Abstrakt
plakát pdf
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.
