Abstract
Plato is commonly taken to be committed to the existence of intermediates , ideal mathematical particulars distinct from Forms. But the main argument by which he is thought to arrive at this commitment makes a problematic assumption about mathematical discourse. By examining the role of mathematics in the philosopher’s education of Republic Bk. VII, I show that Plato does not accept this assumption, and therefore does not endorse the argument for intermediates attributed to him. I then offer a new account on which Plato regards the objects of mathematics as theoretical fictions , objects invented by mathematicians to further their theoretical aims.
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