Synthese

, Volume 190, Issue 14, pp 2731–2748 | Cite as

Epistemic closure under deductive inference: what is it and can we afford it?

Article

Abstract

The idea that knowledge can be extended by inference from what is known seems highly plausible. Yet, as shown by familiar preface paradox and lottery-type cases, the possibility of aggregating uncertainty casts doubt on its tenability. We show that these considerations go much further than previously recognized and significantly restrict the kinds of closure ordinary theories of knowledge can endorse. Meeting the challenge of uncertainty aggregation requires either the restriction of knowledge-extending inferences to single premises, or eliminating epistemic uncertainty in known premises. The first strategy, while effective, retains little of the original idea—conclusions even of modus ponens inferences from known premises are not always known. We then look at the second strategy, inspecting the most elaborate and promising attempt to secure the epistemic role of basic inferences, namely Timothy Williamson’s safety theory of knowledge. We argue that while it indeed has the merit of allowing basic inferences such as modus ponens to extend knowledge, Williamson’s theory faces formidable difficulties. These difficulties, moreover, arise from the very feature responsible for its virtue- the infallibilism of knowledge.

Keywords

Knowledge Inference Modus ponens Infallibilism Lottery propositions Chance Epistemic probability Knowledge safety Single premise closure Multi premise closure 

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References

  1. Alspector-Kelly M. (2011) Why safety doesn’t save closure. Synthese 183(2): 127–142CrossRefGoogle Scholar
  2. Cohen S. (1988) How to be a fallibilist. Philosophical Perspectives, 2: 91–123CrossRefGoogle Scholar
  3. Christensen D. (2004) Putting logic in its place: Formal constraints on rational belief. OUP, New YorkCrossRefGoogle Scholar
  4. Feldman R. (1981) Fallibilism and knowing that one knows. Philosophical Review 90(2): 266–282CrossRefGoogle Scholar
  5. Fumerton R. (2006) Epistemology. Blackwell, Malden, MAGoogle Scholar
  6. Gettier E. L. (1963) Is justified true belief knowledge?. Analysis 23: 121–123CrossRefGoogle Scholar
  7. Hawthorne, J. (2004). Knowledge and lotteries. Oxford: OUP.Google Scholar
  8. Hawthorne, J., & Lasonen-Aarnio, M. (2009). Knowledge and objective chance. In P. Greenough & D. Pritchard (Eds.), Williamson on knowledge (pp. 92–108). Oxford: Oxford University Press.Google Scholar
  9. Hawthorne J., Stanley J. (2008) Knowledge and action. Journal of Philosophy 105(10): 571–590Google Scholar
  10. Kripke, S. (2011). On two paradoxes of knowledge. In Philosophical troubles, collected papers (Vol. I). Oxford: OUP.Google Scholar
  11. Kyburg H. (1961) Probability and the logic of rational belief. Wesleyan University Press, Middletown, CTGoogle Scholar
  12. Kyburg H. (1970) Conjunctivitis. In: Swain M. (eds) Induction, acceptance and rational belief. Reidel, Dordrecht, pp 55–82CrossRefGoogle Scholar
  13. Lewis, D. (1986). A subjectivist’s guide to objective chance. In Philosophical papers (Vol. II, pp. 83–113). Oxford: Oxford University Press.Google Scholar
  14. Lewis, D. (1999). Humean supervenience debugged. (Reprinted from Papers in metaphysics and epistemology, by D. Lewis, Ed., Cambridge: Cambridge University Press).Google Scholar
  15. Makinson D. (1965) The paradox of the preface. Analysis 25: 205–207CrossRefGoogle Scholar
  16. Pagin, P. (1990). Review of Roy Sorenson, Blindspots, Clarendon Press, Oxford 1988. History and Philosophy of Logic, 11, 243–245.Google Scholar
  17. Pryor, J. (2000). The skeptic and the dogmatist. Noûs, 34(4), 517–549.Google Scholar
  18. Sharon, A., & Spectre, L. (forthcoming). Evidence and the openness of knowledge. Philosophical Studies.Google Scholar
  19. Smith M. (2010) What else justification could be. Noûs 44(1): 10–31CrossRefGoogle Scholar
  20. Stanley J. (2005) Fallibilism and concessive knowledge attributions. Analysis, 65: 126–131CrossRefGoogle Scholar
  21. Williamson T. (2000) Knowledge and its limits. OUP, OxfordGoogle Scholar
  22. Williamson, T. (2009). Reply to John Hawthorne and Maria Lasonen-Aarnio. In P. Greenough & D. Pritchard (Eds.), Williamson on knowledge. Oxford: Oxford University Press.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Stanford UniversityStanfordUSA
  2. 2.The Open University of IsraelRaananaIsrael

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