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Knowing the intuition and knowing the counterfactual

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Abstract

I criticize Timothy Williamson’s characterization of thought experiments on which the central judgments are judgments of contingent counterfactuals. The fragility of these counterfactuals makes them too easily false, and too difficult to know.

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Notes

  1. We submitted our paper in 2006; we made limited revisions in 2007, reflecting a draft version of The Philosophy of Philosophy that was informally available at that time. But we did not then have the chance thoroughly to engage with this more authoritative version of Williamson’s project. I am therefore grateful for this opportunity to discuss that project further, in light of both subsequent study of the book, and subsequent conversations with Williamson.

  2. I paraphrase Williamson’s approach, which is given in logical notation, into English. A portion of Williamson’s chapter, along with his Appendix 2, is devoted to a discussion of the logical formulation of the counterfactual (3*); I circumvent that discussion, as I believe it peripheral to the methodological questions that concern us here.

  3. See Williamson (2007), p. 185, and Ichikawa and Jarvis (2009), p. 224.

  4. Ichikawa and Jarvis (2009), p. 226.

  5. This is so on a standard Lewis–Stalnaker semantics for counterfactual conditionals, and on any account in which A & ~C entails the falsity of \( {\text{A}}\square \to {\text{C}} \).

  6. Anna-Sara Malmgren, in a yet-unpublished manuscript, gives an (independently developed) objection to Williamson along similar lines.

  7. Thanks to Crispin Wright here.

  8. pp. 200–204.

  9. p. 200. The quantifiers Williamson here mentions range over subjects and propositions, not over worlds; Williamson’s attempt to characterize the counterfactual is:

    (3*) \( \exists {\text{x}}\exists p\,{\text{GC}}\left( {{\text{x}},p} \right)\square\!\!\to \forall {\text{x}}\forall {{\it p}}\left[ {{\text{GC}}\left( {{\text{x}},p} \right) \supset \left( {{\text{JTB}}\left( {{\text{x}},p} \right)\& \sim {\text{K}}\left( {{\text{x}},p} \right)} \right)} \right]. \)

  10. p. 201.

  11. This is very straightforward on anything in the ballpark of Lewis’s standard (invariantist) semantics for counterfactuals. Things are a bit more complicated on a contextualist semantics, but the ultimate result is the same. Consider some possibility D (deviant), where D together with G (Gettier) result in the negation of C (counterexample). On a contexutalist view, conversational salience of D might make an utterance of ‘\( {\text{G}}\square\!\!\to {\text{C}} \)’ false, even though, had D not been salient, such an utterance would have been true. It is still not the case, however, that the subsequent discussion of D challenges the truth of what was said by the earlier utterance of ‘\( {\text{G}}\square\!\!\to {\text{C}} \)’. What I said was true, though if I used the same words again now I had say something false.

  12. At the Arché workshop on which this symposium is based, Williamson responded to my presentation of such epistemic worries by invoking domain restriction.

  13. One might go on to worry, along similar lines, whether the universal claim (3) that Williamson rejects (p. 185) could be vindicated by this sort of super-robust domain restriction. However, although it easily proven that, with such a restriction, all Gettier subjects are counterexamples to K = JTB, the necessity claim of:

    1. (3)

      \( \square \forall {\text{x}}\forall {\text{p}}\left[ {{\text{GC}}\left( {{\text{x}},p} \right) \supset \left( {{\text{JTB}}\left( {x,p} \right)\& \sim {\text{K}}\left( {{\text{x}},p} \right)} \right)} \right] \)

    is still false. Although the subjects in the domain are, by hypothesis, not actual counterexamples to (3), there are worlds where they are deviantly situated such that they are counterexamples. (Compare: where the domain of the quantifier consists in all faculty members, ‘necessarily, everyone is a faculty member’ is falsified by the possibility that Professor Doddery could have retired last year.)

  14. That this necessity claim is true reflects an important difference between our approach and the super-restricted quantifier one discussed above. See previous footnote.

  15. Williamson offered this objection at the Arché workshop in September 2008.

  16. Sosa (2007) suggests that some apparent disagreement about philosophical thought experiments might be explained in this way.

  17. I presented a version of some of this material at an Arché workshop at the University of St. Andrews, devoted to Williamson’s excellent book. I am grateful to the participants there, and to the AHRC, which funded the event. Thanks also for helpful comments on an earlier version of this paper to Anna-Sara Malmgren and Crispin Wright. I am especially indebted to Benjamin Jarvis, who co-authored the (2009) paper with me, and to Timothy Williamson.

References

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Acknowledgment

I am grateful for the privilege of engaging with Timothy Williamson’s fascinating book, and in such distinguished company.

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Correspondence to Jonathan Ichikawa.

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Ichikawa, J. Knowing the intuition and knowing the counterfactual. Philos Stud 145, 435–443 (2009). https://doi.org/10.1007/s11098-009-9403-9

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