Book contents
- Frontmatter
- Introduction
- 1 Descartes' life and the development of his philosophy
- 2 Descartes and scholasticism
- 3 The nature of abstract reasoning
- 4 Cartesian metaphysics and the role of the simple natures
- 5 The Cogito and its importance
- 6 The idea of God and the proofs of his existence
- 7 The Cartesian circle
- 8 Cartesian dualism
- 9 Descartes' philosophy of science and the scientific revolution
- 10 Descartes' physics
- 11 Descartes' physiology and its relation to his psychology
- 12 Descartes on thinking with the body
- 13 The reception of Descartes' philosophy
- Bibliography
- Index
3 - The nature of abstract reasoning
philosophical aspects of Descartes’ work in algebra
Published online by Cambridge University Press: 28 May 2006
- Frontmatter
- Introduction
- 1 Descartes' life and the development of his philosophy
- 2 Descartes and scholasticism
- 3 The nature of abstract reasoning
- 4 Cartesian metaphysics and the role of the simple natures
- 5 The Cogito and its importance
- 6 The idea of God and the proofs of his existence
- 7 The Cartesian circle
- 8 Cartesian dualism
- 9 Descartes' philosophy of science and the scientific revolution
- 10 Descartes' physics
- 11 Descartes' physiology and its relation to his psychology
- 12 Descartes on thinking with the body
- 13 The reception of Descartes' philosophy
- Bibliography
- Index
Summary
No one contributed more to the early development of algebra than Descartes. In particular, he was able to unify arithmetic and geometry to a significant extent, by showing their mutual connections in terms of an algebraic notation. This was an achievement that eclipsed his other scientific work, and Descartes believed that algebra could serve as a model for his other enterprises. The connection between algebra and his other scientific work was explored, via a consideration of the question of method, in Descartes' first published work, the Discourse on the Method of rightly conducting one's reason and seeking the truth in the sciences, together with the Optics, the Meteorology and the Geometry which are essays in this method (1637). What we are ostensibly presented with here is a general treatise on method, to which are appended three examples of the method.
- Type
- Chapter
- Information
- The Cambridge Companion to Descartes , pp. 91 - 114Publisher: Cambridge University PressPrint publication year: 1992
- 15
- Cited by