, Volume 190, Issue 13, pp 2505–2524 | Cite as

Impossible worlds and logical omniscience: an impossibility result

  • Jens Christian BjerringEmail author


In this paper, I investigate whether we can use a world-involving framework to model the epistemic states of non-ideal agents. The standard possible-world framework falters in this respect because of a commitment to logical omniscience. A familiar attempt to overcome this problem centers around the use of impossible worlds where the truths of logic can be false. As we shall see, if we admit impossible worlds where “anything goes” in modal space, it is easy to model extremely non-ideal agents that are incapable of performing even the most elementary logical deductions. A much harder, and considerably less investigated challenge is to ensure that the resulting modal space can also be used to model moderately ideal agents that are not logically omniscient but nevertheless logically competent. Intuitively, while such agents may fail to rule out subtly impossible worlds that verify complex logical falsehoods, they are nevertheless able to rule out blatantly impossible worlds that verify obvious logical falsehoods. To model moderately ideal agents, I argue, the job is to construct a modal space that contains only possible and non-trivially impossible worlds where it is not the case that “anything goes”. But I prove that it is impossible to develop an impossible-world framework that can do this job and that satisfies certain standard conditions. Effectively, I show that attempts to model moderately ideal agents in a world-involving framework collapse to modeling either logical omniscient agents, or extremely non-ideal agents.


Impossible worlds Logical omniscience Rationality Resource-bounded reasoning Logical reasoning 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Adams R. (1974) Theories of actuality. Noûs 8: 211–231CrossRefGoogle Scholar
  2. Bjerring, J. C. (2010).Non-ideal epistemic spaces. Ph.D. thesis, Australian National University.Google Scholar
  3. Bjerring, J. C. & Tang, W. H. (2011). Undermining the Stalnakerian Solution to the Problem of Logical Omniscience. Manuscript.Google Scholar
  4. Bostock D. (1997) Intermediate logic. Clarendon Press, OxfordGoogle Scholar
  5. Carnap R. (1947) Meaning and necessity, a study in semantics and modal logic. University of Chicago Press, ChicagoGoogle Scholar
  6. Chalmers, D. J. (2011). The nature of epistemic space. In A. Egan & B. Weatherson (Eds.), Epistemic modality. New York: Oxford University Press. (pp. 60-107).Google Scholar
  7. Cherniak C. (1986) Minimal rationality. MIT Press, Cambridge, MAGoogle Scholar
  8. Copi M. I. (1979) Symbolic logic. Macmillian, New YorkGoogle Scholar
  9. Correia F. (1999) Adequacy results for some Priorean modal propositional logics. Notre Dame Journal of Formal Logic 40: 236–249CrossRefGoogle Scholar
  10. Field H. (2001) Truth and the absence of fact. Oxford University Press, OxfordCrossRefGoogle Scholar
  11. Hintikka J. (1962) Belief and knowledge. Cornell University Press, IthacaGoogle Scholar
  12. Hintikka J. (1969) Models for modalities. D. Reidel Publishing Company, DordrechtGoogle Scholar
  13. Hintikka J. (1975) Impossible possible worlds vindicated. Journal of Philosophical Logic 4: 475–484CrossRefGoogle Scholar
  14. Jago M. (2009) Logical information and epistemic space. Synthese 167: 327–341CrossRefGoogle Scholar
  15. Jeffrey R. (1983) The logic of decision. University of Chicago Press, ChicagoGoogle Scholar
  16. Lewis D. (1986) On the plurality of worlds. Blackwell Publishers, OxfordGoogle Scholar
  17. Lewis D. (2004) Letters to Priest and Beall. In: Armour-Garb B., Beall J. C., Priest G. (eds) The law of non-contradiction—new philosophical essays. Oxford University Press, Oxford, pp 176–177CrossRefGoogle Scholar
  18. Nolan D. (1997) Impossible worlds: A modest approach. Notre Dame Journal of Formal Logic 38: 535–572CrossRefGoogle Scholar
  19. Priest G. (2005) Towards non-being: The logic and metaphysics of intentionality. Oxford University Press, OxfordCrossRefGoogle Scholar
  20. Robbins P. (2004) To structure, or not to structure?. Synthese 139: 55–80CrossRefGoogle Scholar
  21. Schotch P., Jensen J., Larsen P., MacLellan E. (1978) A note on three-valued modal logic. Notre Dame Journal of Formal Logic 19: 63–68CrossRefGoogle Scholar
  22. Stalnaker R. (1984) Inquiry. MIT Press, Cambridge, MAGoogle Scholar
  23. Stalnaker R. (1986) Possible worlds and situations. Journal of Philosophical Logic 15: 109–123CrossRefGoogle Scholar
  24. Stanley J. (2010) “Assertion” and intentionality. Philosophical Studies 151: 87–113CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Culture and SocietyAarhus UniversityAarhus CDenmark
  2. 2.Department of PhilosophyAarhus UniversityAarhus CDenmark

Personalised recommendations