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Safety, Skepticism, and Lotteries

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Abstract

Several philosophers have claimed that S knows p only if S’ s belief is safe, where S's belief is safe iff (roughly) in nearby possible worlds in which S believes p, p is true. One widely held intuition many people have is that one cannot know that one's lottery ticket will lose a fair lottery prior to an announcement of the winner, regardless of how probable it is that it will lose. Duncan Pritchard has claimed that a chief advantage of safety theory is that it can explain the lottery intuition without succumbing to skepticism. I argue that Pritchard is wrong. If a version of safety theory can explain the lottery intuition, it will also lead to skepticism.

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Notes

  1. That is (roughly) the principle that for any propositions p, q and r, if S knows p, knows q, and competently deduces r from p and q while retaining her knowledge of p and of q, then S will know r.

  2. I will assume the less controversial single-premise epistemic closure: (roughly) that for any propositions p and q, if S knows p, and competently deduces q from p while retaining her knowledge of p, then S will know q.

  3. Most epistemologists want an account of knowledge which is consistent with the truth of the lottery intuition, and explains why we can’t know that a lottery ticket will lose, prior to the announcement of the winner. In this paper I’m going to ignore philosophers like Hill and Schechter (2007), who deny the truth of the lottery intuition.

  4. Exception: an infinite-ticketed lottery. Here the probability that a ticket will lose will be 1, but I still have the intuition that I can’t know my ticket will lose. To explain this intuition we’d have to change (*) to the following principle: S’s knows p only if S’s evidence entails p. But then the explanation could proceed along the lines I’m about to give for a finite-ticketed lottery. Henceforth I shall be ignoring infinite lotteries in this paper.

  5. Cohen (1999), (2000), Harman (1973), and Hawthorne (2004).

  6. That it does not lead to skepticism seems to me to be asserted or at least presupposed in Dretske (1981), Williamson (2000), and Hawthorne (2004, pp. 91–94). In Dodd (2007) I argue that (*) does lead to skepticism.

  7. Of course Safety Theory is compatible with (*). Williamson (2000) accepts both, for instance.

  8. Note that in this explanation I was using the parenthetical version of (SCK)—S’s must believe truly in all—not nearly all—nearby possible worlds. I think we have to use this version of (SCK) to explain the lottery intuition. More on this later.

  9. It should be pointed out, however, that Lewis’ semantics for might-counterfactuals is controversial. For instance, it is denied by Stalnaker (1981) and DeRose (1999). What I’m doing here is giving one way of arguing for ($). The Safety Theory explanation of the lottery intuition needs ($) to be true.

  10. Please read my quotation marks as corner quotes where appropriate.

  11. For a more detailed discussion on keeping the belief forming method fixed, (see Nozick 1981, p. 179ff).

  12. I also think my arguments would apply to Smith (2010)’s theory of epistemic justification, at least if it entails that one cannot have a justified belief that one’s ticket won’t win the lottery. Applied to Smith’s theory, the arguments would show that it leads to skepticism about epistemic justification, that far fewer of our beliefs are epistemically justified than we normally think.

  13. An anonymous referee for this journal pointed out to me that the argument of this paper was anticipated by Greco (2007). I develop with greater detail and rigor a line of thought Greco presents briefly. Additionally, in sect. 3.3 I respond to an important objection to the line of thought, an objection Greco doesn't consider and which will occur to many readers.

  14. I.e., where L states the laws, and S n+1 is a latter stage than S n (a stage that actually obtains) the system is indeterministic iff \(\diamondsuit\)(L \(\wedge S_n \wedge \neg S_{n+1}\)). This definition is standard (see e.g., Montague 1974; Lewis 1973, pp. 460–461; van Inwagen 1983).

  15. I’m grateful to Martin Smith for helping me to see that whether the system is indeterministic doesn’t matter.

  16. For simplicity, here and elsewhere in the paper I will ignore the necessary parenthetical qualification in EC. Nothing hangs on this. All my arguments could be recast with this simplification removed.

  17. Assuming that there are a large enough number of possible histories. In the argument of this and the next section, we will only be concerned with applications of the model where this assumption is satisfied.

  18. Compare Hawthorne (2004, pp. 4–5).

  19. There is an objection to this claim in the literature based on the notion of quasi-miracles in Lewis (1986) or on the distinction between typicality and atypicality in Williams (2008). I will respond to this objection in Sect. 3.3.

  20. Many readers will find this section superfluous, given that contemporary physics teaches us that subatomic particles and molecules are unpredictable in the relevant way. I encourage such readers to skip ahead to Sect. 3.3.

  21. Actually, all that follows from epistemic closure is that If I know NYC still exists, then I’m in a position to know that we haven’t won a subatomic lottery. However, as I already said in footnote 16, in this paper I’ll be assuming that subjects know whatever they’re in a position to know. This idealization enables me to simplify the presentation of the argument, but nothing hangs on it. My argument could be recast with this idealization eliminated.

  22. Some readers may think it better to say that one must know or be in a position to know the conditional. My statement of 3 reflects my decision, mentioned in previous footnotes, to make the simplifying assumption that subjects know what they’re in a position to know. See footnotes 21 and 16.

  23. I am hoping the reader gets the intuitive idea of how Williams demarcates the distinction between typical and atypical events. For more details, see his paper. The distinction is based on the work of Elga (2004), Gaifman and Snir (1982).

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Acknowledgments

I would like to thank those who attended my presentation of this paper at the Arché Research Centre’s 2008 Reading Party, and at the University of St. Andrews. I am especially indebted to Federico Luzzi, Martin Smith and Jonathan Schaffer for feedback and for discussions of Safety Theory. Additionally, I am grateful to the two anonymous referees at this journal who reviewed my paper. Their comments led to important improvements, including the corrections of some errors.

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  1. Department of Philosophy, Northern Institute of Philosophy, University of Aberdeen, Aberdeen, UK

    Dylan Dodd

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Dodd, D. Safety, Skepticism, and Lotteries. Erkenn 77, 95–120 (2012). https://doi.org/10.1007/s10670-011-9305-z

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