Alethic Reference

Abstract

I put forward precise and appealing notions of reference, self-reference, and well-foundedness for sentences of the language of first-order Peano arithmetic extended with a truth predicate. These notions are intended to play a central role in the study of the reference patterns that underlie expressions leading to semantic paradox and, thus, in the construction of philosophically well-motivated semantic theories of truth.

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Acknowledgements

I am deeply indebted to Volker Halbach, with whom I had countless fruitful discussions on reference and self-reference over the last seven years. I would also like to particularly thank Dan Waxman for extremely helpful comments on the final drafts, Thomas Schindler, for great suggestions and encouragement, and two anonymous referees for serious improvements in clarity and exposition. I should mention as well Eduardo Barrio, Catrin Campbell-Moore, Luca Castaldo, Roy T. Cook, Benedict Eastaugh, Martin Fischer, Hannes Leitgeb, Øystein Linnebo, Carlo Nicolai, Graham Priest, Johannes Stern, Albert Visser, the Buenos Aires Logic Group, the MCMP logic community, and the Oxford logic group. Finally, I would like to thank the Alexander von Humboldt Foundation and, especially, the Deutsche Forschungsgemeinschaft (DFG) for generously funding the research projects “Reference patterns of paradox” (PI 1294/1-1) and “The Logics of Truth: Operational and Substructural Approaches” (GZ HJ 5/1-1, AOBJ 617612).

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Correspondence to Lavinia Picollo.

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Picollo, L. Alethic Reference. J Philos Logic 49, 417–438 (2020). https://doi.org/10.1007/s10992-019-09524-w

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Keywords

  • Semantic paradoxes
  • Reference
  • Self-reference
  • Well-foundedness