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On Generation and corruption   


necessity of atomic magnitudes: we must now show that it conceals a

faulty inference, and exactly where it conceals it.

For, since point is not 'immediately-next' to point, magnitudes

are 'divisible through and through' in one sense, and yet not in

another. When, however, it is admitted that a magnitude is

'divisible through and through', it is thought there is a point not

only anywhere, but also everywhere, in it: hence it is supposed to

follow, from the admission, that the magnitude must be divided away

into nothing. For it is supposed-there is a point everywhere within

it, so that it consists either of contacts or of points. But it is

only in one sense that the magnitude is 'divisible through and

through', viz. in so far as there is one point anywhere within it

and all its points are everywhere within it if you take them singly

one by one. But there are not more points than one anywhere within it,

for the points are not 'consecutive': hence it is not simultaneously

'divisible through and through'. For if it were, then, if it be

divisible at its centre, it will be divisible also at a point

'immediately-next' to its centre. But it is not so divisible: for

position is not 'immediately-next' to position, nor point to

point-in other words, division is not 'immediately-next' to

division, nor composition to composition.

Hence there are both 'association' and 'dissociation', though

neither (a) into, and out of, atomic magnitudes (for that involves

many impossibilities), nor (b) so that division takes place through

and through-for this would have resulted only if point had been

'immediately-next' to point: but 'dissociation' takes place into small

(i.e. relatively small) parts, and 'association' takes place out of

relatively small parts.

It is wrong, however, to suppose, as some assert, that

coming-to-be and passing-away in the unqualified and complete sense

are distinctively defined by 'association' and 'dissociation', while

the change that takes place in what is continuous is 'alteration'.

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