Hilbert's objectivity

Citation data:

Historia Mathematica, ISSN: 0315-0860, Vol: 41, Issue: 2, Page: 188-203

Publication Year:
2014
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Repository URL:
http://philsci-archive.pitt.edu/id/eprint/10607
DOI:
10.1016/j.hm.2014.01.002
Author(s):
Lydia Patton
Publisher(s):
Elsevier BV, Elsevier
Tags:
Arts and Humanities, Mathematics
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article description
Detlefsen (1986) reads Hilbert's program as a sophisticated defense of instrumentalism, but Feferman (1998) has it that Hilbert's program leaves significant ontological questions unanswered. One such question is of the reference of individual number terms. Hilbert's use of admittedly “meaningless” signs for numbers and formulae appears to impair his ability to establish the reference of mathematical terms and the content of mathematical propositions ( Weyl, 2009/1949; Kitcher, 1976 ). The paper traces the history and context of Hilbert's reasoning about signs, which illuminates Hilbert's account of mathematical objectivity, axiomatics, idealization, and consistency.

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