Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser.

INFINITY 811
words, atomic size is not infinitesimal,-it is a variable
but not one having zero, or null size, for limit; we are
told, rightly, that the sum of any finite number of atoms
is finite; we are told that the sum of all the atoms of a
given atomic form is infinite and that, therefore, their
number must be infinite. It is thus evident that the Lucretian conception of an infinite magnitude was that of
a magnitude exceeding the sum of any finite number of
finite quantities none of which surpasses, in respect of
parvitude, a finite size.
It is important to bear in mind that formation of
ideas or possession of them is one thing, and that logically
correct handling of them in argumentation is quite another. The difference is that between conception and
ratiocination. In his use of the ideas in question Lucretius was frequently right and frequently wrong. You
would find it a very edifying discipline to determine all
the instances of both kinds. Of right use some examples
have already been given and it would be easy to cite
others. Let us now consider an instance of erroneous
use. A remarkable example is found in the following
passage (as correctly translated by Munro, page iS)a passage of exceeding interest apart from the error in
question:
Again unless there shall be a least, the very smallest bodies will consist of infinite parts, inasmuch as
half of a half will always have a half and nothing will
set bounds to the division. Therefore between th'e
sum of things and the least of things what difference
will there be? There will be no distinction at all; for
however absolutely infinite soever the whole sum is,
yet the things which are smallest will equally consist
of infinite parts.