Sensitive mathematical objects and intelligible mathematical objects
In this paper we study the concept of mathematical object as it was understood by ancient mathematical thought, particularly by Plato and Aristotle. We are going to prove that it is not right to interpret the duality of this concept in Plato’s works as consequence of an ontological division between two kinds of mathematical objects, i.e. the sensitive and the intelligible ones. We want to prove that such a division is not a real one because, as a matter of fact, Plato is proposing a differentiation between two possible ways to be related with mathematical objects: the way of the philosophers and the way of the non–philosophers. Moreover, we show that our interpretation is able to clarify the ambiguity around the concept of μоνάς and therefore eliminate the false distinction between the two subject matters devoted to the study of discrete mathematical objects: the λоγιστική and the ἀριθμητική.
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