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An Unexplored Aspect of Following a Rule

Driver, Rachael (2020) An Unexplored Aspect of Following a Rule. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Abstract

Though Wittgenstein has been most often identified as opposing Platonism in his writings about mathematics, I argue that Wittgenstein’s radical contextualism about mathematics finds its most natural opponent not in Platonism, but in a variety of formalism. One of Wittgenstein’s obvious formalist targets is his colleague the mathematician G. H. Hardy. If we discard this—still influential—picture of mathematics and replace it with a more nuanced account of mathematical activity as exemplified in the metamathematical thinking of the nineteenth century mathematician Augustus De Morgan, the example of the wayward pupil takes on a different significance. Against a more complex background, the wayward pupil can be reinterpreted as representing an exemplar of mathematical discovery. I consider the example of the nineteenth century engineer Oliver Heaviside whose unconventional approach in mathematics, driven by a need to efficiently elicit results from complex formulae for the purposes of aiding his research in electrical engineering, resulted in extraordinary mathematical advances. Yet, his approach to algebraic manipulation has the aspect of a wayward pupil. The wayward pupil, who may be making an error according to our ordinary criteria of rule-following, may be initiating new and fruitful paths. This possibility is largely unexamined in the larger discussion of Wittgenstein’s remarks on following a rule, and it explains Wittgenstein’s hesitation to label the wayward pupil’s actions straightforwardly incorrect.

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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Driver, Rachaelrachael.e.driver@gmail.comrep350000-0001-7372-5086
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee CoChairRicketts, Thomasricketts@pitt.edu
Committee CoChairWilson, Markmawilson@pitt.edu
Committee MemberBatterman, Robertrbatterm@pitt.edu
Committee MemberGoldfarb, Warrengoldfarb@fas.harvard.edu
Committee MemberShumener, Ericaehs20@pitt.edu
Date: 16 September 2020
Date Type: Publication
Defense Date: 27 July 2020
Approval Date: 16 September 2020
Submission Date: 29 August 2020
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 145
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: Wittgenstein Philosophy of Mathematics
Date Deposited: 16 Sep 2020 13:42
Last Modified: 16 Sep 2020 13:42
URI: http://d-scholarship.pitt.edu/id/eprint/39735

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