Plato’s Mathematical Ontology in Islamic and Western Interpretations

Mathematics has always been considered to be among certain sciences; however, the objects of mathematical knowledge have continually occupied the minds of mathematicians and philosophers of mathematics. The theory stating that the objects of mathematics consist of a number of certain immaterial and separate affairs which are independent of the world of the human mind and thought has been attributed to Plato, and several realist philosophers who, in spite of all their differences, have been called neo-Platonists. Commentators of Plato have failed in providing any clear and consistent interpretation, whether in terms of ontology or semantics, of his philosophy of mathematics, which has resulted in some misunderstandings in this regard and some ambiguity in his whole philosophy. When completing his PhD dissertation at the University of Bristol, Paul Pritchard presented an interpretation of Plato’s ontology, according to which the objects of mathematics are the same sensible things. Here, the allegory of the divided line has been interpreted differently, and the existing ambiguities have been removed. In this paper, the authors have examined this interpretation and compared it with other interpretations of Plato’s ontology of mathematics. They also refer to its effects on Plato’s philosophy of mathematics in general and reveal that, unlike its traditional interpretation, his philosophy of mathematics does not conflict with Benacerraf’s identification problem. Moreover, the authors demonstrate that, based on Mulla Sadra’s arguments, the theory of Ideas is a completely consistent theory in terms of ontology and, thus, Plato’s philosophy of mathematics is a consistent body of philosophy.