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

Fingerprint

Essence
Platonism
Conceptualism
Platonist
Conceptualist
Innate Ideas
Doctrine
Nativism
Ontological
Meditation

ASJC Scopus subject areas

  • Arts and Humanities(all)

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

Descartes on mathematical essences. / de Rosa, Raffaella; Bueno, Otavio.

Philosophy of Mathematics: Set Theory, Measuring Theories, and Nominalism. de Gruyter, 2013. p. 164-182.

Research output: Chapter in Book/Report/Conference proceedingChapter

de Rosa, R & Bueno, O 2013, Descartes on mathematical essences. in Philosophy of Mathematics: Set Theory, Measuring Theories, and Nominalism. de Gruyter, pp. 164-182. https://doi.org/10.1515/9783110323689.164
de Rosa R, Bueno O. Descartes on mathematical essences. In Philosophy of Mathematics: Set Theory, Measuring Theories, and Nominalism. de Gruyter. 2013. p. 164-182 https://doi.org/10.1515/9783110323689.164
de Rosa, Raffaella ; Bueno, Otavio. / Descartes on mathematical essences. Philosophy of Mathematics: Set Theory, Measuring Theories, and Nominalism. de Gruyter, 2013. pp. 164-182
@inbook{1847898f5e5244549cbb3a21ba2068bd,
title = "Descartes on mathematical essences",
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.",
author = "{de Rosa}, Raffaella and Otavio Bueno",
year = "2013",
month = "1",
day = "1",
doi = "10.1515/9783110323689.164",
language = "English (US)",
isbn = "3937202528",
pages = "164--182",
booktitle = "Philosophy of Mathematics",
publisher = "de Gruyter",
address = "Germany",

}

TY - CHAP

T1 - Descartes on mathematical essences

AU - de Rosa, Raffaella

AU - Bueno, Otavio

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85064842389&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064842389&partnerID=8YFLogxK

U2 - 10.1515/9783110323689.164

DO - 10.1515/9783110323689.164

M3 - Chapter

SN - 3937202528

SN - 9783110323092

SP - 164

EP - 182

BT - Philosophy of Mathematics

PB - de Gruyter

ER -