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.
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.
CHAPTER XII.
OF QUANTITY.
[1.] The definition of quantity.—[2.] The exposition of quantity, what it is.—[3.] How line, superficies, and solid, are exposed.—[4.] How time is exposed.—[5.] How number is exposed.—[6.] How velocity is exposed.—[7.] How weight is exposed.—[8.] How the proportion of magnitudes is exposed.—[9.] How the proportion of times and velocities is exposed.
Definition of quantity.
1. What and how manifold dimension is, has been said in the 8th chapter, namely, that there are three dimensions, line or length, superficies, and solid; every one of which, if it be determined, that is, if the limits of it be made known, is commonly called quantity; for by quantity all men understand that which is signified by that word, by which answer is made to the question, How much is it? Whensoever, therefore, it is asked, for example, How long is the journey? it is not answered indefinitely, length; nor, when it is asked, How big is the field? is it answered indefinitely, superficies; nor, if a man ask, How great is the bulk? indefinitely, solid: but it is answered determinately, the journey is a hundred miles; the field is a hundred acres; the bulk is a hundred cubical feet; or at least in some such manner, that the magnitude of the thing enquired after may by certain limits be comprehended in the mind. QUANTITY, therefore, cannot otherwise be defined, than to be a dimension determined, or a dimension, whose limits are set out, either by their place, or by some comparison.