It is now commonly accepted that any adequate history of late nineteenth and early twentieth century philosophy - and thus of the origins of analytic philosophy - must take seriously the role of Neo-Kantianism and Kant interpretation in the period. My dissertation is a contribution to our understanding of this interesting but poorly understood stage in the history of philosophy.
Kant's theory of the concepts, postulates, and proofs of geometry was informed by philosophical reflection on diagram-based geometry in the Greek synthetic tradition. However, even before the widespread acceptance of non-Euclidean geometry, the projective revolution in nineteenth century geometry eliminated diagrams from proofs and introduced "ideal" elements that could not be given a straightforward interpretation in empirical space.
A Kantian like the very early Russell felt forced to regard the ideal elements as convenient fictions. The Marburg Neo-Kantians—the philosophical school that included Ernst Cassirer (1874-1945)—thought that philosophy, as "transcendental logic," needed to take the results of established pure mathematics as a "fact," not a fiction.
Cassirer therefore updates Kant by rejecting the "Transcendental Aesthetic" and by using elements in Richard Dedekind's foundations of arithmetic to rework Kant's idea that the geometrical method is the "construction of concepts". He further argues that geometry is "synthetic" because it progresses when mathematicians introduce new structures (like the complex projective plane) that are not contained in the old structures, but unify them under a new point-of-view.
This new "Kantian" theory of modern mathematics, Cassirer argues, is inconsistent with the traditional theory of concept formation by abstraction. Drawing on earlier Neo-Kantian interpretations, Cassirer argues that Kant's theory of concepts as rules undermines the traditional theory of concept formation and gives a "transcendental" defense of the new logic of Frege and Russell. (In an appendix, I discuss the contemporaneous accounts of concept formation in Gottlob Frege and Hermann Lotze.)
| Identifer | oai:union.ndltd.org:PITT/oai:PITTETD:etd-08232007-132755 |
| Date | 24 January 2008 |
| Creators | Heis, Jeremy Richard |
| Contributors | Mark Wilson, Jeremy Avigad, Stephen Engstrom, Anil Gupta, Kenneth Manders, Thomas Ricketts |
| 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-08232007-132755/ |
| 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. |
Page generated in 0.0019 seconds