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On Discourses Addressed by Infidel Logicians

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Paraconsistency: Logic and Applications

Part of the book series: Logic, Epistemology, and the Unity of Science ((LEUS,volume 26))

Abstract

We here attempt to address certain criticisms of the philosophical import of the so-called Brazilian approach to paraconsistency by providing some epistemic elucidations of the whole enterprise of the logics of formal inconsistency. In the course of this discussion, we substantiate the view that difficulties in reasoning under contradictions in both the Buddhist and the Aristotelian traditions can be accommodated within the precepts of the Brazilian school of paraconsistency.

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Notes

  1. 1.

    It is believed that the “infidel mathematician” in question was either Edmond Halley or Isaac Newton himself.

  2. 2.

    There is some historical evidence that the elements of the infinitesimal calculus, developed between the fourteenth and sixteenth centuries in Kerala, India, may have been transmitted to Europe by Jesuit missionaries (cf. Almeida and Joseph 2007).

  3. 3.

    For some strange reason, this seems to be more acute among writers in certain groups. Although the phenomenon of “relative own-language preference” in citations is well-known, in this case it seems to be one of “relative own-group preference”. As an attitude, it is reminiscent of a whimsical statement by the Brazilian writer Oswald de Andrade, who famously said of a book by a rival: “I didn’t read it, and I didn’t like it”.

  4. 4.

    “da Costa’ systems are, consequently, not treated here from this point on”.

  5. 5.

    “da Costa’s negation is absolutely non-recursive!”.

References

  • Almeida, D.F., and G.G. Joseph. 2007. Kerala mathematics and its possible transmission to Europe. Philosophy of Mathematics Education Journal 20. http://people.exeter.ac.uk/PErnest/pome20/.

  • Alves, E. 1976. Logic and inconsistency (in Portuguese). Ph.D. thesis, University of São Paulo, Brazil.

    Google Scholar 

  • Avron, A., and I. Lev. 2005. Non-deterministic multi-valued structures. Journal of Logic and Computation, 15: 241–261.

    Google Scholar 

  • Berto, F. 2007. How to sell a contradiction: The logic and metaphysics of inconsistency. Studies in logic. London: College Publications.

    Google Scholar 

  • Berkeley, G. 1734. In The Analyst; or, a discourse addressed to an infidel mathematician. ed. D.R. Wilkins. Dublin: School of Mathematics, Trinity College. http://www.maths.tcd.ie/pub/HistMath/People/Berkeley/Analyst/Analyst.html.

  • Bremer, M. 1998. Wahre Widersprüche. Einführung in die parakonsistente Logik. Sankt Augustin: Academia.

    Google Scholar 

  • Bremer, M. 2005. An introduction to paraconsistent logics. Frankfurt: Peter Lang.

    Google Scholar 

  • Carnielli, W.A., and J. Marcos. 2002. A taxonomy of C-systems. In Paraconsistency: The logical way to the inconsistent. Lecture notes in pure and applied mathematics, vol. 228, ed. W.A. Carnielli, M.E. Coniglio, and I.M.L. D’Ottaviano, 1–94. New York: Marcel Dekker.

    Google Scholar 

  • Carnielli, W.A., and M.E. Coniglio. 2008. Aristóteles, Paraconsistentismo e a Tradição Budista. O que nos faz pensar, 23: 163–175.

    Google Scholar 

  • Carnielli, W.A., M.E. Coniglio, and J. Marcos. 2007. Logics of formal inconsistency. In Handbook of philosophical logic, vol. 14, ed. D. Gabbay and F. Guenthner, 1–93. Amsterdam: Springer.

    Google Scholar 

  • Conway, J.H. 1976. On numbers and games. New York: Academic.

    Google Scholar 

  • da Costa, N.C.A., and E. Alves. 1977. A semantical analysis of the calculi C n . Notre Dame Journal of Formal Logic 18(4): 621–630.

    Google Scholar 

  • Deguchi, Y., J.L. Garfield, and G. Priest. 2008. The way of the dialetheist: Contradictions in Buddhism. Philosophy East and West 58(3): 395–402.

    Google Scholar 

  • Derbyshire, J. 2003. Prime obsession: Bernhard Riemann and the greatest unsolved problem in mathematics. New York: Plume/Penguin Group.

    Google Scholar 

  • Dutilh-Novaes, C. 2008. Contradiction: The real philosophical challenge for paraconsistent logic. In Handbook of Paraconsistency, ed. J.-Y. Béziau, W.A. Carnielli, and D. Gabbay, 465–480. Amsterdam: Elsevier.

    Google Scholar 

  • Galloway, B. 1989. Some logical issues in Madhyamaka thought. Journal of Indian Philosophy 17(1): 1–35.

    Google Scholar 

  • Garfield, J.L., and G. Priest. 2002. Nāgārjuna and the limits of thought. In Beyond the limits of thought, ed. G. Priest, 249–270. Oxford: Oxford University Press.

    Google Scholar 

  • Garfield, J.L., and G. Priest. 2003. Nāgārjuna and the limits of thought. Philosophy East and West 53(1): 1–21.

    Google Scholar 

  • Giora, R. 2006. Anything negatives can do affirmatives can do just as well, except for some metaphors. Journal of Pragmatics 38: 981–1014.

    Google Scholar 

  • Gottlieb, P. 2007. Aristotle on non-contradiction. Stanford encyclopedia of philosophy, Feb 2007. http://plato.stanford.edu/entries/aristotle-noncontradiction/#1.

  • Kneale, W., and M. Kneale. 1985. The development of logic. Oxford: Oxford University Press.

    Google Scholar 

  • Knuth, D. 1974. Surreal numbers: How two ex-students turned on to pure mathematics and found total happiness. Reading: Addison-Wesley.

    Google Scholar 

  • Lawvere, F.W. 1998. Outline of synthetic differential geometry. Available at http://www.acsu.buffalo.edu/~wlawvere/SDG_Outline.pdf. Accessed Feb 1998.

  • Marcos, J. 1999. Semânticas de Traduções Possíveis (Possible translations semantics, in Portuguese). Master’s thesis, IFCH-UNICAMP, Campinas, Brazil. http://www.cle.unicamp.br/pub/thesis/J.Marcos/.

  • Naumov, P. 2005. On modal logics of partial recursive functions. Studia Logica 81(3): 295–309.

    Google Scholar 

  • Nearman, H. 2007. Shōbōgenzō: The treasure house of the eye of the true teaching. A trainee’s translation of great master Dogen’s spiritual masterpiece. Mount Shasta: Shasta Abbey Press.

    Google Scholar 

  • Nelson, E. 1977. Internal set theory: A new approach to nonstandard analysis. Bulletin of the American Mathematical Society 83(6): 1165–1198.

    Google Scholar 

  • Newton, I. 1726. Philosophiae Naturalis Principia Mathematica, third edition. Translated in: Isaac Newton’s Philosophiae Naturalis Principia Mathematica, the Third Edition with Variant Readings, ed. A. Koyré and I. B. Cohen, 2 vols., Cambridge: Harvard University Press and Cambridge: Cambridge University Press, 1972.

    Google Scholar 

  • Nishijima, G.W. 1992. Understanding the Shōbōgenzō. London: Windbell Publications.

    Google Scholar 

  • Petrus, A. 1970. Dialectica, ed. L.M. De Rijk, Assen: Van Gorcum. http://individual.utoronto.ca/pking/resources/abelard/Dialectica.txt.

  • Robinson, A. 1966. Non-standard analysis. Princeton: Princeton University Press.

    Google Scholar 

  • Sandifer, E. 2006. Infinitely many primes. MAA online – How Euler did it. Available at http://www.maa.org/news/columns.html. Accessed Mar 2006.

  • Siderits, M. 2008. Contradiction in Buddhist argumentation. Argumentation 22(1): 125–133.

    Google Scholar 

  • Slater, B.H. 1995. Paraconsistent logics? Journal of Philosophical Logic 24: 233–254.

    Google Scholar 

  • Sorensen, R. 2003. A brief history of the paradox. Oxford: Oxford University Press.

    Google Scholar 

  • Tillemans, T. 1999. Is Buddhist logic non-classical or deviant? In Scripture, Logic, Language, ed. T. Tillemans, 187–205. Boston: Wisdom Publications.

    Google Scholar 

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Correspondence to Walter Carnielli .

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Carnielli, W., Coniglio, M.E. (2013). On Discourses Addressed by Infidel Logicians. In: Tanaka, K., Berto, F., Mares, E., Paoli, F. (eds) Paraconsistency: Logic and Applications. Logic, Epistemology, and the Unity of Science, vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4438-7_3

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