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'.