A tortoise agrees to every premise of an argument but won't accept its conclusion. Why?
Achilles wants the Tortoise to accept a basic logical conclusion, Z, from two premises, A and B. The Tortoise happily accepts A and B — but refuses Z unless Achilles also spells out the rule 'if A and B, then Z' as an extra premise, C. Once C is granted, the Tortoise still won't accept Z unless Achilles adds yet another premise linking A, B, and C to Z. Does this ever end?
Reveal the answer
No — the chain never terminates. However many explicit premises Achilles writes down, the Tortoise can always demand one more, generating an infinite regress. Lewis Carroll's 1895 puzzle shows that applying a rule of inference (like modus ponens) isn't itself just another premise you can state — at some point you have to actually perform the inference, not add more things to believe.
— Lewis Carroll, What the Tortoise Said to Achilles — Mind, 1895