Abstract
Descartes seems to hold two inconsistent accounts of the ontological status of mathematical essences. Meditation Five apparently develops a platonist view about such essences, while the Principles seems to advocate some form of “conceptualism”. We argue that Descartes was neither a platonist nor a conceptualist. Crucial to our interpretation is Descartes’ dispositional nativism. We contend that his doctrine of innate ideas allows him to endorse a hybrid view which avoids the drawbacks of Gassendi’s conceptualism without facing the difficulties of platonism. We call this hybrid view “quasi-platonism.” Our interpretation explains Descartes’ account of the nature of mathematical essences, dissolves the tension between the two texts, and highlights the benefits of Descartes’ view.
Original language | English (US) |
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Title of host publication | Philosophy of Mathematics |
Subtitle of host publication | Set Theory, Measuring Theories, and Nominalism |
Publisher | de Gruyter |
Pages | 164-182 |
Number of pages | 19 |
ISBN (Electronic) | 9783110323689 |
ISBN (Print) | 3937202528, 9783110323092 |
DOIs | |
State | Published - Jan 1 2013 |
ASJC Scopus subject areas
- Arts and Humanities(all)