Lewis Carroll showed that accepting a basic rule of logic needs one more rule, forever
Achilles and the Tortoise agree on two premises: 'if A and B, then Z.' The Tortoise accepts both premises are true but refuses to accept the conclusion Z until Achilles also writes down, as a separate premise, the inference rule itself: that A and B together imply Z. But once that's written down as premise C, the Tortoise asks why accepting A, B, and C together should force Z either, demanding yet another premise. Where does this end?
Reveal the answer
It doesn't end on its own: Carroll's 1895 dialogue shows that logical inference can't be reduced to an endless list of premises, because applying any rule requires an act of inference that no further premise can supply. The paper is read today as an early, precise statement of what's now called the regress problem in the philosophy of logic, distinguishing between accepting propositions and actually following a rule.
— Lewis Carroll, What the Tortoise Said to Achilles — Mind, 1895