A liar’s paradox

I will hereby argue that I am the Pope. Consider the following sentence:

If this sentence is true, then I am the Pope.

It is an implication, i.e. a sentence of the form [tex](A\to B)[/tex], where A is “this sentence is true” and B is “I am the Pope”. If we check that whenever A (premise) is true, also B (conclusion) is true, then we have checked that [tex](A\to B)[/tex] is true. So suppose that A is true, i.e. the sentence is true. Because the sentence is true, the implication is also true, so B, the conclusion, is true. So we have verified that [tex](A\to B)[/tex] is true. But the sentence is [tex](A\to B)[/tex], so the premise of the sentence A as well as the sentence [tex](A\to B)[/tex] are both true. This implies that B is true.

Hence I am the Pope!

About Vadim Kulikov

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