
This chapter presents arguments by Syrianus (in his Commentary on Aristotle’s Metaphysics) and Proclus (in his Commentary on Euclid’s Elements) to refute the Aristotelian explanation of the empirical origin of mathematical concepts, known as abstractionism. The authors seek to establish a higher ontological status for mathematical objects. According to Proclus and Syrianus, mathematical objects do not derive from sensible experience but are discursive projections of a priori concepts (ousiodeis logoi) innate in the human soul. These concepts, in turn, originate from a transcendent demiurgic intellect. This Neoplatonic ontology demonstrates how mathematical objects maintain qualities of precision, eternity, and universal validity, while simultaneously allowing for the creative activity of the mathematician. Crucially, this perspective positions mathematics as a fundamental science that serves as a paradigmatic model for physics and a crucial foreshadowing of metaphysics, highlighting its vital role in Proclus’ overall philosophical system.
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