Type of Document Dissertation Author Davey, Kevin Author's Email Address kedst13@pitt.edu URN etd-10292003-081734 Title Problems in Applying Mathematics: On the Inferential and Representational Limits of Mathematics in Physics Degree Doctor of Philosophy Program Philosophy School School of Arts and Sciences Advisory Committee
Advisor Name Title John Norton Committee Chair John Earman Committee Member Kenneth Manders Committee Member Laura Ruetsche Committee Member Mark Wilson Committee Member Robert Geroch Committee Member Keywords
- Path Integral
- Rigor
- Idealizations
- Feynman
- Unphysical
- Unreasonable Effectiveness
- Philosophy
- Physics
- Mathematics
Date of Defense 2003-10-24 Availability unrestricted Abstract It is often supposed that we can use mathematics to capture the time evolution of any physical system. By this, I mean that we can capture the basic truths about the time evolution of a physical system with a set of mathematical assertions, which can then be used as premises in arbitrary mathematical arguments to deduce more complex properties of the system.I would like to argue that this picture of the role of mathematics in physics is incorrect. Specifically, I shall assert:
The Deduction Failure Thesis: Bodies of knowledge in physics are generally not closed under otherwise valid mathematical argument forms.
The Representation Failure Thesis: We cannot assume that the state of any system, together with its fundamental laws, can be captured by some set of mathematical assertions or equations. In fact, it is more likely that the world is not representable by a set of mathematical assertions or equations than that it is.
The dissertation largely consists of arguments for these two theses.
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