The project of constructing a complete system of knowledge---a system capable of integrating all that is and could possibly be known---was common to many early-modern philosophers and was championed with particular alacrity by René Descartes. The inspiration for this project often came from mathematics in general and from geometry in particular: Just as propositions were ordered in a geometrical demonstration, the argument went, so should propositions be ordered in an overall system of knowledge. Science, it was thought, had to proceed `more geometrico'.
I offer a new interpretation of `science emph{more geometrico}' based on an analysis of the explanatory forms used in certain branches of geometry. These branches were optics, astronomy, and mechanics; the so-called subalternate, subordinate, or mixed-mathematical sciences. In Part I, I investigate the nature of the mixed-mathematical sciences according to Aristotle and some `liberal Jesuit' scholastic-Aristotelians. In Part II, the heart of the work, I analyze the metaphysics and physics of Descartes' "Principles of Philosophy" (1644, 1647) in light of the findings of Part I and an example from Galileo. I conclude by arguing that we must broaden our understanding of the early-modern conception of `science more geometrico' to include concepts taken from the mixed-mathematical sciences. These render the geometrical manner more flexible than previously thought.
| Identifer | oai:union.ndltd.org:PITT/oai:PITTETD:etd-03092008-215336 |
| Date | 10 June 2008 |
| Creators | Biener, Zvi |
| Contributors | J. E. McGuire, Paolo Palmieri, Peter Machamer, James G. Lennox, Daniel Garber |
| Publisher | University of Pittsburgh |
| Source Sets | University of Pittsburgh |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.library.pitt.edu/ETD/available/etd-03092008-215336/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to University of Pittsburgh or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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