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Chapter 7 - From the Fifth to the Eighth Deduction

Published online by Cambridge University Press:  22 September 2009

Samuel C. Rickless
Samuel C. Rickless
Affiliation:
University of California, San Diego
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Summary

The last four Deductions take up no more than six or so Stephanus pages (160b5–166c5). Parmenides has lost interest in establishing his results in as virtuosic a fashion as is displayed in the first two Deductions. Still, these Deductions are important to the plan of the dialogue.

THE FIFTH DEDUCTION

D5A1 (160b5–d2)

D5A1 establishes two conclusions, (C1) that if the one is not, then the one is different from the others, and (C2) that if the one is not, then we have knowledge of the one.

Assume (P1) that in saying “the one is not” what we are saying is not is contrary to the not-one. Taken on its own, P1 entails (L1) that if the one is not, then the one and the not-one are contraries. Now, by D2A11P4, the others are those that are not one. Taken on its own, D2A11P4 entails (L2) that the others are the not-one. Hence, by L1 and L2, if the one is not, then the one and the others are contraries. Now, by D4A3P2, if X and Y are contraries, then X is not the same as Y, and, by D2A4P1, if X is not the same as Y, then X is different from Y. Taken together, then, D4A3P2 and D2A4P1 entail (L3) that if X and Y are contraries, then X is different from Y (and hence, if the one and the others are contraries, then the one is different from the others).

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Plato's Forms in Transition
A Reading of the Parmenides
 , pp. 212 - 239
Publisher: Cambridge University Press
Print publication year: 2006

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