Abstract
The assumptions, mostly borrowed from rationalist metaphysics and epistemology for purposes of indirect proof, are sufficiently unlike David Hume's empiricist stance to lend powerful independent collateral support to his central refutation of infinite divisibility and justification of the theory of sensible extensionless indivisibles in the inkspot argument. The premises Hume introduces for indirect proof against infinitist mathematics and metaphysics include the hypothesis that extension in space or time is infinitely divisible, that only unitary things exist, that whatever is clearly conceivable is possible, and, in the case of the geometry dilemma reconstructed as a reductio, that a classical infinitist Euclidean geometry implying the infinite divisibility of extension provides an adequate idea of exact equality and proportion. The impact of Hume's finitism in mathematics and related disciplines is likely to appear liberating or regressive, depending on one's philosophical temperament.Keywords: classical mathematics; David Hume; epistemology; Euclidean geometry; infinite divisibility; inkspot argument; metaphysics
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