DEPARTMENT OF CONTEMPORARY CONTINENTAL PHILOSOPHY

Institute of Philosophy – Czech Academy of Sciences

presents the final Prague lecture

by

prof. Burt C. Hopkins

on

PHILOSOPHICAL PROBLEMS IN THE FOUNDATION OF ARITHMETIC:
ANCIENT AND MODERN

Thursday, 23 May, 2019 from 6pm

Institute of Philosophy CAS, Jilská 1 Prague, seminar room 124a

Abstract
I will address the systematic question of the relationship between arithmetic and philosophy
by exploring the historical justifications for the philosophical engagement with the problems
of the foundation of arithmetic found in the so-called Pythagoreans, Plato, Aristotle, and
modern philosophy culminating in Frege. My focus will be on the being and concept of
number in arithmetic and the philosophical accounts of the intelligibility of both presented
in the ancient and modern traditions. I will argue that the systematic problem of number’s
being and concept cannot be separated from the history of the transformation of the ancient
arithmos (= a determinate amount of determinate units) into the modern symbolic concept
of number (= an indeterminate quantity). I will conclude that both the class and extensional
formulation of the being of number fall short – philosophically speaking – of articulating the
intelligibility of number and that therefore this articulation still awaits a solution.