At Parmenides 13 la5-128. Parmenides contends that if a particular participates in a Form, then either (a) the whole of the Form is present in the particular, or (b) a part of the Form is present in the particular. These disjuncts are the Horns of the so-called Dilemma of Participation ---(a) the First and (b) the Second.' There is little debate about how the reductio of the First Horn works: from the premiss that the whole Form is present in many separate particulars (131a9-10). it seems easy to supply the appropriate assumptions so the conclusion follows that the Form is separate from itself (131b1-2). I show that the logic of the argument depends heavily on our interpretation of two relations---the present-in relation, and the separation relation---and that these relations are not what commentators have been inclined to suppose.
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