Applied Logic without Psychologism

Abstract

Logic is a celebrated representation language because of its formal generality. But there are two senses in which a logic may be considered general, one that concerns a technical ability to discriminate between different types of individuals, and another that concerns constitutive norms for reasoning as such. This essay embraces the former, permutation-invariance conception of logic and rejects the latter, Fregean conception of logic. The question of how to apply logic under this pure invariantist view is addressed, and a methodology is given. The pure invariantist view is contrasted with logical pluralism, and a methodology for applied logic is demonstrated in remarks on a variety of issues concerning non-monotonic logic and non-monotonic inference, including Charles Morgan’s impossibility results for non-monotonic logic, David Makinson’s normative constraints for non-monotonic inference, and Igor Douven and Timothy Williamson’s proposed formal constraints on rational acceptance.

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References

  1. 1.

    Arló-Costa Horacio (2005) ‘Non-adjunctive inference and classical modalities’. Journal of Philosophical Logic 34: 581–605

    Article  Google Scholar 

  2. 2.

    Beall J.C., Greg Restall (2006) Logical Pluralism. Oxford University Press, Oxford

    Google Scholar 

  3. 3.

    Byrd Michael (1989) ‘Russell, logicisn and the choice of logical constants’. Notre Dame Journalof FormalLogic 30(3): 343–361

    Article  Google Scholar 

  4. 4.

    Casanovas Enrique (2007) ‘Logical operations and invariance’. Journal of Philosophical Logic 36(1): 33–60

    Article  Google Scholar 

  5. 5.

    Chellas Brian (1980) Modal Logic. Cambridge University Press, Cambridge

    Google Scholar 

  6. 6.

    Douven Igor, Timothy Williamson (2006) ‘Generalizing the lottery paradox’. The British Journal for the Philosophy of Science Philosophy of Science 57(4):755–779

    Article  Google Scholar 

  7. 7.

    Fisher Ronald A. (1936) ‘Uncertain inference’. Proceedings of the American Academy of Arts and Sciences 71: 245–258

    Google Scholar 

  8. 8.

    Fisher, Ronald A., ‘On the mathematical foundations of theoretical statistics’, in J. H. Bennett, (ed.), CollectedPapers of R.A.Fisher, University of Adelaide, Adelaide, 1971. Originally published in 1922.

  9. 9.

    Frege, Gottlob, The Foundations of Arithmetic, j. l. austin (trans). edn., Basil Blackwell, Oxford, 1893(1950).

  10. 10.

    Gabbay, Dov, ‘Theoretical foundations for nonmonotonic reasoning in expert systems’, in K. Apt, (ed.), Logics and Models of Concurrent Systems, Springer-Verlag, Berlin, 1985.

  11. 11.

    Halpern Joseph Y. (2003) Reasoning about Uncertainty. MIT Press, Cambridge, MA

    Google Scholar 

  12. 12.

    Harman Gilbert (1986) Change in View. MIT Press, Cambridge, MA

    Google Scholar 

  13. 13.

    Harman, Gilbert,and Sanjeev R. Kulkarni, ‘The problem of induction’, Philosophy and Phenomenological Research, (2005). Presented at the 2005 Rutgers Epistemology Workshop.

  14. 14.

    Hawthorne James, David Makinson (2007) ‘The quantitative/qualitative watershed for rules of uncertain inference’. Studia Logica 86(2): 247–297

    Article  Google Scholar 

  15. 15.

    Kraus Sarit, Daniel Lehman, Menachem Magidor (1990) ‘Nonmonotonic reasoning, preferential models and cumulative logics’. Artificial Intelligence 44: 167–207

    Article  Google Scholar 

  16. 16.

    Kyburg, Henry E., Jr., Choh Man Teng,and Gregory Wheeler, ‘Conditionals and consequences’, Journal of Applied Logic, (2007).

  17. 17.

    Lindenbaum, Adolf,and Alfred Tarski, ‘On the limitations of the means of expression of deductive theories’, in John Corcoran, (ed.), Logic, Semantics, Metamathematics, Hackett, Indianapolis, 1983.

  18. 18.

    MacFarlane, John, What does it mean to say that logic is formal, Ph.D. thesis, University of Pittsburgh, 2000.

  19. 19.

    Makinson, David C., ‘General patterns in nonmonotonic reasoning’, in Dov Gabbay, Chris Hogger, and John Alan Robinson, (eds.), Handbook of Logic in Artificial Intelligence and Uncertain Reasoning, vol. 3, Clarendon Press, Oxford, 1994.

  20. 20.

    Makinson David C. (2005) Bridges from Classical to Nonmonotonic Logic. King’s College Publications, London

    Google Scholar 

  21. 21.

    Marek V. Wiktor, Mirosław Truszczyński (1993) Nonmonotonic Logic. Springer-Verlag, Berlin

    Google Scholar 

  22. 22.

    McGee Van (1996) ‘Logicaloperations’. Journal of Philosophical Logic 25: 567–580

    Article  Google Scholar 

  23. 23.

    Morgan Charles G. (1998) ‘Non-monotonic logic is impossible’. Canadian Journal of Artificial Intelligence 42: 19–25

    Google Scholar 

  24. 24.

    Morgan Charles G. (2000) ‘The nature of nonmonotonic reasoning’. Minds and Machines 10: 321–360

    Article  Google Scholar 

  25. 25.

    Pearl Judea (1988) Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann, San Francisco, CA

    Google Scholar 

  26. 26.

    Pearl, Judea, ‘System Z: A natural ordering of defaults with tractable applications to default reasoning’, in Theoretical Aspects of Reasoning about Knowedge, 1990, pp. 121–135.

  27. 27.

    Pratt-Hartmann Ian (2004) ‘Fragments of language’. Logic, Language and Information, 13(2): 207–223

    Article  Google Scholar 

  28. 28.

    Reiter Ray (1980) ‘A logic for default reasoning’. Artificial Intelligence 13: 81–132

    Article  Google Scholar 

  29. 29.

    Restall Greg (2002) ‘Carnap’s tolerance, meaning and logical pluralism’. Journal of Philosophy 99: 426–443

    Article  Google Scholar 

  30. 30.

    Sher Gila (2003) ‘A characterization of logical constants is possible’. Theoria 18(47): 189–198

    Google Scholar 

  31. 31.

    Tamminga, Allard, Belief Dynamics: Epistemological Investigations, Ph.D. thesis, University of Amsterdam, Amsterdam, 2001.

  32. 32.

    van Benthem Johan (1989) ‘Logical constants across varying types’. Notre Dame Journal of Formal Logic 30(3): 315–342

    Article  Google Scholar 

  33. 33.

    Warmbrod Ken (1999) ‘Logical constants’. Mind 108(431): 503–538

    Article  Google Scholar 

  34. 34.

    Wheeler Gregory (2006) ‘Rational acceptance and conjunctive/disjunctive absorption’. Journal of Logic, Language and Information 15(1-2):49–63

    Article  Google Scholar 

  35. 35.

    Wheeler, Gregory, ‘Two puzzles concerning measures of uncertainty and the positive Boolean connectives’, in José Neves, Manuel Santos, and José Machado, (eds.), Progress in Artificial Intelligence, 13th Portuguese Conference on Artificial Intelligence, LNAI 4874, Springer-Verlag, Berlin, 2007, pp. 170–180.

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Correspondence to Gregory Wheeler.

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Edited by Hannes Leitgeb

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Wheeler, G. Applied Logic without Psychologism. Stud Logica 88, 137–156 (2008). https://doi.org/10.1007/s11225-008-9095-8

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Keywords

  • Belief structures
  • non-monotonic logic
  • psychologism
  • pure invariantism
  • sub-System P logics