Counter-Closure

Abstract The focus of this paper is the prima facie plausible view, expressed by the principle of Counter-Closure, that knowledge-yielding competent deductive inference must issue from known premises. I construct a case that arguably falsifies this principle and consider five available lines of response that might help retain Counter-Closure. I argue that three are problematic. Of the two remaining lines of response, the first relies on non-universal intuitions and forces one to view the case I construct as exhibiting a justified, true belief to which none of the usual diagnoses of knowledge failure in Gettier cases apply. The second line involves claiming that Fake Barns and its ilk are misdiagnosed by epistemological orthodoxy as Gettier cases. We are thus confronted by a trilemma: either the case I discuss undermines the first-blush plausible principle of Counter-Closure; or the case I discuss instantiates a novel kind of Gettier case; or a popular conception of a key range of alleged Gettier cases must be rejected. No matter which horn we choose, the case points to a philosophically curious conclusion. Notes 1For prominent endorsements of this view see, e.g., DeRose Citation1995, Williamson Citation2000, and Hawthorne Citation2004 and Citation2005. For prominent opposition see, e.g., Dretske Citation1970 and Citation2005 and Nozick Citation1981. Like many others who discuss closure principles for knowledge, I do not put forward my formulation of Closure with the presumption that it is definitive: it may very well admit further refinement. 2The name 'Counter-Closure' might suggest logical incompatibility with Closure. I do not intend the principle to be read this way—in fact, Counter-Closure is compatible with Closure. Rather, as will become apparent, the prefix 'Counter-' is best read as metaphorically indicating movement in the opposite direction, much like 'counter-clockwise' does with respect to 'clockwise'. 3It may sound obviously true to some. This would partly explain why the view it expresses is sometimes assumed to be true without argument (see, e.g., Armstrong Citation1973: 198–9]; Nozick Citation1981: 231]; Stanley Citation2005: 89–90]). As with Closure, this particular formulation of Counter-Closure may admit of further refinement. However, my argument will depend in no way on such possible refinements. 4As an anonymous referee has pointed out to me, the view expressed by Counter-Closure has come under recent fire: both Warfield Citation2005 and Klein Citation2008 construct and defend cases in which an agent comes to know the conclusion of a deductive inference that contains a false and therefore unknown premise. The challenge I raise to Counter-Closure below importantly differs from these attacks because in the example I will discuss the relevant knowledge-yielding deductive inference contains only true premises. An anonymous referee has also observed that the Gettierized Reliable Reporter case [Coffman Citation2008: 191] seems to undermine Counter-Closure and displays a deductive inference containing only true premises. While there are structural similarities between Gettierized Reliable Reporter and the example I will discuss below, it is worthwhile noting that, while he alludes to this possibility, Coffman does not provide an extended discussion of whether and how his case may undermine the view expressed by Counter-Closure; nor does he consider, as I will below, the interesting philosophical ramifications of insisting that Counter-Closure is true in the light of this kind of challenge. For these reasons, I take the detailed discussion of these issues in what follows to significantly advance the debate over whether we should endorse or reject Counter-Closure. 5See Gettier Citation1963 for the first examples of Gettier cases. 6See, e.g., Nozick Citation1981 and Dretske Citation1971 for endorsements of similar constraints. Differences in their formulations of sensitivity have no significant impact on what follows. 7See, e.g., Sosa Citation1999, Williamson Citation2000, and Pritchard Citation2005 for conceptions of safety. Again, the slight variations in their formulations of safety have no repercussions on my argument. In particular, Ingrid's belief in (1) is not safe even on a formulation of safety that merely requires that in most (as opposed to all) close possible worlds, if S believes that p via M then p is true. 8See, e.g., Lehrer and Paxson Citation1969 and Klein Citation1971. 9While the three constraints just discussed have the virtue of explaining knowledge failure in a range of Gettier cases, I do not mean to suggest that this is their sole or even their main purpose. Their endorsers also believe them to be plausible for independent reasons. 10Goldman attributes this case to Carl Ginet. 11Strictly speaking, to make the analogy tight we would need to posit that Henry, either implicitly or explicitly, relies on an inductive argument along the following lines to justify his belief that there is a barn. '(A*) That object looks like a barn. (B*) When things look like barns, they almost always are barns. So (C*) that object is a barn'. I think it's safe to say that reliance on this argument does not make any difference to our inclination or disinclination to ascribe knowledge to Henry. 12Apart from Goldman Citation1976, see—to name but a few—Plantinga Citation2000: 359–60], Lackey Citation1999: 487 and 2008: 68–9], Pritchard Citation2005: 161–2], Frances Citation2005: 114 (especially footnote 41)] and Gendler and Hawthorne Citation2005. Gendler and Hawthorne report the view that 'the salient proximity of an indistinguishable facsimile is sufficient to indict the casual observer's knowledge' as widespread amongst philosophers [335]. Along similar lines, Fumerton Citation2006: 26] says of this case that 'many epistemologists don't want to allow that [Henry's] apparently justified true belief constitutes knowledge'. 13The strategy that denies (i) that Ingrid knows that if Humphrey is in the lounge, then he is in the house is too implausible to deserve discussion. Furthermore, as stated above, I will leave discussion of the view that affirms the consequent of this instance of Counter-Closure to the final section. 14Thanks to an anonymous referee for raising this third point. 15Other epistemic kinds of luck may fail to transmit across deductive inference. See Pritchard Citation2005: 133–41] for descriptions of these varieties of luck. 16Versions of this paper were presented at the Australian National University Philosophy Society, the Australasian Association of Philosophy Conference at La Trobe University, the 5th Biennial Rochester Epistemology Graduate Conference, the 8th Shapiro Graduate Conference at Brown University, the Arché Basic Knowledge Seminar at the University of St Andrews, the XI Taller d'Investigació en Filosofia at the Universitat de València and the Yale/Uconn Graduate Philosophy Conference. I am grateful to commentators and audiences on these occasions. Thanks to David Chalmers, Paul Dimmock, Douglas Edwards, Stephen Hetherington, Mireia López Amo, Aidan McGlynn, Andreas Stokke, Elia Zardini and two anonymous referees for helpful comments. I am particularly grateful to Leon Leontyev for numerous discussions on the issues of this paper, and to Patrick Greenough and Crispin Wright for discussion, guidance and constant encouragement.