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Modal Logic for Other-World Agnostics: Neutrality and Halldén Incompleteness

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Abstract

The logic of ‘elsewhere,’ i.e., of a sentence operator interpretable as attaching to a formula to yield a formula true at a point in a Kripke model just in case the first formula is true at all other points in the model, has been applied in settings in which the points in question represent spatial positions (explaining the use of the word ‘elsewhere’), as well as in the case in which they represent moments of time. This logic is applied here to the alethic modal case, in which the points are thought of as possible worlds, with the suggestion that its deployment clarifies aspects of a position explored by John Divers un-der the name ‘modal agnosticism.’ In particular, it makes available a logic whose Halldén incompleteness explicitly registers the agnostic element of the position – its neutrality as between modal realism and modal anti-realism.

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References

  1. van Benthem, J. (1985): Modal Logic and Classical Logic, Bibliopolis, Naples.

  2. Boolos, G. (1979): The Unprovability of Consistency, Cambridge University Press.

    Google Scholar 

  3. Boolos, G. (1993): The Logic of Provability, Cambridge University Press.

    Google Scholar 

  4. Divers, J. (2002): Possible Worlds, Routledge, London.

    Google Scholar 

  5. Divers, J. (2003): Possible-worlds semantics without possible worlds, paper presented at the Melbourne University Logic Seminar, November 14.

  6. Divers, J. (2006): Possible-worlds semantics without possible worlds: The agnostic approach, Mind 115, 187–225.

    Article  Google Scholar 

  7. Divers, J. (2005): Agnosticism about other worlds: A new antirealist programme in modality, Philosophy and Phenomenological Research 69, 659–684.

    Google Scholar 

  8. Fine, K. (1970): Propositional quantifiers in modal logic, Theoria 36, 336–346.

    Article  Google Scholar 

  9. Fine, K. (1977): ‘Postscript’ to A. N. Prior and K. Fine, Worlds, Times and Selves, Duckworth, London.

    Google Scholar 

  10. Gabbay, D. (1981): An irreflexivity lemma with applications to axiomatizations of conditions on linear frames, in U. Mönnich (ed.), Aspects of Philosophical Logic, Reidel, Dordrecht, pp. 67–89.

    Google Scholar 

  11. Goranko, V. (1995): A note on derivation rules in modal logic, Bull. Sect. Log. 24, 98–104.

    Google Scholar 

  12. Goranko, V. and Passy, S. (1992): Using the universal modality: Gains and questions, J. Log. Comput. 2, 5–30.

    Google Scholar 

  13. Hughes, G. E. and Cresswell, M. J. (1968): An Introduction to Modal Logic, Methuen, London.

    Google Scholar 

  14. Hughes, G. E. and Cresswell, M. J. (1996): A New Introduction to Modal Logic, Routledge, London.

    Google Scholar 

  15. Humberstone, L. (1983): Inaccessible worlds, Notre Dame J. Form. Log. 24, 346–352.

    Article  Google Scholar 

  16. Humberstone, L. (1987): The modal logic of “all and only”, Notre Dame J. Form. Log. 28, 177–188.

    Article  Google Scholar 

  17. Humberstone, L. (2000): Parts and partitions, Theoria 66, 41–82.

    Article  Google Scholar 

  18. Humberstone, L. (2004): Two-dimensional adventures, Philos. Stud. 118, 17–65.

    Article  Google Scholar 

  19. Humberstone, L. (2004): Yet another “choice of primitives” warning: normal modal logics, Log. Anal. 47, 395–407.

    Google Scholar 

  20. Humberstone, L. (2005): Béziau's translation paradox, Theoria 71, 138–181.

    Article  Google Scholar 

  21. Humberstone, L. (2005): ‘Modality,’ Chapter 20, in F. Jackson and M. Smith (eds.), The Oxford Handbook of Contemporary Philosophy, Oxford University Press, pp. 534–614.

  22. Jansana, R. (1994): Some logics related to von Wright's logic of place, Notre Dame J. Form. Log. 35, 88–98.

    Article  Google Scholar 

  23. Kracht, M. (1999): Tools and Techniques in Modal Logic, North-Holland (Elsevier), Amsterdam.

    Google Scholar 

  24. Kremer, P. (1997): Defining relevant implication in a propositionally quantified S4, J. Symb. Log. 62, 1057–1069.

    Article  Google Scholar 

  25. Kripke, S. A. (1965) Semantical analysis of modal logic II. Non-normal modal propositional calculi, in J. W. Addison, L. Henkin and A. Tarski (eds.), The Theory of Models, North-Holland, Amsterdam, pp. 206–220.

    Google Scholar 

  26. Lambert, K., Leblanc, H. and Meyer, R. K. (1969): A liberated version of S5, Arch. Math. Log. Grundl.forsch. 12, 151–154.

    Article  Google Scholar 

  27. Lemmon, E. J. (1966): A note on Halldén-incompleteness, Notre Dame J. Form. Log. 7, 296–300.

    Article  Google Scholar 

  28. Lemmon, E. J., Meredith, C. A., Meredith, D., Prior, A. N. and Thomas, I. (1969): Calculi of pure strict implication, in J. W. Davis, D. J. Hockney and W. K. Wilson (eds.), Philosophical Logic, Reidel, Dordrecht, pp. 215–250.

    Google Scholar 

  29. Lemmon, E. J. and Scott, D. S. (1966): An introduction to modal logic, in K. Segerberg (ed.), American Philosophical Quarterly Monograph Series, Basil Blackwell, Oxford 1977.

    Google Scholar 

  30. Lemon, O. and Pratt, I. (1997): On the incompleteness of modal logics of space: Advancing complete modal logics of place, in M. Kracht, M. de Rijke, H. Wansing and M. Zakharyeschev (eds.), Advances in Modal Logic '96, CSLI Publications, Stanford, pp. 1–18.

    Google Scholar 

  31. Lewis, C. I. and Langford, C. H. (1959): Symbolic Logic, Dover Publications. (First edn. 1932.)

  32. Lewis, D. (1983): Philosophical Papers, Vol. I, Oxford University Press, New York.

    Google Scholar 

  33. Lewis, D. (1986): On the Plurality of Worlds, Blackwell, Oxford.

    Google Scholar 

  34. Mackie, J. L. (1977): Ethics: Inventing Right and Wrong, Penguin Books, Harmondsworth.

    Google Scholar 

  35. Makinson, D. (1973): A warning about the choice of primitive operators in modal logic, J. Philos. Log. 2, 193–196.

    Google Scholar 

  36. Meredith, C. A. and Prior, A. N. (1965): Modal logic with functorial variables and a contingent constant, Notre Dame J. Form. Log. 6, 99–109.

    Article  Google Scholar 

  37. Meredith, C. A. and Prior, A. N. (1964): Investigations into implicational S5, Z. math. Log. Grundl. Math. 10, 203–220.

    Article  Google Scholar 

  38. McKinsey, J. C. C. (1953): Systems of modal logic not unreasonable in the sense of Halldén, J. Symb. Log. 18, 109–113.

    Article  Google Scholar 

  39. Morgan, C. G. (1974): Liberated brouwerian modal logic, Dialogue 13, 505–514.

    Article  Google Scholar 

  40. Morgan, C. G. (1975): Liberated versions of T, S4 and S5, Arch. Math. Log. Grundl. forsch. 17, 85–90.

    Article  Google Scholar 

  41. Morgan, C. G. (1975): Weak liberated versions of T and S4, J. Symb. Log. 40, 25–30.

    Article  Google Scholar 

  42. Morgan, C. G. (1979): Note on a strong liberated modal logic and its relevance to possible world scepticism, Notre Dame J. Form. Log. 20, 718–722.

    Article  Google Scholar 

  43. Pizzi, C. (1999): Contingency logics and propositonal quantification, Manuscrito, CLE (UNICAMP, São Paulo) 22, 283–303.

    Google Scholar 

  44. Prior, A. N. (1967): Past, Present and Future, Clarendon, Oxford.

    Google Scholar 

  45. Prior, A. N. (1971): Objects of Thought, Clarendon, Oxford.

    Google Scholar 

  46. de Rijke, M. (1992): The modal logic of inequality, J. Symb. Log. 57, 566–584.

    Article  Google Scholar 

  47. Schumm, G. F. (1993): Why does Halldén-completeness matter? Theoria 59, 192–206.

    Article  Google Scholar 

  48. Segerberg, K. (1976): “Somewhere else” and “Some other time”, in Wright and Wrong: Mini-Essays in Honor of George Henrik von Wright on his Sixtieth Birthday, Publications of the Group in Logic and Methodology of Real Finland, Vol. 3, Åbo Akademi, pp. 61–64.

  49. Segerberg, K. (1980): A note on the logic of elsewhere, Theoria 46, 183–187.

    Article  Google Scholar 

  50. Venema, Y. (1993): Derivation rules as anti-axioms in modal logic, J. Symb. Log. 58, 1003–1034.

    Article  Google Scholar 

  51. von Wright, G. H. (1979): A modal logic of place, in E. Sosa (ed.), The Philosophy of Nicholas Rescher: Discussions and Replies, Reidel, Dordrecht, pp. 65–73.

    Google Scholar 

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  1. Monash University, Victoria, Australia

    Lloyd Humberstone

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Humberstone, L. Modal Logic for Other-World Agnostics: Neutrality and Halldén Incompleteness. J Philos Logic 36, 1–32 (2007). https://doi.org/10.1007/s10992-005-9020-9

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