Roles, Rigidity, and Quantification in Epistemic Logic

Part of the Outstanding Contributions to Logic book series (OCTR, volume 5)


Epistemic modal predicate logic raises conceptual problems not faced in the case of alethic modal predicate logic: Frege’s “Hesperus-Phosphorus” problem—how to make sense of ascribing to agents ignorance of necessarily true identity statements—and the related “Hintikka-Kripke” problem—how to set up a logical system combining epistemic and alethic modalities, as well as others problems, such as Quine’s “Double Vision” problem and problems of self-knowledge. In this paper, we lay out a philosophical approach to epistemic predicate logic, implemented formally in Melvin Fitting’s First-Order Intensional Logic, that we argue solves these and other conceptual problems. Topics covered include: Quine on the “collapse” of modal distinctions; the rigidity of names; belief reports and unarticulated constituents; epistemic roles; counterfactual attitudes; representational versus interpretational semantics; ignorance of co-reference versus ignorance of identity; two-dimensional epistemic models; quantification into epistemic contexts; and an approach to multi-agent epistemic logic based on centered worlds and hybrid logic.


Quantified modal logic Epistemic logic Frege’s puzzle Hintikka-Kripke problem Quine on modality 



For helpful discussion or comments on this paper, we thank Johan van Benthem, Russell Buehler, Thomas Icard, David Israel, Ethan Jerzak, Alex Kocurek, Daniel Lassiter, John MacFarlane, Michael Rieppel, Shane Steinert-Threlkeld, Justin Vlasits, and Seth Yalcin.


  1. 1.
    Aloni M (2005) Individual concepts in modal predicate logic. J Philos Log 34(1):1–64CrossRefGoogle Scholar
  2. 2.
    Areces C, ten Cate B (2006) Hybrid logic. In: van Benthem J, Wolter F, Blackburn P (eds) Handbook of modal logic. Elsevier, Amsterdam, pp 821–868Google Scholar
  3. 3.
    Arló-Costa H, Pacuit E (2006) First-order classical modal logic. Studia Logica 84:171–210CrossRefGoogle Scholar
  4. 4.
    Barnes KT (1976) Proper names, possible worlds, and propositional attitudes. Philosophia 6(1):29–38CrossRefGoogle Scholar
  5. 5.
    Barwise J, Perry J (1983) Situations and attitudes. MIT Press, CambridgeGoogle Scholar
  6. 6.
    Belardinelli F, Lomuscio A (2009) Quantified epistemic logics for reasoning about knowledge in multi-agent systems. Artif Intell 173:982–1013CrossRefGoogle Scholar
  7. 7.
    van Benthem J (1985) Modal logic and classical logic. Bibliopolis, NapoliGoogle Scholar
  8. 8.
    van Benthem J (1993) Beyond accessibility: functional models for modal logic. In: de Rijke M (ed) Diamonds and defaults. Kluwer Academic, Dordrecht, pp 1–18CrossRefGoogle Scholar
  9. 9.
    van Benthem J (2010a) Frame correspondences in modal predicate logic. In: Feferman S, Sieg W (eds) Proofs, categories and computations: essays in honor of Grigori Mints. College Publications, LondonGoogle Scholar
  10. 10.
    van Benthem J (2010b) Modal logic for open minds. CSLI Publications, StanfordGoogle Scholar
  11. 11.
    van Benthem J (2011) Logical dynamics of information and interaction. Cambridge University Press, CambridgeGoogle Scholar
  12. 12.
    Braüner T, Ghilardi S (2006) First-order modal logic. In: van Benthem J, Wolter F, Blackburn P (eds) Handbook of modal logic. Elsevier, Amsterdam, pp 549–620Google Scholar
  13. 13.
    Burge T (1973) Reference and proper names. J Philos 70(14):425–439CrossRefGoogle Scholar
  14. 14.
    Carlson L (1988) Quantified Hintikka-style epistemic logic. Synthese 74(2):223–262CrossRefGoogle Scholar
  15. 15.
    Carnap R (1947) Meaning and necessity. University of Chicago Press, ChicagoGoogle Scholar
  16. 16.
    Castañeda HN (1966) ‘He’: a study in the logic of self-consciousness. Ratio 7:130–157Google Scholar
  17. 17.
    Cresswell MJ, von Stechow A (1982) De Re belief generalized. Linguist Philos 5:503–535CrossRefGoogle Scholar
  18. 18.
    Crimmins M (1992) Talk about belief. MIT Press, CambridgeGoogle Scholar
  19. 19.
    Crimmins M, Perry J (1989) The prince and the phone booth: reporting puzzling beliefs. J Philos 86(12):685–711CrossRefGoogle Scholar
  20. 20.
    Cumming S (2008) Variabilism. Philos Rev 117(4):525–554CrossRefGoogle Scholar
  21. 21.
    Davies M, Humberstone L (1980) Two notions of necessity. Philos Stud 38:1–30CrossRefGoogle Scholar
  22. 22.
    Etchemendy J (1999) The concept of logical consequence. CSLI Publications, StanfordGoogle Scholar
  23. 23.
    Fitting M, Thalmann L, Voronkov A(2001) Term-modal logics. Studia Logica 69(1): 133–169Google Scholar
  24. 24.
    Fitting M (2004) First-order intensional logic. Ann Pure Appl Log 127(1–3):171–193CrossRefGoogle Scholar
  25. 25.
    Fitting M (2006) FOIL axiomatized. Studia Logica 84(1):1–22CrossRefGoogle Scholar
  26. 26.
    Fitting M, Mendelsohn RL (1998) First-order modal logic. Kluwer, DordrechtCrossRefGoogle Scholar
  27. 27.
    Føllesdal D (1961) Referential opacity and modal logic. Routledge, London (published 2004)Google Scholar
  28. 28.
    Frege G (1892) Über Sinn und Bedeutung. Zeitschrift für Philosophie und philosophische Kritik 100:25–50Google Scholar
  29. 29.
    Garson JW (2001) Quantification in modal logic. In: Gabbay D, Guenthner E (eds) Handbook of philosophical logic, 2nd edn, vol 3. Kluwer, Dordrecht, pp 267–323Google Scholar
  30. 30.
    Garson JW (2006) Modal logic for philosophers. Cambridge Universtiy Press, CambridgeGoogle Scholar
  31. 31.
    Grove AJ (1995) Naming and identity in epistemic logic part II: a first-order logic for naming. Artif Intell 74:311–350CrossRefGoogle Scholar
  32. 32.
    Hintikka J (1962) Knowledge and belief: an introduction to the logic of the two notions. College Publications, London (Republished 2005)Google Scholar
  33. 33.
    Hintikka J (1969) On the logic of perception. Models for modalities. Reidel, Dordrecht, pp 151–183Google Scholar
  34. 34.
    Hintikka J (1970) Objects of knowledge and belief: acquaintances and public figures. J Philos 67:869–883CrossRefGoogle Scholar
  35. 35.
    Holliday WH (2014) Epistemic closure and epistemic logic I: relevant alternatives and subjunctivism. J Philos Log (forthcoming). doi: 10.1007/s10992-013-9306-2
  36. 36.
    Holliday WH (2014) Epistemic logic and epistemology. In: Hansson SO, Hendricks VF (eds) Handbook of formal philosophy. Springer (forthcoming)Google Scholar
  37. 37.
    Hughes GE, Cresswell MJ (1996) A new introduction to modal logic. Routledge, LondonGoogle Scholar
  38. 38.
    Israel D, Perry J (1996) Where monsters dwell. In: Seligman J, Westerståhl D (eds) Proceedings of the logic, language and computation: the 1994 Moraga, CSLI Publications, pp 303–316Google Scholar
  39. 39.
    Kaplan D (1968) Quantifying In. Synthese 19:178–214CrossRefGoogle Scholar
  40. 40.
    Kaplan D (1989) Demonstratives. In: Perry J, Wettstein H, Almog J (eds) Themes from Kaplan. MIT Press, Cambridge, pp 481–563Google Scholar
  41. 41.
    Kripke S (1980) Naming and necessity. Harvard University Press, CambridgeGoogle Scholar
  42. 42.
    Lehmann S (1978) The Hintikka-Kripke problem. Philosophia 8:59–70CrossRefGoogle Scholar
  43. 43.
    Lewis D (1977) Possible-world semantics for counterfactual logics: a rejoinder. J Philos Log 6:359–363CrossRefGoogle Scholar
  44. 44.
    Lewis D (1979) Attitudes De Dicto and De Se. Philos Rev 88(4):513–543CrossRefGoogle Scholar
  45. 45.
    Lewis D (1983) Individuation by acquaintance and by stipulation. Philos Rev 92(1):3–32CrossRefGoogle Scholar
  46. 46.
    Linsky L (1979) Believing and necessity. Theory Decis 11:81–94CrossRefGoogle Scholar
  47. 47.
    Ninan D (2012) Counterfactual attitudes and multi-centered worlds. Semant Pragmat 5(5):1–57Google Scholar
  48. 48.
    Parks Z (1974) Semantics for contingent identity systems. Notre Dame J Formal Log 15(2): 333–334Google Scholar
  49. 49.
    Perry J (1977) Frege on demonstratives. Philos Rev 86:474–497CrossRefGoogle Scholar
  50. 50.
    Perry J (1986) Thought without representation. Proc Aristotelian Soc 60:137–151Google Scholar
  51. 51.
    Perry J (2009) Hintikka on demonstratives. Revue internationale de philosophie 4(250): 369–382Google Scholar
  52. 52.
    Perry J (2012) Reference and reflexivity, 2nd edn. CSLI Publications, StanfordGoogle Scholar
  53. 53.
    Perry J (2013) Føllesdal and Quine’s slingshot. In: Frauchiger M (ed) Reference, rationality, and phenomenology: themes from Føllesdal. Ontos Verlag, Frankfurt, pp 237–258Google Scholar
  54. 54.
    Priest G (2002) The hooded man. J Philos Log 31(5):445–467CrossRefGoogle Scholar
  55. 55.
    Quine W (1953) Three grades of modal involvement. In: Proceedings of the 11th international congress of philosophy, vol 14. North-Holland Publishing, Amsterdam, pp 158–176Google Scholar
  56. 56.
    Quine W (1956) Quantifiers and propositional attitudes. J Philos 53(5):177–187CrossRefGoogle Scholar
  57. 57.
    Rabinowicz W, Segerberg K (1994) Actual truth, possible knowledge. Topoi 13:101–105CrossRefGoogle Scholar
  58. 58.
    Richard M (1983) Direct reference and ascriptions of belief. J Philos Log 12:425–452CrossRefGoogle Scholar
  59. 59.
    Russell B (1905) On denoting. Mind 14(4):479–493CrossRefGoogle Scholar
  60. 60.
    Russell B (1911) Knowledge by acquaintance and knowledge by description. Proc Aristotelian Soc 11:108–128Google Scholar
  61. 61.
    Schroeter L (2012) Two-dimensional semantics. In: Zalta EN (ed) The stanford encyclopedia of philosophy (winter 2012 edn)Google Scholar
  62. 62.
    Soames S (1989) Direct reference and propositional attitudes. In: Perry J, Wettstein H, Almog J (eds) Themes from kaplan. MIT Press, Cambridge, pp 393–419Google Scholar
  63. 63.
    Stalnaker RC (1984) Inquiry. MIT Press, CambridgeGoogle Scholar
  64. 64.
    Stalnaker RC (2010) Our knowledge of the internal world. Oxford University Press, BostonGoogle Scholar
  65. 65.
    Wettstein H (1988) Cognitive significance without cognitive content. Mind 97(385):1–28CrossRefGoogle Scholar
  66. 66.
    Wishon D (2012) Russellian acquaintance and Frege’s puzzle (manuscript)Google Scholar
  67. 67.
    Yalcin S (2012) Quantifying in from a Fregean perspective (manuscript)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of PhilosophyUniversity of CaliforniaRiversideUSA

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