possess an attribute which it or its genus would naturally possess.
E.g., a blind man is not "deprived" of sight in the same sense that a mole is; the latter is "deprived" in virtue of its genus, but the former in virtue of himself. i.e., a mole is blind as being a member of a blind genus, whereas a man is blind only as an individual. Of course moles are not really blind, but we still speak as though they were. (c) If a thing has not an attribute which it would naturally possess, and when it would naturally possess it (for blindness is a form of privation; but a man is not blind at any age, but only if he lacks sight at the age when he would naturally possess it The qualification refers, I suppose, to the fact that an embryo does not naturally possess sight. ), and similarly if it The subject seems to be indefinite, but no doubt Aristotle is thinking primarily of the particular example which he has just given. A man "is not called blind if he does not see in the dark, or if he does not see with his ears, or if he does not see sound, or if he does not see what is behind him or too far away" ( Ross). lacks an attribute in the medium and organ and relation and manner in which it would naturally possess it. (d) The forcible removal of anything is called privation. (e) Privation has as many senses as there are senses of negation derived from the negative affix ( a) -). For we call a thing "unequal" because it does not possess equality (though it would naturally do so); and "invisible" either because it has no color at all or because it has only a faint one; and "footless" either because it has no feet at all or because it has rudimentary feet. Again, a negative affix may mean "having something in a small degree"—e.g.
"stoneless"— that is, having it in some rudimentary manner. Again, it may mean having it "not easily" or "not well"; e.g., "uncutable" means not only that which cannot be cut, but that which cannot be cut easily or well. And again, it may mean not having a thing at all; for it is not the one-eyed man, but the man who lacks sight in both eyes, who is called blind. Hence not every man is good or bad, moral or immoral; there is also the intermediate state. "To have" <or "possess"> is used in various senses. (a) To direct in accordance with one's own nature or impulse; whence we say that fever "possesses" a man, and despots "possess" cities, and people who wear clothes "possess" them. (b) We speak of anything as "having" in which, as receptive material, something is present. E.g., the bronze "has" the shape of the statue, and the body "has" the disease. (c) In the sense that the container holds the contained; for when A is contained in B, we say that A is held by B.
E.g., we say that the vessel holds the liquid, and the city holds men, and the ship holds sailors, and so too that the whole "holds" the parts. (d) The same term is applied to that which prevents anything from moving or acting in accordance with its own impulse; as pillars hold <up> the weights which are imposed upon them, and as the poets make Atlas Cf. Hes. Th.
517. hold up the heaven, because otherwise it would fall upon the earth (as some of the physicists e.g., Empedocles held that the heavens were kept in place by the velocity of their rotation; Aristot. De Caelo 284a 24, 295a 16 (Ritter and Preller, 170 b). maintain also). It is in this sense that we say that "that which holds together" holds what it holds together; because otherwise the latter would disperse, each part in accordance with its own impulse. "To be in a thing" is used similarly in senses corresponding to those of "to have." "To come from something" means: (a) In one sense, to come from something as matter, and this in two ways: in respect either of the primary genus or of the ultimate species. E.g., in the one sense everything liquefiable comes from water, and in the other the statue comes from bronze. (b) To come from something as the first moving principle; e.g., "from what comes fighting?" From abuse; because this is the beginning of a fight. (c) To come from the combination of matter and form (as the parts come from the whole, and the verse from the Iliad , and the stones from the house); for the shape is an end, and that is a complete thing which has attained its end. (d) In the sense that the form is made out of the part of its definition; as, e.g., "man" is made out of "two-footed " and the syllable out of its element In the sense that stoixei=on ("letter") forms part of the definition of "syllable." (this is a different way from that in which the statue is made out of the bronze; for the composite entity is made out of perceptible material, but the form is also made out of the material of the form). These, then, are some of the meanings of "from" <or "out of">, but (e) sometimes one of these senses only partially applies; e.g., the child comes from the father and mother, and plants from the earth, because they come from some part of those things. (f) It means "after" in time; e.g., we say that night comes from day, and storm from fine weather, because one comes after the other. And we speak thus of some of these things in view of their alternation with each other, as in the examples just mentioned, and of others in view merely of their succession in time; e.g., "the voyage was made from the equinox," meaning that it was made after it; and "the Thargelia are from the Dionysia," meaning after the Dionysia. The (city) Dionysia were celebrated in March; the Thargelia (a festival in honor of Apollo and Artemis) at the end of May. "Part" means: (a) That into which a quantity can be in any way divided; for that which is taken from a quantity qua quantity is always called a part of that quantity—e.g., we call 2 part (in a sense) of 3. (b) In another sense the term is only applied to those "parts" in sense (a) which measure the whole; hence in one sense we call 2 part of 3, and in another not. Again, (c) those divisions into which the form, apart from quantity, can be divided, are also called parts of the form. Hence species are called parts of their genus. (d) That into which the whole (either the form or that which contains the form) is divided, or of which it is composed. E.g., of a bronze sphere or cube not only is the bronze (i.e. the material which contains the form) a part, but also the angle. (e) The elements in the definition of each thing are also called parts of the whole. Hence the genus is even called a part of the species, whereas in another sense the species is part of the genus. "Whole" means: (a) That from which no part is lacking of those things as composed of which it is called a natural whole. (b) That which so contains its contents that they form a unity; and this in two ways, either in the sense that each of them is a unity, or in the sense that the unity is composed of them. For (i) the universal, or term generally applied as being some whole thing, is universal in the sense that it contains many particulars; because it is predicated of each of them, and each and all of them (e.g. man, horse, god) are one; because they are all living things. And (2) that which is continuous and limited is a whole when it is a unity composed of several parts (especially if the parts are only potentially present in it; but otherwise even if they are present actually). And of these things themselves, those which are so naturally are more truly wholes than those which are so artificially; just as we said of "the one," because "wholeness" is a kind of "oneness." Again, since a quantity has a beginning, middle and end, those to which position makes no difference we describe as "all," and those to which position makes a difference we describe as "whole," and those to which both descriptions can be applied, as both "all" and "whole." These are all things whose nature remains the same in transposition, but whose shape does not; e.g. wax or a coat. They are described as both "whole" and "all"; for they have both characteristics. Water, however, and all liquids, and number, are described as "all"; we do not speak of a "whole number" or "whole water" except by an extension of meaning. Things are described as "all" in the plural qua differentiated which are described as "all" in the singular qua one; all this number, all these units. We do not describe any chance quantity as "mutilated"; it must have parts, and must be a whole. The number 2 is not mutilated if one of its 1's is taken away—because the part lost by mutilation is never equal to the remainder—nor in general is any number mutilated; because the essence must persist. If a cup is mutilated, it must still be a cup; but the number is no longer the same. Moreover, not even all things which have dissimilar parts are mutilated; for a number has in a sense dissimilar as well as similar parts—e.g. 2, 3. But in general of things whose position makes no difference, e.g. water or fire, none is mutilated;— to be mutilated, things must be such as have their position according to their essence. Further, they must be continuous; for a musical scale is composed of dissimilar parts, and has position; but it does not become mutilated. Moreover, even things which are wholes are not mutilated by the removal of any of their parts; the parts removed must be neither proper to their essence nor in any chance location. E.g., a cup is not mutilated if a hole is made in it, but only if the handle or some projection is broken; and a man is not mutilated if he loses flesh or his spleen, but if he loses some extremity; and not every extremity, but only such as cannot grow again when completely removed. Hence bald people are not mutilated. The term "genus" <or "race"> is used: (a) When there is a continuous generation of things of the same type; e.g., "as long as the human race exists" means "as long as the generation of human beings is continuous." (b) Of anything from which things derive their being as the prime mover of them into being. Thus some are called Hellenes by race, and others Ionians, because some have Hellen and others Ion as their first ancestor. (Races are called after the male ancestor rather than after the material. Aristotle regards the mother as providing the material, and the father the formal element of the child. Cf. Aristot. Met.
1.6.8, Aristot. Met. 8.4.5.
Some derive their race from the female as well; e.g. "the descendants of Pyrrha Wife of Deucalion, the Greek Noah..") (c) In the sense that the plane is the "genus" of plane figures, and the solid of solids (for each one of the figures is either a particular plane or a particular solid); i.e., that which underlies the differentiae. (d) In the sense that in formulae the first component, which is stated as part of the essence, is the genus, and the qualities are said to be its differentiae. The term "genus," then, is used in all these senses—(a) in respect of continuous generation of the same type; (b) in respect of the first mover of the same type as the things which it moves; (c) in the sense of material. For that to which the differentia or quality belongs is the substrate, which we call material. Things are called "generically different" whose immediate substrates are different and cannot be resolved one into the other or both into the same thing. E.g., form and matter are generically different, and all things which belong to different categories of being; for some of the things of which being is predicated denote the essence, others a quality, and others the various other things which have already been distinguished. For these also cannot be resolved either into each other or into any one thing. "False" means: (i) false as a thing; (a) because it is not or cannot be substantiated; such are the statements that the diagonal of a square is commensurable, or that you are sitting. Of these one is false always, and the other sometimes; it is in these senses that these things are not facts. (b) Such things as really exist, but whose nature it is to seem either such as they are not, or like things which are unreal; e.g. chiaroscuro and dreams. For these are really something, but not that of which they create the impression. Things, then, are called false in these senses: either because they themselves are unreal, or because the impression derived from them is that of something unreal. (2.) A false statement is the statement of what is not, in so far as the statement is false. Hence every definition is untrue of anything other than that of which it is true; e.g., the definition of a circle is untrue of a triangle. Now in one sense there is only one definition of each thing, namely that of its essence; but in another sense there are many definitions, Here Aristotle is using the word lo/gos not in the strict sense of "definition" but in the looser sense of "a statement about something." since the thing itself, and the thing itself qualified (e.g. "Socrates" and "cultured Socrates") are in a sense the same. But the false definition is not strictly a definition of anything. Hence it was foolish of Antisthenes The Cynic; contemporary and renegade "disciple" of Socrates. He taught that definition, and even predication, are strictly speaking impossible. A simple entity can only be named; a complex entity can only be "defined" by naming its simple constituents. Cf.
Aristot. Met. 8.3.7, 8; Plat. Theaet. 201d-202c, Plat. Soph.
251b, c. to insist that nothing can be described except by its proper definition: one predicate for one subject; from which it followed that contradiction is impossible, and falsehood Cf. Plat. Euthyd. 283e-284c, 286c, d. nearly so. But it is possible to describe everything not only by its own definition but by that of something else; quite falsely, and yet also in a sense truly—e.g., 8 may be described as "double" by the definition of 2. Such are the meanings of "false" in these cases. (3.) A false man is one who readily and deliberately makes such statements, for the sake of doing so and for no other reason; and one who induces such statements in others—just as we call things false which induce a false impression. Hence the proof in the Hippias Plat. Hipp. Min 365-375. that the same man is false and true is misleading; for it assumes (a) that the false man is he who is able to deceive, i.e. the man who knows and is intelligent; (b) that the man who is willingly bad is better. This false assumption is due to the induction; for when he says that the man who limps willingly is better than he who does so unwillingly, he means by limping pretending to limp. For if he is willingly lame, he is presumably worse in this case just as he is in the case of moral character. "Accident" <or "attribute"> means that which applies to something and is truly stated, but neither necessarily nor usually; as if, for example, while digging a hole for a plant one found a treasure. Then the finding of treasure is an accident to the man who is digging the hole; for the one thing is not a necessary consequence or sequel of the other, nor does one usually find treasure while planting. And a cultured man might be white; but since this does not happen necessarily or usually, we call it an accident.
Thus since there are attributes and subjects, and some attributes apply to their subjects only at a certain place and time, any attribute which applies to a subject, but not because it was a particular subject or time or place, will be an accident. Nor is there any definite cause for an accident, but only a chance, i.e. indefinite, cause. It was by accident that X went to Aegina if he arrived there, not because he intended to go there but because he was carried out of his course by a storm, or captured by pirates. The accident has happened or exists, but in virtue not of itself but of something else; for it was the storm which was the cause of his coming to a place for which he was not sailing—i.e. Aegina. "Accident" has also another sense, i.e. "property." namely, whatever belongs to each thing in virtue of itself, but is not in its essence; e.g. as having the sum of its angles equal to two right angles belongs to the triangle. Accidents of this kind may be eternal, but none of the former kind can be. There is an account of this elsewhere. The reference is probably to the Aristot. Analytica Posteriora 75a 18, 39-41.
It is the principles and causes of the things which are that we are seeking; and clearly of the things which are qua being. There is a cause of health and physical fitness; and mathematics has principles and elements and causes; and in general every intellectual science or science which involves intellect deals with causes and principles, more or less exactly or simply considered. But all these sciences single out some existent thing or class, and concern themselves with that; not with Being unqualified, nor qua Being, nor do they give any account of the essence; but starting from it, some making it clear to perception, and others assuming it as a hypothesis, they demonstrate, more or less cogently, the essential attributes of the class with which they are dealing. Hence obviously there is no demonstration of substance or essence from this method of approach, but some other means of exhibiting it. And similarly they say nothing as to whether the class of objects with which they are concerned exists or not; because the demonstration of its essence and that of its existence belong to the same intellectual process. And since physical science also happens to deal with a genus of Being (for it deals with the sort of substance which contains in itself the principle of motion and rest), obviously it is neither a practical nor a productive science. For in the case of things produced the principle of motion (either mind or art or some kind of potency) is in the producer; and in the case of things done the will is the agent—for the thing done and the thing willed are the same. Thus if every intellectual activity is either practical or productive or speculative, physics will be a speculative science; but speculative about that kind of Being which can be moved, and about formulated substance for the most part only qua inseparable from matter. But we must not fail to observe how the essence and the formula exist, since without this our inquiry is ineffectual. Now of things defined, i.e. of essences, some apply in the sense that "snub" does, and some in the sense that "concave" does. The difference is that "snub" is a combination of form with matter; because the "snub" is a concave nose, whereas concavity is independent of sensible matter. Now if all physical terms are used in the same sense as "snub"—e.g. nose, eye, face, flesh, bone, and in general animal; leaf, root, bark, and in general vegetable (for not one of these has a definition without motion; the definition invariably includes matter)—it is clear how we should look for and define the essence in physical things, and why it is the province of the physicist to study even some aspects of the soul, so far as it is not independent of matter. It is obvious, then, from these considerations, that physics is a form of speculative science. And mathematics is also speculative; but it is not clear at present whether its objects are immutable and separable from matter; it is clear, however, that some branches of mathematics study their objects qua immutable and qua separable from matter. Obviously it is the province of a speculative science to discover whether a thing is eternal and immutable and separable from matter; not, however, of physics (since physics deals with mutable objects) nor of mathematics, but of a science prior to both. For physics deals with things which exist separately but are not immutable; and some branches of mathematics deal with things which are immutable, but presumably not separable, but present in matter; but the primary science treats of things which are both separable and immutable. Now all causes must be eternal, but these especially; since they are the causes of what is visible of things divine. Hence there will be three speculative philosophies: mathematics, physics, and theology— since it is obvious that if the divine is present anywhere, it is present in this kind of entity; and also the most honorable science must deal with the most honorable class of subject. The speculative sciences, then, are to be preferred to the other sciences, and "theology" to the other speculative sciences. One might indeed raise the question whether the primary philosophy is universal or deals with some one genus or entity; because even the mathematical sciences differ in this respect—geometry and astronomy deal with a particular kind of entity, whereas universal mathematics applies to all kinds alike. Then if there is not some other substance besides those which are naturally composed, physics will be the primary science; but if there is a substance which is immutable, the science which studies this will be prior to physics, and will be primary philosophy, and universal in this sense, that it is primary. And it will be the province of this science to study Being qua Being; what it is, and what the attributes are which belong to it qua Being. But since the simple term "being" is used in various senses, of which we saw that one was accidental, and another true (not-being being used in the sense of "false"); and since besides these there are the categories, e.g. the "what," quality, quantity, place, time, and any other similar meanings; and further besides all these the potential and actual: since the term "being" has various senses, it must first be said of what "is" accidentally, that there can be no speculation about it. This is shown by the fact that no science, whether practical, productive or speculative, concerns itself with it. The man who produces a house does not produce all the attributes which are accidental to the house in its construction; for they are infinite in number. There is no reason why the house so produced should not be agreeable to some, injurious to others, and beneficial to others, and different perhaps from every other existing thing; but the act of building is productive of none of these results. In the same way the geometrician does not study the accidental attributes of his figures, nor whether a triangle is different from a triangle the sum of whose angles is equal to two right angles. And this accords with what we should reasonably expect, because "accident" is only, as it were, a sort of name. Hence in a way Plato Cf. Plat. Soph.
254a. was not far wrong in making sophistry deal with what is nonexistent; because the sophists discuss the accident more, perhaps, than any other people—whether "cultured" and "grammatical," i.e. able to read and write. The sophistic argument is given by Alexander as follows: A is grammatical; therefore grammatical A=A. A is cultured; therefore cultured A=A. Therefore grammatical=cultured, and he who is grammatical must be cultured. But B, though grammatical, is not cultured. Therefore the grammatical is not the same as the cultured. and "cultured Coriscus" and "Coriscus," If Coriscus is the same as cultured Coriscus, he is the same as cultured cultured Coriscus, and soad infinitum.
Cf. Soph. Elench. 173a 34. are the same or different; and whether everything that is, but has not always been, has come into being, so that if a man who is cultured has become grammatical, he has also, being grammatical, become cultured If A, being cultured, has become grammatical, then being cultured he is grammatical. Then being grammatical he is cultured. But he has not always, being grammatical, been cultured. So if that which is but has not always been must have come to be, then being grammatical he has become cultured; i.e., he must have been both grammatical before he was cultured and cultured before he was grammatical; which is absurd ( Ross).; and all other such discussions. Indeed it seems that the accidental is something closely akin to the nonexistent. This is clear too from such considerations as the following: of things which are in other senses there is generation and destruction, but of things which are accidentally there is not. i.e., the process of becoming or change takes place in the subject—the man, who is accidentally cultured, becomes grammatical, and when the process is complete "the cultured" is accidentally grammatical; but it does not become so. Nevertheless we must state further, so far as it is possible, with regard to the accidental, what its nature is and through what cause it exists. At the same time it will doubtless also appear why there is no science of it. Since, then, there are among existing things some which are invariable and of necessity (not necessity in the sense of compulsion, Cf. Aristot. Met. 5.5.2. but that by which we mean that it cannot be otherwise Aristot. Met. 5.5.3 ), and some which are not necessarily so, nor always, but usually: this is the principle and this the cause of the accidental.
For whatever is neither always nor usually so, we call an accident. E.g., if in the dog-days The period from July 3 to August 11, during which the dog-star Sirius rises and sets with the sun. we have storm and cold, we call it an accident; but not if we have stifling and intense heat, because the latter always or usually comes at this time, but not the former. It is accidental for a man to be white (since this is neither always nor usually so), but it is not accidental for him to be an animal.
It is by accident that a builder restores to health, because it is not a builder but a doctor who naturally does this; but the builder happened accidentally to be a doctor. A confectioner, aiming at producing enjoyment, may produce something health-giving; but not in virtue of his confectioner's art. Hence, we say, it was accidental; and he produces it in a sense, but not in an unqualified sense. For there are potencies which produce other things, but there is no art or determinate potency of accidents, since the cause of things which exist or come to be by accident is also accidental. Hence, since not everything is or comes to be of necessity and always, but most things happen usually, the accidental must exist. E.g., the white man is neither always nor usually cultured; but since this sometimes happens, it must be regarded as accidental. Otherwise, everything must be regarded as of necessity. Therefore the cause of the accidental is the matter, which admits of variation from the usual. We must take this as our starting-point: Is everything either "always" or "usually"? This is surely impossible. Then besides these alternatives there is something else: the fortuitous and accidental. But again, are things usually so, but nothing always, or are there things which are eternal? These questions must be inquired into later Cf. Aristot. Met. 12.6-8.; but it is clear that there is no science of the accidental—because all scientific knowledge is of that which is always or usually so.
How else indeed can one learn it or teach it to another? For a fact must be defined by being so always or usually; e.g., honey-water is usually beneficial in case of fever. But science will not be able to state the exception to the rule: when it is not beneficial—e.g. at the new moon; because that which happens at the new moon also happens either always or usually; but the accidental is contrary to this. We have now explained the nature and cause of the accidental, and that there is no science of it. It is obvious that there are principles and causes which are generable and destructible apart from the actual processes of generation and destruction On the analogy of accidental events; see 2. 5.; for if this is not true, everything will be of necessity: that is, if there must necessarily be some cause, other than accidental, of that which is generated and destroyed. Will A be, or not? Yes, if B happens; otherwise not. And B will happen if C does. It is clear that in this way, as time is continually subtracted from a limited period, we shall come to the present. Accordingly So-and-so will die by disease or violence if he goes out; and this if he gets thirsty; and this if something else happens; and thus we shall come to what is the case now, or to something which has already happened. E.g. "if he is thirsty"; this will happen if he is eating pungent food, and this is either the case or not. Thus of necessity he will either die or not die. And similarly if one jumps over to the past, the principle is the same; for this—I mean that which has just happened—is already present in something. Everything, then, which is to be, will be of necessity; e.g., he who is alive must die—for some stage of the process has been reached already; e.g., the contraries are present in the same body—but whether by disease or violence is not yet determined; it depends upon whether so-and-so happens. Clearly, then, the series goes back to some starting-point, which does not go back to something else. This, therefore, will be the starting-point of the fortuitous, and nothing else is the cause of its generation. But to what sort of starting-point and cause this process of tracing back leads, whether to a material or final or moving cause, is a question for careful consideration. So much, then, for the accidental sense of "being"; we have defined it sufficiently. As for "being" qua truth, and "not-being" qua falsity, since they depend upon combination and separation, and taken together are concerned with the arrangement of the parts of a contradiction (since the true has affirmation when the subject and predicate are combined, and negation where they are divided; but the false has the contrary arrangement. How it happens that we combine or separate in thought is another question. By "combining or separating in thought" I mean thinking them not as a succession but as a unity sc., "or not as a unity but as a succession" (this is separating in thought). ); for "falsity" and "truth" are not in things —the good, for example, being true, and the bad false—but in thought; and with regard to simple concepts and essences there is no truth or falsity even in thought; —what points we must study in connection with being and not-being in this sense, we must consider later. But since the combination and separation exists in thought and not in things, and this sense of "being" is different from the proper senses (since thought attaches or detaches essence or quality or quantity or some other category), we may dismiss the accidental and real senses i.e., the senses in which the verb "to be" is used to express an accidental or a true relation. of "being." For the cause of the one is indeterminate and of the other an affection of thought; and both are connected with the remaining genus of "being," and do not indicate any objective reality. Let us therefore dismiss them, and consider the causes and principles of Being itself qua Being. [We have made it clear in our distinction of the number of senses in which each term is used that "being" has several senses.] This sentence is almost certainly a later and clumsy addition to show the connection with the following book.
The term "being" has several senses, which we have classified in our discussion Aristot. Met.
5.7. of the number of senses in which terms are used. It denotes first the " what " of a thing, i.e. the individuality; and then the quality or quantity or any other such category. Now of all these senses which "being" has, the primary sense is clearly the "what," which denotes the substance (because when we describe the quality of a particular thing we say that it is "good or bad," and not "five feet high" or "a man"; but when we describe what it is, we say not that it is "white" or "hot" or "five feet high," but that it is "a man" or "a god"), and all other things are said to "be" because they are either quantities or qualities or affections or some other such thing. Hence one might raise the question whether the terms "to walk" and "to be well" and "to sit" signify each of these things as "being," or not; and similarly in the case of any other such terms; for not one of them by nature has an independent existence or can be separated from its substance. Rather, if anything it is the thing which walks or sits or is well that is existent. The reason why these things are more truly existent is because their subject is something definite; i.e. the substance and the individual, which is clearly implied in a designation of this kind, since apart from it we cannot speak of "the good" or "sitting." Clearly then it is by reason of the substance that each of the things referred to exists. Hence that which is primarily, not in a qualified sense but absolutely, will be substance. Now "primary" has several meanings; but nevertheless substance is primary in all senses, both in definition and in knowledge and in time. For none of the other categories can exist separately, but substance alone; and it is primary also in definition, because in the formula of each thing the formula of substance must be inherent; and we assume that we know each particular thing most truly when we know what "man" or "fire" is— rather than its quality or quantity or position; because we know each of these points too when we know what the quantity or quality is. Indeed, the question which was raised long ago, is still and always will be, and which always baffles us—"What is Being?"—is in other words "What is substance?" Some say that it is one The Milesians and Eleatics.; others, more than one; some, finite The Pythagoreans and Empedocles.; others, infinite. Anaxagoras and the Atomists. And so for us too our chief and primary and practically our only concern is to investigate the nature of "being" in the sense of substance. Substance is thought to be present most obviously in bodies. Hence we call animals and plants and their parts substances, and also natural bodies, such as fire, water, earth, etc., and all things which are parts of these or composed of these, either of parts or them or of their totality; e.g. the visible universe and its parts, the stars and moon and sun. We must consider whether (a) these are the only substances, or (b) these and some others, or (c) some of these, or (d) some of these and some others, or (e) none of these, but certain others. Some The Pythagoreans. hold that the bounds of body—i.e.
the surface, line, point and unit—are substances, and in a