What Hume said to the Tortoise

Hume argues that induction cannot be justified to someone who is not already willing to accept induction, and as a result, it cannot be justified at all. In Lewis Carroll's ‘What the Tortoise said to Achilles’ (Citation1895), the Tortoise argues that deduction cannot be justified to someone who is not already willing to accept deduction, and as a result, it cannot be justified at all. In each case, it seems that we require some further premise in order to license the proposed form of inference; but in each case, the appeal to that further premise merely opens up the same sort of inferential gap all over again.Thus far, Hume and the Tortoise might seem like natural allies. However, Hume suggests that, while induction lacks any basis in reason, demonstration—the Humean analogue of deduction—does have such a basis. I examine Hume’s account of the difference between the two cases, and consider how he might reply to Carroll’s ‘paradox of inference’. Hume’s vindication of demonstrative reasoning turns, I suggest, on his understanding of the reciprocal relationship between our powers of conception and the facts about absolute necessity.