• Korean Journal of Logic
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• v.20 no.2
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• pp.241-271
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• 2017

Dialetheism is the view that there exists a true contradiction. This paper ventures to suggest that Priest's argument for Dialetheism from $G{\ddot{o}}del^{\prime}s$ theorem is unconvincing as the lesson of $G{\ddot{o}}del^{\prime}s$ 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 $G{\ddot{o}}del$ sentence to the inconsistent and complete theory of arithmetic. We argue, however, that the alternative argument raises a circularity problem. In sum, $G{\ddot{o}}del^{\prime}s$ and its related theorem merely show the relation between a complete and a consistent theory. A contradiction derived by the application of $G{\ddot{o}}del$ sentence has the value of true sentences, i.e. the both-value, only under the inconsistent models for arithmetic. Without having the assumption of inconsistency or completeness, a true contradiction is not derivable from the application of $G{\ddot{o}}del$ sentence. Hence, $G{\ddot{o}}del^{\prime}s$ and its related theorem never can be a ground for Dialetheism.