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On Generation and corruption   


admitted that neither a body nor a magnitude will remain, and yet

division is to take place, the constituents of the body will either be

points (i.e. without magnitude) or absolutely nothing. If its

constituents are nothings, then it might both come-to-be out of

nothings and exist as a composite of nothings: and thus presumably the

whole body will be nothing but an appearance. But if it consists of

points, a similar absurdity will result: it will not possess any

magnitude. For when the points were in contact and coincided to form a

single magnitude, they did not make the whole any bigger (since,

when the body was divided into two or more parts, the whole was not

a bit smaller or bigger than it was before the division): hence,

even if all the points be put together, they will not make any

magnitude.

But suppose that, as the body is being divided, a minute section-a

piece of sawdust, as it were-is extracted, and that in this sense-a

body 'comes away' from the magnitude, evading the division. Even

then the same argument applies. For in what sense is that section

divisible? But if what 'came away' was not a body but a separable form

or quality, and if the magnitude is 'points or contacts thus

qualified': it is paradoxical that a magnitude should consist of

elements, which are not magnitudes. Moreover, where will the points

be? And are they motionless or moving? And every contact is always a

contact of two somethings, i.e. there is always something besides

the contact or the division or the point.

These, then, are the difficulties resulting from the supposition

that any and every body, whatever its size, is divisible through and

through. There is, besides, this further consideration. If, having

divided a piece of wood or anything else, I put it together, it is

again equal to what it was, and is one. Clearly this is so, whatever

the point at which I cut the wood. The wood, therefore, has been

divided potentially through and through. What, then, is there in the

wood besides the division? For even if we suppose there is some

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