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A Formalist Philosophy of Mathematics Part I: Arithmetic

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Abstract

In this paper I present a formalist philosophy mathematics and apply it directly to Arithmetic. I propose that formalists concentrate on presenting compositional truth theories for mathematical languages that ultimately depend on formal methods. I argue that this proposal occupies a lush middle ground between traditional formalism, fictionalism, logicism and realism.

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References

  1. Enderton, H. B., A Mathematical Introduction to Logic, Academic Press, 2 edition, 2001.

  2. Kripke, S., ‘Is there a problem about substitutional quantification?’ in G. Evans and J. McDowell (eds.), Truth and Meaning: Essays in Semantics, Oxford University Press, 1976.

  3. Sainsbury, R. M., Reference without Referents, Oxford University Press, 2005.

  4. van Benthem, J., ‘Higher-order logic’, in D. M. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd Edition, volume 1, Kluwer, 2001, pp. 189–244.

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  1. Department of Philosophy, Kings College London, The Strand, London, England

    Michael Gabbay

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  1. Michael Gabbay
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Correspondence to Michael Gabbay.

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Gabbay, M. A Formalist Philosophy of Mathematics Part I: Arithmetic. Stud Logica 96, 219–238 (2010). https://doi.org/10.1007/s11225-010-9283-1

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  • DOI: https://doi.org/10.1007/s11225-010-9283-1

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