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Hilbert's objectivity

Patton, Lydia (2014) Hilbert's objectivity. Historia Mathematica. ISSN 03150860

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Abstract

Abstract

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 and 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.

Resumi

Detlefsen (1986) legge il programma di Hilbert come una sofisticata difesa dello strumentalismo, ma Feferman (1998) sostiene che il programma di Hilbert lascia senza risposta alcune significative questioni ontologiche. Una fra queste è il riferimento dei termini individuali numerici. L'impiego da parte di Hilbert di simboli per i numeri e formule per la matematica finistista esplicitamente “privi di senso,” sembra impedire la possibilitá di stabilire un riferimento per i termini matematici e un contenuto per le proposizioni (Weyl, 2009/1949 and Kitcher, 1976). Questo articolo ripercorre la storia e il contesto del pensiero di Hilbert concernente i simboli; tale contesto getta luce sulla concezione Hilbertiana dell'oggettivitá matematica.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Patton, Lydia
Keywords: hilbert, formalism, instrumentalism, objectivity, realism, axiomatics
Subjects: Specific Sciences > Mathematics
General Issues > Operationalism/Instrumentalism
General Issues > Realism/Anti-realism
Depositing User: Dr Lydia Patton
Date Deposited: 11 Apr 2014 13:17
Last Modified: 11 Apr 2014 13:17
Item ID: 10607
Journal or Publication Title: Historia Mathematica
Publisher: Elsevier
Official URL: http://dx.doi.org/10.1016/j.hm.2014.01.002
DOI or Unique Handle: https://doi.org/10.1016/j.hm.2014.01.002
Subjects: Specific Sciences > Mathematics
General Issues > Operationalism/Instrumentalism
General Issues > Realism/Anti-realism
Date: 2014
ISSN: 03150860
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/10607

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