, Volume 28, Issue 6, pp 549-558

Semantic Closure, Descriptions and Non-Triviality

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It is known that a semantically closed theory with description may well be trivial if the principles concerning denotation and descriptions are formulated in certain ways, even if the underlying logic is paraconsistent. This paper establishes the non-triviality of a semantically closed theory with a natural, but non-extensional, description operator.