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On Alternative Geometries, Arithmetics, and Logics; a Tribute to Łukasiewicz

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Abstract

The paper discusses the similarity between geometry, arithmetic, and logic, specifically with respect to the question of whether applied theories of each may be revised. It argues that they can - even when the revised logic is a paraconsistent one, or the revised arithmetic is an inconsistent one. Indeed, in the case of logic, it argues that logic is not only revisable, but, during its history, it has been revised. The paper also discusses Quine's well known argument against the possibility of “logical deviancy”.

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References

  1. Anderson, A., and N. Belnap, Entailment, Vol. I, Princeton University Press, 1975.

  2. Borkowski, L., and J. SŁupecki, ‘The Logical Works of J. Łukasiewicz’, Studia Logica 8 (1958), 7-56.

    Google Scholar 

  3. Bell, E. T., Men of Mathematics, Pelican Books, 1953.

  4. Benacerraf, P., and H. Putnam, Philosophy of Mathematics; Selected Readings, Oxford University Press, 1964.

  5. CastaÑeda, H.-N., ‘Arithmetic and Reality’, Australasian Journal of Philosophy 37 (1959), 92-107; reprinted in Benacerraf and Putnam (1964), 404–71.

    Google Scholar 

  6. Dancy, R. M., Sense and Contradiction: a Study in Aristotle, Reidel, 1975.

  7. Denyer, N., ‘Priest's Paraconsistent Arithmetic’, Mind 104 (1995), 567-75.

    Google Scholar 

  8. Dummett, M., Elements of Intuitionism, Oxford University Press, 1977.

  9. Dummett, M., ‘Is Logic Empirical?’, ch. 16 of Truth and Other Enigmas, Duckworth, 1978.

  10. Etchemendy, J., The Concept of Logical Consequence, Harvard University Press, 1990.

  11. Feyerabend, P., Against Method, New Left Books, 1975.

  12. Gasking, D. A. T., ‘Mathematics and the World’, Australasian Journal of Philosophy 18 (1940), 97-116; reprinted in Benacerraf and Putnam (1964), 390–403.

    Google Scholar 

  13. Goddard, L., ‘The Inconsistency of Aristotelian Logic?’, Australasian Journal of Philosophy 78 (2000), 434-7.

    Google Scholar 

  14. Goodstein, R. L., ‘Multiple Successor Arithmetics’, in J. Crossley and M. Dummett (eds.), Formal Systems and Recursive Functions, North Holland Publishing Company, 1965, 265-71.

  15. Gray, J. J., ‘Euclidean and Non-Euclidean Geometry’, sect. 7.4 of I. Grattan-Guiness (ed.), Companion Encyclopedia of the History and Philosophy of Mathematical Sciences, Routledge, 1994.

  16. Haack, S., Deviant Logic, Cambridge University Press, 1974.

  17. Hinckfuss, I., ‘Instrumentalist Theories: Possibilities and Space and Time’, in P. Riggs (ed.), Natural Kinds, Laws of Nature and Scientific Methodology, Kluwer Academic Publishers, 1996, 187-209.

  18. Kneale, W., and M. Kneale, The Development of Logic, Oxford University Press, 1962.

  19. KotarbiŃski, T., ‘Jan Łukasiewicz's Works on the History of Logic’, Studia Logica 8 (1958), 57-62.

    Google Scholar 

  20. Kuhn, T., The Structure of Scientific Revolutions, Chicago University Press, 1962.

  21. Łukasiewicz, J., Aristotle's Syllogistic, Clarendon Press, 1957.

  22. Łukasiewicz, J., ‘Philosophische Bemargungen zu Mehrwertigen des Aussagenkalküls’, Comptes Rendus des Séances de la Societé des Sciences et des Lettres de Varsovie, Cl. iii, 23 (1930), 51-77, translated into English as ‘Philosophical Remarks on the Many-Valued Systems of Propositional Logic’, ch. 3 of McCall (1967).

    Google Scholar 

  23. McCall, S., Polish Logic 1920–1939, Oxford University Press, 1967.

  24. Mortensen, C., Inconsistent Mathematics, Kluwer Academic Publishers, 1995.

  25. Nerlich, G., The Shape of Space, Cambridge University Press, 1976.

  26. PoincarÉ, H., La Science et L'Hypothèse, Paris: Ernest Flammmarian (no date); translated into English as Science and Hypothesis, Dover Publications, 1952.

  27. Priest, G., ‘Two Dogmas of Quineanism’, Philosophical Quarterly 29 (1979), 289-301.

    Google Scholar 

  28. Priest, G., In Contradiction, Martinus Nijhoff, 1987.

  29. Priest, G., ‘Classical Logic Aufgehoben’, ch. 4 of G. Priest, R. Routley and J. Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent, Philosophia Verlag, 1989.

  30. Priest, G., ‘Is Arithmetic Consistent?’, Mind 103 (1994), 337-49.

    Google Scholar 

  31. Priest, G., ‘Etchemendy and the Concept of Logical Validity’, Canadian Journal of Philosophy 25 (1995), 283-92.

    Google Scholar 

  32. Priest, G., ‘On Inconsistent Arithmetics: Reply to Denyer’, Mind 105 (1996), 649-59.

    Google Scholar 

  33. Priest, G., ‘Inconsistent Models of Arithmetic; I Finite Models’, Journal of Philosophical Logic 26 (1997), 223-35.

    Google Scholar 

  34. Priest, G., ‘What not? A Defence of a Dialetheic Account of Negation’, in D. Gabbay and H. Wansing (eds.), What is Negation?, Kluwer Academic Publishers, 1999.

  35. Priest, G., ‘Inconsistent Models of Arithmetic; II, the General Case’, Journal of Symbolic Logic 65 (2000), 1519-29.

    Google Scholar 

  36. Prior, A., ‘Logic, Traditional’, in P. Edwards (ed.), Encyclopedia of Philosophy, Collier-MacMillan, 1967.

  37. Putnam, H., ‘It Ain't Necessarily So’, Journal of Philosophy 59 (1962), 658-71; reprinted as ch. 15 of Putnam (1975).

    Google Scholar 

  38. Putnam, H., ‘Is Logic Empirical?’, in R. Cohen and M. Wartofsky (eds.), Boston Studies in the Philosophy of Science, Vol. V, Reidel, 1969; reprinted under the title ‘The Logic of Quantum Mechanics’ as ch. 10 of Putnam (1975).

  39. Putnam, H., Mathematics, Matter and Method; Philosophical Papers, Vol. I, Cambridge University Press, 1975.

  40. Quine, W. V., ‘Two Dogmas of Empiricism’, Philosophical Review 60 (1951), 20-43; reprinted in From a Logical Point of View, Harvard University Press, 1953.

    Google Scholar 

  41. Quine, W. V., Word and Object, MIT Press, 1960.

  42. Quine, W. V., Philosophy of Logic, Prentice Hall, 1970.

  43. Rescher, N., Many-Valued Logic, McGraw Hill, 1969.

  44. Ryle, G., ‘Formal and Informal Logic’, ch. 8 of Dilemmas, Cambridge University Press, 1954.

  45. Slater, B. H., ‘Paraconsisent Logic?’, Journal of Philosophical Logic 24 (1995), 451-4.

    Google Scholar 

  46. SobociŃski, B., ‘In Memoriam Jan Łukasiewicz’, Philosophical Studies (Dublin) 6 (1956), 3-49.

    Google Scholar 

  47. Strawson, P., Introduction to Logical Theory, Methuen and Co., 1952.

  48. Tarski, A., ‘On the Concept of Logical Consequence’, ch. 14 of Logic, Semantics and Metamathematics, Oxford University Press, 1956.

  49. Van Bendegem, J.-P., Finite, Empirical Mathematics; Outline of a Model, Rijksuniversiteit Gent, 1987.

  50. Wright, C., Frege's Conception of Numbers as Objects, Aberdeen University Press, 1983.

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  1. Department of Philosophy, University of Melbourne, USA

    Graham Priest

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  1. Graham Priest
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Priest, G. On Alternative Geometries, Arithmetics, and Logics; a Tribute to Łukasiewicz. Studia Logica 74, 441–468 (2003). https://doi.org/10.1023/A:1025123418085

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