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There are many things in the world, including the standard rod in Paris, that are one meter long. The length of each of these, call it ‘L’, is identical to one meter. Suppose there were a second length of one meter, qualitatively-identical to L but numerically-different from it, call it ‘L'’. Since both these lengths are qualitatively the same, their length would be common to both, call it ‘L''’. Neither L nor L' could be identical to L''; and it would now be L'' that is identical to one meter. Why? This is the realisation Plato made about the Forms: each Form is qualitatively and numerically unique. Plato gives the argument in Republic X. In brief, and simplifi ed, the argument is that there is only one Form F for f-similar things, e.g. for beds, all of which are likenesses of that Form. If there were two Forms of Bed, they would be qualitatively-identical to one another, but numerically-different from each other. Their qualitative identity and numerical distinctness would point to a further entity, which would be the Form whose instances they both are. The reason is that their qualitative identity requires a common Form to explain it. Their numerical difference prevents either of them from being this common Form; i.e., from being identical to what is common between the two of them without thereby violating their qualitative identity. Forms explain the resemblance between their instances. Whatever, in the instances of a Form, makes them numerically different from one another also makes the instances different from their Form.

Is Being One Only One? The Uniqueness of Platonic Forms