Semantic closure

This paper argues for tlie claims that a) a natural language such as English is semanticaly closed b) semantic closure implies inconsistency. A corollary of these is that the semantics of English must be paraconsistent. The first part of the paper formulates a definition of semantic closure which applies to natural languages and shows that this implies inconsistency. The second section argues that English is semeantically closed. The preceding discussion is predicated on the assumption that there are no truth value gaps. The next section of the paper considers whether the possibility of these makes any difference to the substantive conclusions of the previous sections, and argues that it does not. The crux of the preceding arguments is that none of the consistent semantical accounts that have been offered for solving the semantical paradoxes is a semantic ofEnglish. The final section of the paper produces a general argument as to why this must always be the case.