Abstract
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.
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References
Y. Bar-Hillel,New light on the liar,Analysis 18 (1957), pp. 1–6.
T. Burge,Semantical paradox,Journal of Philosophy 76 (1979), pp. 169–198.
R. Carnap,Logical Synthax of Language, Kegan Paul, Trench, Trubner, 1937.
J. M. Dunn,Intuitive semantics for first degree entailments and “coupled trees” Philosophical Studies, 29 (1976), pp. 149–168.
F. B. Fitch,Symbolic Logic, Donald Press Co, 1952.
F. B. Fitch,Universal, metalanguages for Philosophy,Review of Metaphysics, 17 (1964), pp. 396–402.
B. van Fraassen,Presupposition implication and self reference,Journal of Philosophy, 65 (1968), pp. 136–151.
B. van Fraassen,Truth and paradoxical consequences inThe Paradox of the Liar, R. L. Martin, Yale University Press, 1970.
L. Goddard andGoldstein,Strengthened paradoxes,Australasian Journal of Philosophy, 58 (1980), pp. 211–221.
R. J. Haack andS. Haack,Token sentences, translation and truth value,Mind, 79 (1967), pp. 40–57.
H. Herzberger,The truth-conditional consistency of natural languages Journal of Philosophy, 64 (1967), pp. 29–35.
H. Herzberger,Paradoxes of grounding in semantics,Journal of Philosophy, 67 (1970), pp. 145–167.
S, Kripke,Outline of a theory of truth,Journal of Philosophy, 72 (1975), pp. 690–716.
R. L. Martin,Towards a solution to the liar paradox,Philosophical Review, 76 (1967), pp. 279–311.
R. L. Martin,Are natural languages universal,Synthese, 32 (1976), pp. 271–291.
K. R. Popper,Self reference and meaning,Mind 1954. Reprinted inConjectures and Refutations Routledge and Kegan Paul 1963.
G. Priest,Logic of paradox,Journal of Philosophical Logic, 8 (1979), pp, 219–41.
G. Priest,Sense, entailment and Modus Ponens,Journal of Philosophical Logic, 8, pp. 219–41.
G. Priest,Logical paradoxes and the law of excluded middle,Philosophical Quarterly, (forthcoming).
G. Priest, R. Routley andJ. Norman,Paraconsistent Logic, Philosophia Verlag, 1985.
R. Routley,Ultralogic as universal,Relevance Logic Newsletter, 2, pp. 50–89, pp. 138–175. Reprinted as an appendix inExploring Meinong's Jungle and Beyond, A.N.U. 1980.
G. Ryle,Heterologicality Analysis, 11 (1950), pp. 61–69.
A. Tarski,Der Wahreitsbegriff in den formalisierten Sprachen,Studia Philosophica, 1 (1936), pp. 261–405. Reprinted in English inLogic Semantics and Metamathematics, Oxford University Press 1956.
A. Tarski,The Semantic concept of truth and the foundations of semantics,Philosophical and Phenomenological Research, 4 (1944), pp. 341–376. Reprinted inSemantics and the Philosophy of Language, ed. L. Linsky, University of Illinois Press. 1952.
Wittgenstein L. Remarks on the Foundations of Mathematics, Blackwell, 1953.
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Priest, G. Semantic closure. Stud Logica 43, 117–129 (1984). https://doi.org/10.1007/BF00935745
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DOI: https://doi.org/10.1007/BF00935745