# ABSTRACT

### RALPH E. KENYON JR.

B.A., B.S., MIAMI UNIVERSITY

M.A., PEPPERDINE UNIVERSITY

M.S., OLD DOMINION UNIVERSITY

M.A, UNIVERSITY OF MASSACHUSETTS AMHERST

### Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST

Directed by: Bruce Aune

This work analyzes two perspectives, Atomism and Infinite Divisibility, in
the light of modern mathematical knowledge and recent developments in computer
graphics. A developmental perspective is taken which relates ideas leading to
atomism and infinite divisibility. A detailed analysis of and a new resolution
for Zeno's paradoxes are presented. Aristotle's arguments are analyzed. The
arguments of some other philosophers are also presented and discussed. All
arguments purporting to prove one position over the other are shown to be
faulty, mostly by question begging. Included is a sketch of the consistency of
infinite divisibility and a development of the atomic perspective modeled on
computer graphics screen displays. The Pythagorean theorem is shown to depend
upon the assumption of infinite divisibility. The work concludes that Atomism
and infinite divisibility are independently consistent, though mutually
incompatible, not unlike the wave/particle distinction in physics.

A printed copy of this dissertation can be be ordered from University
Microfilms International. Request order number 9420641.