Variations of the Socratic peritrope-- if it is the case that there is no truth, then isn't the very assertion that "there is no truth" itself a truth?!--has been a staple of many formal attacks on relativism. Such a self-referential critique of relativism, I believe, is not conclusive as the same critique can well be deployed against the epistemic positions opposing relativism e.g. absolutism, realism etc. Consider:

Relativism about truth: " A statement is true iff it corresponds to the (epistemic) norms of a given community."

Realism about truth: " A statement is true iff it corresponds to a fact."

The opponents of relativism object, and rightly so, that relativism's truth theory is self-referentially incoherent i.e. in what way is the statement " A statement is true iff it corresponds to the (epistemic) norms of a given community" itself "true"? If the statement, as it asserts, is true only because it somehow corresponds to the "(epistemic) norms of a given community", most probably a community of relativists in this case, then we, the opponents of relativism, need not heed relativism as a serious epistemic position because after all it is true only relative to the relativists' insular self-justifying epistemic norms. If, on the other hand, the statement is true in a non-relative universal way, then the relativist has already refuted himself by asserting an absolutely true statement.

Now, can't exactly the same be said of the realist truth theory? In what way is the statement "A statement is true iff it corresponds to a fact" itself "true"? Is this statement "true" in virtue of its correspondence to a fact? But what chuck of the perceivable space-time does, in fact, testify to the objective truth of this statement?Alternatively, what abstract entities e.g. geometric shapes, numbers, sets, substances etc. might be said to be the truth-makers of the statement in question? The realist truth theory, therefore, is either "true" in virtue of its "correspondence to a fact" of the universe--and there are no such facts;for one thing, if there were, there would have arisen no rational debates about truth to begin with-- or in virtue of it standing in no relation to facts i.e. Reality! in which case the realist has already refuted himself by asserting a non-realistically true statement.

Would you say that the peritrope cuts both ways?

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