This paper introduces a new argument against Richard Foley’s threshold view of belief.  His view is based on the Lockean Thesis (LT) and the Rational Threshold Thesis (RTT).  The argument introduced here shows that the views derived from the LT and the RTT violate the safety condition on knowledge in way that threatens the LT and/or the RTT

Shaffer, Michael J.

English

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FOLEYS THRESHOLD VIEW OF BELIEF AND THE SAFETYCONDITION ON KNOWLEDGEMICHAEL J. SHAFFERAbstract: This paper introduces a new argument against Richard Foleysthreshold view of belief. Foleys view is based on the Lockean Thesis (LT) and theRational Threshold Thesis (RTT). The former thesis is the claim that it isepistemically rational to believe a proposition if and only if it is epistemicallyrational 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 aproposition if and only if it is epistemically rational to have a degree ofconfidence in that proposition that meets or exceeds a specified threshold. Theargument introduced here shows that the views derived from the jointendorsement of the LT and the RTT violate the safety condition on knowledge inway that threatens the LT and/or the RTT.Keywords: belief, credence, safety, rationality.Richard Foley (1992) has famously attempted to integrate views aboutthe epistemology of full belief and views about probabilistic credencesby 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 rationalfor A to have a degree of confidence in p sufficient for belief.The LT is then supplemented by the Rational Threshold Thesis, andthis fleshes out the relevant notion of rational belief employed in theLT:(RTT) It is (epistemically) rational for A to believe p if and onlyif it is (epistemically) rational for A to have a degree of confi-dence y in p, where y x.So, where As degree of confidence in p is equal to or exceeds x, Ahas full belief in p. But, we should not set x5 1 (for this is too high),and we cant let x be set too low (as we would then believe virtuallyVC 2018 Metaphilosophy LLC and John Wiley & Sons LtdVC 2018 Metaphilosophy LLC and John Wiley & Sons LtdMETAPHILOSOPHYVol. 49, No. 4, July 20180026-1068everything) (Foley 1992, 112). On Foleys view one can then have fullbelief in a proposition where the threshold x is met, but where x is lessthan probability 1. This requires only that x be set at some value thatis less than 1 but that, in accord with the LT, is sufficiently high. Thecombination of the LT and the RTT is supposed to allow for the kindof integrated view that Foley believes we must have in order to makesense of our epistemic behavior. This is important because he believesthat the LT allows us to make sense of rational cognitive behavior with-out the unrealistic and unduly complex assumption that we actuallyhave fully formed and numerically precise degrees of confidence withrespect to the propositions that we entertain in many epistemic endeav-ors. In many of those cases we appear to employ what we might callbelief simpliciter. On this view we simply believe, disbelieve, or suspendjudgment about a proposition, rather than having more fine-graineddegrees of belief with respect to that proposition. This simpler conceptof belief is then the more or less all-or-nothing belief of the sort thatcan be generated from applying the RTT and the LT to our beliefs.A number of objections have been raised against the view stemmingfrom the lottery and preface paradoxes, as well as other sources. Foleyhas addressed many of these worries (see Foley 2009). There is, how-ever, one glaring problem with the RTT. This problem arises when oneattempts to deploy Foleys view. In order to deploy the RTT we mustspecify a value for x. Suppose then that one argues that the thresholdfor full belief should be x5 0.90. Now, unless the selection of x5 0.90as the appropriate threshold is grounded in some good reasons R, itwill be arbitrary and hence will not explain why that level of confidenceis epistemically rational and sufficient for full belief, and the same willgo for any selection of a value for x. So, it would appear that any suchselection must ultimately be grounded in some such reasons. Where theselection of x is grounded in such reasons R, however, it is totallyunreasonable to suppose that those reasons would not also be equallycompelling reasons to set x at x5 0.90 – d or x5 0.901 d where d isrelatively small. Surely this will be the case where d is infinitesimallysmall. As a result, the reasoned fixing of x at least appears to beproblematic.Foley attempts to dodge this particular and deep problem byunabashedly embracing the idea that there need be no good reasons forthe selection of any particular value for x. Foley explicitly states thathis defense of the LT and the RTT involves the stipulation of x andsays, “Once such a threshold x is stipulated, we can use the Lockeanthesis to say what is required for rational belief: it is rational for you tobelieve p just in case it is rational for you to have degree of confidencey in p, where y x” (Foley 1992, 112). Elsewhere, of the integration ofthe LT and the RTT, Foley claims: “This is a tidy result, but it doesinvite the follow-up question, what degree of confidence is sufficientMICHAEL J. SHAFFER590VC 2018 Metaphilosophy LLC and John Wiley & Sons Ltdfor belief? But even if it proves difficult to identify a precise thresholdfor belief, this in itself wouldnt seem to constitute a serious objectionto the Lockean thesis. It only illustrates what should have been obviousfrom the start, namely, the vagueness of belief talk” (Foley 2009, 37).Of course, Foley is correct here. This worry is not a direct objectionto the LT, but it is a substantive objection to the RTT. Foley thenattempts to disarm this objection: “Still, it seems as if we should beable to say something, if only very general, about the threshold abovewhich ones level of confidence in a proposition must rise in order forsomeone to believe that proposition. What to say is not immediatelyobvious, however, since there does not seem to be any non-arbitraryway of identifying a threshold. But perhaps we dont need a non-arbitrary threshold anyway. Why not just stipulate a threshold? Wedeal with other kinds of vagueness by stipulation. Why not do thesame here?” (Foley 2009, 38). Foley goes on to say: “Indeed, it mightnot even matter much where the threshold is as long as we are consist-ent in applying it. We wont want to require subjective certainty forbelief. So, the threshold shouldnt be that high. On the other extreme,we will want to stipulate that for belief one needs to have more confi-dence in a proposition than its negation. But except for these tworestrictions, we would seem to be pretty much on our own” (Foley2009, 38).So, for full belief, ones degree of rational credence must meet orexceed x, and the same will be true for full beliefs that count as knowl-edge. 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 whoreject conventionalism, contextualism, and related views. But, it turnsout that this view of belief is subject to additional problematic implica-tions that are perhaps less easily dealt with than the more standardobjections stemming from the lottery and preface paradoxes, pragmaticencroachment, and stipulative nature of thresholds in the thresholdview. Specifically, here it will be shown that Foleys suggestion runsafoul of the safety condition on knowledge no matter what value isstipulated for x.This problem arises in virtue of the following basic contention thatFoley appears to be committed to:ðDÞ KAp ! FBAp:This is simply the doxastic assumption that knowledge requires fullbelief. The idea then is that knowledge is the maximally valedictoryform of rational belief. As Kripke (2011) has shown, however, if oneFOLEYS THRESHOLD VIEW OF BELIEF 591VC 2018 Metaphilosophy LLC and John Wiley & Sons Ltdaccepts factivity and the idea that knowledge entails belief, then one isthereby committed to the safety condition on knowledge (see Shaffer2017). We have seen that Foley is implicitly committed to the formeridea, and denying factivity invites all sorts of problematic Morreancontradictions of the form “I know that p, but :p.” So, it is reasonableto suppose that Foley is committed to safety, if only by implication.The safety condition on knowledge is a necessary condition for know-ing that recently has been systematically defended by Williamson(2000), Sosa (1999), and Pritchard (2007, 2008, 2009a and 2009b), andtheir endorsements of this condition stem from Noziks (1981) work onknowledge. It is supposed to reflect the basic idea of the sort of reli-ability associated with bona fide knowledge. The safety condition canbe 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 moreprecise as follows:ðSafetyÞ ðwiKApÞ ! :½<wi> ðBAp &:pÞ:Here “<wi>” is the set of world sufficiently close to wi and “BAp” rep-resents that A believes that p. So understood, the safety condition isthe claim that if A knows that p at wi, then A does not believe that pwhen p is false in worlds sufficiently similar to wi. This regimentationcaptures the core idea of the safety condition well. Safety has inde-pendent merit as a condition on knowledge as it reflects a primitivenotion of reliability, but it is an unavoidable consequence of accountsof knowledge that involve the contentions that knowledge entails bothtruth and belief.Notice then that FB and D entail the following principle aboutknowledge 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 ofsafety no matter what value has been stipulated for x. Suppose, forexample, that by stipulation we set the threshold value x at 0.98. Wethen get the following specific version of FK:ðFK0:98Þ KAp ! PAðpÞ  0:98:Suppose then that we have a case where in world w1 As evidence forp is such that it meets or exceeds the probability 0.98 threshold. So,in accordance with FB, A fully believes p. Suppose also that thisMICHAEL J. SHAFFER592VC 2018 Metaphilosophy LLC and John Wiley & Sons Ltdstipulation about x is also sufficient for knowing as FK0.98 implies. Theproblem is then that all of this can be true, while A fully believes pwhile it is false in worlds close to w1. More formally, given Foleystheory, it can be the case that wi  KAp &<wi> (FBAp & :p). Thiswill occur in cases where wi  KAp because A meets or exceeds thethreshold for full belief and meets whatever other conditions there arefor knowing and where <wi> FBAp but where in at least one ofthose worlds close to wi :p is true because an improbable conditionobtains. Given our “x5 0.98 model” this might plausibly occur as fol-lows. Sally plans to draw a ball from an urn containing ninety-ninewhite balls and one black ball. On this basis and given Foleys pre-ferred epistemological views, Sally fully believes that she will draw awhite ball and even knows this. There are, however, close worlds to w1where Sallys counterpart fully believes she will draw a white ball butthis is false, for drawing a black ball is surely a thing that happens insome 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 theimprobable outcome occurs in some of those worlds that are virtuallyidentical in all respects to the indexed world where she knows the drawwill 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 knowingimplies believing and the truth of the known proposition. In turn, thisspells very specific trouble for the LT and the RTT. What we have is aplethora of cases that can easily be generated for any x that show thatFK and safety are incompatible. But safety follows from the doxasticand factive conditions on knowledge, and it is hard to see how onemight cede either of those orthodoxies. So, this casts deeply seriousdoubts on either or both the LT and the RTT, whatever independentplausibility they might enjoy as an analysis of everyday belief.Department of Philosophy, CH 365St. Cloud State University720 4th Ave. SouthSt. Cloud, MN 56301USAshaffermphil@hotmail.comReferencesFoley, R. 1992. “The Epistemology of Belief and the Epistemology ofDegrees of Belief.” American Philosophical Quarterly 29:111–21.——––. 2009. “Belief, Degrees of Belief and the Lockean Thesis.” InF. Huber and C. Schmidt-Petri (eds.), Degrees of Belief, 37–47.New York: Springer.FOLEYS THRESHOLD VIEW OF BELIEF 593VC 2018 Metaphilosophy LLC and John Wiley & Sons LtdKripke, S. 2011. “Nozik on Knowledge.” In Saul Kripke: CollectedPapers, 1:162–224. Oxford: Oxford University Press.Nozik, R. 1981. Philosophical Explanations. Cambridge, Mass.: Har-vard University Press.Pritchard, D. 2007. “Anti-Luck Epistemology.” Synthese 158:277–98.——––. “Knowledge, Luck, and Lotteries.” In V. Hendricks andD. Pritchard (eds.), New Waves in Epistemology, 28–51. London:Palgrave Macmillan.——––. 2009a. “Safety-Based Epistemology: Whither Now?” Journal ofPhilosophical Research 34:33–45.——––. 2009b. Knowledge. London: Palgrave Macmillan.Shaffer, M. 2017. “An Argument for the Safety Condition.” Logos andEpisteme 8:517–20.Sosa, E. 1999. “How to Defeat Opposition to Moore.” PhilosophicalPerspectives 13:141–54.Williamson, T. 2000. Knowledge and Its Limits. Oxford: Oxford Univer-sity Press.MICHAEL J. SHAFFER594VC 2018 Metaphilosophy LLC and John Wiley & Sons Ltd

Foley’s Threshold View of Belief and the Safety Condition on Knowledge

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Foley’s Threshold View of Belief and the Safety Condition on Knowledge

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