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.

Downloads

Abstract views: 35

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

Metrics

Downloads

Download data is not yet available.

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.


    Authors who publish with this journal agree to the following terms:
  • Authors retain copyright and grant the journal right of first publication.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
Crossref
Scopus
Google Scholar
Europe PMC