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The Psychologistic Foundations of Hume's Critique of Mathematical Philosophy

The Psychologistic Foundations of Hume's Critique of Mathematical Philosophy Hume Studies Volume XXII, Number 1, April 1996, pp. 123-167 WAYNE WAXMAN Nearly every philosopher has encountered positions or arguments that seem fatally flawed yet been at a loss to diagnose the precise causes of the debility. There are cases, too, where a broad consensus exists that something is defective but, even after centuries of trying, no agreement as to why. So, when an author arrives claiming to establish a definitive diagnosis, as James Franklin does in "Achievements and Fallacies in Hume's Account of Infinite Divisibility,"1 one can only respond with hope and anticipation. Alas, once Franklin's case is subjected to scrutiny, most readers will, I believe, conclude that their hopes were misplaced. Nevertheless, its examination offers an excellent opportunity to improve our understanding of why Hume's reasons for denying infinite divisibility seem so uncharacteristically weak, while the source of the apparent infirmity remains so frustratingly elusive. In this paper, I shall advance a new diagnosis, locating the trouble not in Hume's argumentation but in the way readers tend to approach it. The error consists in treating the demonstrations of T I ii as self-contained exercises in philosophy of mathematics: so long as we remain wedded to the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Hume Studies Hume Society

The Psychologistic Foundations of Hume's Critique of Mathematical Philosophy

Hume Studies , Volume 22 (1) – Jan 26, 1996

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Hume Society
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Copyright © Hume Society
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1947-9921
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Abstract

Hume Studies Volume XXII, Number 1, April 1996, pp. 123-167 WAYNE WAXMAN Nearly every philosopher has encountered positions or arguments that seem fatally flawed yet been at a loss to diagnose the precise causes of the debility. There are cases, too, where a broad consensus exists that something is defective but, even after centuries of trying, no agreement as to why. So, when an author arrives claiming to establish a definitive diagnosis, as James Franklin does in "Achievements and Fallacies in Hume's Account of Infinite Divisibility,"1 one can only respond with hope and anticipation. Alas, once Franklin's case is subjected to scrutiny, most readers will, I believe, conclude that their hopes were misplaced. Nevertheless, its examination offers an excellent opportunity to improve our understanding of why Hume's reasons for denying infinite divisibility seem so uncharacteristically weak, while the source of the apparent infirmity remains so frustratingly elusive. In this paper, I shall advance a new diagnosis, locating the trouble not in Hume's argumentation but in the way readers tend to approach it. The error consists in treating the demonstrations of T I ii as self-contained exercises in philosophy of mathematics: so long as we remain wedded to the

Journal

Hume StudiesHume Society

Published: Jan 26, 1996

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