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) |
|---|---|
| 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 |
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ASJC Scopus subject areas
- Arts and Humanities(all)
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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 proceeding › Chapter
}
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.
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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 -