• Korean Journal of Logic
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• v.16 no.3
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• pp.381-406
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• 2013

This paper deals with the question whether the para-completeness theory of Kripkian style can avoid the revenge problem. According to the para-completeness theory, there are some sentences that are neither true nor false. And the liar sentence is the exemplar of such sentences. But the para-completeness theory has been criticised to give rise to the revenge problem, since Kripke suggested his theory. Maudlin argues that he can construct the para-completeness theory which avoids the problem by appealing to his foundationalist semantics. The aim of this paper shows that the para-completeness theory, including Maudlin's, cannot avoid the problem. Furthermore, it is argued that Maudlin's view is ad hoc suggestion just to avoid the problem.

• Korean Journal of Logic
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• v.21 no.1
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• pp.59-96
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• 2018

${\bot}$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 (${\perp}$). The result shows that the restriction of the Double Negation Elimination (DNE) fails to block the inference to ${\perp}$. It is, however, not the problem of the intuitionistic approaches to the liar-type paradoxes but the lack of expressive power of the standard intuitionistic natural deduction system. We introduce a meta-level negation, ⊬$_s$, for a given system S and a meta-level absurdity, ⋏, to the intuitionistic system. We shall show that in the system, the inference to ${\perp}$ is not given without the assumption that the system is complete. Moreover, we consider the Double Meta-Level Negation Elimination rules (DMNE) which implicitly assume the completeness of the system. Then, the restriction of DMNE can rule out the inference to ${\perp}$.