equally reliable, e.g. as to whether a man will get well or not. And again in the case of the senses themselves, our perception of a foreign object and of an object proper to a given sense, or of a kindred object and of an actual object of that sense itself, is not equally reliable An object of taste is foreign to the sense of sight; a thing may look sweet without tasting sweet. Similarly although the senses of taste and smell (and therefore their objects) are kindred ( Aristot. De Sensu 440b 29 ), in judging tastes the sense of taste is the more reliable.; but in the case of colors sight, and not taste, is authoritative, and in the case of flavor taste, and not sight. But not one of the senses ever asserts at the same time of the same object that it is "so and not so." Nor even at another time does it make a conflicting statement about the quality, but only about that to which the quality belongs. I mean, e.g., that the same wine may seem, as the result of its own change or of that of one's body, at one time sweet and at another not; but sweetness, such as it is when it exists, has never yet changed, and there is no mistake about it, and that which is to be sweet is necessarily of such a nature. Yet all these theories destroy the possibility of anything's existing by necessity, inasmuch as they destroy the existence of its essence; for "the necessary" cannot be in one way and in another; and so if anything exists of necessity, it cannot be "both so and not so." And in general, if only the sensible exists, without animate things there would be nothing; for there would be no sense-faculty. That there would be neither sensible qualities nor sensations is probably true Cf. Aristot. De Anima 425b 25-426b 8. (for these depend upon an effect produced in the percipient), but that the substrates which cause the sensation should not exist even apart from the sensation is impossible. For sensation is not of itself, but there is something else too besides the sensation, which must be prior to the sensation; because that which moves is by nature prior to that which is moved, and this is no less true if the terms are correlative. But there are some, both of those who really hold these convictions and of those who merely profess these views, who raise a difficulty; they inquire who is to judge of the healthy man, and in general who is to judge rightly in each particular case. But such questions are like wondering whether we are at any given moment asleep or awake; and all problems of this kind amount to the same thing. These people demand a reason for everything. They want a starting-point, and want to grasp it by demonstration; while it is obvious from their actions that they have no conviction. But their case is just what we have stated before Aristot. Met. 4.4.2.; for they require a reason for things which have no reason, since the starting-point of a demonstration is not a matter of demonstration. The first class, then, may be readily convinced of this, because it is not hard to grasp. But those who look only for cogency in argument look for an impossibility, for they claim the right to contradict themselves, and lose no time in doing so. Yet if not everything is relative, but some things are self-existent, not every appearance will be true; for an appearance is an appearance to someone. And so he who says that all appearances are true makes everything relative. Hence those who demand something cogent in argument, and at the same time claim to make out a case, must guard themselves by saying that the appearance is true; not in itself, but for him to whom it appears, and at, the time when it appears, and in the way and manner in which it appears. And if they make out a case without this qualification, as a result they will soon contradict themselves; for it is possible in the case of the same man for a thing to appear honey to the sight, but not to the taste, and for things to appear different to the sight of each of his two eyes, if their sight is unequal. For to those who assert (for the reasons previously stated Aristot. Met. 4.5.7-17.
) that appearances are true, and that all things are therefore equally false and true, because they do not appear the same to all, nor always the same to the same person, but often have contrary appearances at the same time (since if one crosses the fingers touch says that an object is two, while sight says that it is only one Cf. Aristot. Problemata 958b 14, 959a 5, 965a 36. ), we shall say "but not to the same sense or to the same part of it in the same way and at the same time"; so that with this qualification the appearance will be true.
But perhaps it is for this reason that those who argue not from a sense of difficulty but for argument's sake are compelled to say that the appearance is not true in itself, but true to the percipient; and, as we have said before, are compelled also to make everything relative and dependent upon opinion and sensation, so that nothing has happened or will happen unless someone has first formed an opinion about it; otherwise clearly all things would not be relative to opinion. Further, if a thing is one, it is relative to one thing or to something determinate. And if the same thing is both a half and an equal, yet the equal is not relative to the double. If to the thinking subject "man" and the object of thought are the same, "man" will be not the thinking subject but the object of thought; and if each thing is to be regarded as relative to the thinking subject, the thinking subject will be relative to an infinity of specifically different things. That the most certain of all beliefs is that opposite statements are not both true at the same time, and what follows for those who maintain that they are true, and why these thinkers maintain this, may be regarded as adequately stated. And since the contradiction of a statement cannot be true at the same time of the same thing, it is obvious that contraries cannot apply at the same time to the same thing. For in each pair of contraries one is a privation no less than it is a contrary—a privation of substance. And privation is the negation of a predicate to some defined genus. Therefore if it is impossible at the same time to affirm and deny a thing truly, it is also impossible for contraries to apply to a thing at the same time; either both must apply in a modified sense, or one in a modified sense and the other absolutely. Nor indeed can there be any intermediate between contrary statements, but of one thing we must either assert or deny one thing, whatever it may be.
This will be plain if we first define truth and falsehood. To say that what is is not, or that what is not is, is false; but to say that what is is, and what is not is not, is true; and therefore also he who says that a thing is or is not will say either what is true or what is false. But neither what is nor what is not is said not to be or to be.
Further, an intermediate between contraries will be intermediate either as grey is between black and white, or as "neither man nor horse" is between man and horse. If in the latter sense, it cannot change (for change is from not-good to good, or from good to not-good); but in fact it is clearly always changing; for change can only be into the opposite and the intermediate. And if it is a true intermediate, in this case too there would be a kind of change into white not from not-white; but in fact this is not seen. It is not qua grey (i.e.
intermediate between white and black) that grey changes to white, but qua not-white (i.e. containing a certain proportion of black).
Further, the understanding either affirms or denies every object of understanding or thought (as is clear from the definition Aristot. Met.
4.7.1. ） whenever it is right or wrong. When, in asserting or denying, it combines the predicates in one way, it is right; when in the other, it is wrong. Again, unless it is maintained merely for argument's sake, the intermediate must exist beside all contrary terms; so that one will say what is neither true nor false.
And it will exist beside what is and what is not; so that there will be a form of change beside generation and destruction. Again, there will also be an intermediate in all classes in which the negation of a term implies the contrary assertion; e.g., among numbers there will be a number which is neither odd nor not-odd. But this is impossible, as is clear from the definition. What definition Aristotle had in mind we cannot tell; but it must have stated that every number is either even or odd. Again, there will be an infinite progression, and existing things will be not only half as many again, but even more. For again it will be possible to deny the intermediate in reference both to its assertion and to its negation, and the result will be something If besides A and not-A there is an intermediate B, besides B and not-B there will be an intermediate C which is neither B nor not-B; and so on.; for its essence is something distinct. Again, when a man is asked whether a thing is white and says "no," he has denied nothing except that it is <white>, and its not-being <white> is a negation. Now this view has occurred to certain people in just the same way as other paradoxes have also occurred; for when they cannot find a way out from eristic arguments, they submit to the argument and admit that the conclusion is true. Some, then, hold the theory for this kind of reason, and others because they require an explanation for everything. In dealing with all such persons the starting-point is from definition; and definition results from the necessity of their meaning something; because the formula, which their term implies, will be a definition. Cf. Aristot. Met. 4.4.5, 6. The doctrine of Heraclitus, which says that everything is and is not, Cf.
Aristot. Met. 4.3.10. seems to make all things true; and that of Anaxagoras Cf. Aristot. Met.
4.4.28. seems to imply an intermediate in contradiction, so that all things are false; for when things are mixed, the mixture is neither good nor not-good; and so no statement is true. It is obvious from this analysis that the one-sided and sweeping statements which some people make cannot be substantially true—some maintaining that nothing is true (for they say that there is no reason why the same rule should not apply to everything as applies to the commensurability of the diagonal of a square A stock example of impossibility and falsity; see Index. ), and some that everything is true. These theories are almost the same as that of Heraclitus. For the theory which says that all things are true and all false also makes each of these statements separately; so that if they are impossible in combination they are also impossible individually. And again obviously there are contrary statements, which cannot be true at the same time. Nor can they all be false, although from what we have said, this might seem more possible. But in opposing all such theories we must demand, as was said in our discussion above, Aristot. Met. 4.4.5.
not that something should be or not be, but some significant statement; and so we must argue from a definition, having first grasped what "falsehood" or "truth" means. And if to assert what is true is nothing else than to deny what is false, everything cannot be false; for one part of the contradiction must be true. Further, if everything must be either asserted or denied, both parts cannot be false; for one and only one part of the contradiction is false. Indeed, the consequence follows which is notorious in the case of all such theories, that they destroy themselves; for he who says that everything is true makes the opposite theory true too, and therefore his own untrue (for the opposite theory says that his is not true); and he who says that everything is false makes himself a liar. And if they make exceptions, the one that the opposite theory alone is not true, and the other that his own theory alone is not false, it follows none the less that they postulate an infinite number of true and false statements. For the statement that the true statement is true is also true; and this will go on to infinity. Nor, as is obvious, are those right who say that all things are at rest; nor those who say that all things are in motion. For if all things are at rest, the same things will always be true and false, whereas this state of affairs is obviously subject to change; for the speaker himself once did not exist, and again he will not exist. And if all things are in motion, nothing will be true, so everything will be false; but this has been proved to be impossible. Again, it must be that which is that changes, for change is from something into something. And further, neither is it true that all things are at rest or in motion sometimes, but nothing continuously; for there is something The sphere of the fixed stars; cf. Aristot. Met. 12.6, 12.7.1, 12.8.18. which always moves that which is moved, and the "prime mover" is itself unmoved. Cf. Aristot. Met.
12.7.
"Beginning" a)rxh/ means "starting-point," "principle," "rule" or "ruler." means: (a) That part of a thing from which one may first move; eg., a line or a journey has one beginning here, and another at the opposite extremity. (b) The point from which each thing may best come into being; e.g., a course of study should sometimes be begun not from what is primary or from the starting-point of the subject, but from the point from which it is easiest to learn.
(c) That thing as a result of whose presence something first comes into being; e.g., as the keel is the beginning of a ship, and the foundation that of a house, and as in the case of animals some thinkers suppose the heart This was Aristotle's own view, Aristot. De Gen. An. 738b 16. to be the "beginning," others the brain, So Plato held, Plat. Tim. 44 d. and others something similar, whatever it may be. (d) That from which, although not present in it, a thing first comes into being, and that from which motion and change naturally first begin, as the child comes from the father and mother, and fighting from abuse. (e) That in accordance with whose deliberate choice that which is moved is moved, and that which is changed is changed; such as magistracies, authorities, monarchies and despotisms. (f) Arts are also called "beginnings," As directing principles. especially the architectonic arts.
(g) Again, "beginning" means the point from which a thing is first comprehensible, this too is called the "beginning" of the thing; e.g.
the hypotheses of demonstrations. ("Cause" can have a similar number of different senses, for all causes are "beginnings.") It is a common property, then, of all "beginnings" to be the first thing from which something either exists or comes into being or becomes known; and some beginnings are originally inherent in things, while others are not. Hence "nature" is a beginning, and so is "element" and "understanding" and "choice" and "essence" and "final cause"—for in many cases the Good and the Beautiful are the beginning both of knowledge and of motion. "Cause" means: (a) in one sense, that as the result of whose presence something comes into being—e.g. the bronze of a statue and the silver of a cup, and the classes sc. of material—metal, wood, etc. which contain these; (b) in another sense, the form or pattern; that is, the essential formula and the classes which contain it—e.g. the ratio 2:1 and number in general is the cause of the octave—and the parts of the formula. (c) The source of the first beginning of change or rest; e.g. the man who plans is a cause, and the father is the cause of the child, and in general that which produces is the cause of that which is produced, and that which changes of that which is changed. (d) The same as "end"; i.e. the final cause; e.g., as the "end" of walking is health. For why does a man walk? "To be healthy," we say, and by saying this we consider that we have supplied the cause. (e) All those means towards the end which arise at the instigation of something else, as, e.g. fat-reducing, purging, drugs and instruments are causes of health; for they all have the end as their object, although they differ from each other as being some instruments, others actions. These are roughly all the meanings of "cause," but since causes are spoken of with various meanings, it follows that there are several causes (and that not in an accidental sense) of the same thing. E.g., both statuary and bronze are causes of the statue; not in different connections, but qua statue. However, they are not causes in the same way, but the one as material and the other as the source of motion. And things are causes of each other; as e.g. labor of vigor, and vigor of labor—but not in the same way; the one as an end, and the other as source of motion. And again the same thing is sometimes the cause of contrary results; because that which by its presence is the cause of so-and-so we sometimes accuse of being, by its absence, the cause of the contrary—as, e.g., we say that the absence of the pilot is the cause of a capsize, whereas his presence was the cause of safety. And both, presence and privation, are moving causes. Now there are four senses which are most obvious under which all the causes just described may be classed. The components of syllables; the material of manufactured articles; fire, earth and all such bodies; the parts of a whole; and the premisses of a syllogistic conclusion; are causes in the material sense. Of these some are causes as substrate: e.g. the parts; and others as essence: the whole, and the composition, and the form. The seed and the physician and the contriver and in general that which produces, all these are the source of change or stationariness. The remainder represent the end and good of the others; for the final cause tends to be the greatest good and end of the rest. Let it be assumed that it makes no difference whether we call it "good" or "apparent good." In kind, then, there are these four classes of cause. The modes of cause are numerically many, although these too are fewer when summarized. For causes are spoken of in many senses, and even of those which are of the same kind, some are causes in a prior and some in a posterior sense; e.g., the physician and the expert are both causes of health; and the ratio 2:1 and number are both causes of the octave; and the universals which include a given cause are causes of its particular effects. Again, a thing may be a cause in the sense of an accident, and the classes which contain accidents; e.g., the cause of a statue is in one sense Polyclitus and in another a sculptor, because it is an accident of the sculptor to be Polyclitus. And the universal terms which include accidents are causes; e.g., the cause of a statue is a man, or even, generally, an animal; because Polyclitus is a man, and man is an animal. And even of accidental causes some are remoter or more proximate than others; e.g., the cause of the statue might be said to be "white man" or "cultured man," and not merely "Polyclitus" or "man." And besides the distinction of causes as proper and accidental, some are termed causes in a potential and others in an actual sense; e.g., the cause of building is either the builder or the builder who builds. And the same distinctions in meaning as we have already described will apply to the effects of the causes; e.g. to this statue, or a statue, or generally an image; and to this bronze, or bronze, or generally material. Effects, just like causes (10), may be particular or general. The metal-worker produces (a) the bronze for a particular statue by the sculptor, (b) bronze for a statue, (c) metal for an image. And it is the same with accidental effects. Again, the proper and accidental senses will be combined; e.g., the cause is neither "Polyclitus" nor "a sculptor" but "the sculptor Polyclitus." However, these classes of cause are in all six in number, each used in two senses. Causes are (1.)
particular, (2.) generic, (3.) accidental, (4.) generically accidental; and these may be either stated singly or (5, 6) in combination The cause of a statue may be said to be (1) a sculptor, (2) an artist, (3) Polyclitus, (4) a man, (5) the sculptor Polyclitus (combination of (1) and (3)), (6) an artistic man (combination of (2) and (4)).; and further they are all either actual or potential. And there is this difference between them, that actual and particular causes coexist or do not coexist with their effects (e.g. this man giving medical treatment with this man recovering his health, and this builder with this building in course of erection); but potential causes do not always do so; for the house and the builder do not perish together. "Element" means (a) the primary immanent thing, formally indivisible into another form, of which something is composed. E.g., the elements of a sound are the parts of which that sound is composed and into which it is ultimately divisible, and which are not further divisible into other sounds formally different from themselves. If an element be divided, the parts are formally the same as the whole: e.g., a part of water is water; but it is not so with the syllable. (b) Those who speak of the elements of bodies similarly mean the parts into which bodies are ultimately divisible, and which are not further divisible into other parts different in form. And whether they speak of one such element or of more than one, this is what they mean. (c) The term is applied with a very similar meaning to the "elements" of geometrical figures, and generally to the "elements" of demonstrations; for the primary demonstrations which are contained in a number of other demonstrations are called "elements" of demonstrations. Cf. Aristot. Met. 3.3.1. Such are the primary syllogisms consisting of three terms and with one middle term. (d) The term "element" is also applied metaphorically to any small unity which is useful for various purposes; and so that which is small or simple or indivisible is called an "element." (e) Hence it comes that the most universal things are elements; because each of them, being a simple unity, is present in many things—either in all or in as many as possible. Some too think that unity and the point are first principles. (f) Therefore since what are called genera This must refer to the highest genera, which have no definition because they cannot be analyzed into genus and differentia ( Ross). are universal and indivisible (because they have no formula), some people call the genera elements, and these rather than the differentia, because the genus is more universal. For where the differentia is present, the genus also follows; but the differentia is not always present where the genus is. And it is common to all cases that the element of each thing is that which is primarily inherent in each thing. "Nature" On the meaning of fu/sis cf. Burnet, E.G.P. pp. 10-12, 363-364.
means: (a) in one sense, the genesis of growing things—as would be suggested by pronouncing the u of fu/sis long—and (b) in another, that immanent thing Probably the seed (Bonitz). from which a growing thing first begins to grow. (c) The source from which the primary motion in every natural object is induced in that object as such. All things are said to grow which gain increase through something else by contact and organic unity (or adhesion, as in the case of embryos). Organic unity differs from contact; for in the latter case there need be nothing except contact, but in both the things which form an organic unity there is some one and the same thing which produces, instead of mere contact, a unity which is organic, continuous and quantitative (but not qualitative). Again, "nature" means (d) the primary stuff, shapeless and unchangeable from its own potency, of which any natural object consists or from which it is produced; e.g., bronze is called the "nature" of a statue and of bronze articles, and wood that of wooden ones, and similarly in all other cases. For each article consists of these "natures," the primary material persisting. It is in this sense that men call the elements of natural objects the "nature," some calling it fire, others earth or air or water, others something else similar, others some of these, and others all of them. Again in another sense "nature" means (e) the substance of natural objects; as in the case of those who say that the "nature" is the primary composition of a thing, or as Empedocles says: Of nothing that exists is there nature, but only mixture and separation of what has been mixed; nature is but a name given to these by men. Empedocles Fr. 8 (Diels). Hence as regards those things which exist or are produced by nature, although that from which they naturally are produced or exist is already present, we say that they have not their nature yet unless they have their form and shape. That which comprises both of these exists by nature; e.g. animals and their parts. And nature is both the primary matter (and this in two senses: either primary in relation to the thing, or primary in general; e.g., in bronze articles the primary matter in relation to those articles is bronze, but in general it is perhaps water—that is if all things which can be melted are water) and the form or essence, i.e.
the end of the process, of generation. Indeed from this sense of "nature," by an extension of meaning, every essence in general is called "nature," because the nature of anything is a kind of essence. From what has been said, then, the primary and proper sense of "nature" is the essence of those things which contain in themselves as such a source of motion; for the matter is called "nature" because it is capable of receiving the nature, and the processes of generation and growth are called "nature" because they are motions derived from it. And nature in this sense is the source of motion in natural objects, which is somehow inherent in them, either potentially or actually. "Necessary" means: (a) That without which, as a concomitant condition, life is impossible; e.g. respiration and food are necessary for an animal, because it cannot exist without them. (b) The conditions without which good cannot be or come to be, or without which one cannot get rid or keep free of evil—e.g., drinking medicine is necessary to escape from ill-health, and sailing to Aegina is necessary to recover one's money. (c) The compulsory and compulsion; i.e. that which hinders and prevents, in opposition to impulse and purpose. For the compulsory is called necessary, and hence the necessary is disagreeable; as indeed Evenus Of Poros; sophist and poet, contemporary with Socrates. says: "For every necessary thing is by nature grievous." Evenus Fr. 8 (Hiller). And compulsion is a kind of necessity, as Sophocles says: "Compulsion makes me do this of necessity." Soph. El. 256 (the quotation is slightly inaccurate). And necessity is held, rightly, to be something inexorable; for it is opposed to motion which is in accordance with purpose and calculation. (d) Again, what cannot be otherwise we say is necessarily so. It is from this sense of "necessary" that all others are somehow derived; for the term "compulsory" is used of something which it is necessary for one to do or suffer only when it is impossible to act according to impulse, because of the compulsion: which shows that necessity is that because of which a thing cannot be otherwise; and the same is true of the concomitant conditions of living and of the good. For when in the one case good, and in the other life or existence, is impossible without certain conditions, these conditions are necessary, and the cause is a kind of necessity. (e) Again, demonstration is a "necessary" thing, because a thing cannot be otherwise if the demonstration has been absolute. And this is the result of the first premisses, when it is impossible for the assumptions upon which the syllogism depends to be otherwise. Thus of necessary things, some have an external cause of their necessity, and others have not, but it is through them that other things are of necessity what they are. Hence the "necessary" in the primary and proper sense is the simple, for it cannot be in more than one condition. Hence it cannot be in one state and in another; for if so it would ipso facto be in more than one condition. Therefore if there are certain things which are eternal and immutable, there is nothing in them which is compulsory or which violates their nature. The term "one" is used (1.) in an accidental, (2.) in an absolute sense. (1.) In the accidental sense it is used as in the case of "Coriscus" Coriscus of Scepsis was a Platonist with whom Aristotle was probably acquainted; but the name is of course chosen quite arbitrarily. and "cultured" and "cultured Coriscus" (for "Coriscus" and "cultured" and "cultured Coriscus" mean the same); and "cultured" and "upright" and "cultured upright Coriscus." For all these terms refer accidentally to one thing; "upright" and "cultured" because they are accidental to one substance, and "cultured" and "Coriscus" because the one is accidental to the other. And similarly in one sense "cultured Coriscus" is one with "Coriscus," because one part of the expression is accidental to the other, e.g. "cultured" to "Coriscus"; and "cultured Coriscus" is one with "upright Coriscus," because one part of each expression is one accident of one and the same thing. It is the same even if the accident is applied to a genus or a general term; e.g., "man" and "cultured man" are the same, either because "cultured" is an accident of "man," which is one substance, or because both are accidents of some individual, e.g. Coriscus. But they do not both belong to it in the same way; the one belongs presumably as genus in the substance, and the other as condition or affection of the substance. Thus all things which are said to be "one" in an accidental sense are said to be so in this way. (2.) Of those things which are said to be in themselves one, (a) some are said to be so in virtue of their continuity; e.g., a faggot is made continuous by its string, and pieces of wood by glue; and a continuous line, even if it is bent, is said to be one, just like each of the limbs; e.g. the leg or arm. And of these things themselves those which are naturally continuous are one in a truer sense than those which are artificially continuous. "Continuous" means that whose motion is essentially one, and cannot be otherwise; and motion is one when it is indivisible, i.e.
indivisible in time. Things are essentially continuous which are one not by contact only; for if you put pieces of wood touching one another you will not say that they are one piece of wood, or body, or any other continuous thing. And things which are completely continuous are said to be "one" even if they contain a joint, and still more those things which contain no joint; e.g., the shin or the thigh is more truly one than the leg, because the motion of the leg may not be one. And the straight line is more truly one than the bent. We call the line which is bent and contains an angle both one and not one, because it may or may not move all at once; but the straight line always moves all at once, and no part of it which has magnitude is at rest while another moves, as in the bent line. (b) Another sense of "one" is that the substrate is uniform in kind. Things are uniform whose form is indistinguishable to sensation; and the substrate is either that which is primary, or that which is final in relation to the end. For wine is said to be one, and water one, as being something formally indistinguishable. And all liquids are said to be one (e.g. oil and wine), and melted things; because the ultimate substrate of all of them is the same, for all these things are water or vapor. (c) Things are said to be "one" whose genus is one and differs in its opposite differentiae. All these things too are said to be "one" because the genus, which is the substrate of the differentiae, is one (e.g., "horse," "man" and "dog" are in a sense one, because they are all animals); and that in a way very similar to that in which the matter is one. Sometimes these things are said to be "one" in this sense, and sometimes their higher genus is said to be one and the same (if they are final species of their genus)—the genus, that is, which is above the genera of which their proximate genus is one; e.g., the isosceles and equilateral triangles are one and the same figure (because they are both triangles), but not the same triangles. (d) Again, things are said to be "one" when the definition stating the essence of one is indistinguishable from a definition explaining the other; for in itself every definition is distinguishable <into genus and differentiae>. In this way that which increases and decreases is one, because its definition is one; just as in the case of planes the definition of the form is one. And in general those things whose concept, which conceives the essence, is indistinguishable and cannot be separated either in time or in place or in definition, are in the truest sense one; and of these such as are substances are most truly one. For universally such things as do not admit of distinction are called "one" in so far as they do not admit of it; e.g., if "man" qua "man" does not admit of distinction, he is one man; and similarly if qua animal, he is one animal; and if qua magnitude, he is one magnitude. Most things, then, are said to be "one" because they produce, or possess, or are affected by, or are related to, some other one thing; but some are called "one" in a primary sense, and one of these is substance. It is one either in continuity or in form or in definition; for we reckon as more than one things which are not continuous, or whose form is not one, or whose definition is not one. Again, in one sense we call anything whatever "one" if it is quantitative and continuous; and in another sense we say that it is not "one" unless it is a whole of some kind, i.e. unless it is one in form (e.g., if we saw the parts of a shoe put together anyhow, we should not say that they were one — except in virtue of their continuity; but only if they were so put together as to be a shoe, and to possess already some one form). Hence the circumference of a circle is of all lines the most truly one, because it is whole and complete. The essence of "one" is to be a kind of starting point of number; for the first measure is a starting point, because that by which first we gain knowledge of a thing is the first measure of each class of objects. "The one," then, is the starting-point of what is knowable in respect of each particular thing. But the unit is not the same in all classes, for in one it is the quarter-tone, and in another the vowel or consonant; gravity has another unit, and motion another. But in all cases the unit is