by Aristotle
17 · We call a limit the last point of each thing, i.e. the first point beyond which it is not possible to find any part, and the first point within which every part [5] is; it is applied to the form, whatever it may be, of a spatial magnitude or of a thing that has magnitude, and to the end of each thing (and of this nature is that towards which the movement and the action are—not that from which they are, though sometimes it is both, that from which and that to which the movement is—and that for the sake of which), and to the substance of each thing, and the essence of each; [10] for this is the limit of knowledge; and if of knowledge, of the thing also. Evidently, therefore, ‘limit’ has as many senses as ‘beginning’, and yet more; for the beginning is a limit, but not every limit is a beginning.
18 · ‘That in virtue of which’ has several meanings, (1) the form or [15] substance of each thing, e.g. that in virtue of which a man is good is the good itself, (2) the proximate subject in which an attribute is naturally found, e.g. colour in a surface. ‘That in virtue of which’, then, in the primary sense is the form, and in a secondary sense the matter of each thing and the proximate substratum of each.—In general ‘that in virtue of which’ will be found in the same number of [20] senses as ‘cause’; for we say ‘in virtue of what has he come’? or ‘for what end has he come’? and ‘in virtue of what has he inferred wrongly, or inferred at all’? or ‘what is the cause of the inference, or of the wrong inference’?—Further (3) ‘that in virtue of which’ is used in reference to position, e.g. ‘in which he stands’ or ‘in which he walks’; for all such phrases indicate place and position.
[25] Therefore ‘in virtue of itself’ must have several meanings. It applies to (1) the essence of each thing, e.g. Callias is in virtue of himself Callias and the essence of Callias; (2) whatever is present in the ‘what’, e.g. Callias is in virtue of himself an animal. For ‘animal’ is present in the formula that defines him; Callias is a [30] particular animal.—(3) Whatever attribute a thing receives in itself directly or in one of its parts, e.g. a surface is white in virtue of itself, and a man is alive in virtue of himself; for the soul, in which life directly resides, is a part of the man.—(4) That which has no cause other than itself; man has more than one cause—animal, two-footed—but man is man in virtue of himself.—(5) Whatever attributes belong [35] to a thing alone and qua alone; hence also that which exists separately is ‘in virtue of itself’.
[1022b1] 19 · We call a disposition the arrangement of that which has parts, in respect either of place or of capacity or of kind; for there must be a certain position, as the word ‘disposition’ shows.
20 · We call a having (1) a kind of activity of the haver and the had—something [5] like an action or movement. When one thing makes and one is made, between them there is a making; so too between him who has a garment and the garment which he has there is a having. This sort of having, then, evidently we cannot have; for the process will go on to infinity, if we can have the having of what [10] we have.—(2) ‘Having’ means a disposition according to which that which is disposed is either well or ill disposed, either in itself or with reference to something else, e.g. health is a having; for it is such a disposition.—(3) We speak of a having if there is a portion of such a disposition; therefore the excellence of the parts is a having.
21 · We call an affection (1) a quality in respect of which a thing can be [15] altered, e.g. white and black, sweet and bitter, heaviness and lightness, and all others of the kind.—(2) The already actualized alterations.—(3) Especially, injurious alterations and movements, and, above all, painful injuries.—(4) Experienees [20] pleasant or painful when on a large scale are called affections.
22 · We speak of privation (1) if something has not one of the attributes which a thing might naturally have, even if this thing itself would not naturally have it, e.g. a plant is said to be deprived of eyes.—(2) If, though either the thing itself or its genus would naturally have an attribute, it has it not, e.g. a blind man and a mole [25] are in different senses deprived of sight; the latter in contrast with its genus, the former in contrast with his own normal nature.—(3) If, though it would naturally have the attribute, and when it would naturally have it, it has it not; for blindness is a privation, but one is not blind at any and every age, but only if one has not sight at the age at which one would naturally have it. Similarly a thing suffers privation when it has not an attribute in those circumstances, or in that respect and in that [30] relation and in that sense, in which it would naturally have it.—(4) The violent taking away of anything is called privation.
There are just as many kinds of privations as there are of words with negative prefixes; for a thing is called unequal because it has not equality though it would naturally have it, and invisible either because it has no colour at all or because it has [35] a poor colour, and footless either because it has no feet at all or because it has imperfect feet. Again, a privative term may be used because the thing has little of the attribute (and this means having it in a sense imperfectly), e.g. kernelless; or [1023a1] because it has it not easily or not well (e.g. we call a thing indivisible not only if it cannot be divided but also if it cannot be easily or well divided); or because it has not the attribute at all; for it is not the one-eyed man but he who is sightless in both eyes [5] that is called blind. This is why not every man is good or bad, just or unjust, but there is also an intermediate state.
23 · ‘To have’ means many things. (1) To treat a thing according to one’s own nature or according to one’s own impulse, so that fever is said to have a man, [10] and tyrants to have their cities, and people to have the clothes they wear.—(2) That in which a thing is present as in something receptive is said to have the thing, e.g. the bronze has the form of the statue, and the body has the disease.—(3) As that which contains has that which is contained; for a thing is said to be had by that in which it is contained, e.g. we say that the vessel has the liquid and the city has men [15] and the ship sailors; and so too that the whole has the parts.—(4) That which hinders a thing from moving or acting according to its own impulse is said to have it, as pillars have the incumbent weights, and as the poets make Atlas have the heavens, implying that otherwise they would collapse on the earth, as some of the [20] natural philosophers also say. In this way that which holds things together is said to have the things it holds together, since they would otherwise separate, each according to its own impulse.
‘Being in something’ has similar and corresponding meanings to ‘having’. [25]
24 · To come from something means (1) to come from something as from matter, and this in two senses, either in respect of the highest genus or in respect of the lowest species, e.g. in a sense all things that can be melted come from water, but in a sense the statue comes from bronze.—(2) As from the first moving principle, [30] e.g. what does the fight stem from?—from abusive language, because this is the source of the fight.—(3) From the compound of matter and shape, as the parts come from the whole and the verse from the Iliad and the stones from the house; for the form is an end, and only that which attains an end is complete.—(4) As the form from its part, e.g. man from two-footed and syllable from letter; for this is a [1023b1] different sense to that in which the statue comes from bronze; for the composite substance comes from the sensible matter, but the form also comes from the matter of the form.—These, then, are some of the meanings of ‘from’, but sometimes (5) one of these senses is applicable only to part of a whole, e.g. the child comes from its [5] father and mother and plants come from the earth, because they come from a part of those things.—(6) It means coming after a thing in time, e.g. night comes from day and storm from fine weather, because the one comes after the other. Of these things some are so described because they admit of change into one another, as in the cases now mentioned; some merely because they are successive in time, e.g. the [10] voyage took place ‘from’ the equinox, because it took place after the equinox, and the Thargelia come ‘from’ the Dionysia, because
after the Dionysia.
25 · We call a part (1) that into which a quantity can in any way be divided; for that which is taken from a quantity qua quantity is always called a part of it, e.g. two is called in a sense a part of three.—(2) It means, of the parts in the first sense, [15] only those which measure the whole; this is why two, though in one sense it is, in another is not, a part of three.—(3) The elements into which the kind might be divided apart from the quantity, are also called parts of it; for which reason we say the species are parts of the genus.—(4) The elements into which the whole is [20] divided, or of which it consists—‘the whole’ meaning either the form or that which has the form; e.g. of the bronze sphere or of the bronze cube both the bronze—i.e. the matter in which the form is—and the characteristic angle are parts.—(5) The elements in the formula which explains a thing are parts of the whole; this is why the genus is called a part of the species, though in another sense the species is part of the [25] genus.
26 · We call a whole (1) that from which is absent none of the parts of which it is said to be naturally a whole, and (2) that which so contains the things it contains that they form a unity; and this in two senses—either as each and all one, or as making up the unity between them. For (a) that which is true of a whole class [30] and is said to hold good as a whole (which implies that it is a kind of whole) is true of a whole in the sense that it contains many things by being predicated of each, and that each and all of them, e.g. man, horse, god, are one, because all are living things. But (b) the continuous and limited is a whole, when there is a unity consisting of several parts present in it, especially if they are present only potentially, but, failing this, even if they are present actually. Of these things themselves, those which are so by nature are wholes in a higher degree than those which are so by art, as we said in [35] the case of unity also, wholeness being in fact a sort of oneness.
Again, as quantities have a beginning and a middle and an end, those to which [1024a1] the position does not make a difference are called totals, and those to which it does, wholes, and those which admit of both descriptions are both wholes and totals. These are the things whose nature remains the same after transposition, but whose form does not, e.g. wax or a coat; they are called both wholes and totals; for they [5] have both characteristics. Water and all liquids and number are called totals, but ‘the whole number’ or ‘the whole water’ one does not speak of, except by an extension of meaning. To things, to which qua one the term ‘total’ is applied, the term ‘all’ is applied when they are treated as separate; ‘this total number’, ‘all these units’. [10]
27 · It is not any chance quantitative thing that can be said to be mutilated; it must be both divisible and a whole. For two is not mutilated if one of the two ones is taken away (for the part removed by mutilation is never equal to the remainder), nor in general is any number thus mutilated; for it is also necessary that the substance remain; if a cup is mutilated, it must still be a cup; but the number is no [15] longer the same. Further, even if things consist of unlike parts, not even these things can all be said to be mutilated, for in a sense a number has unlike parts, e.g. two and three. But in general of the things to which their position makes no difference, e.g. water or fire, none can be mutilated; to be mutilated, things must be such as in virtue of their substance have a certain position. Again, they must be continuous; [20] for a musical scale consists of unlike parts and has position, but cannot become mutilated. Besides, not even the things that are wholes are mutilated by the privation of any part. For the parts removed must be neither those which determine the substance nor any chance parts, irrespective of their position; e.g. a cup is not mutilated if it is bored through; but only if the handle or a projecting part is [25] removed. And a man is mutilated not if the flesh or the spleen is removed, but if an extremity is, and that not every extremity but one which when completely removed cannot grow again. Therefore baldness is not a mutilation.
28 · We call something a kind (1) if there is continuous generation of things which have the same form, e.g. ‘while mankind lasts’ means ‘while the generation of [30] them goes on continuously’.—(2) A kind is that which first brought things into existence; for so some are called Hellenes in kind and others Ionians, because the former proceed from Hellen and the latter from Ion as their first begetter. And the word is used in reference to the begetter more than to the matter, though people also [35] get a kind-name from the female, e.g. the descendants of Pyrrha.—(3) There are kinds in the sense in which plane is the kind of plane figures and solid of solids; for [1024b1] each of the figures is in the one case a plane of such and such a kind, and in the other a solid of such and such a kind; and this is what underlies the differentiae. Again, in formulae their first constituent element, which is included in the essence, is the [5] kind, whose differentiae the qualities are said to be.—Kind then is used in all these ways, (1) in reference to continuous generation of the same sort, (2) in reference to the first mover which is of the same sort as the things it moves, (3) as matter; for that to which the differentia or quality belongs is the substratum, which we call matter.
[10] Those things are said to be other in kind whose ultimate substratum is different, and which are not analysed the one into the other nor both into the same thing (e.g. form and matter are different in kind); and things which belong to different categories of being; for some of the things that are said to be signify essence, others a quality, others the other categories we have before distinguished; [15] these also are not analysed either into one another or into some one thing.
29 · We call false (1) that which is false as a thing, and that (a) because it is not put together or cannot be put together, e.g. ‘that the diagonal of a square is [20] commensurate with the side’ or ‘that you are sitting’; for one of these is false always, and the other sometimes; it is in these two senses that they are non-existent, (b) There are things which exist, but whose nature it is to appear either not to be such as they are or to be things that do not exist, e.g. a sketch or a dream; for these are something, but are not the things the appearance of which they produce in us. We [25] call things false in this way, then,—either because they themselves do not exist, or because the appearance which results from them is that of something that does not exist.
(2) A false formula is the formula of non-existent objects, in so far as it is false. Hence every formula is false when applied to something other than that of which it is true, e.g. the formula of a circle is false when applied to a triangle. In a sense there is one formula of each thing, i.e. the formula of its essence, but in a sense there are [30] many, since the thing itself and the thing itself modified in a certain way are somehow the same, e.g. Socrates and musical Socrates. The false formula is not the formula of anything, except in a qualified sense. Hence Antisthenes foolishly claimed that nothing could be described except by its own formula,—one formula to one thing; from which it followed that there could be no contradiction, and almost [35] that there could be no error. But it is possible to describe each thing not only by its own formula, but also by that of something else. This may be done altogether falsely indeed, but in some ways it may be done truly, e.g. eight may be described as a [1025a1] double number by the use of the formula of two.
These things, then, are called false in these senses, but (3) a false man is one who is ready at and fond of such formulae, not for any other reason but for their own sake, and one who is good at impressing such formulae on other people, just as we [5] say things are false, which produce a false appearance. This is why the proof in the Hippias that the same man is false and true is misleading. For it assumes that he is false who can deceive (i.e. the man who knows and is wise); and further that he who [10] is willingly bad is better. This is a false result of induction; for a man who limps willingly is better than one who does so unwillingly; by ‘limping’ Plato means ‘mimicking a limp’, for if the man were actually lame willingly, he would perhaps be worse in this case as in the correspondin
g case of character.
30 · We call an accident that which attaches to something and can be truly asserted, but neither of necessity nor usually, e.g. if one in digging a hole for a plant [15] found treasure. This—the finding of treasure—happens by accident to the man who digs the hole; for neither does the one come of necessity from the other or after the other, nor, if a man plants, does he usually find treasure. And a musical man might be white; but since this does not happen of necessity nor usually, we call it an [20] accident. Therefore since there are attributes and they attach to a subject, and some of them attach in a particular place and at a particular time, whatever attaches to a subject, but not because it is this subject, at this time or in this place, will be an accident. Therefore there is no definite cause for an accident, but a chance cause, [25] i.e. an indefinite one. Going to Aegina was an accident, if the man went not in order to get there, but because he was carried out of his way by a storm or captured by pirates. The accident has happened or exists,—not in virtue of itself, however, but of something else; for the storm was the cause of his coming to a place for which he was not sailing, and this was Aegina.
‘Accident’ has also another meaning, i.e. what attaches to each thing in virtue [30] of itself but is not in its substance, as having its angles equal to two right angles attaches to the triangle. And accidents of this sort may be eternal, but no accident of the other sort is. This is explained elsewhere.