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
Summary of existential and predicate models.
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.
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