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Reasoning about Arbitrary Natural Numbers from a Carnapian Perspective

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Abstract

Inspired by Kit Fine’s theory of arbitrary objects, we explore some ways in which the generic structure of the natural numbers can be presented. Following a suggestion of Saul Kripke’s, we discuss how basic facts and questions about this generic structure can be expressed in the framework of Carnapian quantified modal logic.

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Acknowledgements

We want to thank audience of the Philosophy of Mathematics Seminar at the University of Oxford (in particular, Timothy Williamson), Jan Heylen, Philip Welch and Hazel Brickhill for providing constructive comments. The work was partially carried out during S. O. Speranski’s visit to the Department of Philosophy at the University of Bristol, which took place in Summer 2017 and was supported by an IAS Benjamin Meaker Visiting Professorship.

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Authors and Affiliations

  1. University of Bristol, Cotham House, Cotham Hill, Bristol, BS6 6JL, UK

    Leon Horsten

  2. St. Petersburg State University, 29B Line 14th, Vasilyevsky Island, Saint Petersburg, 199178, Russia

    Stanislav O. Speranski

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  1. Leon Horsten
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  2. Stanislav O. Speranski
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Correspondence to Stanislav O. Speranski.

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Horsten, L., Speranski, S.O. Reasoning about Arbitrary Natural Numbers from a Carnapian Perspective. J Philos Logic 48, 685–707 (2019). https://doi.org/10.1007/s10992-018-9490-1

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  • DOI: https://doi.org/10.1007/s10992-018-9490-1

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