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Infinite Liar in a (Modal) Finitistic Setting

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Logic and Its Applications (ICLA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11600))

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Abstract

Yablo’s paradox results in a set of formulas which (with local disquotation in the background) turns out consistent, but \(\omega \)-inconsistent. Adding either uniform disquotation or the \(\omega \)-rule results in inconsistency. One might think that it doesn’t arise in finitary contexts. We study whether it does. It turns out that the issue turns on how the finitistic approach is formalized.

This research has been supported by the FWO postdoctoral research grant and the National Science Centre SONATA BIS research grant number 2016/22/E/HS1/00304. The second author has been supported by the National Science Centre OPUS research grant number 2014/13/B/HS1/02892.

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Notes

  1. 1.

    The methods we develop here – especially the semantics of quantifiers in FM-domains – is similar to the framework of modal potentialism developed independently in [2].

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Author information

Authors and Affiliations

  1. University of Warsaw, Warsaw, Poland

    Michał Tomasz Godziszewski

  2. University of Gdańsk, Gdańsk, Poland

    Rafal Urbaniak

  3. Ghent University, Ghent, Belgium

    Rafal Urbaniak

Authors
  1. Michał Tomasz Godziszewski
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  2. Rafal Urbaniak
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Corresponding author

Correspondence to Rafal Urbaniak .

Editor information

Editors and Affiliations

  1. Indian Institute of Technology Indore, Madhya Pradesh, India

    Md. Aquil Khan

  2. Indian Institute of Technology Goa, Goa, India

    Amaldev Manuel

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Godziszewski, M.T., Urbaniak, R. (2019). Infinite Liar in a (Modal) Finitistic Setting. In: Khan, M., Manuel, A. (eds) Logic and Its Applications. ICLA 2019. Lecture Notes in Computer Science(), vol 11600. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-58771-3_3

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  • DOI: https://doi.org/10.1007/978-3-662-58771-3_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-58770-6

  • Online ISBN: 978-3-662-58771-3

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