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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.

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    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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    Item Type: University of Pittsburgh ETD
    ETD Committee:
    ETD Committee TypeCommittee MemberEmailORCID
    Committee ChairNorton, John Djdnorton@pitt.edu
    Committee MemberEarman, Johnjearman@pitt.edu
    Committee MemberManders, Kennethmandersk@pitt.edu
    Committee MemberRuetsche, Lauraruetsche@pitt.edu
    Committee MemberWilson, Markmawilson@pitt.edu
    Committee MemberGeroch, Robertgeroch@midway.uchicago.edu
    Title: Problems in Applying Mathematics: On the Inferential and Representational Limits of Mathematics in Physics
    Status: Unpublished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.
    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; The work is available for access worldwide immediately.
    Patent pending: No
    Institution: University of Pittsburgh
    Thesis Type: Doctoral Dissertation
    Refereed: Yes
    Degree: PhD - Doctor of Philosophy
    URN: etd-10292003-081734
    Uncontrolled Keywords: Feynman; Mathematics; Path Integral; Philosophy; Rigor; Unphysical; Unreasonable Effectiveness; Idealizations; Physics
    Schools and Programs: Dietrich School of Arts and Sciences > Philosophy
    Date Deposited: 10 Nov 2011 15:03
    Last Modified: 08 May 2012 11:31
    Other ID: http://etd.library.pitt.edu/ETD/available/etd-10292003-081734/, etd-10292003-081734

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