Philosophical Studies

, Volume 163, Issue 2, pp 429–452 | Cite as

Rational self-doubt and the failure of closure

Article

Abstract

Closure for justification is the claim that thinkers are justified in believing the logical consequences of their justified beliefs, at least when those consequences are competently deduced. Many have found this principle to be very plausible. Even more attractive is the special case of Closure known as Single-Premise Closure. In this paper, I present a challenge to Single-Premise Closure. The challenge is based on the phenomenon of rational self-doubt—it can be rational to be less than fully confident in one’s beliefs and patterns of reasoning. In rough outline, the argument is as follows: Consider a thinker who deduces a conclusion from a justified initial premise via an incredibly long sequence of simple competent deductions. Surely, such a thinker should suspect that he has made a mistake somewhere. And surely, given this, he should not believe the conclusion of the deduction even though he has a justified belief in the initial premise.

Keywords

Single-premise closure Justification Competent deduction Deductive inference Long sequence argument Rational self-doubt 

References

  1. Alston, W. (1980). Level confusions in epistemology. Midwest Studies in Philosophy, 5, 143–145.CrossRefGoogle Scholar
  2. Boghossian, P. (1989). The rule following considerations. Mind, 98, 507–549.CrossRefGoogle Scholar
  3. Boghossian, P. (Ed.). (2008). Epistemic rules. In Content and justification (pp. 109–134). Oxford: Oxford University Press.Google Scholar
  4. Carroll, L. (1895). What the tortoise said to Achilles. Mind, 4, 278–280.CrossRefGoogle Scholar
  5. Cheng, P., & Holyoak, K. (1985). Pragmatic reasoning schemas. Psychology, 17, 391–416.Google Scholar
  6. Christensen, D. (2004). Putting logic in its place. Oxford: Oxford University Press.CrossRefGoogle Scholar
  7. Christensen, D. (2008). Does Murphy’s law apply in epistemology? Self-doubt and rational ideals. Oxford Studies in Epistemology, 2, 3–31.Google Scholar
  8. Christensen, D. (2010). Higher-order evidence. Philosophy and Phenomenological Research, 81, 185–215.CrossRefGoogle Scholar
  9. Cosmides, L. (1989). The logic of social exchange. Cognition, 31, 187–276.CrossRefGoogle Scholar
  10. Dretske, F. (1970). Epistemic operators. Journal of Philosophy, 67, 1007–1023.CrossRefGoogle Scholar
  11. Elga, A. (2010). How to disagree about how to disagree. In R. Feldman & T. Warfield (Eds.), Disagreement. Oxford: Oxford University Press.Google Scholar
  12. Elga, A. (unpublished). Lucky to be rational. http://www.princeton.edu/~adame/papers/bellingham-lucky.pdf.
  13. Evans, J., Newstead, S., & Byrne, R. (1993). Human reasoning: The psychology of deduction. Hillsdale: Lawrence Erlbaum.Google Scholar
  14. Evnine, S. (1999). Believing conjunctions. Synthese, 118, 201–227.CrossRefGoogle Scholar
  15. Field, H. (2000). A prioricity as an evaluative notion. In P. Boghossian & C. Peacocke (Eds.), New essays on the a priori (pp. 117–149). Oxford: Oxford University Press.CrossRefGoogle Scholar
  16. Field, H. (2009a). Epistemology without metaphysics. Philosophical Studies, 143, 249–290.CrossRefGoogle Scholar
  17. Field, H. (2009b). What is the normative role of logic? Proceedings of the Aristotelian Society Supplementary Volume, 133, 251–268.CrossRefGoogle Scholar
  18. Harman, G. (1986). Change in view: Principles of reasoning. Cambridge, MA: MIT Press.Google Scholar
  19. Harman, G. (1995). Rationality. In E. Smith & D. Oshershon (Eds.), Thinking: An invitation to cognitive science (Vol. 3, pp. 175–211). Cambridge, MA: The MIT Press.Google Scholar
  20. Hawthorne, J. (2004). Knowledge and lotteries. Oxford: Oxford University Press.Google Scholar
  21. Kripke, S. (1982). Wittgenstein on rules and private language. Cambridge, MA: Harvard University Press.Google Scholar
  22. Kyburg, H. (1970). Conjunctivitis. In M. Swain (Ed.), Induction, acceptance, and rational belief (pp. 55–82). New York: Humanities Press.CrossRefGoogle Scholar
  23. Lasonen-Aarnio, M. (2008). Single premise deduction and risk. Philosophical Studies, 141, 157–173.CrossRefGoogle Scholar
  24. Lewis, D. (1971). Immodest inductive methods. Philosophy of Science, 38, 54–63.CrossRefGoogle Scholar
  25. Makinson, D. (1965). The paradox of the preface. Analysis, 25, 205–207.CrossRefGoogle Scholar
  26. Nelkin, D. (2000). The lottery paradox, knowledge, and rationality. The Philosophical Review, 109, 373–409.Google Scholar
  27. Nozick, R. (1981). Philosophical explanations. Cambridge, MA: Harvard University Press.Google Scholar
  28. Pollock, J. (1983). Epistemology and probability. Synthese, 55, 231–252.CrossRefGoogle Scholar
  29. Pollock, J. (1986). Contemporary theories of knowledge (1st ed.). Towota, NJ: Rowman and Littlefield Publishers.Google Scholar
  30. Vogel, J. (1990). Are there counterexamples to the closure principle? In M. Roth & G. Ross (Eds.), Doubting: Contemporary perspectives on skepticism (pp. 13–27). Dordrecht: Kluwer.Google Scholar
  31. Williamson, T. (2000). Knowledge and its limits. Oxford: Oxford University Press.Google Scholar
  32. Williamson, T. (2009). Reply to Hawthorne and Lasonen-Aarnio. In P. Greenough & D. Pritchard (Eds.), Williamson on knowledge (pp. 313–329). Oxford: Oxford University Press.Google Scholar
  33. Williamson, T. (forthcoming). Very improbable knowing. In T. Dougherty (Ed.), Evidentialism and its discontents. Oxford: Oxford University Press.Google Scholar
  34. Wright, C. (1985). Facts and certainty. Proceedings of the British Academy, 7, 429–472.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of PhilosophyBrown UniversityProvidenceUSA

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