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Problems in Applying Mathematics: On the Inferential and Representational Limits of Mathematics in Physics

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 (Unpublished)

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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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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Davey, Kevinkedst13@pitt.eduKEDST13
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairNorton, John Djdnorton@pitt.eduJDNORTON
Committee MemberEarman, Johnjearman@pitt.eduJEARMAN
Committee MemberManders, Kennethmandersk@pitt.eduMANDERSK
Committee MemberRuetsche, Lauraruetsche@pitt.eduRUETSCHE
Committee MemberWilson, Markmawilson@pitt.eduMAWILSON
Committee MemberGeroch,
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:, etd-10292003-081734
Date Deposited: 10 Nov 2011 20:03
Last Modified: 15 Nov 2016 13:51


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