Antique origins of the relations between Modern philosophy and mathematics

Authors

  • Kostiantyn Uzbek Mykhailo Tuhan-Baranovskyi Donetsk National University of Economics and Trade

DOI:

https://doi.org/10.31649/sent05.01.044

Keywords:

method, rationalism , mathesis universalis , analytic geometry

Abstract

The article discusses the ancient origins of the mathematical foundations of Cartesian rationalism. The author concludes that Cartesian project of «mathesis universalis»  synthesised the ideas of many ancient thinkers. In particular, the idea of coordinates comes from Apollonius, the use of motion in mathematics from Archimedes, and the concept of modelling mathematical objects (Cartesius uses geometric shapes) from the Pythagoreans. The author, while acknowledging the conventionality of these parallels, concludes that without the ancient union of philosophy and mathematics, this unity could not have developed in the modern era.

References

Aristotle. (1978). Posterior Analytics. [In Russian]. In Aristotle, Works in 4 vol. (Vol. 2, pp. 255-346). Moscow: Mysl.

Aronov, R. A. (1996). Pythagorean Syndrome in Science and Philosophy [In Russian]. Voprosy philosophii, (4), 134-146.

Bacon, F. (1938). New Organon. [In Russian]. Moscow: Sotsekzis.

Descartes, R. (1938). Geometry. [In Russian]. Moscow & Leningrad: Gostekhizdat.

Descartes, R. (1989). Discourse on Method. [In Russian]. In R. Descartes, Works in 2 vol. (Vol. 1, pp. 250-298). Moscow: Mysl.

Descartes, R. (1989). Principles of Philosophy. [In Russian]. In R. Descartes, Works in 2 vol. (Vol. 1, pp. 298-422). Moscow: Mysl.

Descartes, R. (1989). Rules for the Direction of the Mind. [In Russian]. In R. Descartes, Works in 2 vol. (Vol. 2, pp. 77-153). Moscow: Mysl.

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Published

2002-04-22

How to Cite

Uzbek, K. (2002). Antique origins of the relations between Modern philosophy and mathematics. Sententiae, 5(1), 44–50. https://doi.org/10.31649/sent05.01.044

Issue

Vol. 5 No. 1 (2002): SENTENTIAE

Section

ARTICLES

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