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

INFINITY 315
What we assert is that after we have divided a body
into a certain finite number of constituent parts called
molecules, then any further division of these molecules
will deprive them of the properties which give rise to
the phenomena observed in the substance.
The traditional form of the thesis tacitly invoked by
Lucretius to fortify his "other" grounds for holding that
among the parts of an atom there is a least part, is exceedingly vague: all infinites are equal. Its vagueness
helps to account for its ages-long and world-wide vogue.
Thus Kanadi, an old Hindu author, employs the thesis
to prove that, if every body be infinitely divisible, there
can be "no difference of magnitude between a mustard
seed and a mountain" (Daubeny's Introduction to Atomic
Theory, p. 5). In this connection, anyone, philosopher
or mathematician, if he be at all interested in the history
of the idea of infinity, will be glad to have his attention
called to a little-known letter of Newton dealing with the
idea. The letter, which is addressed to Richard Bentley
(Works of, Vol. III, p. 207), is interesting on several
accounts: it points out the vagueness and falseness of the
above-mentioned thesis, which Dr. Bentley had assumed
to be true; it itself repeatedly employs the term "infinite"
in a sense not less vague and indeterminate; and it virtually asserts that, if two infinite magnitudes be equal, the
addition of any finite magnitude to either of them will
destroy the equality-a proposition which we now know
to be false.
I have said that a thorough-going Critical History
of the Concept of Infinity would be a highly valuable contribution to our knowledge and understanding of humankind. The account I have now given of the rôle of infinity in the work of Lucretius is submitted, let me say