Davey, Kevin
(2004)
Problems in Applying Mathematics: On the Inferential and Representational Limits of Mathematics in Physics.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
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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Details
Item Type: 
University of Pittsburgh ETD

Status: 
Unpublished 
Creators/Authors: 

ETD Committee: 

Date: 
16 January 2004 
Date Type: 
Completion 
Defense Date: 
24 October 2003 
Approval Date: 
16 January 2004 
Submission Date: 
29 October 2003 
Access Restriction: 
No restriction; Release the ETD for access worldwide immediately. 
Institution: 
University of Pittsburgh 
Schools and Programs: 
Dietrich School of Arts and Sciences > Philosophy 
Degree: 
PhD  Doctor of Philosophy 
Thesis Type: 
Doctoral Dissertation 
Refereed: 
Yes 
Uncontrolled Keywords: 
Feynman; Mathematics; Path Integral; Philosophy; Rigor; Unphysical; Unreasonable Effectiveness; Idealizations; Physics 
Other ID: 
http://etd.library.pitt.edu/ETD/available/etd10292003081734/, etd10292003081734 
Date Deposited: 
10 Nov 2011 20:03 
Last Modified: 
15 Nov 2016 13:51 
URI: 
http://dscholarship.pitt.edu/id/eprint/9534 
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