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

FINFIIY 813
as such is no less than the sum of all matter." The error
to which I desire to invite your attention,-an error in
the poet's use of the concept of infinity,-is his assertion
italicised in the foregoing paraphrase. The error is not
due to wrong conception of infinity, whether of multitude
or of magnitude; it is due solely to the tacit assumption
that the sum of the elements of any infinite multitude of
elements is infinite,-an assumption which, as you are
aware, is false, for, for example, the sum of the elements
of the infinite multitude of elements (-, 4, -,...) is,
as you learned in high school, not infinite but is Iin other words, the limit of the sum, i —7, of the first
I I I I
n terms of the series, -+ 22++.*, - n+t2 2 23 2
is i. Such a series,-any series such that the sum of
the first n terms has a finite limit for n increasing limitlessly,-is said to be convergent. An obvious moral is
that a little knowledge of the convergence of series
would greatly improve the philosophy of poets and the
science of philosophers.
It is astonishing that the mentioned fallacy occurs, as
it does, in immediate conscious connection with a line
seeming (to us) to refute it: the half of the half will
always have a half and nothing will set bounds to the
division. What is the explanation? It is not to be found
in any supposition of stupidity or of momentary nodding.
It is doubtless to be found in the author's purpose and
point of view. He was here exclusively concerned with
natural phenomena, with what he deemed to be existing
entities-with bodies (and parts thereof) occupying
space, actually filling what would else have been absolute
emptiness or void. And so, if you had tried to refute