Rerum formae: What is François Viète’s Logistice Speciosa about?

This paper aims to clarify the philosophical content of the terms employed in the description of the opposition between intuitionism and the view called “Platonism” concerning whether mathematical truth depends on the human mind or expresses properties of eternal abstract objects. We argue that reconstructed in terms of its historical origin, Aristotelian aphairesis characterizes the mathematical practice not only of the ancient Greeks, but likewise of mathematicians of all time. To this end, we analyze the emergence of mathematical aphairesis in Aristotle’s criticism of Plato’s account of what mathematics is about and describe the mathematical being of Viète’s Logistica Speciosa in terms of Aristotelian aphairesis.