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Deflationism and Instrumentalism

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Unifying the Philosophy of Truth

Part of the book series: Logic, Epistemology, and the Unity of Science ((LEUS,volume 36))

Abstract

Deflationist theories of truth have become increasingly popular. In this paper we are going to pursue an instrumentalist reading of deflationism. This reading is particularly interesting considering the role a truth predicate can have in facilitating proofs. Based on an instrumentalist conception we will provide a new answer to one of the arguments challenging deflationism.

Thanks to the organizers of the conference ‘Axiomatic Theories of Truth’ at Oxford for the invitation and to the members of the MCMP and participants of the Plurals, Predicates and Paradox Seminar for valuable comments, especially Johannes Stern, Sean Walsh and Florian Steinberger. The research was carried out in the project ‘Syntaktische Ansätze für interagierende Modalitäten’ financed by the DFG. For their financial support I wanted to thank the DFG and the Alexander von Humboldt foundation.

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Notes

  1. 1.

    See for instance Horsten (1995), Shapiro (1998) and Ketland (1999).

  2. 2.

    Shapiro (1998) and Ketland (1999).

  3. 3.

    See for example Halbach (1999).

  4. 4.

    For example Hilbert (1923,1926).

  5. 5.

    For example Hilbert (1926, p. 179).

  6. 6.

    For a different interpretation see Detlefsen (1990).

  7. 7.

    See also Ignjatović (1994). Another line of reasoning is given in Niebergall and Schirn (2002).

  8. 8.

    Compare Smoryński (1977).

  9. 9.

    Smoryński (1977, p. 824).

  10. 10.

    Compare Caldon and Ignjatović (2005, p. 7).

  11. 11.

    See for example Feferman (2000).

  12. 12.

    The line taken in this paper is only one of many possible connections. As was pointed out by one of the referees Reinhardt (1986) had an interesting proposal of connecting theories of truth and Hilbert’s program. Reinhardt compared Hilbert’s ideal part with meaningful, but nonsignificant sentences, i.e. sentences such as the liar that are wellformed formulas but are neither true nor false. Reinhardt proposed to use the theory \(\mathrm{IKF}\), which is the inner logic of \(\mathrm{KF}\) as the real part. Reinhardt’s proposal has some problems that were pointed out by Halbach and Horsten (2006). They show that many derivations of significant statements in \(\mathrm{IKF}\) necessarily contain nonsignificant statements.

  13. 13.

    Compare Hilbert (1926, p. 175).

  14. 14.

    Horsten (2011) already suggested connections of truth and inferentialism in the context of deflationism.

  15. 15.

    Caldon and Ignjatović (2005) combine mathematical instrumentalism and speed-up.

  16. 16.

    Also \(\mathrm{KF}_t\) and \(\mathrm{CT}{upharpoonright}\) + ‘all axioms of \(\mathrm{PA}\) are true’, are viable candidates.

  17. 17.

    For details see Fischer (2014).

  18. 18.

    Under the condition that the theory of truth satisfies some minimal criteria, such as containing all T-sentences for the arithmetical language.

  19. 19.

    See Artemov (2001, p. 6).

  20. 20.

    Compare ‘Ein formalisierter Beweis ist … ein konkreter und überblickbarer Gegenstand’ Hilbert (1926, p. 179).

  21. 21.

    For a proof see Fischer(2014).

  22. 22.

    See Guaspari and Solovay (1979, p. 83).

  23. 23.

    See Guaspari and Solovay (1979).

  24. 24.

    \(\Sigma_0^{exp}\) allows only bounded quantifiers but the the exponentiation function. By Craig’s theorem we can find for a deductively closed set of sentences T, which is \(\Sigma_1\), a \(\Sigma_0^{exp}\) set of axioms t, such that the deductive closure of t is T.

  25. 25.

    See Hájek and Pudlák (1993, Chap. III. 3)

  26. 26.

    See Hájek and Pudlák (1993, Chap. III. 3).

  27. 27.

    See Hájek and Pudlák (1993, Chap. III. 3).

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Authors and Affiliations

  1. MCMP, LMU-Munich, Germany

    Martin Fischer

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  1. Martin Fischer
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Correspondence to Martin Fischer .

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Editors and Affiliations

  1. Philosophy, ILLC & AUC - University of Amsterdam, Amsterdam, The Netherlands

    Theodora Achourioti

  2. PHIER, Université Blaise Pascal, Clermont Ferrrand, France

    Henri Galinon

  3. Lògica, Història i Filosofia de la Ciència, Universitat de Barcelona, Barcelona, Barcelona, Spain

    José Martínez Fernández

  4. Department of Mathematics and Department of Philosophy, University of Bristol, Bristol, United Kingdom

    Kentaro Fujimoto

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Fischer, M. (2015). Deflationism and Instrumentalism. In: Achourioti, T., Galinon, H., Martínez Fernández, J., Fujimoto, K. (eds) Unifying the Philosophy of Truth. Logic, Epistemology, and the Unity of Science, vol 36. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9673-6_14

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