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Descartes on Mathematical Reasoning and the Truth Principle
University of Southern California, Trousdale Parkway, Los Angeles, CA, USA
- 1 University of Southern California, Trousdale Parkway, Los Angeles, CA, USA
Open Journal of Philosophy·Volume 10 (2020)·Pages 388–410·Published 23 June 2020·DOI10.4236/ojpp.2020.103026
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Abstract
The main purpose of this paper is to examine and assess the plausibility of Descartes’ thesis that it is by mathematical reasoning that we ultimately justify the Truth Principle, which is a metaphysical claim. Drawing upon contemporary logic and philosophy of mathematics, the paper argues that Descartes’ understanding of mathematical reasoning, especially concerning infinity, enables him to justifiably conclude that the Truth Principle is indubitable.
KeywordsTruthReasoningInfinityNatural Light
- Arnauld, A. (1641). Fourth Set of Objections. In J. Cottingham et al. (Eds.), The Philosophical Writings of Descartes (Vol. II, (1984), pp. 138-153). Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9780511818998.019
- Arnauld, A., & Nicole, P. (1683). La logique ou l’art de pensser. In A. Antoine, P. Nicole, & J. Buroker (Trans. and Eds.), Logic or the Art of Thinking (5nd ed., p. 94f). Cambridge: Cambridge University Press.
- Ayer (1956). I Think, Therefore I Am. In W. Doney (Ed.), Descartes: A Collection of Critical Essays (pp. 81-87 (1967)). New York: Doubleday & Company. (Reprinted From: Ayer, A.J., The Problem of Knowledge, New York, St. Martin’s Press, Inc., pp. 45-54)
- Beth, E. (1965). The Foundations of Mathematics (2nd ed., pp. 510-513). Amsterdam: North-Holland Publishing Co.
- Burman, F. (1648). Conversation with Burman. In J. Cottingham (Trans. and Ed.), Descartes’ Conversation with Burman, 1976 (pp. xif, 47f.). Oxford: Clarendon Press.
- Cottingham, J. (Trans. and Ed.) (1976). Descartes’ Conversation with Burman (pp. xif, 47f). Oxford: Clarendon Press.
- Cottingham, J. et al. (1984). The Philosophical Writings of Descartes (Vol. I, pp. 111-151, 192-193). Cambridge: Cambridge University Press.
- Curley, E. (1986). Analysis in the Meditations: The Quest for Clear and Distinct Ideas. In A. Rorty (Ed.), Essays on Descartes’ Meditations (pp. 153-176). Berkeley, CA: University of California Press. https://doi.org/10.1525/9780520907836-010
- Descartes, R. (1637, 1984). Discourse on Method. In J. Cottingham et al. (Eds.), The Philosophical Writings of Descartes (Vol. I, pp. 111-151). Cambridge: Cambridge University Press.
- Descartes, R. (1641, 1984a). Meditations on First Philosophy. In J. Cottingham et al. (Eds.), The Philosophical Writings of Descartes (Vol. I, pp. 3-62). Cambridge: Cambridge University Press.
- Descartes, R. (1641a, 1984a). Second Set of Replies. In J. Cottingham et al. (Eds.), The Philosophical Writings of Descartes (Vol. II, pp. 87-92). Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9780511818998.016
- Descartes, R. (1644, 1984). Principles of Philosophy. In J. Cottingham et al. (Eds.), The Philosophical Writings of Descartes (Vol. I, pp. 193-292). Cambridge: Cambridge University Press.
- Dreher, J. (2017). The Circle, from Descartes Point of View. Open Journal of Philosophy, 7, 202-216.