Boolean negation and all that
- Graham Priest
- … show all 1 hide
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
We have seen that proofs of soundness of (Boolean) DS, EFQ and of ABS — and hence the legitimation of these inferences — can be achieved only be appealing to the very form of reasoning in question. But this by no means implies that we have to fall back on classical reasoning willy-nilly. Many logical theories can provide the relevant boot-strapping. Decision between them has, therefore, to be made on other grounds. The grounds include the many criteria familiar from the philosophy of science: theoretical integrity (e.g., paucity of ad hoc hypotheses), adequacy to the data (explaining the data of inference —all inferences, not just those chosen from consistent domains!) and so on. This paper has not attempted to address these issues in general. All it demonstrates is that the charge that a dialetheist solution to the semantic paradoxes can be maintained only by making some intelligible notion ineffable cannot be made to stick. The dialetheist has a coherent position, endorsing the T-scheme, but rejecting DS, EFQ (even Boolean DS and EFQ) and ABS. And any argument to the effect that the relevant notions are both ineffable and intelligible begs the question. The case against consistent “solutions” to the semantic paradoxes therefore remains intact.
- Belnap, N. (1962) ‘Tonk, Plonk and Plink’, Analysis 22, 130–134. Reprinted in Strawson (1967).
- Brady, R. (1983) ‘The Simple Consistency of a Set Theory Based on the Logic CSQ’, Notre Dame Journal of Formal Logic 24, 431–449.
- Brady, R. (1988) ‘The Non-Triviality of Dialectical Set Theory’, in Priest et al. (1988).
- Dowden, B. (1984) ‘Accepting Inconsistencies from the Paradoxes’, Journal of Philosophical Logic 13, 125–130.
- Dummett, M. (1978a) ‘The Philosphical Basis of Intuitionist Logic’, ch. 14 of Truth and Other Enigmas, Duckworth, 1978.
- Dummett, M. (1978b) ‘The Justification of Deduction’, ch. 17 of Truth and Other Enigmas, Duckworth, 1978.
- Dunn, J. M. (1986) ‘Relevance Logic and Entailment’, in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, Vol. 3, D. Reidel.
- Haack, S. (1976) ‘The Justification of Deduction’, Mind 85, 112–119.
- Meyer, R. (1974) ‘New Axiomatics for Relevant Logics I’, Journal of Philosophical Logic 3 (1974), 53–86.
- Meyer, R. (1985) ‘Boole Bights Back’, a paper read at a meeting of the Austrlasian Association of Philosophy, Canberra, 1985.
- Meyer, R., Dunn, J. M., and Routley, R. (1979) ‘Curry's Paradox’, Analysis 39, 124–128.
- Meyer, R. and Routley, R. (1972) ‘Classical Relevant Logics I’, Studia Logica 32, 51–68.
- Meyer, R. and Routley, R. (1973) ‘Classical Relevant Logic II’, Studia Logica 33, 183–94.
- Priest, G. (1979) ‘Logic of Paradox’, Journal of Philosophical Logic 8, 219–241.
- Priest, G. (1980) ‘Sense, Entailment and Modus Ponens’, Journal of Philosophical Logic 9, 415–435.
- Priest, G. (1984a) ‘Semantic Closure’, Studia Logica 43, 117–129.
- Priest, G. (1984b) ‘Logic of Paradox Revisited’, Journal of Philosophical Logic 12, 153–179.
- Priest, G. (1986) Review of A Companion to Modal Logic, by G. Hughes and M. J. Cresswell, Australasian Journal of Philosophy 64, 220–221.
- Priest, G. (1987a) ‘Unstable Solutions to the Liar Paradox’, in Self Reference: Reflections and Reflexivity, S. J. Bartlett and P. Suber (eds.), Nijhoff.
- Priest, G. (1987b) In Contradiction: a Study of the Transconsistent, Nijhoff.
- Priest, G. (1988) ‘Reductio ad Absurdum et Modus Tollendo Ponens’, in Priest et al. (1988).
- Priest, G. (1989) ‘Intensional Paradoxes’, A paper read to a meeting of the Australasian Association for Logic, Perth, 1988. To appear.
- Priest, G., Routley, R., and Norman, J. (eds.) (1988) Paraconsistent Logics, Philosophia Verlag.
- Prior, A. (1960) ‘The Runabout Inference Ticket’, Analysis 21, 38–39. Reprinted in Strawson (1967).
- Routley, R. et al. (1982) Revelant Logics and Their Rivals, Ridgeview.
- Stevenson, J. (1961) ‘Roundabout the Runabout Inference Ticket’, Analysis 21, 124–128. Reprinted in Strawson (1967).
- Stawson, P. (1967) Philosophical Logic, Oxford U.P.
- Thomason, R. (1986) ‘Paradoxes and Semantic Representation’, in J. Y. Halpern Reasoning about Knowledge, Morgan Kaufman.
- White, R. B. (1979) ‘The Consistency of the Axiom of Comprehension in the Infinite Valued Predicate Logic of Łukasiewicz’, Journal of Philosophical Logic 8, 509–534.
- Boolean negation and all that
Journal of Philosophical Logic
Volume 19, Issue 2 , pp 201-215
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- Graham Priest (1)
- Author Affiliations
- 1. Department of Philosophy, University of Queensland, 4067, St Lucia, Queensland, Australia