followed a second use of the term, so that nature came to mean the principle of generation from which a thing comes to be, or that from which as from an intrinsic principle something born is first generated.

810. And as a result of the likeness between birth and other kinds of motion the meaning of the term nature has been extended farther, so that in a third sense it means the source from which motion begins in any being according to its nature, provided that it is present in it insofar as it is such a being and not accidentally. For example, the principle of health, which is the medical art, is not present in a physician who is ill insofar as he is ill but insofar as he is a physician. And he is not healed insofar as he is a physician but insofar as he is ill; and thus the source of motion is not in him insofar as he is moved. This is the definition of nature given in Book II of the Physics.

811. And because he mentioned things that are born, he also shows what it means in the proper sense “to be born,” as another text says, and in place of which this text incorrectly says “to be generated.” For the generation of living things differs from that of non-living things, because a non-living thing is not generated by being joined or united to its generator, as fire is generated by fire and water by water. But the generation of a living thing comes about through some kind of union with the principle of generation. And because the addition of quantity to quantity causes increase, therefore in the generation of living things there seems to be a certain increase, as when a tree puts forth foliage and fruit. Hence he says that those things are said to be born which “increase,” i.e., have some increase together with the principle of generation [i.e. multiply].

812. But this kind of increase differs from that class of motion which is called increase [or augmentation], by which things that are already born are moved or changed. For a thing that increases within itself does so because the part added passes over into the substance of that thing, as food passes over into the substance of the one nourished. But anything that is born is added to the thing from which it is born as something other and different, and not as something that passes over into its substance. Hence he says that it increases “through something distinct” or something else, as if to say that this increase comes about through the addition of something that is other or different.

813. But addition that brings about increase can be understood to take place in two ways: in one way, “by touching,” i.e., by contact alone; in another way, “by existing together,” i.e., by the fact that two things are produced together and naturally connected with each other, as the arms and sinews; “and by being joined,” i.e., by the fact that something is naturally adapted to something else already existing, as hair to the head and teeth to the gums. In place of this another text reads, more appropriately, “by being born together with,” and “by being connected with at birth.” Now in the generation of living things addition comes about not only by contact but also by a kind of joining together or natural connection, as is evident in the case of embryos, which are not only in contact in the womb, but are also bound to it at the beginning of their generation.

814. Further, he indicates the difference between these two, saying that “being fused,” i.e., being bound together, or “being connected at birth,” as another text says, differs from contact, because in the case of contact there need be nothing besides the things in contact which makes them one. But in the case of things which are bound together, whether naturally connected or born together and joined at birth, there must be some one thing “instead of contact,” i.e., in the place of contact, which causes them “to be naturally joined,” i.e., joined or bound together or born together. Moreover, it must be understood that the thing which causes them to be one makes them one in quantity and continuity but not in quality; because a bond does not alter the things bound from their own dispositions.

815. And from this it is evident that anything that is born is always connected with the thing from which it is born. Hence nature never means an extrinsic principle, but in every sense in which it is used it is taken to mean an intrinsic principle.

816. (4) And from this third meaning of nature there follows a fourth. For if the source of motion in natural bodies is called their nature, and it seemed to some that the principle of motion in natural bodies is matter, it was for this reason that matter came to be called nature, which is taken as a principle of a thing both as to its being and as to its becoming. And it is also considered to be without any form, and is not moved by itself but by something else. He accordingly says that nature is spoken of as that primary thing of which any being is composed or from which it comes to be.

817. He says this because matter is a principle both of being and of becoming. Hence he says that “it is without order,” i.e., form; and for this reason another text says “when it is unformed”; for in the case of some things their order (or arrangement) is regarded as their form, as in the case of an army or of a city. And for this reason he says that it is “immutable by its own power,” i.e., it cannot be moved by its own power but by that of a higher agent. For matter does not move itself to acquire a form but is moved by a higher and extrinsic agent. For instance, we might say that “bronze is the nature of a statue or of bronze vessels” or “wood of wooden,” as if such vessels were natural bodies. The same is true of everything else that is composed of or comes to be from matter; for each comes to be from its matter though this is preserved. But in the process of generation the dispositions of a form are not preserved; for when one form is introduced another is cast out. And for this reason it seemed to some thinkers that forms are accidents and that matter alone is substance and nature, as he points out in the Physics, Book II

818. They held this view because they considered the matter and form of natural bodies in the same way as they did the matter and form of things made by art, in which forms are merely accidents and matter alone is substance. It was in this sense that the philosophers of nature said that the elements are the matter of things which come to be by nature, i.e., water, air, or fire, or earth, which no philosopher has held to be the element of natural beings all by itself, although some of those who were not philosophers of nature did hold this, as was stated in Book I (134). And some philosophers, such as Parmenides, held that some of these are the elements and natures of things; others, such as Empedocles, held that all four are the elements of things; and still others, such as Heraclitus, held that something different is the element of things, for he claimed that vapor plays this role.

819. (5) Now because motion is caused in natural bodies by the form rather than by the matter, he therefore adds a fifth sense in which the term nature is used: that in which nature means the form of a thing. Hence in another sense nature means “the substance of things,” i.e., the form of things, which are by nature. It was in this sense that some said that the nature of things is the composition of mixed bodies, as Empedocles said that there is nothing absolute in the world, but that only the alteration or loosening (or mixing, according to another text) of what has been mixed is called nature by men. For they said that things composed of different mixtures have different natures.

820. Now they were led to hold that form is nature by this process of reasoning: whatever things exist or come to be by nature are not said to have a nature, even though the matter from which they are naturally disposed to be or to come to be is already present, unless they have a proper species and a form through which they acquire their species. Now the term species seems to be given in place of substantial form and the term form in place of figure, which is a natural result of the species and a sign of it. Hence, if form is nature, a thing cannot be said to have a nature unless it has a form. Therefore, that which is composed of matter and form “is said to be by nature,” i.e., according to nature, as animals and the parts of animals, such as flesh and bones and the like.

821. Again, nature (414).

Then he gives two meanings of nature which are connected with the last two preceding ones, and the first of these is added to the fourth sense of nature, in which it means the matter of a thing. And he says that not every kind of matter is said to be the nature of a thing but only first matter. This can be understood in two senses: either with reference to something generic, or with reference to something that is first absolutely or without qualification. For example, the first matter generically of artificial things produced from bronze is bronze; but their first matter without qualification is water; for all things which are liquefied by heat and solidified by cold have the character of water, as he says in Book IV of the Meteors.

822. He links up the second of these additional meanings with the fifth sense of nature mentioned above, according to which nature means form. And in this sense not only the form of a part (forma partis) is called nature but the species is the form of the whole (forma totius). For example, we might say that the nature of man is not only a soul but humanity and the substance signified by the definition. For it is from this point of view that Boethius says that the nature of a thing is the specific difference which informs each thing, because the specific difference is the principle that completes a thing’s substance and gives it its species. And just as form or matter is called nature because it is a principle of generation, which is the meaning of nature according to the original use of the term, in a similar way the species or substance of a thing is called its nature because it is the end of the process of generation. For the process of generation terminates in the species of the thing generated, which is a result of the union of matter and form.

823. And because of this every substance is called nature according to a kind of metaphorical and extended use of the term; for the nature which we spoke of as the terminus of generation is a substance. Thus every substance is similar to what we call nature. Boethius also gives this meaning of the term. Moreover, it is because of this meaning that the term nature is distinguished from other common terms. For it is common in this way just as substance also is.

824. Hence, from what (415).

Then he reduces all of the foregoing senses of the term nature to one common notion. But it must be noted that the reduction of the other senses to one primary sense can happen in two ways: in one way, with reference to the order which things have; and in another way, with reference to the order which is observed in giving names to things. For names are given to things according as we understand them, because names are signs of what we understand; and sometimes we understand prior things from subsequent ones. Hence something that is prior for us receives a name which subsequently fits the object of that name. And this is what happens in the present case; for since the forms and powers of things are known from their activities, the process of generation or birth of a thing is the first to receive the name of nature and the last is the form.

825. But with reference to the order which things have in reality the concept of nature primarily fits the form, because, as has been said (808), nothing is said to have a nature unless it has a form.

826. Hence from what has been said it is evident that “in its primary and proper sense nature is the substance,” i.e., the form, of those things which have within themselves as such the source of their motion. For matter is called nature because it is receptive of form; and processes of generation get the name of nature because they are motions proceeding from a form and terminating in further forms. And this, namely, the form, is the principle of motion in those things which are by nature, either potentially or actually. For a form is not always the cause of actual motion but sometimes only of potential motion, as when a natural motion is prevented by an external obstacle, or even when a natural action is prevented by a defect in the matter.

LESSON 6

Four Senses of the Term Necessary. Its First and Proper Sense. Immobile Things, though Necessary, Are Exempted from Force

ARISTOTLE'S TEXT Chapter 5: 1015a 20-1015b 15

416. Necessary means that without which, as a contributing cause, a thing cannot be or live; for example, breathing and food are necessary to an animal because it cannot exist without them.

417. And it also means that without which the good for man cannot be or come to be, and that without which one cannot get rid of or remain free of some evil; for example, the drinking of some drug is necessary in order that one may not be in distress, and sailing to Aegina is necessary in order that one may collect money.

418. Again, it means what applies force and force itself, and this is something which hinders and prevents, in opposition to desire and choice. For that which applies force is said to be necessary, and for this reason anything necessary is also said to be lamentable, as Evenus says, "For every necessary thing is mournful." And force is a kind of necessity, as Sophocles says, "But force compels me to do this." And necessity seems to be something blameless, and rightly so, for it is contrary to motion which stems from choice and from knowledge.

419. Again, we say that anything which cannot be otherwise is necessarily so.

420. And from this sense of the term necessary all the other senses are derived. For whatever is forced is said either to do or to undergo something necessary when it cannot do something according to its inclination as a result of force, as if there were some necessity by reason of which the thing could not be otherwise. The same thing applies to the contributing causes of life and of good. For when in the one case good, and in the other life or being, is impossible without certain contributing causes, these are necessary; and this cause is a kind of necessity.

421. Further, demonstration belongs to the class of necessary things, because whatever has been demonstrated in the strict sense cannot be otherwise. The reason for this is the principles, for the principles from which a syllogism proceeds cannot be otherwise.

422. Now of necessary things some have something else as the cause of their necessity and others do not, but it is because of them that other things are necessary. Hence what is necessary in the primary and proper sense is what is simple, for this cannot be in more ways than one. Therefore it cannot be in one state and in another; otherwise there would be more ways than one. If, then, there are any beings which are eternal and immobile, in them nothing forced or contrary to nature is found.

COMMENTARY

Necessary

827. Having distinguished the different senses of the terms which signify causes, the Philosopher now gives the different senses of a term which designates something pertaining to the notion of cause, i.e., the term necessary; for a cause is that from which something else follows of necessity. In regard to this he does two things. First, he distinguishes the different senses of the term necessary. Second (836), he reduces all of these to one primary sense (“And from this sense”).

In the first part he gives four senses in which the term necessary is used:

First, it means that without which a thing cannot be or live; and even when this is not the principal cause of a thing, it is still a contributing cause. Breathing, for example, is necessary to an animal which breathes, because it cannot live without this. And while breathing is not the [principal] cause of life, nonetheless it is still a contributing cause inasmuch as it helps to restore what is lost and prevents the total consumption of moisture, which is a cause of life. Hence things of this kind are said to be necessary because it is impossible for things to exist without them.

828. And it also means (417).

Then he gives a second sense in which things are said to be necessary. He says that in a second way those things are said to be necessary without which some good cannot be or come about, or some evil be avoided or expelled. For example, we say that “the drinking of some drug,” i.e., a laxative medicine, is necessary, not because an animal cannot live without it, but because it is required to expel something, namely, an evil, illness, or even to avoid it. For this is necessary “in order that one may not be in distress,” i.e., to avoid being ill. And similarly “sailing to Aegina,” i.e., to a definite place, is necessary, not because a man cannot exist without this, but because he cannot acquire some good, i.e., money, without doing this. Hence, such a voyage is said to be necessary in order to collect a sum of money.

829. Again, it means (418).

Here he gives a third sense in which things are said to be necessary. He says that anything which exerts force, and even force itself, is termed necessary. For force is said to be necessary, and one who is forced is said to do of necessity whatever he is compelled to do. He shows what is meant by something that exerts force both in the case of natural beings and in that of beings endowed with will. In natural beings there is a desire for or an inclination toward some end or goal, to which the will of a rational nature corresponds; and for this reason a natural inclination is itself called an appetite. For both of these, i.e., both the desire of a natural inclination and the intention of the will, can be hindered and prevented—hindered in carrying out a motion already begun, and prevented from initiating motion. Therefore, that is said to be forced “which is done in opposition to desire,” ‘ i.e., against the inclination of a natural being; and it is “something that hinders choice,” i.e., the end intended in executing a voluntary motion already begun, and also something that prevents it from beginning. Another text says, “and this is according to impetuousness,” i.e., according to impulse. For force is found when something is done through the impulse of an external agent and is opposed to the will and power of the subject. And that is forced which is done as a result of an impulse applying force.

830. Now from this definition of the forced he draws two conclusions. The first is that everything forced is sad or mournful. He proves this by using the statement of a certain poet or teacher, saying that everything which is necessary or forced is sad or lamentable; for force is a kind of necessity, as the poet Sophodes says: “Force,” i.e., necessity, “compelled me to do this.” For it has been said that force is something which hinders the will; and things which are opposed to the will cause sorrow, because sorrow has to do with things which happen to us against our will.

831. The second conclusion is that anything which is necessary is rightly said to be without blame or reproach. For it is said that necessity deserves forgiveness rather than blame; and this is true because we deserve to be blamed only for the things which we do voluntarily and for which we may also be reasonably rebuked. But the kind of necessity which pertains to force is opposed to the will and to reason, as has been stated (829); and thus it is more reasonable to say that things done by force are not subject to blame.

832. Again, we say (419).
He gives a fourth sense in which things are said to be necessary. He says that being in such a state that it cannot be otherwise we also call necessary, and this is what is necessary in an absolute sense. Things necessary in the first senses, however, are necessary in a relative sense.

833. Now whatever is absolutely necessary differs from the other types of necessity, because absolute necessity belongs to a thing by reason of something that is intimately and closely connected with it, whether it be the form or the matter or the very essence of a thing. For example, we say that an animal is necessarily corruptible because this is a natural result of its matter inasmuch as it is composed of contraries; and we say that an animal is necessarily capable of sensing because this is a result of its form; and we also say that an animal is necessarily a living sensible substance because this is its essence.

834. However, the necessity of something which is necessary in a relative sense and not absolutely depends on an extrinsic cause. And there are two kinds of extrinsic causes—the end and the agent. The end is either existence taken absolutely, and the necessity taken from this end pertains to the first kind; or it is well disposed existence or the possession of some good, and necessity of the second kind is taken from this end.

835. Again, the necessity which comes from an external agent pertains to the third kind of necessity. For force exists when a thing is moved by an external agent to something which it has no aptitude for by its own nature. For if something is disposed by its own nature to receive motion from an external agent, such motion will not be forced but natural. This is evident in the motion of the celestial bodies by separate substances, and in that of lower bodies by higher ones.

836. And from this (420).
Here he reduces all of the senses in which things are necessary to one; and in regard to this he does three things. First (836), he shows that all the types of necessity found in reality pertain to this last type. Second (838), he shows that necessity in matters of demonstration is taken in this last sense (“Further, demonstration”). Third (839), he draws a corollary from what has been set down above (“Now of necessary things”).

He accordingly says, first, that all the other senses of the term necessary are somehow referred to this last sense. He makes this clear, first, with reference to the third way in which things are said to be necessary. For whatever is forced is said to do or to undergo something of necessity on the grounds that it cannot act through its own power because of the force exerted on it by an agent; and this is a kind of necessity by which it cannot be otherwise than it is.

837. Then he shows that the same thing is true of the first and second ways in which things are said to be necessary: in the first way with reference to the causes of living and being absolutely, and in the second with reference to the causes of good. For the term necessary was so used in these other ways: in one way to designate that without which a thing cannot be well off, and in the other to designate that without which a thing cannot live or exist. Hence that cause without which a thing cannot live or exist or possess a good or avoid an evil is said to be necessary; the supposition being that the primary notion of the necessary derives from the fact that something cannot be otherwise.

838. Further, demonstration (421).
Then he shows that the necessary in matters of demonstration is taken from this last sense, and this applied both to principles and to conclusions. For demonstration is said to be about necessary things, and to proceed from necessary things. At is said to be about necessary things because what is demonstrated in the strict sense cannot be otherwise. He says “demonstrated in the strict sense” in order to distinguish this from what is demonstrated by the kind of demonstration which refutes an opponent, and does not strictly demonstrate. In the fourth book (609) he called this an ad hominem argument. In demonstrations of this kind which refute an opponent we conclude to the impossible from certain impossible premises. But since in demonstrations the premises are the causes of the conclusion, for demonstrations in the strict sense are productive of science and this is had only by way of a cause, the principles from which a syllogism proceeds must also be necessary and thus cannot be otherwise than they are. For a necessary effect cannot come from a non-necessary cause.

839. Now of necessary things (422).
Here he draws three conclusions from the points set down above, one of which follows from the other. The first is that, since in demonstrations the premises are the causes of the conclusion and both of these are necessary, it follows that some things are necessary in one of two ways. For there are (1) some things whose necessity is caused by something else, and there are (2) others whose necessity has no cause; and such things are necessary of themselves. This is said against Democritus, who claimed that we must not look for the causes of necessary things, as is stated in Book VIII of the Physics.

840. The second conclusion is that, since there must be one first necessary being from which other beings derive their necessity (for there cannot be an infinite regress in causes, as was shown in the second book (301), this first necessary being, which is also necessary in the most proper sense because it is necessary in all ways, must be simple. For composite things are changeable and thus can be in more ways than one. But things which can be in more ways than one can be now in one way and now in another, and this is opposed to the notion of necessity; for that is necessary which cannot be otherwise. Hence the first necessary being must not be now in one way and now in another, and consequently cannot be in more ways than one. Thus he must be simple.

841. The third conclusion is that, since the forced is something which is moved by an external agent in opposition to its own nature, and necessary principles are simple and unchangeable, as has been shown (422:C 840), therefore if there are certain eternal and unchangeable beings, as the separate substances are, in them there must be nothing forced or contrary to their nature. He says this lest a mistake should be made in the case of the term necessity, since it is predicated of immaterial substances without implying on this account that anything forced is found in them.

LESSON 7

The Kinds of Accidental Unity and of Essential Unity

ARISTOTLE'S TEXT Chapter 6: 1015b 16-1016b 3

423. The term one is used both of what is accidentally one and of what is essentially one. A thing is said to be accidentally one, for example, when we say "Coriscus" and "musical" and "musical Coriscus." For to say "Coriscus" and "musical" and "musical Coriscus" amounts to the same thing; and this is also true when we say "just" and "musical" and "just musical Coriscus." For all of these are said to be accidentally one; just and musical because they are accidents of one substance, and musical and Coriscus because the one is an accident of the other. And similarly in a sense musical Coriscus is one with Coriscus, because one of the parts of this expression is an accident of the other. Thus musical is an accident of Coriscus and musical Coriscus is an accident of just Coriscus, because one part of each expression is an accident of one and the same subject. For it makes no difference whether musical is an accident of Coriscus [or whether just Coriscus is an accident of musical Coriscus]. The same thing also holds true if an accident is predicated of a genus or of any universal term, for example, when one says that man and musical man are the same; for this occurs either because musical is an accident of man, which is one substance, or because both are accidents of some singular thing, for example, Coriscus. Yet both do not belong to it in the same way, but one perhaps as the genus and substance, and the other as a habit or modification of the substance. Therefore whatever things are said to be accidentally one are said to be such in this way.

424. But in the case of things which are said to be essentially one, some are said to be such by nature of their continuity; for example, a bundle becomes one by means of a binding, and pieces of wood become one by means of glue. And a continuous line, even if it is bent, is said to be one, just as each part [of the human body] is, for example, a leg or an arm. And of these things themselves those which are continuous by nature are one to a greater degree than those which are continuous by art. And that is said to be continuous whose motion is essentially one and cannot be otherwise. And motion is one when it is indivisible, i.e., indivisible in time.

425. Again, all those things are essentially continuous which are one not merely by contact; for if you place pieces of wood so that they touch each other, you will not say that they are one, either one board or one body or any other continuous thing. Hence those things which are continuous throughout are said to be one even though they are bent. And those which are not bent are one to an even greater degree; for example, the lower leg or the thigh is one to a greater degree than the leg, because the motion of the leg may not be one. And a straight line is one to a greater degree than a bent line. But what is bent and angular we refer to as either one or not one, because its motion may be either simultaneous or not. But the motion of a straight line is always simultaneous, and no part of it which has extension is at rest when another moves, as in a bent line.

426. Again, a thing is said to be one in another sense because its underlying subject is uniform in species; and it is uniform in species as those things whose form is indivisible from the viewpoint of sensory perception. And the underlying subject is either one that is primary or one that is last in relation to the end. For wine is said to be one and water is said to be one inasmuch as they are indivisible in species. And all liquids are said to be one, as oil, wine and fluids, because the ultimate subject of all is the same; for all of these are made up of water or of air.

427. And those things are said to be one whose genus is one and differs by opposite differences. And all these things are said to be one because the genus, which is the subject of the differences, is one; for example, man, dog and horse are one because all are animals; and it is such in a way closest to that in which matter is one. And sometimes these things are said to be one in this way, and sometimes in their higher genus, which is said to be the same if those which are higher than these are the last species of the genus; for example, the isosceles and the equilateral triangle are one and the same figure because both are triangles; but they are not the same triangles.

428. Further, any two things are said to be one when the definition expressing the essence of one is indistinguishable from that signifying the essence of the other. For in itself every definition is divisible. And what has increased and what has decreased are one in this way, because their definition is one. An example of this is found in plane figures, which are one in species.

429. And those things are altogether one and in the highest degree whose concept, which grasps their essence, is indivisible and cannot be separated either in time or in place or in its intelligible structure; and of these, all those which are substances are especially such.

COMMENTARY

842. Having given the various senses of the terms which signify causes, the Philosopher now proceeds to do the same thing with those terms which signify in some way the subject of this science. This is divided into two parts. In the first (423:C 843) he gives or distinguishes the different senses of the terms which signify the subject of this science; and in the second (445:C 908) he distinguishes the different senses of the terms which signify the parts of this subject ("Things are said to be the same").

Now the subject of this science can be taken either as that which has to be considered generally in the whole science, and as such it is unity and being, or as that with which this science is chiefly concerned, and this is substance. Therefore, first (423), he gives the different senses of the term one; second (435:C 885) of the term being ("The term being"); and third (440:C 898), of the term substance ("The term substance").

In regard to the first part of this division he does two things. First, he makes a distinction between what is essentially one and what is accidentally one, and he also indicates the various senses in which things are said to be accidentally one. Second (42VC 848), he notes the various senses in which things are said to be essentially one ("But in the case").

843. He says (423), then, that the term one signifies both what is essentially one and what is accidentally one. And he tells us that what is accidentally one we should consider first in the case of singular terms. Now singular terms can be accidentally one in two ways: in one way according as an accident is related to a subject; and in another way according as one accident is related to another. And in both cases three things have to be considered—one composite thing and two simple ones. For if what is accidentally one is considered to be such according as an accident is related to a subject, then there are, for example, these three things: first, Coriscus; second, musical; and third, musical Coriscus. And these three are accidentally one; for Coriscus and what is musical are the same in subject. Similarly when an accident is related to an accident, three terms must be considered: first, musical; second, just; and third, just musical Coriscus. And all these atle said to be accidentally one, but for different reasons.

844. For just and musical, which are two simple terms in the second way, are said to be accidentally one because both are accidents of one and the same subject. But musical and Coriscus, which are two simple terms in the first way, are said to be accidentally one because "the one," namely, musical, "is an accident of the other," namely, of Coriscus. And similarly in regard to the relationship of musical Coriscus to Coriscus (which is the relationship of a composite term to one of two simple terms), these are said to be accidentally one in the first way, because in this expression, i.e., in the complex term, musical Coriscus, one of the parts, namely, musical, is an accident of the other, which is designated as a substance, namely, Coriscus. And for the same reason it can be said that musical Coriscus is one with just Coriscus, which are two composites in the second way, because two of the parts of each composite are accidents of one subject, Coriscus. For if musical and musical Coriscus, and just and just Coriscus, are the same, then whatever is an accident of musical is also an accident of musical Coriscus; and whatever is an accident of Coriscus is also an accident of just Coriscus. Hence, if musical is an accident of Coriscus, it follows that musical Coriscus is an accident of just Coriscus. Therefore it makes no difference whether we say that musical Coriscus is an accident of just Coriscus, or that musical is an accident of Coriscus.

845. But because accidental predicates of this kind are first applied to singular things and then to universals (although the reverse is true of essential predicates), he therefore makes clear that what he showed in the case of singular terms also applies in that of universal terms. He says that, if an accident is used along with the name of a genus or of any universal term, accidental unity is taken in the same way as it is in the above cases when an accident is joined to a singular term; for example, when it is said that man and musical man are accidentally one, although they differ in some respect.

846. For singular substances are neither present in a subject nor predicated of a subject, so that while they are the subject of other things, they themselves do not have a subject. Now universal substances are predicated of a subject but are not present in a subject, so that while they are not the subjects of accidents, they have something as their subject. Hence, when an accident is joined to a singular substance, the expression stating this can only mean that an accident belongs to a singular substance, as musical belongs to Coriscus when Coriscus is said to be musical.

847. But when we say musical man, the expression can mean one of two things: either that musical is an accident of man, by which substance is designated, and from this it derives its ability to be the subject of an accident; or it means that both of these, man and musical, belong to some singular thing, for example, Coriscus, in the way that musical was predicated of just, because these two belong to the same singular thing and in the same way, i.e., accidentally. But perhaps the one term does not belong to the other in the same way, but in the way that universal substance belongs to the singular as a genus, as the term animal, or if it is not a genus, it at least belongs to the substance of the subject, i.e., as an essential predicate, as the term man. But the other term, namely, musical, does not have the character of a genus or essential predicate, but that of a habit or modification of the subject, or whatever sort of accident it may be. He gives these two, habit and modification, because there are some accidents which remain in their subject, such as habits, which are moved with difficulty, and others which are not permanent but transient, such as modifications. It is clear, then, that these are the ways in which things are said to be accidentally one.

Kinds of unity

848. But in the case (424).

Then he gives the ways in which things are essentially one, and in regard to this he does two things. First, he indicates the different senses in which the term one is used; and second (880), the different senses in which the term many is used (“Moreover, it is evident”).

In regard to the first he does two things. First, he gives the different senses in which things arc one from the viewpoint of nature, i.e., according to the conditions found in reality; and second (876), from the viewpoint of logic, i.e., according to the considerations of logic (“Further, some things”).

In regard to the first he does two things. First, he distinguishes the different senses in which things are said to be one. Second (872), he indicates a property which accompanies unity (“But the essence of oneness”).

In regard to the first he does two things. First, he sets down the different senses in which things are said to be one. Second (866), he reduces all of them to a single sense (“For in general”).

In the first part he gives five senses in which the term one is used.

849. (1) The first is this: some of the things which are said to be essentially one are such “by nature of their continuity,” i.e., by being continuous, or “because they are continuous,” as another translation says. But things are said to be continuous in two ways; for, as another text says, some things are continuous by reason of something other than themselves, and some in themselves.

850. First, he proceeds to deal with those things which are continuous (a) by reason of something other than themselves. He says that there are things which are continuous as a result of something else; for example, a bundle of sticks is continuous by means of a cord or binding; and in this way too pieces of wood which have been glued together are said to be one by means of the glue. Now there are also two ways in which this occurs, because the continuity of things which are fastened together (i) sometimes takes the form of a straight line, and (ii) sometimes that of a line which is not straight. This is the case, for example, with a bent line having an angle, which results from the contact of two lines in one surface in such a way that they are not joined in a straight line. And it is in this way that the parts of an animal are said to be one and continuous; for example, the leg, which is bent, and contains an angle at the knee, is said to be one and continuous; and it is the same with the arm.

851. But since this kind of continuity which comes about by reason of something else can exist or come to be both by nature and by art, (b) those things which are continuous by nature are one to a greater degree than those which are continuous by art; for the unity that accounts for the continuity of things which are continuous by nature is not extrinsic to the nature of the thing which is made continuous by it, as happens in the case of things which are one by art, in which the binding or glue or something of the sort is entirely extrinsic to the nature of, the things which are joined together. Hence those things which are joined by nature hold the first place among those which are essentially continuous, which are one in the highest degree.

852. In order to make this clear he defines the continuous. He says that that is said to be continuous which has only one motion essentially and cannot be otherwise. For the different parts of any continuous thing cannot be moved by different motions, but the whole continuous thing is moved by one motion. He says “essentially” because a continuous thing can be moved in one way essentially and in another or others accidentally. For example, if a man in a ship moves against the motion of the ship essentially, he is still moved accidentally by the motion of the ship.

853. Now in order for motion to be one it must be indivisible; and by this I mean from the viewpoint of time, in the sense that at the same time that one part of a continuous thing is moved another is also moved. For it is impossible that one part of a continuous thing should be in motion and another at rest, or that one part should be at rest and another in motion, so that the motion of the different parts should take place in different parts of time.

854. Therefore the Philosopher defines the continuous here by means of motion, and not by means of the oneness of the boundary at which the parts of the continuous things are joined, as is stated in the Categories, and in the Physics; because from this definition he can consider different grades of unity in different continuous things (as will be made clear later on [856]), but he cannot do this from the definition given there.

855. Moreover, it should be noted that what is said here about the motion of a continuous thing being indivisible from the viewpoint of time is not opposed to the point proved in Book VI of the Physics, that the time of a motion is divided according to the parts of the thing moved. For here the Philosopher is speaking of motion in an unqualified sense, because one part of a continuous thing does not begin to be moved before another part does; but there he is speaking of some designation which is made in the continuous quantity over which motion passes. For that designation, which is the first part of a continuous quantity, is traversed in a prior time, although in that prior time other parts of the continuous thing that is in motion are also moved.

856. Again, all those (425).

Then he proceeds to deal with things which are essentially continuous. He says that those things are essentially continuous which are said to be one not by contact. He proves this as follows: things which touch each other, as two pieces of wood, are not said to be one piece of wood or one body or any other kind of one which belongs to the class of the continuous. Hence it is evident that the oneness of things which are continuous differs from that of things which touch each other. For those things which touch each other do not have any unity of continuity of themselves but by reason of some bond which unites them; but those things which are continuous are said to be essentially one even though they are bent. For two bent lines are continuous in relation to one common boundary, which is the point at which the angle is formed.

857. Yet those things are one to a greater degree which are essentially continuous and without a bend. The reason is that a straight line can have only one motion in all of its parts, whereas a bent line can have one or two motions. For the whole of a bent line can be understood to be moved in one part; and it can also be understood that when one part is at rest, the other part, which makes an angle with the part at rest, can come closer by its motion to the unmoved part; for example, when the lower leg or shin is bent in the direction of the upper leg, which here is called the thigh. Hence each of these—the shin and thigh—is one to a greater degree “than the scelos,” as the Greek text says, i.e. the whole composed of the shin and thigh.

858. Further, it must be noted that the text which reads “curved” instead of “bent” is false. For, since the parts of a curved line do not contain an angle, it is evident that they must be in motion together or at rest together, just as the parts of a straight line are; but this does not happen in the case of a bent line, as has been stated (857).

859. Again, a thing (426).

(2) Here he gives the second way in which things are one. He says that a thing is said to be one in a second way not merely by reason of continuous quantity but because of the fact that the whole subject is uniform in species. For some things can be continuous even though they differ in species; for example, when gold is continuous with silver or something of this kind. And then two such things will be one if quantity alone is considered but not if the nature of the subject is considered. But if the whole continuous subject is uniform in species, it will be one both from the viewpoint of quantity and from that of nature.

860. Now a subject is said to be uniform in species when the same sensible form is not divided in such a way that there are different sensible forms in different parts of the subject, as it sometimes happens, for example, that one part of a sensible body is white and another black. And this subject, which does not differ in species, can be taken in two ways: in one way as the first subject, and in another as the last or ultimate subject which is reached at the end of a division. It is evident, for example, that a whole amount of wine is said to be one because its parts are parts of one common subject which is undifferentiated specifically. The same is true of water. For all liquids or moist things are said to be one insofar as they have a single ultimate subject. For oil and wine and the like are ultimately dissolved into water or air, which is the root of moistness in all things.

861. And those things (427).

(3) Then he indicates the third way in which things are said to be one. He says that those things are said to be one whose genus is one, even though it is divided by opposite differences. And this way resembles the preceding one; for some things were said to be one in the preceding way because their subject-genus is one, and now some things are said to be one because their genus, which is the subject of differences, is one; for example, a man and a horse and a dog are said to be one because they have animality in common as one genus, which is the subject of differences. Yet this way differs from the preceding, because in the preceding way the subject was one thing which was not differentiated by forms; but here the subject-genus is one thing which is differentiated by various differences, as though by various forms.

862. Thus it is evident that some things are said to be one in genus in a most proximate sense, and in a way similar to that in which some things are said to be one in matter. For those things which are said to be one in matter are also differentiated by forms. For even though a genus is not matter, because it would then not be predicated of a species since matter is part of a thing, still the notion of a genus is taken from what is material in a thing, just as the notion of a difference is taken from what is formal. For the rational soul is not the difference of man (since it is not predicated of man), but something having a rational soul (for this is what the term rational signifies). Similarly, sensory nature is not the genus of man but a part. But something having a sensory nature, which the term animal Signifies, is the genus of man. In a similar fashion, then, the way in which things are one in matter is closely related to that in which they are one in genus.

863. But it must be borne in mind that to he one in generic character has two meanings. For sometimes some things are said to be one in genus, as has been stated, because they belong to one genus, whatever it may be. But sometimes some things are said to be one in genus only in reference to a higher genus, which, along with the designation “one” or “the same,” is predicated of the last species of a lower genus when there are other higher species in one of which the lower species agree. For example, figure is one supreme genus which has many species under it, namely, circle, triangle, square, and the like. And triangle also has different species, namely, the equilateral, which is called iso-pleural and the triangle with two equal sides, which is called equi-legged or isosceles. Hence these two triangles are said to be one figure, which is their remote genus, but not one triangle, which is their proximate genus. The reason for this is that these two triangles do not differ by any differences which divide figure, but by differences which divide triangle. And the term same means that from which something does not differ by a difference.

864. (4) He now describes the fourth way in which things are said to be one. He says that things such that the definition of one (which is the concept signifying its quiddity) is not distinguished from the definition of the other (which also signifies its quiddity) are also said to be one. For while every definition must be divisible or distinguishable in itself, or essentially, since it is composed of genus and difference, it is possible for the definition of one thing to be indistinguishable from that of another when the two have one definition. And this applies (a) whether those definitions signify the total [intelligible structure] of the thing defined, as tunic and clothing (and then things whose definition is one are one in an absolute sense), or (b) whether that common definition does not totally comprehend the intelligible structure of the two things which have it in common, as an ox and a horse have in common the one definition of animal. Hence they are never one in an absolute sense, but only in a relative sense inasmuch as each is an animal. The same applies in the case of increase and decrease; for there is one common definition of the genus, because each is a motion relating to quantity. And the same thing is true of plane figures, for there is one definition of the species, plane figure.

865. And those things (429).

(5) He gives the fifth way in which things are one. He says that those things are “altogether” one, i.e., perfectly, and in the highest degree, whose concept, which grasps their quiddity, is altogether indivisible, like simple things, which are not composed of material and formal principles. Hence the concept which embraces their quiddity does not comprehend them in such a way as to form a definition of them from different principles, but (a) rather grasps them negatively, as happens in the case of a point, which has no parts; or (b) it even comprehends them by relating them to composite things, as happens, for example, when someone defines the unit as the principle of number. And because such things have in themselves an indivisible concept, and things which are divided in any way at all can be understood separately, it therefore follows that such things are indivisible both in time and in place and in their intelligible structure. Hence these things are one in the highest degree, and especially those which are indivisible in the genus of substance. For even though what is indivisible in the genus of accident is not composite in itself, nonetheless it does form a composite with something else, namely, the subject in which it inheres. But an indivisible substance is neither composite in itself nor does it form a composite with something else. Or the term substance can be taken in the ablative case, and then the sense is that, even though some things are said to be one because they are indivisible in time and in place and in definition, still those things in this class which are indivisible in substance are said to be one in the highest degree. This sense is reduced to the preceding one.

LESSON 8

The Primary Sense of One. One in the Sense of Complete. One as the Principle of Number. The Ways in Which Things Are One. The Ways in Which Things Are Many

ARISTOTLE'S TEXT Chapter 6: 1016b 3-1017a 6

430. For in general those things which do not admit of division are said to be one insofar as they do not admit of division. Thus, if two things do not admit of division insofar as they are man, they are one man; and if they do not admit of division insofar as they are animal, they are one animal; and if they do not admit of division insofar as they have continuous quantity, they are one continuous quantity. Hence many things are said to be one because they do or undergo or