Abstract

In On Ideas, Aristotle presents and criticizes an argument for ideas referred to as “the One-over-Many.” On the basis of an uncontroversial fact concerning a group (for instance, the fact that each of the many men is a man), the One-over-Many infers that there is something predicated of each of the members of the group (for instance, that there is something predicated of each of the many men). It then tries to show that the thing predicated in common is an idea. Aristotle criticises this argument by claiming that if it were sound it would show that there are ideas of negations, a result which the Platonists should reject. Since Aristotle himself refuses the existence of “common things,” i.e., Aristotelian universals, of negations, he is committed to the view that the One-over-Many fails to prove the existence not only of ideas, but also of “common things.”