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Ideal rationality and logical omniscience

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Abstract

Does rationality require logical omniscience? Our best formal theories of rationality imply that it does, but our ordinary evaluations of rationality seem to suggest otherwise. This paper aims to resolve the tension by arguing that our ordinary evaluations of rationality are not only consistent with the thesis that rationality requires logical omniscience, but also provide a compelling rationale for accepting this thesis in the first place. This paper also defends an account of apriori justification for logical beliefs that is designed to explain the rational requirement of logical omniscience. On this account, apriori justification for beliefs about logic has its source in logical facts, rather than psychological facts about experience, reasoning, or understanding. This account has important consequences for the epistemic role of experience in the logical domain. In a slogan, the epistemic role of experience in the apriori domain is not a justifying role, but rather an enabling and disabling role.

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Notes

  1. This informal statement of the axioms is taken from Christensen (2004, p. 16).

  2. See Hajek (2010) for discussion of the link between probability and modality in connection with the regularity thesis—that is, the thesis that if pr (P) \(=\) 1, then it is necessary that P.

  3. The requirement of logical omniscience is also a consequence of deductive theories of rationality that require logical consistency and closure.

  4. Not all apriori truths are epistemically necessary in the sense that they are conclusively justified, including Hawthorne’s (2002) examples of what he calls “deeply contingent apriori knowledge”.

  5. I am particularly interested in the extension to apriori epistemic principles. See Titelbaum (forthcoming) for relevant discussion.

  6. See Kahneman et al. (1982) for scientific evidence that we routinely violate probabilistic coherence.

  7. I am indebted here to discussion with Roger White. See also Jarvis and Ichikawa (2013, Chap. 12–13) for related discussion in the context of their critique of what they call ‘experiential rationalism’.

  8. See Boghossian (2000) in defense of rule-circular justification for logical beliefs.

  9. See Casullo (2003, Chap. 2) for the traditional definition and discussion of the distinction between broad and narrow conceptions of experience.

  10. See BonJour (1998), Huemer (2001), Chudnoff (2013), and Bengson (forthcoming) for versions of experientialism.

  11. Alston considers truth-sufficiency as an account of privileged introspective access to one’s mental states. See Smithies (2012a) for a truth-sufficiency account of introspective justification that provides a model for the truth-sufficiency account of apriori logical justification proposed here.

  12. This may have been Frege’s view. See Burge (1998) for discussion.

  13. We need some restriction because every concept can figure in some logical truth, but rationality does not require grasping every concept. So the scope of the logical omniscience requirement should be restricted to propositions composed from concepts that the subject actually grasps or would if she were ideally rational.

  14. See Feldman and Conee (1985, p. 17), Alston (1988, pp. 286–288), Pryor (2001, pp. 114–115), and Christensen (2004, pp. 161–162) for additional examples of this kind.

  15. Compare Pryor (2001, p. 115, fn. 36) for a related distinction between thick and thin senses of ‘obligation’.

  16. See Schoenfield (2012) for a related distinction between two notions of rationality: what your evidence supports versus what you ought to believe given your evidence. See also Schoenfield (2013) for further development of her proposal.

  17. See Sect. 6 for an account of good reasoning.

  18. On Kratzer’s (1981) semantics, ‘S ought to do A,’ is true in a context C if S does A in all of the possible worlds in the contextually relevant modal base that are optimal according to the contextually relevant ordering source. Using Kratzer’s framework, we can model ideal and non-ideal standards of rationality using the same ordering source but a different modal base. In contexts where ideal standards are relevant, the modal base includes worlds in which the subject takes options that are beyond her actual capacities, whereas these worlds are excluded in contexts were ordinary standards are relevant.

  19. See Kvanvig and Menzel (1990) for the proposal that doxastic justification is propositional justification plus basing. Turri (2010) proposes counterexamples, but as far as I can see, they do not satisfy the proper basing condition proposed here. But I am not sure that the proper basing condition can be understood independently of doxastic justification and so immunity from counterexample may be gained at the cost of reduction.

  20. See Sosa (2003) and Smithies (2012b) for more detailed discussion of the problem of the speckled hen and its implications for the basing relation.

  21. See Burge (1993, p. 460), BonJour (1998, pp. 9–10) and Chalmers (2012, pp. 189–190).

  22. See Peacocke (2004, pp. 205–207), Chalmers (2012, pp. 185–198) and Ichikawa and Jarvis (2013, pp. 166–170) for similarly expansive conceptions of the enabling role of experience, although none of them goes so far as to endorse the claims about the disabling role of experience proposed in Sects. 7 and 8.

  23. See also Feldman (2005), Christensen (2010), and Kelly (2010), although all of these authors acknowledge that evidence of one’s cognitive imperfection is in some respects different from more standard examples of undercutting defeaters.

  24. Compare Pryor’s (2004) account of what’s wrong with Moore’s argument for the existence of the external world. According to Pryor, there is nothing wrong with the justificatory structure of the argument, although there are limits on its dialectical effectiveness: “Anyone who had doubts about its conclusion couldn’t use the argument to rationally overcome those doubts” (2004, p. 363).

  25. This account of the function of evidence of one’s cognitive imperfection has more general implications for debates about the epistemic significance of disagreement, but I do not have space to explore them here. See Van Wietmarschen (2013) for an account that is broadly congenial to mine.

  26. Hawthorne (2007) uses the example of “apriori gas” to argue that apriori knowledge does not supervene on one’s intrinsic properties given a safety condition for knowledge. However, the safety condition is not violated in the presence of apriori gas so long as it is formulated in a basis-sensitive way.

  27. This fits with a version of access internalism on which propositional justification but not doxastic justification is accessible by reflection alone. See Smithies (2012c).

  28. See Schaffer (2010) for the debasing demon.

  29. Compare Chalmers’s (2012, pp. 101–107) response to the problem of self-doubt by postulating ideal insulated cognizers: “cognizers whose rational processes are practically insulated from higher-order beliefs...but otherwise ideal.”

  30. See Lasonen Aarnio (2014) for criticism of this proposal.

  31. I am grateful to audiences in 2012 and 2013 at Ohio State, Cologne, Oxford, Aberdeen, and MIT for feedback on this paper. Many thanks especially to Magdalena Balcerak Jackson, Albert Casullo, David Chalmers, David Christensen, Jeremy Fantl, John Hawthorne, Brian Hedden, Sophie Horowitz, Jonathan Ichikawa, Carrie Jenkins, Brian Kim, Chris Pincock, Bernhard Salow, Miriam Schoenfield, Jack Spencer, Roger White, Crispin Wright, and the referees for Synthese. The Templeton Foundation supported work on this paper during a visit to Oxford University in Trinity 2013.

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  1. Department of Philosophy, The Ohio State University, 350 University Hall, 230 North Oval Mall, Columbus, OH, 43210, USA

    Declan Smithies

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Smithies, D. Ideal rationality and logical omniscience. Synthese 192, 2769–2793 (2015). https://doi.org/10.1007/s11229-015-0735-z

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