Parmenides and a Definition of Truth

In Plato’s writing, Parmenides, Socrates paid a visit to Parmenides and Zeno.  As Zeno was explaining Parmenides’ views to some listeners, Socrates spoke up and presented an alternative to Parmenides’ theory.  Old Parmenides was impressed by Socrates when he came out and listened so he questioned Socrates until Socrates was unable to answer because of how difficult Parmenides’ questions were.

Socrates believed that what made a good deed a good deed was its similarity to the form “goodness.”  What made a hula-hoop circular was its similarity to the form “circularity.”  Parmenides asked Socrates what made a hula-hoop similar to circularity, and, in doing so, Parmenides pointed out the need for an additional form “similarity” to which all similar things had to be similar.  And then a form was needed for being similar to similar things, and so on ad infinitum.

The easiest response to this objection seems, to me, to be that the form “goodness” is not actually similar to good deeds at all.  After all, how can a form which can only exist in a soul be similar at all to good actions?  But Socrates does not agree with this.  The reason I think he doesn’t want to drop “similarity” is because he wants to preserve some correspondence between the lower world of sensation and the higher world of the forms.  Until I got out of the shower this afternoon, I did not see the connection between this story in Plato’s Parmenides and the modern and ancient debate on the nature of truth.  A correspondence theorist would define truth something like:

Truth:  Propositions which correspond to reality

Here is my paraphrase of Parmenides’ argument applied against correspondence theory.  Assume that if one thing corresponds to another, it is also similar to it in some sense.  Thus the man Parmenides corresponds to the man Gordon Clark in that they are similarly men and that they are similarly philosophers, but they need not be similar in weight or in their beliefs.  Now I think I can use “similar” instead of “corresponds.” If we assume that truth consists of propositions which share similarity with reality, we seem to be led to an infinite regress.  If the proposition (P1) “Parmenides is a man” is similar to (R1) Parmenides actually being a man, a new proposition exists.  The proposition

P2:  Parmenides is a man is similar to Parmenides actually being a man.


P2:  P1 is similar to R1

If P2 is true, it must correspond to a reality as well.  This reality (R2) is the reality of P2 being similar to Parmenides is a man actually being similar to Parmenides actually being a man.  This introduces another proposition.

P3:  P2 is similar to R2

And this continues ad infinitum such that there must exist an infinite amount of realities {R}, similarities {S}, and propositions {P} for each truth.


Perhaps this is not a problem.  For whether or not one holds a correspondence theory of truth, he might end up with an infinite amount of true propositions {P}.  For we have:

P1: P

P2: P1 is true

P3: P2 is true


For the coherence theorist and the Scripturalist, this may not be hard to accept, nor particularly hard to refute.  But, depending on what a given correspondence theorist takes to be the nature of similarity and of reality, an infinite amount of similarities {S} and realities {R} may pose a problem.  For example, if a person believes that all reality is spatial, he needs somewhere to put {R} and he needs to decide if {S} and {P} are real or not.

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