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

INFINITY 807
indispensable to the prosperity of his great undertaking.
This is not the place to give a detailed account of
the Lucretian principles and procedure. For our present
purpose it is sufficient to point out that among the propositions of De Rerumn Natura there are three major ones
and that these owe their efficacy and indeed their control
of the entire discourse to the fact of their postulating
the existence of infinite multitude and infinite magnitude.
"Postulating" I have said, although Lucretius regarded
the propositions, not as mere hypotheses or assumptions,
but as indubitable certitudes. What are these three basic
propositions? They are: that the universe of space is a
region or room of infinite capacity-infinite extent; that
time is an infinite duration composed of a beginningless
infinite past and an endless infinite future; and that the
universe's matter consists of an infinite multitude of absolutely solid (non-porous) and non-decomposable atoms
-"seeds of things"-always moving hither and thither
in an infinite variety of ways and ever so distributed
throughout infinite space that of all spheres none but such
as are microscopically minute could at any instant fail
to enclose one or more of the "seeds." Without these
infinitudes, explanation of the phenomena of the world
was, in the poet's belief, impossible; with them, supplemented by certain other principles, such explanation was
possible. In the view of Lucretius cosmic history was an
eternal (infinite) drama enacted by an infinitude of unoriginated and indestructible "seeds," atoms, or elements
operating upon an infinite stage. The drama was not to
be understood except by help of the concept of infinity;
and so De Rerum Natutra may be not unjustly said to be
a kind of poetic celebration of what the poet deemed to
be the scientific efficacy of that concçpt,