Abstract
To refute the infinite divisibility of extension, David Hume argues not only that a correct epistemology precludes the idea, but that the concept is internally inconsistent. The importance of Bayle's trilemma to Hume's critique of infinity explains the relation between Hume's central inkspot argument and the reductio proofs. The reductio arguments thereby uphold the inkspot argument in the negative task of refuting the concept of infinite divisibility in Hume's critique. The reductio arguments in Hume's critique help prove the existence of extensionless indivisibles. But only Hume's inkspot experiment establishes extensionless indivisibles more particularly as sensible, phenomenal, or experienceable, rather than ideal, abstract, or mathematical. Hume attributes his second reductio argument to Nicholas de Malezieu. The argument occurs immediately after the first reductio from the addition of infinite parts. Hume regards the argument as Very strong and beautiful.Keywords: Bayle's trilemma; critique of infinity; David Hume; inkspot argument; Nicholas de Malezieu; reductio arguments
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