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Sensitivity, Safety, and Closure

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Abstract

It is widely thought that if knowledge requires sensitivity, knowledge is not closed because sensitivity is not closed. This paper argues that there is no valid argument from sensitivity failure to non-closure of knowledge. Sensitivity does not imply non-closure of knowledge. Closure considerations cannot be used to adjudicate between safety and sensitivity accounts of knowledge.

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Notes

  1. For a systematic treatment of the interplay between epistemology and (epistemic) logic see De Bruin (2008), Hendricks and Symons (2006), and Van Benthem (2006).

  2. One of the problems with the method-relativization of modal knowledge conditions (such as sensitivity and adherence) is that it involves the individuation of belief forming methods which, in turn, involves the infamous generality problem. The generality problem is the problem of categorizing belief forming process-tokens into process-types for the purposes of epistemic evaluation. The crux is that there are indefinitely many ways to categorize belief forming process-tokens into types.

  3. McGinn gives basically the same argument against closure: “The following seems an intuitively correct principle: one can know that p only if one can tell whether p – I can know (e.g.) It is raining outside only if I can tell whether it is raining outside. Let us apply this principle to my putative knowledge that there is a table in front of me and that I am not a brain in a vat. Can I tell whether there is a table there? I think that in the ordinary use of the phrase ‘tell whether,’ what this requires is that I can distinguish there being a table from there being a chair or dog or some such. So, granted that conditions are normal – there is a table there, my eyes are functioning normally, etc. – I can tell whether there is a table there. But can I tell whether I am a brain in a vat? … [W]hat is required for telling whether I am a brain in a vat is that I be able to distinguish my being a brain in a vat from my not being a brain in a vat. But it seems clear that I lack this ability – I cannot tell whether I am a brain in a vat because I have no means of distinguishing being in that condition from not being in that condition” (1984: 543).

  4. This is not Roush’s final analysis but only a first approximation. Note that ‘S knows that p implies q’ in the recursive clause is not analyzed as tracking knowledge, for this would lead to circularity.

  5. Among the proponents of safety-based accounts of knowledge are Luper (2003: 189–91), Pritchard (2005: 161–73), Sainsbury (1997), Sosa (1999; 2002), and Williamson (2000: 123–8).

  6. We cannot make the problem go away by claiming that entailment is not a kind of implication. Even if entailment isn’t a form of implication there are no close possible worlds where, contrary to fact, p doesn’t entail q.

  7. Necessary truths are not the only ones to cause problems for sensitivity. Contingent truths whose negations are nomologically or metaphysically impossible are just as problematic. Sensitivity needs to be restricted to fully contingent propositions, that is, propositions that are neither logically, nor nomologically, nor metaphysically necessary.

  8. DeRose (1995: 22–3) weakens the sensitivity condition in the following way: S knows that p only if either S sensitively believes that p or, where ~p implies some q and we take it that S knows that ~q, ~p fails to explain how S came falsely to believe that ~q. For a critical discussion of this revised sensitivity condition see Black and Murphy (2007: 55).

  9. The example is inspired by Goldman (1976: 779) and adapted from Murphy (2006: 372). Similar examples can be found in Kvanvig (2004: 209; 2008: 465–71) and Murphy (2005: 333–4).

  10. Cf. Pritchard 2005: 156, 168; Sosa 2002: 267–9; Weatherson 2004: 378–9; Williamson 2000: 179–82. Instead of method-relativizing the safety condition one can also method-relativize the closure principle. Black (2008: 609) proposes a restriction of the closure principle to the same belief-formation process: If S knows via belief-producing mechanism k that p, and if S knows via k+ (which need not be distinct from k) that p entails q, and if k or k+ will allow S reasonably to believe that q, then S knows that q.

  11. Alspector-Kelly (2011) provides a different argument to the effect that safety violates closure: Is it possible to safely believe p and safely believe that p entails q but unsafely believe q? The belief in q is unsafe only if S believes q and q is false. But if q is false, p must be false as well, for p entails q. So the close not-q world in which S believes q is also a not-p world. Since S’s belief in p is safe, S doesn’t believe p in the not-q world. “The question whether safety implies closure turns, then, on whether the fact that S does not believe p in every nearly world in which q is false implies that S also does not believe q in every such world” (2011: 133). Alspector-Kelly argues that just because S doesn’t believe p in not-q worlds doesn’t mean that S doesn’t believe q in not-q worlds.

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Acknowledgement

Earlier drafts of this paper were presented at the 34th International Wittgenstein Symposium in Kirchberg am Wechsel (2011) and the University of Connecticut (2011). Travel expenses related to this project were supported by a UC Irvine Chancellor’s Fellowship. For helpful comments on earlier drafts of this paper I am grateful to Peter Baumann, Paul Bloomfield, Tom Bontly, Fred Dretske, John Greco, Michael Lynch, Lionel Shapiro, Sam Wheeler, and an anonymous referee for this journal.

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  1. Department of Philosophy, University of California, Irvine, Irvine, CA, 92697-4555, USA

    Sven Bernecker

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Bernecker, S. Sensitivity, Safety, and Closure. Acta Anal 27, 367–381 (2012). https://doi.org/10.1007/s12136-011-0137-x

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