On the Compatibility between Euclidean Geometry and Hume's Denial of Infinite Divisibility

Hume Studies 34 (2):231-244 (2010)
Abstract
In the Treatise, David Hume denies the thesis that extension is infinitely divisible, even though it can be derived as a theorem of Euclidean geometry. This clearly shows that he rejects some of the theorems of Euclidean geometry. What is less clear is the extent to which he thinks geometry needs to be revised. It has been argued that Hume's rejection of infinite divisibility entails that most of the familiar theorems of Euclidean geometry, including the Pythagorean theorem and the bisection theorem, are false, a view that is normally associated with Berkeley's earlier writings.I argue that Hume's denial of infinite divisibility is not incompatible with the Pythagorean theorem and other central theorems of ..
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Emil Badici (2011). Standards of Equality and Hume's View of Geometry. Pacific Philosophical Quarterly 92 (4):448-467.
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