In his Soliloquies Augustine offers an argument which may be paraphrased like this:

Suppose there are no truths. Then it’s a truth that there are no truths. So there’s at least one truth. So there’s at least one truth.

That nice piece of reasoning involves something which the Greeks called a περιτροπή or reversal. There are dozens of things like it in ancient philosophical texts. Scholars tend to refer to them as self-refutation arguments, and so Luca Castagnoli says of his book about reversals that it ‘aims to provide a comprehensive survey and analysis of the history and logic of ancient self-refutation’ from the beginning to the age of Augustine (p. 2). The survey, which considers more than a hundred texts, divides into three parts: part one deals with arguments which turn about the notions of truth and falsehood; part two discusses ‘pragmatic, ad hominem and...

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