The fundamental question, in dealing with all these
difficulties, is this: 'Do things come-to-be and "alter" and grow, and
undergo the contrary changes, because the primary "reals" are
indivisible magnitudes? Or is no magnitude indivisible?' For the
answer we give to this question makes the greatest difference. And
again, if the primary 'reals' are indivisible magnitudes, are these
bodies, as Democritus and Leucippus maintain? Or are they planes, as
is asserted in the Timaeus?
To resolve bodies into planes and no further-this, as we have also
remarked elsewhere, in itself a paradox. Hence there is more to be
said for the view that there are indivisible bodies. Yet even these
involve much of paradox. Still, as we have said, it is possible to
construct 'alteration' and coming-to-be with them, if one 'transposes'
the same by 'turning' and 'intercontact', and by 'the varieties of the
figures', as Democritus does. (His denial of the reality of colour
is a corollary from this position: for, according to him, things get
coloured by 'turning' of the 'figures'.) But the possibility of such a
construction no longer exists for those who divide bodies into planes.
For nothing except solids results from putting planes together: they
do not even attempt to generate any quality from them.
Lack of experience diminishes our power of taking a comprehensive
view of the admitted facts. Hence those who dwell in intimate
association with nature and its phenomena grow more and more able to
formulate, as the foundations of their theories, principles such as to
admit of a wide and coherent development: while those whom devotion to
abstract discussions has rendered unobservant of the facts are too
ready to dogmatize on the basis of a few observations. The rival
treatments of the subject now before us will serve to illustrate how
great is the difference between a 'scientific' and a 'dialectical'
method of inquiry. For, whereas the Platonists argue that there must
be atomic magnitudes 'because otherwise "The Triangle" will be more
than one', Democritus would appear to have been convinced by arguments
appropriate to the subject, i.e. drawn from the science of nature. Our
meaning will become clear as we proceed. For to suppose that a body
(i.e. a magnitude) is divisible through and through, and that this
division is possible, involves a difficulty. What will there be in the
body which escapes the division?
If it is divisible through and through, and if this division is
possible, then it might be, at one and the same moment, divided
through and through, even though the dividings had not been effected
simultaneously: and the actual occurrence of this result would involve
no impossibility. Hence the same principle will apply whenever a
body is by nature divisible through and through, whether by bisection,
or generally by any method whatever: nothing impossible will have
resulted if it has actually been divided-not even if it has been
divided into innumerable parts, themselves divided innumerable
times. Nothing impossible will have resulted, though perhaps nobody in
fact could so divide it.