David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Philosophical Review 97 (1):47-69 (1988)
Since both berkeley and hume are committed to the view that a line is composed of finitely many fundamental parts, They must find responses to the standard geometrical proofs of infinite divisibility. They both repeat traditional arguments intended to show that infinite divisibility leads to absurdities, E.G., That all lines would be infinite in length, That all lines would have the same length, Etc. In each case, Their arguments rest upon a misunderstanding of the concept of a limit, And thus are not successful. Berkeley, However, Adds a further ingenious argument to the effect that the standard geometrical proofs of infinite divisibility misread the unlimited representational capacity of geometrical diagrams as a substantive feature of the objects that these diagrams represent. The article concludes that berkeley is right on this matter, And that the traditional proofs of infinite divisibility do not show what they are intended to show
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Emil Badici (2011). Standards of Equality and Hume's View of Geometry. Pacific Philosophical Quarterly 92 (4):448-467.
Stefan Storrie (2012). What is It the Unbodied Spirit Cannot Do? Berkeley and Barrow on the Nature of Geometrical Construction. British Journal for the History of Philosophy 20 (2):249-268.
Dale Jacquette (1995). Hume's Aesthetic Psychology of Distance, Greatness and the Sublime. British Journal for the History of Philosophy 3 (1):89 – 112.
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