Abstract
This paper focuses on the categoricity of arithmetic and determinacy of arithmetical truth. Several ‘internal’ categoricity results have been discussed in the recent literature. Against the background of the philosophical position called internalism, we propose and investigate truth-theoretic versions of internal categoricity based on a primitive truth predicate. We argue for the compatibility of a primitive truth predicate with internalism and provide a novel argument for (and proof of) a truth-theoretic version of internal categoricity and internal determinacy with some positive properties.
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Acknowledgements
Versions of this article have been presented at research seminars in Bristol, Konstanz, and Warsaw and a workshop in Helsinki. Thanks to the audience for their helpful comments and discussion. In particular, we are thankful to Philip Welch, Sean Walsh, Cezary Cieśliński, and the two anonymous referees of this journal.
Martin Fischer thankfully acknowledges the financial support by the DFG, “Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 407312485”. Matteo Zicchetti is grateful to the South, West and Wales Doctoral Training Partnership and the Arts and Humanities Research Council for their financial support (AH/L503939/1)
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Martin Fischer: Deutsche Forschungsgemeinschaft (407312485). Matteo Zicchetti Arts and Humanities Research Council (AH/L503939/1)
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Fischer, M., Zicchetti, M. Internal Categoricity, Truth and Determinacy. J Philos Logic 52, 1295–1325 (2023). https://doi.org/10.1007/s10992-023-09707-6
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DOI: https://doi.org/10.1007/s10992-023-09707-6