Recalling our earlier discussions of the problems for the existential position, and given the explicit formulation of each of the interpretations, we should be able to better deal with them, discern where the problems lie, and propose some solutions or qualifications.  Our naïve criticisms have already informed us that the difficulties lie in 2a and, perhaps less obviously, 2b­the formulations for sensibles, the objects of opinion.  The apparent problem is this: How can something both exist and not exist, or be both F and not F?  While the notion of something both existing and not existing seems more absurd, it is not any more problematic, logically speaking, than something having the qualities F and not F. But why are these formulations problematic in the first place?

Table 1
Summary of existential and predicate models.

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Note:
By substituing "exists" for "is" in Plato's object model, we get the existential interpretation.  With X, Y, and Z standing for the objects of knowledge, opinion, and ignorance respectively.

The answer seems to be, as many commentators have suggested, that they are not really problematic so long as we qualify them temporally, spatially, or relatively.   That is, the formulations are only absurd if they are considered apart from time, space, or perspective­in a vacuum so to speak. Given a more complex account, the formulations can be rendered entirely coherent. For instance, something can exist at time t1 and not exist at time t2.   The same applies for the predicative formula. Something can be F at one time and not F at another.  If temporality is included as part of the contexts of the formulae, they are entirely consistent.  But it seems 2a cannot easily be rendered coherent by appeal to perspective, while 2b can.59  I would argue that this does not furnish grounds for eliminating the existential interpretation, since Plato does not even bother to qualify his expression at all.  We cannot readily reject 2a because we cannot reconcile it with relative perspective.  Plato does not take care to explain the conditions for qualifying the objects of knowledge, opinion, and ignorance, so we cannot justifiably throw out the existential interpretation because of its failure to measure up to conditions that Plato does not himself bother to specify.

Types of Change­2a and 2b

For evaluative purposes, we must further discuss the issue of change and its relation to the two formulae for sensibles. Earlier, we briefly discussed Plato's classification of the objects of knowledge, opinion, and ignorance.  Plato's basic epistemological idea is that only perfect, unchanging Forms can be the proper objects of knowledge. 

Those objects which undergo constant change, or embody opposite properties, cannot furnish grounds for knowledge, since whatever propositions one constructs in reference to them are always false, or, rather, become false due to change.  Some X may be F at time t1 and not F at time t2; X may be F from one person's point of view and not F from another's; X may be F in one respect and not F in another.60  In short, it seems that sensibles­objects which undergo some type of change­can never be proper objects of knowledge if we can never give an accurate, indubitable description of them.  From this reasoning we get 2a and 2b as possibilities.  In Republic Bk. V, rather than giving us an exposition of change, or flux, Plato gives us "that which is and is not."  By looking further into types of flux, and making some distinctions between two types of change, we should see how this affects our evaluation of 2a and 2b

T.H. Irwin, in "Plato's Heracleiteanisim," outlines two types of flux: self-change (s-change) and aspect-change (a-change). S-change amounts to constant "qualitative alteration." Some X is F at one time, not F at another:

X s-changes iff at time t1 X is F and at time t2 X is not-F, and X itself is not in the same condition at t2 as it was at t1.61

This does not exhaust the kinds of change attributed to Heracleitus, whose "unity of opposites" also includes things with "compresent opposite properties." This is a-change.

X a-changes iff X is F in one aspect, not-F in another, and X is in the same condition when it is F and when it is not-F.

What is the difference between the two types of change?  As Irwin suggests, s-change is change through time, while in a-change, time is static.  Both involve the "presence of opposite properties in different situations," but in a-change these opposite properties are not derived by comparing the object with itself at some previous time.  According to Irwin, we can safely infer that Plato recognized the differences between s-change and a-change, and that he clearly refers to both types.  However, Plato does not clearly distinguish them.62  This is critical for our understanding of Bk. V and for evaluating the existential and predicative formulae in 2a and 2b.

What kinds of change are consistent with the existential and predicative models?  It should be clear that

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Robert Elkins - Degrees of Reality in the Republic [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]