CHAPTER XI.
OF IDENTITY AND DIFFERENCE.
1. What it is for one thing to differ from another.—2. To differ in number, magnitude, species, and genus, what.—3. What is relation, proportion, and relatives.—4. Proportionals, what.—5. The proportion of magnitudes to one another, wherein it consists.—6. Relation is no new accident, but one of those that were in the relative before the relation or comparison was made. Also the causes of accidents in the correlatives, are the cause of relation.—7. Of the beginning of individuation.
[Sidenote: What it is for one thing to differ from another.]
1. Hitherto I have spoken of body simply, and accidents common to all bodies, as _magnitude_, _motion_, _rest_, _action_, _passion_, _power_, _possible_, _&c._; and I should now descend to those accidents by which one body is distinguished from another, but that it is first to be declared what it is to be _distinct_ and _not distinct_, namely, what are the SAME and DIFFERENT; for this also is common to all bodies, that they may be distinguished and differenced from one another. Now, two bodies are said to _differ_ from one another, when something may be said of one of them, which cannot be said of the other at the same time.
[Sidenote: To differ in number, magnitude, species, and genus, what.]
2. And, first of all, it is manifest that no two bodies are the _same_; for seeing they are two, they are in two places at the same time; as that, which is the _same_, is at the same time in one and the same place. All bodies therefore differ from one another in _number_, namely, as one and another; so that the _same_ and _different in number_, are names opposed to one another by contradiction.
In _magnitude_ bodies differ when one is greater than another, as _a cubit long_, and _two cubits long_, of _two pound weight_, and of _three pound weight_. And to these, _equals_ are opposed.
Bodies, which differ more than in magnitude, are called _unlike_; and those, which differ only in magnitude, _like_. Also, of unlike bodies, some are said to differ in the _species_, others in the _genus_; in the _species_, when their difference is perceived by one and the same sense, as _white_ and _black_; and in the _genus_, when their difference is not perceived but by divers senses, as _white_ and _hot_.
[Sidenote: What is relation, proportion, and relatives.]
3. And the _likeness_, or _unlikeness_, _equality_, or _inequality_ of one body to another, is called their RELATION; and the bodies themselves _relatives_ or _correlatives_; _Aristotle_ calls them τὰ πρὸς τί; the first whereof is usually named the _antecedent_, and the second the _consequent_; and the _relation_ of the antecedent to the consequent, according to magnitude, namely, the equality, the excess or defect thereof, is called the PROPORTION of the antecedent to the consequent; so that _proportion_ is nothing but the equality or inequality of the magnitude of the antecedent compared to the magnitude of the consequent by their difference only, or compared also with their difference. For example, the _proportion_ of three to two consists only in this, that three _exceeds_ two by unity; and the proportion of two to five in this, that two, compared with five, is _deficient_ of it by three, either simply, or compared with the numbers different; and therefore in the proportion of unequals, the proportion of the less to the greater, is called DEFECT; and that of the greater to the less, EXCESS.
[Sidenote: Proportionals, what.]
4. Besides, of unequals, some are more, some less, and some equally unequal; so that there is _proportion of proportions_, as well as of _magnitudes_; namely, where two unequals have relation to two other unequals; as, when the inequality which is between 2 and 3, is compared with the inequality which is between 4 and 5. In which comparison there are always four magnitudes; or, which is all one, if there be but three, the middlemost is twice numbered; and if the proportion of the first to the second, be equal to the proportion of the third to the fourth, then the four are said to be _proportionals_; otherwise they are not proportionals.
[Sidenote: The proportion of magnitudes to one another, wherein it consists.]
5. The proportion of the antecedent to the consequent consists in their difference, not only simply taken, but also as compared with one of the relatives; that is, either in that part of the greater, by which it exceeds the less, or in the remainder, after the less is taken out of the greater; as the proportion of two to five consists in the three by which five exceeds two, not in three simply only, but also as compared with five or two. For though there be the same difference between two and five, which is between nine and twelve, namely three, yet there is not the same inequality; and therefore the proportion of two to five is not in all relation the same with that of nine to twelve, but only in that which is called arithmetical.
[Sidenote: Relation is no new accident, but one of those that were in the relative, before the relation or comparison was made. Also the causes of accidents in correlatives are the cause of relation.]
6. But we must not so think of relation, as if it were an accident differing from all the other accidents of the relative; but one of them, namely, that by which the comparison is made. For example, the likeness of one _white_ to another _white_, or its unlikeness to _black_, is the same accident with its _whiteness_; and _equality_ and _inequality_, the same accident with the _magnitude_ of the thing compared, though under another name: for that which is called _white_ or _great_, when it is not compared with something else, the same when it is compared, is called _like_ or _unlike_, _equal_ or _unequal_. And from this it follows that the causes of the accidents, which are in relatives, are the causes also of _likeness_, _unlikeness_, _equality_ and _inequality_; namely, that he, that makes two unequal bodies, makes also their inequality; and he, that makes a rule and an action, makes also, if the action be congruous to the rule, their congruity; if incongruous, their incongruity. And thus much concerning _comparison_ of one body with another.
[Sidenote: Of the beginning of individuation.]
7. But the same body may at different times be compared with itself. And from hence springs a great controversy among philosophers about the _beginning of individuation_, namely, in what sense it may be conceived that a body is at one time the same, at another time not the same it was formerly. For example, whether a man grown old be the same man he was whilst he was young, or another man; or whether a city be in different ages the same, or another city. Some place _individuity_ in the unity of _matter_; others, in the unity of _form_; and one says it consists in the unity of the _aggregate of all the accidents together_. For _matter_, it is pleaded that a lump of wax, whether it be spherical or cubical, is the same wax, because the same matter. For _form_, that when a man is grown from an infant to be an old man, though his matter be changed, yet he is still the same numerical man; for that _identity_ which cannot be attributed to the matter, ought probably to be ascribed to the form. For the _aggregate of accidents_, no instance can be made; but because, when any new accident is generated, a new name is commonly imposed on the thing, therefore he, that assigned this cause of _individuity_, thought the thing itself also was become another thing. According to the first opinion, he that sins, and he that is punished, should not be the same man, by reason of the perpetual flux and change of man's body; nor should the city, which makes laws in one age and abrogates them in another, be the same city; which were to confound all civil rights. According to the second opinion, two bodies existing both at once, would be one and the same numerical body. For if, for example, that ship of Theseus, concerning the difference whereof made by continual reparation in taking out the old planks and putting in new, the sophisters of Athens were wont to dispute, were, after all the planks were changed, the same numerical ship it was at the beginning; and if some man had kept the old planks as they were taken out, and by putting them afterwards together in the same order, had again made a ship of them, this, without doubt, had also been the same numerical ship with that which was at the beginning; and so there would have been two ships numerically the same, which is absurd. But, according to the third opinion, nothing would be the same it was; so that a man standing would not be the same he was sitting; nor the water, which is in the vessel, the same with that which is poured out of it. Wherefore the beginning of _individuation_ is not always to be taken either from matter alone, or from form alone.
But we must consider by what name anything is called, when we inquire concerning the _identity_ of it. For it is one thing to ask concerning Socrates, whether he be the same man, and another to ask whether he be the same body; for his body, when he is old, cannot be the same it was when he was an infant, by reason of the difference of magnitude; for one body has always one and the same magnitude; yet, nevertheless, he may be the same man. And therefore, whensoever the name, by which it is asked whether a thing be the same it was, is given it for the matter only, then, if the matter be the same, the thing also is _individually_ the same; as the water, which was in the sea, is the same which is afterwards in the cloud; and any body is the same, whether the parts of it be put together, or dispersed; or whether it be congealed, or dissolved. Also, if the name be given for such form as is the beginning of motion, then, as long as that motion remains, it will be the same _individual_ thing; as that man will be always the same, whose actions and thoughts proceed all from the same beginning of motion, namely, that which was in his generation; and that will be the same river which flows from one and the same fountain, whether the same water, or other water, or something else than water, flow from thence; and that the same city, whose acts proceed continually from the same institution, whether the men be the same or no. Lastly, if the name be given for some accident, then the _identity_ of the thing will depend upon the matter; for, by the taking away and supplying of matter, the accidents that were, are destroyed, and other new ones are generated, which cannot be the same numerically; so that a ship, which signifies matter so figured, will be the same as long as the matter remains the same; but if no part of the matter be the same, then it is numerically another ship; and if part of the matter remain and part be changed, then the ship will be partly the same, and partly not the same.
-------