Page 188 - Encyclopedia of Philosophy of Language

Truth and Meaning
in the Tarskian hierarchy. In response to the same problem in connection with ramified type theory, Rus- sell introduced the idea of 'typical ambiguity.' As an alternative, Barwise and Etchemendy have suggested that some occurrences of 'is true' be interpreted as transcending the Tarskian hierarchy altogether. Para- doxes can be avoided by denying such transcendent status to the relevant occurrences of 'is true' in para- doxical statements.
McGee (1991) offers a suggestion along these lines inspired by Carnap's idea of the partial definition of theoretical predicates. McGee distinguishes between truthanddefinite truth:theLiarmaybeeithertrueor false (we cannot say which), but it is neither definitely true nor definitely not true. McGee agrees with Tarski that natural language is inconsistent, since the ordi- nary notion of truth carries with it Tarski's T schema, which leads to inconsistency. McGee urges that we replace this ordinary concept with a scientifically respectable but only partially defined predicate. We should no longer assert the Tarski biconditionals, although we can continue to use the corresponding inference rules (from 'p' to infer 'True(p)', and vice versa) outside hypothetical contexts. Wecannot assert that the Liar (and other pathological propositions) are not true, but we can assert that they are not defi- nitely true. McGee avoids a paradox involving definite truth ('This sentence is not definitely true') by denying that we can assert all instances of the schema DT: if 'p' is definitely true, then p. The set of definite truths
may be inconsistent, if the meaning postulates embed- ded in our current scientific language are (unbe- knownst to us) inconsistent.
See also: Categories and Types; Formal Semantics; Metalanguage versus Object Language; Pre- supposition; Truth and Paradox.
Bibliography
Barwise J, Etchemendy J 1987 The Liar: An Essay on Truth and Circularity. Oxford University Press, New York
Burge T 1979 Semantical paradox. Journal of Philosophy 76: 169-98
Church A 1979 A comparison of Russell's resolution of
the semantical antinomies with that of Tarski. Journal of
Symbolic Logic41: 747-60
Donnellan K 1957 A note on the liar paradox. The Philo-
sophical Review 65: 394-97
Feferman S 1984 Toward useful type-free theories, I. Journal
of Symbolic Logic 49: 75-111
Gaifman H 1988 Operational pointer semantics: Solution to
the self-referential puzzles, I. In: Vardi M (ed.) Proceedings of the Second Conference on Theoretical Aspects of Reason- ing About Knowledge. Morgan Kaufman, Los Altos, CA
Grelling K, Nelson L 1908 Bemerkungen zu den Paradoxien von Russell und Burali-Forti. Abhandlungen der Frie- sischen Schule 1: 301-34
Gupta A 1982 Truth and paradox. Journal of Philosophical Logic 11: 61-102
Herzberger H G 1982 Notes on naive semantics. Journal of Philosophical Logic 11: 1-60
Koons R 1990 Three solutions to the liar paradox. In: Cooper R, Mukai K., Perry P (eds.) Situation Theory and Its Applications. Center for the Study of Language and Information, Stanford, CA
Koons R 1992 Paradoxes of Belief and Strategic Rationality. Cambridge University Press, New York
Kripke S 1975 Outline of a theory of truth. Journal of Phil- osophy 72: 690-716
Martin R L (ed.) 1984 Recent Essays on Truth and the Liar Paradox. Clarendon Press, Oxford
McGee V 1991 Truth, Vagueness and Paradox. Hackett Pub- lishing Company, Indianapolis, IN
Moody E A 1953 Truth and Consequence in Medieval Logic. North Holland, Amsterdam
Parsons C 1974 The liar paradox. Journal of Philosophical Logic 3: 381-412
Parsons T 1984 Assertion, denial and the liar paradox. Jour- nal of Philosophical Logic 13: 137-52
Priest G 1984 Logic of paradox revisited. Journal of Philo- sophical Logic 13: 153-79
Prior A N 1961 On a family of paradoxes. Notre Dame Journal of Formal Logic 2: 16-32
Richard J 1906 Les Principes des mathematiques et le pro- bleme des ensembles. Acta Mathematica 30: 295-%
Russell B 1908 Mathematical logic as based on the theory of types. American Journal of Mathematics 30: 222-62
Simmons K 1990 The diagonal argument and the liar. Jour- nal of Philosophical Logic 19: 277-304
Ushenko 1957 An addendum to the note on the liar paradox. The Philosophical Review 65: 394-97
Yablo S 1985 Truth and reflection. Journal of Philosophical Logic 14: 297-349
The term 'meaning' is susceptible of many different and sometimes conflicting characterizations. The term 'picture,' by contrast, seems more intuitively accessible,
and naturally suggests something visible. The term 'picture theory of meaning,' therefore, signals an analogy if not a metaphor which purports to elucidate
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Picture Theory of Meaning D. E. B. Pollard