The foundations of arithmetic in ibn Sīnā
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).
Tahiri, H. (2018)., The foundations of arithmetic in ibn Sīnā, in H. Tahiri (ed.), The philosophers and mathematics, Dordrecht, Springer, pp. 297-314.
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