Skip to main content
Log in

The Problem of Rational Knowledge

  • Original Article
  • Published:
Erkenntnis Aims and scope Submit manuscript

Abstract

Real-world agents do not know all consequences of what they know. But we are reluctant to say that a rational agent can fail to know some trivial consequence of what she knows. Since every consequence of what she knows can be reached via chains of trivial cot be dismissed easily, as some have attempted to do. Rather, a solution must give adequate weight to the normative requirements on rational agents’ epistemic states, without treating those agents as mathematically ideal reasoners. I’ll argue that agents can fail to know trivial consequences of what they know, but never determinately. Such cases are epistemic oversights on behalf of the agent in question, and the facts about epistemic oversights are always indeterminate facts. As a result, we are never in a position to assert that such-and-such constitutes an epistemic oversight for agent i (for we may rationally assert only determinate truths). I then develop formal epistemic models according to which epistemic accessibility relations are vague. Given these models, we can show that epistemic oversights always concern indeterminate cases of knowledge.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Belnap, N. (1977). A useful four-valued logic. In J. Dunn & G. Epstein (Eds.), Modern use of multiple-valued logic. Dordrecht: Reidel.

    Google Scholar 

  • Bjerring, J. (2011). Impossible worlds and logical omniscience: an impossibility result. Synthese. doi:10.1007/s11229-011-0038-y.

  • Chalmers, D. (2010). The nature of epistemic space. In A. Egan & B. Weatherson (Eds.), Epistemic modality. Oxford: Oxford University Press.

    Google Scholar 

  • Fagin, R., & Halpern, J. (1988). Belief, awareness and limited reasoning. Artificial Intelligence, 34, 39–76.

    Article  Google Scholar 

  • Fagin, R., Halpern, J., Moses, Y., & Vardi, M. (1995). Reasoning about knowledge. Cambridge: MIT press.

    Google Scholar 

  • Fagin, R., Halpern, J., & Vardi, M. (1990). A nonstandard approach to the logical omniscience problem. In R. Parikh (Ed.), Proceedings of the 3rd conference on theoretical aspects of reasoning about knowledge (pp. 41–55). Burlington: Morgan Kaufmann.

  • Hintikka, J. (1962). Knowledge and belief: An introduction to the logic of the two notions. Ithaca: Cornell University Press.

    Google Scholar 

  • Hintikka, J. (1975). Impossible possible worlds vindicated. Journal of Philosophical Logic, 4, 475–484.

    Article  Google Scholar 

  • Jago, M. (2009). Logical information and epistemic space. Synthese, 167(2), 327–341.

    Article  Google Scholar 

  • Jago, M. (2012). Constructing worlds. Synthese, 189(1), 59–74.

    Article  Google Scholar 

  • Jago, M. (2013). The content of deduction. Journal of Philosophical Logic, 42(2), 317–334.

    Article  Google Scholar 

  • Kleene, S.C. (2002). Mathematical logic. New York: Dover.

    Google Scholar 

  • Lakemeyer, G. (1986). Steps towards a first-order logic of explicit and implicit belief. In J. Y. Halpern (Ed.), Proceedings of the first conference on theoretical aspects of reasoning about knowledge (pp. 325–340) San Francisco, California: Morgan Kaufmann.

  • Lakemeyer G. (1987). Tractable metareasoning in propositional logic of belief. In Proceedings of the 10th international joint conference on artificial intelligence, pp. 401–408.

  • Levesque, H. J. (1984). A logic of implicit and explicit belief. In Proceedings of the 4th national conference on artificial intelligence, pp. 198–202.

  • Lewis, D. (1982). Logic for equivocators. Noûs, 16(3), 431–441.

    Article  Google Scholar 

  • Lewis, D. (1986). On the plurality of worlds. Oxford: Blackwell.

    Google Scholar 

  • Lewis, D. (2004). Letters to priest and beall. In B. Armo-Garb, J. Beall & G. Priest & (Eds.), The law of non-contradiction—New philosophical essays (pp. 176–177). Oxford: Oxford University Press.

    Chapter  Google Scholar 

  • Rantala, V. (1975). Urn models. Journal of Philosophical Logic, 4, 455–474.

    Article  Google Scholar 

  • Rantala, V. (1982). Impossible worlds semantics and logical omniscience. Acta Philosophica Fennica, 35, 18–24.

    Google Scholar 

  • Restall, G. (2005). Multiple conclusions. In Proceedings of the 12th international congress of logic, methodology and philosophy of science, pp. 189–205.

  • Restall, G. (2008a). Assertion and denial, commitment and entitlement, and incompatibility (and some consequence). Studies in Logic, 1, 26–36.

    Google Scholar 

  • Restall, G. (2008b). Assertion, denial and non-classical theories. Proceedings of the 4th world congress of paraconsistency, Melbourne.

  • Stalnaker, R. (1984). Inquiry. Cambridge, MA: MIT Press.

    Google Scholar 

  • Williamson, T. (1992). Inexact knowledge. Mind, 101(402), 217–242.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mark Jago.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jago, M. The Problem of Rational Knowledge. Erkenn 79 (Suppl 6), 1151–1168 (2014). https://doi.org/10.1007/s10670-013-9545-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10670-013-9545-1

Keywords

Navigation