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  1. Can Gödel's Incompleteness Theorem Be a Ground for Dialetheism?Seungrak Choi - 2017 - Korean Journal of Logic 20 (2):241-271.
    Dialetheism is the view that there exists a true contradiction. This paper ventures to suggest that Priest’s argument for Dialetheism from Gödel’s theorem is unconvincing as the lesson of Gödel’s proof (or Rosser’s proof) is that any sufficiently strong theories of arithmetic cannot be both complete and consistent. In addition, a contradiction is derivable in Priest’s inconsistent and complete arithmetic. An alternative argument for Dialetheism is given by applying Gödel sentence to the inconsistent and complete theory of arithmetic. We argue, (...)
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  2. Liar-Type Paradoxes and Intuitionistic Natural Deduction Systems.Seungrak Choi - 2018 - Korean Journal of Logic 21 (1):59-96.
    It is often said that in a purely formal perspective, intuitionistic logic has no obvious advantage to deal with the liar-type paradoxes. In this paper, we will argue that the standard intuitionistic natural deduction systems are vulnerable to the liar-type paradoxes in the sense that the acceptance of the liar-type sentences results in inference to absurdity (⊥). The result shows that the restriction of the Double Negation Elimination (DNE) fails to block the inference to ⊥. It is, however, not the (...)
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    Logical Revision by Counterexamples: A Case Study of the Paraconsistent Counterexample to Ex Contradictione Quodlibet.Seungrak Choi - 2019 - In Proceedings of the 14th and 15th Asian Logic Conferences. pp. 141-167.
    It is often said that a correct logical system should have no counterexample to its logical rules and the system must be revised if its rules have a counterexample. If a logical system (or theory) has a counterexample to its logical rules, do we have to revise the system? In this paper, focussing on the role of counterexamples to logical rules, we deal with the question. -/- We investigate two mutually exclusive theories of arithmetic - intuitionistic and paraconsistent theories. The (...)
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