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Truth Meets Vagueness. Unifying the Semantic and the Soritical Paradoxes

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  • Published: 09 October 2023
  • Volume 52, pages 1637–1671, (2023)
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Journal of Philosophical Logic Aims and scope Submit manuscript
Truth Meets Vagueness. Unifying the Semantic and the Soritical Paradoxes
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  • Riccardo Bruni  ORCID: orcid.org/0000-0003-2695-00581 &
  • Lorenzo Rossi  ORCID: orcid.org/0000-0002-1932-54842 

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Abstract

Semantic and soritical paradoxes display remarkable family resemblances. For one thing, several non-classical logics have been independently applied to both kinds of paradoxes. For another, revenge paradoxes and higher-order vagueness—among the most serious problems targeting solutions to semantic and soritical paradoxes—exhibit a rather similar dynamics. Some authors have taken these facts to suggest that truth and vagueness require a unified logical framework, or perhaps that the truth predicate is itself vague. However, a common core of semantic and soritical paradoxes has not been identified yet, and no explanation of their relationships has been provided. Here we aim at filling this lacuna, in the framework of many-valued logics. We provide a unified diagnosis of semantic and soritical paradoxes, identifying their source in a general form of indiscernibility. We then develop our diagnosis into a theory of paradoxicality, which formalizes both semantic and soritical paradoxes as arguments involving specific instances of our generalized indiscernibility principle, and correctly predicts which logics can non-trivially solve them.

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Acknowledgements

The authors would like to thank two anonymous referees for their useful comments over a previous version of the paper. They also wish to express their gratitude to Paul Égré and David Ripley, for commenting on an early version of the paper, and to Damian Szmuc for his feedback and his important suggestion to extend our unification proposal from revenge and higher-order vagueness to ‘ordinary’ semantic and soritical paradoxes. Finally, they would like to thank Kentaro Fujimoto, Simone Picenni, and Johannes Stern for a useful discussion concerning the reduction of the T-Schema to indiscernibility.

Funding

Open access funding provided by Università degli Studi di Firenze within the CRUI-CARE Agreement. For Riccardo Bruni: this work was supported by the Italian Ministry of Education, University and Research through the PRIN 2017 program “The Manifest Image and the Scientific Image” prot. 2017ZNWW7F_004.

For Lorenzo Rossi: this work was supported by the Research Grant MSCA Staff Exchanges 2021 (HORIZON-MSCA-2021-SE-01) no. 1010866295 “PLEXUS: Philosophical, Logical, and Experimental Routes to Substructurality”.

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  1. Dipartimento di Lettere e Filosofia (DILEF), Università degli Studi di Firenze, via della Pergola 60, 50134 Firenze, Italy

    Riccardo Bruni

  2. Dipartimento di Filosofia e Scienze dell’Educazione (DFE) and Center for Logic, Language, and Cognition (LLC), Università degli Studi di Torino, via Sant’Ottavio 20, Palazzo Nuovo, 10124, Torino, Italy

    Lorenzo Rossi

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Correspondence to Riccardo Bruni.

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Bruni, R., Rossi, L. Truth Meets Vagueness. Unifying the Semantic and the Soritical Paradoxes. J Philos Logic 52, 1637–1671 (2023). https://doi.org/10.1007/s10992-023-09721-8

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  • Received: 27 February 2022

  • Accepted: 27 August 2023

  • Published: 09 October 2023

  • Issue Date: December 2023

  • DOI: https://doi.org/10.1007/s10992-023-09721-8

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