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.
References
[1]
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
[2]
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.
[3]
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)
[4]
Beth, E. (1965). The Foundations of Mathematics (2nd ed., pp. 510-513). Amsterdam: North-Holland Publishing Co.
[5]
Burman, F. (1648). Conversation with Burman. In J. Cottingham (Trans. and Ed.), Descartes’ Conversation with Burman, 1976 (pp. xif, 47f.). Oxford: Clarendon Press.
[6]
Cottingham, J. (Trans. and Ed.) (1976). Descartes’ Conversation with Burman (pp. xif, 47f). Oxford: Clarendon Press.
[7]
Cottingham, J. et al. (1984). The Philosophical Writings of Descartes (Vol. I, pp. 111-151, 192-193). Cambridge: Cambridge University Press.
[8]
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
[9]
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.
[10]
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.
[11]
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
[12]
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.
[13]
Dreher, J. (2017). The Circle, from Descartes Point of View. Open Journal of Philosophy, 7, 202-216.
[14]
Gassendi, P. (1641, 1984a). Fifth Set of Objections. Second Set of Replies. In J. Cottingham et al. (Eds.), The Philosophical Writings of Descartes (Vol. II, pp. 199ff, 251-257). Cambridge: Cambridge University Press.
[15]
Hintikka, J. (1962). Cogito Ergo Sum: Inference or Performance. The Philosophical Review, Vol. LXXI, No. 1. In W. Doney (Ed.), Descartes: A Collection of Critical Essays (pp. 108-130). New York: Doubleday & Company.
[16]
Hobbes, T. (1641, 1984a). The Third Set of Objections. In J. Cottingham et al. (Eds.), The Philosophical Writings of Descartes (Vol. II, pp. 121-137). Cambridge: Cambridge University Press.
[17]
Jenkinson, A. J. (trans.) (1966). Aristotle Stagiritis Son of Nicomachus. In R. McKeon (Ed.), Prior Analytics (c.350 BCE). The Basic Works of Aristotle (pp. 65-109). New York: Random House.
[18]
Pascal, B. (1670). Pensées. In P. Blaise, & H. Levi (Trans., Eds.), Pensées and Other Writings (pp. 5-181, (1995), pp. 1-181). New York: Oxford University Press.
[19]
Russell, B. (1919). Introduction to Mathematical Philosophy (pp. 63-96). London: George Allen and Unwin, Ltd.
[20]
von Lindemann, F. (1882). Uber die Zahl π. Mathematische Annalen, 20, 213-225.
https://doi.org/10.1007/BF01446522
[21]
Williams, B. (1978). “The Certainty of the Cogito”. In Doney, Willis, ed., Descartes: A Collection of Critical Essays, (1967), Garden City, New York, Anchor, Doubleday & Company, pp. 88-107.
[22]
Wittgenstein, L. (1929). Lecture on Ethics. In S. Cahn, & J. Haber (Eds.), Twentieth Century Ethical Theory 1995 (pp. 81-87). Englewood Cliffs, NJ: Prentice Hall.
