Page 284 - Encyclopedia of Philosophy of Language

Language and Logic
by ruling, consonant with his account of ground- edness, that the predicate 'truth-valueless' belongs not to the object- but to the meta-language; but this is undeniably disappointing, given that the idea was to avoid the artificiality of the Tarskian hierarchy of languages.
The solution proposed by 'dialethic' logicians, that the Liar should be acknowledged to be both true and false, since no disastrous consequences need follow in a paraconsistent logic, may provoke outrage rather than disappointment. Dialethists see the semantic paradoxes, as Tarski did, as indicating the incon- sistency of natural languages; but here intuition favors the Tarskian, Regimentalist response—'so much the worse for natural languages!'—over the dialethist's
hospitality to contradictions.
4. A Challenge to Deviant Logic from Considerations
of Language: The 'Meaning-Variance' Argument
The argument, due to Quine, is this: the deviant logi- cian proposes a system in which some classical prin- ciples ostensibly fail; trying to 'deny the doctrine,' however, he succeeds only in 'changing the subject.' What he denies when he denies, say, that 'p or not p' is always true, is not what the classical logician asserts when he asserts that classical logic is always true; the fact that 'p v -p' is not a theorem shows that it is not the LEMthat the 'deviant' logician denies, rather he is giving 'v' or'-' or both a new meaning.
Quine offers the example of a fictional, ostensibly deviant logic where the wff 'p & -p' is a theorem, but '&' turns out to be merely a 'perverse notation' for 'v,' and the appearance of disagreement mere appearance. The argument, however, shows less than Quine supposes. Granted—at least if one takes the meaning of logical connectives to be determined primarily by the syntax and/or semantics of the system in which they occur, rather than by the natural-language read- ings they are given—there may be room for doubt whether, say, the intuitionist logician means by his negation, for example, exactly what the classical logi- cian means by his. (The more so because it is possible to represent Heyting's logic as a notational variant of the modal system S4, which might suggest that the Intuitionist's 'it is not the case that' could be construed as 'it is impossible that.') But it wouldn't follow that ostensibly deviant logics are really no more than a re- presentation of classical logic in a nonclassical notation; only, at most, that the distinction between a challenge to the correctness of classical logic and a challenge to the adequacy of its vocabulary, be- tween deviant and extended logics, would begin to blur.
5. Conclusion
Before the development of modem formal logic, in his Logik of 1800, Kant wrote that '[tjhere are...few sciences that can come into a permanent state, which
admit of no further alteration.' But logic, he continued, was such a science: 'Aristotle has omitted no essential point — ' 'In our own times,' he went on, 'there has been no famous logician, and indeed we do not require any newdiscoveries in logic....'
Less than a century later, with the work of Boole, Peirce and Frege, logic had been transformed by the new, powerful vocabulary and techniques of what is now called 'classical logic.' By 1923 C. I. Lewis was insisting that 'those who suppose that there is a logic which everyone would agree to if he understood i t . . . are more optimistic than those versed in the his- tory of logic have a right to be.' Even if none of the deviant logics so far devised seem either so appealing mathematically or so well-motivated philosophically as seriously to threaten the position of classical logic, it is as well to recall Russell's observation, made in 1906, that 'since one never knows what will be the line of advance, it is always most rash to condemn what is not quite in the fashion of the moment.'
See also: Fiction, Logic of; Intuitionism; Paradoxes, Semantic; Relevant Logic.
Bibliography
Anderson A R, Belnap, N D Jr 1975 Entailmenf. volume 1. Princeton University Press, Princeton, NJ
Anderson A R, Belnap N D Jr, Dunn J M 1992 Entailment, volume 2. Princeton University Press, Princeton.
Burdick H 1982 A logical form for the prepositional atti- tudes. Synthese 52:185-230
Dunn J M, Epstein G 1977 Modern Uses of Multiple-Valued Logic. Reidel, Dordrecht
Fisch M, Turquette A 1961 Peirce's triadic logic. Trans- actions of the C. S. Peirce Society 2: 71-85
Fraassen B C Van 1969 Presuppositions, supervaluations and free logic. In: Lambert K (ed.) The Logical Way of Doing Things. Yale University Press, New Haven, CT
Gabbay D, Guenther F, eds 1986 Handbook of Philosophical Logic, volume 3, Alternatives to Classical Logic. Reidel, Dordrecht
Haack S 1978 Philosophy of Logics. Cambridge University Press, Cambridge
Haack S 1996 Deviant Logic,Fuzzy Logic: Beyond theFor- malism. University of Chicago Press, Chicago
Heyting A 1966 Intuitionism. North Holland, Amsterdam Kosko B 1993 Fuzzy Thinking: The New Science of Fuzzy
Logic. Hyperion, New York
Lane R forthcoming Peirce's 'Entanglement' with the Prin-
ciples of Excluded Middle and Contradiction. Trans-
actions of the C. S. Peirce Society
Norman J, Sylvan R, eds 1989 Directions in Relevant Logic.
Reidel, Dordrecht. [Sylvan R was formerly known as
Routley R.]
Parsons T 1980 Non-Existent Objects. Yale University Press,
New Haven, CT
Priest G, Routley R, Norman J (eds.) 1989 Paraconsistent
Logic. Philosophia Verlag, Munich
Priest G 1987 In Contradiction: A Study of the Trans-
consistent.MartinusNijhofT, Dordrecht
Quine W V O 1970 Philosophy of Logic. Prentice Hall, Engte-
wood Cliffs, NJ
262