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Distributed Knowability and Fitch’s Paradox

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Abstract

Recently predominant forms of anti-realism claim that all truths are knowable. We argue that in a logical explanation of the notion of knowability more attention should be paid to its epistemic part. Especially very useful in such explanation are notions of group knowledge. In this paper we examine mainly the notion of distributed knowability and show its effectiveness in the case of Fitch’s paradox. Proposed approach raised some philosophical questions to which we try to find responses. We also show how we can combine our point of view on Fitch’s paradox with the others. Next we give an answer to the question: is distributed knowability factive? At the end, we present some details concerning a construction of anti-realist modal epistemic logic.

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References

  1. Brogaard, B., and J. Salerno, ‘Fitch’s paradox of knowability’, Stanford Encyclopedia of Philosophy.

  2. Brogaard B., Salerno J. (2002) ‘Clues to the paradoxes of knowability: Reply to Dummett and Tennant’. Analysis 62 (2): 143–150

    Article  Google Scholar 

  3. Cook R.T. (2006) ‘Knights, knaves and unknowable truths’. Analysis 66 (1): 10–16

    Article  Google Scholar 

  4. Douven I. (2005) ‘A principled solution to Fitch’s paradox’. Erkenntnis 62 (1): 47–69

    Article  Google Scholar 

  5. Dummett M. (2001) ‘Victor’s error’. Analysis 61(1): 1–2

    Article  Google Scholar 

  6. Fagin, R., J. Y. Halpern, Y. Moses,and M. Y. Vardi, Reasoning About Knowledge, 2 edn., MIT Press Cambridge, 2003.

  7. Fagin, R., J. Y. Halpern, and M. Y. Vardi, ‘What can machines know? On the properties of knowledge in distributed systems’, Journal of the ACM, 39 (1992), 2, 328–376.

    Google Scholar 

  8. Fitch F.B. (1963) ‘A logical analysis of some value concepts’. The Journal of Symbolic Logic 28 (2): 135–142

    Article  Google Scholar 

  9. Gabbay, D. M., ‘Fibred semantics and the weaving of logics part I: Modal and intuitionistic logics’, The Journal of Symbolic Logic, 61 (1996), 4, 1057–1120.

    Google Scholar 

  10. Halpern J.Y. (1996) ‘Should knowledge entail belief?’. Journal of Philosophical Logic 25, 483–494

    Article  Google Scholar 

  11. Halpern, J. Y., and Y. Moses, ‘Knowledge and common knowledge in a distributed environment’, Journal of the ACM, 37 (1990), 3, 549–587.

    Google Scholar 

  12. Halpern, J. Y., and Y. Moses, ‘A guide to completeness and complexity for modal logics of knowledge and belief’, Artificial Intelligence, 54 (1992), 319–379.

    Google Scholar 

  13. Hand M., Kvanvig J.L. (1999) ‘Tennant on knowability’. Australasian Journal of Philosophy 77 (4): 422–428

    Article  Google Scholar 

  14. Kracht M., Wolter F. (1991) ‘Properties of indepedently axiomatizable bimodal logics’. The Journal of Symbolic Logic 56 (4): 1469–1485

    Article  Google Scholar 

  15. Kvanvig, J. L., ‘Restriction strategies for knowability: Some lessons in false hope’, Online Papers in Philosophy, 6 April 2004.

  16. Martinez C., Sagüillo J.-M., Vilanova J. (1997) ‘Fitch’s problem and the knowability paradox: Logical and philosophical remarks’. Logica Trianguli 1: 73–91

    Google Scholar 

  17. Palczewski, R., ‘On aporetical relations between realist and anti-realist theories’, In preparation.

  18. Percival P. (1990) ‘Fitch and intuitionistic knowability’. Analysis 50: 182–187

    Article  Google Scholar 

  19. Polacik, T., ‘Propositional quantification in the monadic fragment of intuitionistic logic’, Journal of Symbolic Logic, 63 (1998), 1, 269–300.

    Google Scholar 

  20. Rosenkranz S. (2004) ‘Fitch back in action again?’. Analysis 64: 67–71

    Article  Google Scholar 

  21. Tennant, N., The Taming of the True, Oxford: larendon Press, 1997.

  22. Tennant N. (2000) ‘Anti-realist aporias’. Mind 109 (436): 825–854

    Article  Google Scholar 

  23. Tennant N. (2001) ‘Is every truth knowable? Reply to Hand and Kvanvig’. Australasian Journal of Philosophy 79 (1): 107–113

    Article  Google Scholar 

  24. Tennant, N., ‘Is every truth Knowable? Reply to Williamson’, Ratio (new series), 14 (2001), 3, 263–280.

  25. van Benthem J. (2004) ‘What one may come to know’. Analysis 64 (2): 95–105

    Article  Google Scholar 

  26. van der Hoek, W.,and J.-J. Meyer, Epistemic Logic for AI and Computer Science, 2 edn., Cambridge University Press, 2004.

  27. van der Hoek, W., B. van Linder,and J.-J. Meyer, ‘Group knowledge is not always distributed (neither is it always implicit)’, Mathematical Social Sciences,38 (1999), 215–240.

    Google Scholar 

  28. Wansing, H., ‘Diamonds are a philosopher’s best friends. The knowability paradox and modal epistemic relevance logic’, Journal of Philosophical Logic, 31 (2002), 591– 612.

    Google Scholar 

  29. Williamson T. (1982) ‘Intuitionism disproved?’. Analysis 42: 203–207

    Article  Google Scholar 

  30. Williamson, T., ‘Two complete anti-realist modal epistemic logic’, The Journal of Symbolic Logic, 55 (1990), 1, 297–314.

    Google Scholar 

  31. Williamson T. (1992) ‘On intuitionistic modal epistemic logic’. Journal of Philosophical Logic 21:63–89

    Google Scholar 

  32. Williamson, T., ‘Verificationism and non-distributive knowledge’, Australasian Journal of Philosophy, 71 (1993), 1, 78–86.

    Google Scholar 

  33. Williamson T. (1994) ‘Never say never’. Topoi 13: 135–145

    Article  Google Scholar 

  34. Williamson, T., Knowledge and its Limits, Oxford University Press, Oxford, 2000.

  35. Williamson, T., ‘Tennant on knowable truth’, Ratio (new series), 13 (2000), 2, 99–114.

  36. Wright C. (1992) Truth and Objectivity. Harvard University Press, Harvard

    Google Scholar 

  37. Wright, C., Saving the Differences: Essays on Themes from “Truth and Objectivity”, Harvard University Press, 2003.

Download references

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Correspondence to Rafał Palczewski.

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Special Issue Formal Epistemology II. Edited by Branden Fitelson

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Palczewski, R. Distributed Knowability and Fitch’s Paradox. Stud Logica 86, 455–478 (2007). https://doi.org/10.1007/s11225-007-9070-9

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