FOLEYS THRESHOLD VIEW OF BELIEF AND THE SAFETY CONDITION ON KNOWLEDGE MICHAEL J. SHAFFER Abstract: This paper introduces a new argument against Richard Foleys threshold view of belief. Foleys view is based on the Lockean Thesis (LT) and the Rational Threshold Thesis (RTT). The former thesis is the claim that it is epistemically rational to believe a proposition if and only if it is epistemically rational to have a degree of confidence in that proposition sufficient for belief. The latter thesis is the claim that it is epistemically rational to believe a proposition if and only if it is epistemically rational to have a degree of confidence in that proposition that meets or exceeds a specified threshold. The argument introduced here shows that the views derived from the joint endorsement of the LT and the RTT violate the safety condition on knowledge in way that threatens the LT and/or the RTT. Keywords: belief, credence, safety, rationality. Richard Foley (1992) has famously attempted to integrate views about the epistemology of full belief and views about probabilistic credences by means of what he calls the Lockean Thesis: (LT) For any subject A and proposition p, it is (epistemically) rational for A to believe p if and only if it is epistemically rational for A to have a degree of confidence in p sufficient for belief. The LT is then supplemented by the Rational Threshold Thesis, and this fleshes out the relevant notion of rational belief employed in the LT: (RTT) It is (epistemically) rational for A to believe p if and only if it is (epistemically) rational for A to have a degree of confidence y in p, where y x. So, where As degree of confidence in p is equal to or exceeds x, A has full belief in p. But, we should not set x 5 1 (for this is too high), and we cant let x be set too low (as we would then believe virtually VC 2018 Metaphilosophy LLC and John Wiley & Sons Ltd VC 2018 Metaphilosophy LLC and John Wiley & Sons Ltd METAPHILOSOPHY Vol. 49, No. 4, July 2018 0026-1068 everything) (Foley 1992, 112). On Foleys view one can then have full belief in a proposition where the threshold x is met, but where x is less than probability 1. This requires only that x be set at some value that is less than 1 but that, in accord with the LT, is sufficiently high. The combination of the LT and the RTT is supposed to allow for the kind of integrated view that Foley believes we must have in order to make sense of our epistemic behavior. This is important because he believes that the LT allows us to make sense of rational cognitive behavior without the unrealistic and unduly complex assumption that we actually have fully formed and numerically precise degrees of confidence with respect to the propositions that we entertain in many epistemic endeavors. In many of those cases we appear to employ what we might call belief simpliciter. On this view we simply believe, disbelieve, or suspend judgment about a proposition, rather than having more fine-grained degrees of belief with respect to that proposition. This simpler concept of belief is then the more or less all-or-nothing belief of the sort that can be generated from applying the RTT and the LT to our beliefs. A number of objections have been raised against the view stemming from the lottery and preface paradoxes, as well as other sources. Foley has addressed many of these worries (see Foley 2009). There is, however, one glaring problem with the RTT. This problem arises when one attempts to deploy Foleys view. In order to deploy the RTT we must specify a value for x. Suppose then that one argues that the threshold for full belief should be x 5 0.90. Now, unless the selection of x 5 0.90 as the appropriate threshold is grounded in some good reasons R, it will be arbitrary and hence will not explain why that level of confidence is epistemically rational and sufficient for full belief, and the same will go for any selection of a value for x. So, it would appear that any such selection must ultimately be grounded in some such reasons. Where the selection of x is grounded in such reasons R, however, it is totally unreasonable to suppose that those reasons would not also be equally compelling reasons to set x at x 5 0.90 – d or x 5 0.90 1 d where d is relatively small. Surely this will be the case where d is infinitesimally small. As a result, the reasoned fixing of x at least appears to be problematic. Foley attempts to dodge this particular and deep problem by unabashedly embracing the idea that there need be no good reasons for the selection of any particular value for x. Foley explicitly states that his defense of the LT and the RTT involves the stipulation of x and says, "Once such a threshold x is stipulated, we can use the Lockean thesis to say what is required for rational belief: it is rational for you to believe p just in case it is rational for you to have degree of confidence y in p, where y x" (Foley 1992, 112). Elsewhere, of the integration of the LT and the RTT, Foley claims: "This is a tidy result, but it does invite the follow-up question, what degree of confidence is sufficient MICHAEL J. SHAFFER590 VC 2018 Metaphilosophy LLC and John Wiley & Sons Ltd for belief? But even if it proves difficult to identify a precise threshold for belief, this in itself wouldnt seem to constitute a serious objection to the Lockean thesis. It only illustrates what should have been obvious from the start, namely, the vagueness of belief talk" (Foley 2009, 37). Of course, Foley is correct here. This worry is not a direct objection to the LT, but it is a substantive objection to the RTT. Foley then attempts to disarm this objection: "Still, it seems as if we should be able to say something, if only very general, about the threshold above which ones level of confidence in a proposition must rise in order for someone to believe that proposition. What to say is not immediately obvious, however, since there does not seem to be any non-arbitrary way of identifying a threshold. But perhaps we dont need a nonarbitrary threshold anyway. Why not just stipulate a threshold? We deal with other kinds of vagueness by stipulation. Why not do the same here?" (Foley 2009, 38). Foley goes on to say: "Indeed, it might not even matter much where the threshold is as long as we are consistent in applying it. We wont want to require subjective certainty for belief. So, the threshold shouldnt be that high. On the other extreme, we will want to stipulate that for belief one needs to have more confidence in a proposition than its negation. But except for these two restrictions, we would seem to be pretty much on our own" (Foley 2009, 38). So, for full belief, ones degree of rational credence must meet or exceed x, and the same will be true for full beliefs that count as knowledge. Accordingly, this yields the following condition for full belief: ðFBÞ FBAp  PAðpÞ  x; such that 1 > x > 0:5: Now, this view will be exceptionally unpalatable to epistemologists who reject conventionalism, contextualism, and related views. But, it turns out that this view of belief is subject to additional problematic implications that are perhaps less easily dealt with than the more standard objections stemming from the lottery and preface paradoxes, pragmatic encroachment, and stipulative nature of thresholds in the threshold view. Specifically, here it will be shown that Foleys suggestion runs afoul of the safety condition on knowledge no matter what value is stipulated for x. This problem arises in virtue of the following basic contention that Foley appears to be committed to: ðDÞ KAp ! FBAp: This is simply the doxastic assumption that knowledge requires full belief. The idea then is that knowledge is the maximally valedictory form of rational belief. As Kripke (2011) has shown, however, if one FOLEYS THRESHOLD VIEW OF BELIEF 591 VC 2018 Metaphilosophy LLC and John Wiley & Sons Ltd accepts factivity and the idea that knowledge entails belief, then one is thereby committed to the safety condition on knowledge (see Shaffer 2017). We have seen that Foley is implicitly committed to the former idea, and denying factivity invites all sorts of problematic Morrean contradictions of the form "I know that p, but :p." So, it is reasonable to suppose that Foley is committed to safety, if only by implication. The safety condition on knowledge is a necessary condition for knowing that recently has been systematically defended by Williamson (2000), Sosa (1999), and Pritchard (2007, 2008, 2009a and 2009b), and their endorsements of this condition stem from Noziks (1981) work on knowledge. It is supposed to reflect the basic idea of the sort of reliability associated with bona fide knowledge. The safety condition can be understood simply as follows: If A knows that p, then A could not easily have falsely believed that p. This relatively nontechnical gloss on safety and it can be made more precise as follows: ðSafetyÞ ðwiKApÞ ! :1⁄2<wi> ðBAp &:pÞ: Here "<wi>" is the set of world sufficiently close to wi and "BAp" represents that A believes that p. So understood, the safety condition is the claim that if A knows that p at wi, then A does not believe that p when p is false in worlds sufficiently similar to wi. This regimentation captures the core idea of the safety condition well. Safety has independent merit as a condition on knowledge as it reflects a primitive notion of reliability, but it is an unavoidable consequence of accounts of knowledge that involve the contentions that knowledge entails both truth and belief. Notice then that FB and D entail the following principle about knowledge that Foley is unavoidably committed to: ðFKÞ KAp ! PAðpÞ  x; such that 1 > x > 0:5: The problem then is that it is easy to see that FK entails violations of safety no matter what value has been stipulated for x. Suppose, for example, that by stipulation we set the threshold value x at 0.98. We then get the following specific version of FK: ðFK0:98Þ KAp ! PAðpÞ  0:98: Suppose then that we have a case where in world w1 As evidence for p is such that it meets or exceeds the probability 0.98 threshold. So, in accordance with FB, A fully believes p. Suppose also that this MICHAEL J. SHAFFER592 VC 2018 Metaphilosophy LLC and John Wiley & Sons Ltd stipulation about x is also sufficient for knowing as FK0.98 implies. The problem is then that all of this can be true, while A fully believes p while it is false in worlds close to w1. More formally, given Foleys theory, it can be the case that wi  KAp &<wi> (FBAp & :p). This will occur in cases where wi  KAp because A meets or exceeds the threshold for full belief and meets whatever other conditions there are for knowing and where <wi> FBAp but where in at least one of those worlds close to wi :p is true because an improbable condition obtains. Given our "x 5 0.98 model" this might plausibly occur as follows. Sally plans to draw a ball from an urn containing ninety-nine white balls and one black ball. On this basis and given Foleys preferred epistemological views, Sally fully believes that she will draw a white ball and even knows this. There are, however, close worlds to w1 where Sallys counterpart fully believes she will draw a white ball but this is false, for drawing a black ball is surely a thing that happens in some of those worlds that do not differ in almost any way from w1. They are thus close worlds, but it just happens to be the case that the improbable outcome occurs in some of those worlds that are virtually identical in all respects to the indexed world where she knows the draw will be a white ball and it is. But then we have a violation of safety, and that spells trouble for any theory of knowledge in which knowing implies believing and the truth of the known proposition. In turn, this spells very specific trouble for the LT and the RTT. What we have is a plethora of cases that can easily be generated for any x that show that FK and safety are incompatible. But safety follows from the doxastic and factive conditions on knowledge, and it is hard to see how one might cede either of those orthodoxies. So, this casts deeply serious doubts on either or both the LT and the RTT, whatever independent plausibility they might enjoy as an analysis of everyday belief. Department of Philosophy, CH 365 St. Cloud State University 720 4th Ave. South St. Cloud, MN 56301 USA shaffermphil@hotmail.com References Foley, R. 1992. "The Epistemology of Belief and the Epistemology of Degrees of Belief." American Philosophical Quarterly 29:111–21. --––. 2009. "Belief, Degrees of Belief and the Lockean Thesis." In F. Huber and C. Schmidt-Petri (eds.), Degrees of Belief, 37–47. New York: Springer. FOLEYS THRESHOLD VIEW OF BELIEF 593 VC 2018 Metaphilosophy LLC and John Wiley & Sons Ltd Kripke, S. 2011. "Nozik on Knowledge." In Saul Kripke: Collected Papers, 1:162–224. Oxford: Oxford University Press. Nozik, R. 1981. Philosophical Explanations. Cambridge, Mass.: Harvard University Press. Pritchard, D. 2007. "Anti-Luck Epistemology." Synthese 158:277–98. --––. "Knowledge, Luck, and Lotteries." In V. Hendricks and D. Pritchard (eds.), New Waves in Epistemology, 28–51. London: Palgrave Macmillan. --––. 2009a. "Safety-Based Epistemology: Whither Now?" 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