Quantity

1. Quantity two-fold, discrete and continuous; of parts occupying relative position, and the contrary.

Of Quantity, one kind is discrete, and another continuous

The one consists of parts, holding position with respect to each other, but the other of parts, which have not that position.

2. Examples discrete.Discrete quantity is, as number and sentence, but continuous, as line, superficies, body, besides place and time.

3. Number.For, of the parts of number, there is no common term, by which its parts conjoin, as if five be a part of ten, five and five, conjoin at no common boundary, but are separated. Three, and seven, also conjoin at no common boundary, nor can you at all take a common limit of parts, in number, but they are always separated, whence number is of those things which are discrete.

4. Oratio.

In like manner a sentence, for that a sentence is quantity is evident, since it is measured by a short and long syllable;[25] but I mean a sentence produced by the voice, as its parts concur at no common limit, for there is no common limit, at which the syllables concur, but each is distinct by itself. 3. Examples continuous.

1. A line.A line, on the contrary, is continuous, for you may take a common term, at which its parts meet, namely, a point, and of a superficies, a line, for the parts of a superficies coalesce in a certain common term. 2. A superficies.So also you can take a common term in respect of body, namely, a line, or a superficies, by which the parts of body are joined. Of the same sort are time and place, for the present time is joined both to the past and to the future. 3. Time and place.Again, place is of the number of continuous things, for the parts of a body occupy a certain place, which parts join at a certain common boundary, wherefore also the parts of place, which each part of the body occupies, join at the same boundary as the parts of the body, so that place will also be continuous, since its parts join at one common boundary.

2. Relation position to some of the parts as to the above.Moreover, some things consist of parts, having position with respect to each other, but others of parts not having such position.

Thus, the parts of a line have relative position, for each of them lies some where, and you can distinguish, and set out, where each lies, in a superficies, and to which part of the rest, it is joined.

So also the parts of a superficies, have a certain position, for it may be in like manner pointed out where each lies, and what have relation to each other, and the parts of a solid, and of a place, in like manner.

5. Parts have no relation in respect to number or time.On the contrary, in respect of number, it is impossible for any one to show that its parts have any relative position, or that they are situated any where, or which of the parts are joined to each other.

Nor as regards parts of time, for not one of the parts of time endures, but that which does not endure, how can it have any position? you would rather say, that they have a certain order, inasmuch as one part of time is former, but another latter.

In the same manner is it with number, because one, is reckoned before two, and two, before three, and so it may have a certain order, but you can, by no means, assume, that it has position. 6. Oratio.A speech likewise, for none of its parts endures, but it has been spoken, and it is no longer possible to bring back what is spoken, so that there can be no position of its parts, since not one endures: some things therefore consist of parts having position, but others of those which have not position.

7. The above-named are the only proper quanta—all others reducible to these.—Examples.What we have enumerated are alone properly termed quantities; all the rest being so denominated by accident, for looking to these, we call other things quantities, as whiteness is said to be much, because the superficies is great, and an action long, because of its time being long, and motion also, is termed, much.

Yet each of these is not called a quantity by itself, for if a man should explain the quantity of an action, he will define it by time, describing it as yearly, or something of the sort; and if he were to explain the quantity of whiteness, he will define it by the superficies, for as the quantity of the superficies, so he would say is the quantity of the whiteness; whence the particulars we have mentioned are alone properly of themselves termed quantities, none of the rest being so of itself, but according to accident.

8. Quantity, per se, has no contrary.Again, nothing is contrary to quantity,[27] for in the definite it is clear there is nothing contrary, as to “two cubits” or to “three,” or to “superficies,” or to any thing of this kind, for there is no contrary to them; except indeed a man should allege that “much” was contrary to “little,” or the “great” to the “small.” Of these however, none is a quantity, but rather belongs to relatives, since nothing, itself by itself, is described as great or small, but from its being referred to something else.

9. Reply to objection, founded upon the contrariety of great to small.A mountain, for instance, is called “little,” but a millet seed “large,” from the fact of the one being greater, but the other less, in respect of things of the same nature, whence the relation is to something else, since if each were called “small” or “great” of itself, the mountain would never have been called “small,” nor the seed “large.”

We say also that there are “many” men in a village, but “few” at Athens, although these last are more numerous, and “many” in a house, but “few” in a theatre, although there is a much larger number in the latter. Besides, “two cubits,” “three,” and every thing of the kind signify quantity, but “great” or “small” does not signify quantity, but rather relation, for the “great” and “small” are viewed in reference to something else, so as evidently to appear relatives. 10.Whether however any one does, or does not, admit such things to be quantities, still there is no contrary to them, for to that which cannot of itself be assumed, but is referred to another, how can there be a contrary?

11.Yet more, if “great” and “small” be contraries, it will happen, that the same thing, at the same time, receives contraries, and that the same things are contrary to themselves, for it happens that the same thing at the same time is both “great” and “small.” Something in respect of this thing is “small,” but the same, in reference to another, is “large,” so that the same thing happens at the same time to be both “great” and “small,” by which at the same moment it receives contraries.

12. Simultaneous contrariety impossible.Nothing however appears to receive contraries simultaneously, as in the case of substance, for this indeed seems capable of contraries, yet no one is at the same time “sick” and “healthy,” nor a thing “white” and “black” together, neither does any thing else receive contraries at one and the same time. 13.It happens also, that the same things are contrary to themselves, since if the “great” be opposed to the “small,” but the same thing at the same time be great and small, the same thing would be contrary to itself, but it is amongst the number of impossibilities, that the same thing should be contrary to itself, wherefore the great is not contrary to the small, nor the many to the few, so that even if some one should say that these do not belong to relatives, but to quantity, still they will have no contrary.

13. The contrariety of quantity chiefly subsistent in space.The contrariety however of quantity seems especially to subsist about place, since men admit “upward” to be contrary to “downward,” calling the place toward the middle “downward,” because there is the greatest distance from the middle, to the extremities of the world;[28] they appear also to deduce the definition of the other contraries from these, for they define contraries to be those things which, being of the same genus, are most distant from each other.

14. Quantity is incapable of degree.Nevertheless quantity does not appear capable of the greater and the less, as for instance “two cubits,” for one thing is not more “two cubits” than another; neither in the case of number, since “three” or “five” are not said to be more than “three” or “five,” neither “five” more “five” than “three” “three;” one time also is not said to be more “time” than another; in short, of none that I have mentioned is there said to be a greater or a less, wherefore quantity is not capable of the greater and less.

15. But of equality and inequality.Still it is the especial peculiarity of quantity to be called “equal” and “unequal,"[29] for each of the above-mentioned quantities is said to be “equal” and “unequal,” thus body is called “equal” and “unequal,” and number, and time, are predicated of as “equal” and “unequal;” likewise in the case of the rest enumerated, each one is denominated “equal” and “unequal.” Of the remainder, on the contrary, such as are not quantities, do not altogether appear to be called “equal” and “unequal,” as for instance, disposition is not termed entirely “equal” and “unequal,” but rather “similar” and “dissimilar;” and whiteness is not altogether “equal” and “unequal,” but rather “similar” and “dissimilar;” hence the peculiarity of quantity will especially consist in its being termed “equal” and “unequal.”