PYTHAGORAS TO PLATO In the passage I have cited, Plato arrives at the Idea of circle after starting from a consideration of the word ‘circle’ as it occurs in the subject-place of a sentence such as A circle is a plane Wgure whose circumference is everywhere equidistant from its centre However, he sometimes introduces the Idea of X by reXection on sentences in which ‘X’ appears not in subject-place, but as a predicate Consider the following Socrates, Simmias, and Cebes are all called ‘men’; they have it in common that they are all men Now when we say ‘Simmias is a man’ we may wonder whether the word ‘man’ names or stands for something in the way that the name ‘Simmias’ stands for the individual man Simmias? If so, what? Is it the same thing as the word ‘man’ stands for in ‘Cebes is a man’? In order to deal with questions of this kind, Plato introduces the Idea of Man It is that which makes Simmias, Cebes, and Socrates all men; it is the prime bearer of the name ‘Man’ In many cases where we would say that a common predicate was true of a number of individuals, Plato will say that they are all related to a certain Idea or Form: where A, B, C, are all F, they are related to a single Form of F Sometimes he will describe this relation as one of imitation: A, B, C, all resemble F Sometimes he will talk rather of participation: A, B, C all share in F, they have F in common between them It is not clear how universally we are to apply the principle that behind common predication there lies a common Idea Sometimes Plato states it universally, sometimes he hesitates about applying it to certain particular sorts of predicate Certainly he lists Ideas of many diVerent types, such as the Idea of Good, the Idea of Bed, the Idea of Circle, the Idea of Being He is prepared to extend the theory beyond single-place predicates such as ‘is round’ to two-place predicates like ‘is distinct from’ When we say that A is distinct from B and when we say that B is distinct from A, although we use the word ‘distinct’ twice, each time we are applying it to a single entity We may state a number of Platonic theses about Ideas and their relations to ordinary things in the world (1) The Principle of Commonality Wherever several things are F, this is because they participate in or imitate a single Idea of F (Phd 100c; Men 72c, 75a; Rep 476a10, 597c) 51