Descartes on mathematical essences

Raffaella de Rosa, Otavio Bueno

Research output: Chapter in Book/Report/Conference proceedingChapter

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 languageEnglish (US)
Title of host publicationPhilosophy of Mathematics
Subtitle of host publicationSet Theory, Measuring Theories, and Nominalism
Publisherde Gruyter
Pages164-182
Number of pages19
ISBN (Electronic)9783110323689
ISBN (Print)3937202528, 9783110323092
DOIs
StatePublished - Jan 1 2013

ASJC Scopus subject areas

  • Arts and Humanities(all)

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  • Cite this

    de Rosa, R., & Bueno, O. (2013). Descartes on mathematical essences. In Philosophy of Mathematics: Set Theory, Measuring Theories, and Nominalism (pp. 164-182). de Gruyter. https://doi.org/10.1515/9783110323689.164