The foundations of arithmetic in ibn Sīnā

Hassan Tahiri

pp. 297-314

in: Hassan Tahiri (ed), The philosophers and mathematics, Berlin, Springer, 2018

Abstract

Ibn Sīnā (980–1037), one of the most influential philosopher-scientists who was known to the West by the Latinised name Avicenna, has introduced a major shift in the philosophy of mathematics. His conception of number is structured into 5 main conceptual developments: (1) the recognition of mathematical objects as intentional entities and the acknowledgment that this amounts to provide an intentional notion of existence; (2) the link between the intentional act of apprehending unity and the generation of numbers by means of a specific act of repetition made possible by memory; (3) the identification of a specific intentional act that explains how the repetition operator can be performed by an epistemic agent; (4) the development of a notion of aggregate (or constructive set) that assumes an inductive operation for the generation of its elements and an underlying notion of equivalence relation; (5) the claim that plurality and unity should be understood interdependently (we grasp plurality by grasping it as instantiating an invariant).

Cited authors

Avicenne