The Uniqueness Proof for Forms in Republic 10

The Uniqueness Proof for Forms in Republic lo RICHARD D. PARRY IN THIS PAPER I offer an interpretation of the argument at the beginning of Repttblic lo (597cl-d3). The argument--sometimes called the Third Bed Argument (TBA)--shows that the Form of bed is unique. The argument is interesting because it uses the One-Over-Many principle (OM), which justifies positing Forms. But unlike the use of OM in the first Third Man Argument (TMA) of Parmenides (131al-b2), the use of the OM in TBA does not produce an argument which is liable to becoming an infinite regress. Since the TBA is in every other respect a classic statement of the theory of Forms usually associated with the middle dialogues, we can conclude that this theory is not metaphysically bankrupt, as it is sometimes claimed. Whatever the problems with the TMA, they do not infect the whole theory of Forms in the middle dialogues because there is at least one instance of a clear enunciation of the theory which does not fall prey to the infinite regress of the TMA. In Section 1 of this paper, we analyze the TBA and add three assumptions necessary to make it valid. As well, we explain these assumptions and offer textual evidence for them. In Section 9, we survey recent commentaries on the TBA and defend our interpretation against these commentaries. In particular we show that, under our interpretation, the TBA is not liable to being turned into an infinite regress of Forms of bed. In Section 3, we see what implications this latter fact has for a theory of Forms which holds that the Form of f is, in some way, itself f. We show in what way this central doctrine of the middle dialogues theory of Forms can be held without threat of inconsistency or infinite regress. In Section 4, we apply our interpretation of the TBA to the TMA, showing that the fallacious step of the TMA can be I would like to thank Anthony Nemetz, Nicholas Smith, and E. W. van Steenburgh who were kind enough to discuss this paper with me, as wellas an anonymous referee for theJournal of the History of Philosophy. All internal references to the Greek text are from Burnet's edition. [133] I34 JOURNAL OF THE HISTORY OF PHILOSOPHY brought to light by considering the important differences between the two arguments. 1, At Republic lO (597cl-d3) Socrates argues that there will be only one Form of bed, which he calls that which is bed. He says that the god will not make more than one bed in nature--by the latter phrase is meant a Form--nor will two such things arise. The argument to back up at least the first part of this claim is simply put: if he made as few as two ~then again a one (bed in nature) would arise, whose form the two (original beds) would have, and this one would be that which is bed and not the two. So, the god, knowing all this and wishing to be the real bed maker of the real being and not (just) a maker of a bed, makes one (bed) in nature. The calculation involved in this passage could be rendered: (I) If he made as few as two (x) (a) again a one (bed) would appear (b) whose form the two would have and (2) (a) this one would be that which is bed and (b) not the two. If we look at the calculation closely we see that some assumptions are made. For the calculation to work, then, these suppressed assumptions need to be added to derive both part (1) and part (2). In this section we add these assumptions. In effect, the assumptions show that the one which appears is the one Form over many and that everything which is a bed besides this one Form derives its character from this Form. The latter assumption is of crucial importance because it allows the Form of f to be f without participating in another Form of f; the Form is non-derivatively f. The significance of this assumption will be explored in subsequent sections; but...