Conditionals, curry, and consequence: embracing deduction

Nicholas Tourville, Roy T. Cook

Research output: Contribution to journalArticlepeer-review


We extend the Embracing Revenge account of the semantic paradoxes by constructing two distinct consequence relations that reflect, in different ways, the transfinitely-many-valued semantics developed in earlier work. In particular, we adapt the underlying ideas of “gappy” approaches based on K3, and “glutty” approaches based on LP, to the Embracing Revenge framework, by treating the infinitely many non-classical truth values as infinitely many ways that a sentence might fail to receive a classical truth value in the former case, and as infinitely many ways that a sentence might receive both classical truth values in the latter. In order to obtain deductive systems that are very nearly classical, we need to utilize different conditionals (and different negations) in each logic.

Original languageEnglish (US)
Article number52
Issue number2
StatePublished - Feb 2023

Bibliographical note

Funding Information:
We would like to thank the audiences at the 2018 Semantic Paradox and Revenge Conference at the University of Salzburg, Austria; the 2016 International Conference on Paradoxes, Logic, and Philosophy at the Department of Philosophy and Institute of Foreign Philosophy, Peking University, China; the 2016 5th Workshop on Philosophical Logic at SADAF, Buenos Aires, Argentina; and the 2016 ASL Logic Colloquium at the University of Leeds, England for helpful and generous feedback. Thanks are also owed to a number of extremely helpful referees.

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature B.V.


  • Conditional
  • Curry paradox
  • Deduction
  • Logic
  • Logical consequence
  • Many-valued logic
  • Negation


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