Nicholas of Cusa and Aristotle's philosophy of mathematics

Abstract

One of the basic elements of Nicholas of Cusa's philosophy of mathematics is his theory of mathematical objects as “entities-of-reason” (entia rationis). He refers to these as being “abstracted from sensible things”. That is why it is possible to assume that Nicholas bases his theory of mathematics on Aristotle's philosophy of mathematics. Aristotle too describes mathematical objects as coming into being through abstraction (ex aphaireseos). The author analyses Cusa's understanding of abstraction in De docta ignorantia and De mente and tries to show that – according to Nicholas of Cusa – the abstraction, which is ens rationis, simultaneously stimulates the human mind to produce mathematical objects from within itself. The author attempts to show how Cusa's philosophy of mathematics is not directly based on Aristotle's philosophy of mathematics – Aristotle is not an abstractionist and does not ascribe the existence of mathematical objects to the mind of the mathematician – but on the abstractionist interpretation of Aristotle by Alexander of Aphodisias, who was followed by the predominantly neoplatonist commentators of Aristotle. These commentators did not see any important differences in the metaphysical or epistemological underpinnings of abstractionism and the so-called projectionism, i.e. the theory according to which mathematical objects pre-exist in the soul.