Descartes' Philosophical Grounds for Algebra and Geometry Public Deposited
- Last Modified
- March 20, 2019
- Creator
-
Liu, Cathay Ming Lih
- Affiliation: College of Arts and Sciences, Department of Philosophy
- Abstract
- Though neither Descartes nor Fermat developed analytic geometry as we understand the mathematical discipline today, they each developed a different central feature of it. But history of mathematics has not explained their differences in mathematical aims and practice in terms of philosophical commitments. Generally, Descartes' metaphysics has not played a role in the explication of his mathematical emphasis. While it is undisputed that Descartes placed a lot of emphasis on the geometrical aspect of analytic geometry over the algebraic component, I explain his mathematical practice by appealing to his philosophical views. I argue that Descartes views geometry to be more basic than algebra. Algebra, and its significance, depended on geometrical objects. I have defend this view by appealing to Descartes metaphysical and epistemological commitments, but I also defend this view against a possible alternative interpretation of Descartes' philosophy that would allow algebra not to depend on geometry.
- Date of publication
- August 2008
- DOI
- Resource type
- Rights statement
- In Copyright
- Advisor
- Nelson, Alan Jean
- Language
- Access
- Open access
- Parents:
This work has no parents.
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Descartes philosophical grounds for algebra and geometry | 2019-04-08 | Public |
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