Abstract
The paper introduces a new problem for fallibilist and infallibilist epistemologies—the diachronic threshold problem. As the name suggests, this is a problem similar to the well-known threshold problem for fallibilism. The new problem affects both fallibilism and infallibilism, however. The paper argues that anyone who worries about the well known problem for fallibilism should also worry about this new, diachronic version of the problem.
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11 November 2021
A Correction to this paper has been published: https://doi.org/10.1007/s11098-021-01749-3
Notes
See Hetherington (2006) for an apt discussion of the synchronic threshold problem in qualitative terms.
The ‘P( )’ function refers here to what is sometimes called evidential probability (broadly speaking): when we say that p is probable given e, for example, we are saying something like ‘Any reasonable person who considers p in light of e carefully enough will find believing p to be more reasonable than believing not-p.’ ‘Reasonable’ and ‘more reasonable than’ are primitive epistemological concepts as in Chisholm (1966).
See Kotzen (2019) for a similar account of justification and defeat.
See Dougherty (2011) for a discussion of fallibilism that goes beyond my focus on fallibilism qua fallibilism.
Remember: we are ignoring the Gettier Problem. We are also ignoring global forms of skepticism (e.g., Cartesian skepticism).
But see a few paragraphs down (and footnote 11) for more on the similarity between the vagueness of ‘know’ and ‘bald.’
The claim that the problems of vagueness and of the threshold are the same is controversial. The idea that those problems are structurally similar is more widely accepted in the literature on the threshold problem. See Hannon (2017, footnote 4) for a similar view on the relationship between the two problems.
See Hannon (2019, p. 57) for a similar characterization of the problem. Of course, this way of putting the problem should not be taken to imply that the fallibilist can solve the threshold problem by saying that the threshold is ‘not precise,’ or ‘too vague.’ I agree with Hannon (2019, p. 64), Bonjour (2010) and others that the fallibilist does not solve the problem in this way.
See also Hawthorne (2004, p. 73) for the same point.
This case is adapted from Williamson (2000, p. 205).
If you think that knowledge is vulnerable to new evidence in the way suggested by the fallibilist, but you do not think that two hundred and fifty consecutive draws of a red marble are enough to defeat Liz’s justification, then change the case so that the number of consecutive draws of a red marble matches your epistemological sensibilities. Alternatively, if you think that there is no number of drawings of a red marble that is sufficient to lower Liz’s justification below n, then you might be an infallibilist. There is nothing wrong with being an infallibilist, but then this argument is not designed to convince you of anything. The impatient infallibilist should simply skip to the next paragraph where I argue that fallibilism and defeasibilism belong together.
To the extent that the marbles case deals with the border between ignorance and knowledge, it resembles some cases discussed in the literature on inductive knowledge. For example, Cian Door, Jeremy Goodman and John Hawthorne discuss a case where the subject seems to learn that a certain double-headed coin is not fair by flipping it repeatedly and seeing it land heads each time. According to Door et al., ‘[i]n any such case, there must be a first flip of the coin after which you are in a position to know that the coin is not fair’ Door et al. (2014, p. 283). Similarly, Bacon (2020) asks how one could come to know, after observing emeralds e1 ... en to be green, that a law explains all of one’s observations, rather than mere chance. Bacon asks how one observation could make a difference. The cases discussed by Door et al. and Bacon are similar to the marbles case, in that they all feature the inductive and gradual crossing of the border between ignorance and knowledge. But, even though the cases are similar in this way, they are being used to ask importantly different questions. On the one hand, Door et al. and Bacon’s cases are being used to probe fallibilism with the question ‘How is inductive knowledge possible in a fallibilist framework (i.e., in a framework in which knowledge-level justification does not require probability 1)?’ On the other hand, I use the marbles case to probe defeasibilism (in its fallibilist and infallibilist varieties) with the question ‘How is defeat possible in a defeasibilist framework (i.e., in a framework where new misleading evidence is allowed to defeat existing knowledge)?’ The result is that the cases Door et al. and Bacon discuss are similar to the marbles case in broad outline, but they are being used to raise different questions about theories that are trying to explain different epistemological phenomena. While the theoretical target in the Door et al. and Bacon cases is the crossing of the border between ignorance and knowledge in the ignorance-to-knowledge direction, the theoretical target in the marbles case is the crossing of the same border but in the opposite direction; i.e., in the knowledge-to-ignorance direction. The direction in which the crossing occurs matters (among other reasons) because one may cross into ignorance (from knowledge) with respect to p by suspending judgment about p, but one cannot cross into knowledge that p (from ignorance about p) in the same way. The use I make of the marbles case poses a new challenge to defeasibilism, a challenge that threatens to undercut the claim that infallibilists need not worry about the problem of the threshold. If am right, some prominent infallibilists need to worry about a version of the problem, a version of the problem that comes into focus as one thinks carefully about Liz’s crossing of the threshold between ignorance and knowledge in the knowledge-to-ignorance direction. The traditional threshold problem for fallibilism, as well as the cases in Door et al. and Bacon, do no such thing. Many thanks to a reviewer for bringing these cases to my attention.
One might worry that the case, as described, does not work because of the ‘mere probabilistic nature’ of the misleading evidence. However, one may change the case so that this worry disappears but the result remains (i.e., Liz’s knowledge is defeated by new evidence). Consider. Liz is drawing marbles with replacement from a normal, opaque bag. She takes careful notes describing each draw. She put a red and a black marble in the bag herself, and she knows that the bag has no abnormalities (pockets, etc.). After a few draws with replacement, her trustworthy butler, Paul, walks into the room and tells Liz that she should not drink from the bottles of water he bought the day before, since he just found out that they are tainted with a substance that causes prolonged periods of hallucination. Chief among them is color confusion: things that are not really red, look red. Now, what Paul says is true (the bottles he bought contain the hallucinogen), and Liz did drink the tainted water. However, what neither one of them knows is that Liz is iron-deficient, and that iron-deficient individuals are not affected by the hallucinogen in the water. Now, a skeptic might object that Liz did not lose any knowledge because of Paul’s testimony, since she never had any knowledge to begin with—‘Liz is in a Gettier case,’ he might try to convince us, ‘similar to the Fake Barn case.’ I do not find this claim plausible, since both Barney and Liz strike me as knowing the target proposition.’ However, I know that this will sound controversial to many (but see Sosa (2007) and Gendler and Hawthorne (2005) for a similar view of Barn cases). So, instead, I suggest that the skeptic change the case so as to make Paul’s testimony false but justified. In that case his testimony is misleading because what he says is false, while in the original case his testimony is misleading because it suggests something false (namely, that Liz is hallucinating red objects). Either way, Liz knows at first but not after Paul’s testimony; but, in this latter version of the case we avoid Barn-like worries. Thanks to John Biro for discussion here.
Many thanks to a reviewer for prompting me to be explicit about this issue.
Of course, we can also understand defeasibilism synchronically (i.e., one is justified in believing that p at time, t, only if there is no defeater of one’s justification for p at t). That is not the relevant version of defeasibilism being discussed here, however. For synchronic defeasibilism, see, among others, Lehrer and Thomas (1969), Pollock and Cruz (1999) and Klein (2008).
Bonjour (2010, p. 59).
Dretske (1981, p. 364).
This characterization of infallibilism is good enough for my purposes here, since it is a sine qua non for any infallibilist view. However, much more needs to be said in order to make infallibilism plausible, as a whole. For a careful presentation of infallibilism that aims to do just that, see, e.g., Dretske (1971), Williamson (2000), Neta (2009) and Pritchard (2016).
It might be argued that setting the threshold for justification at 1 is as arbitrary as any other value between .5 and 1 (at least at a first glance). Consider: Liz puts 99 black marbles and 1 red marble in a bag. She knows this to be the case; and, she knows that the bag has no internal pockets or any other abnormality. Liz shakes the bag, places her hand inside and grabs one marble. As she does that, she comes to believe (truly) at t that she is holding a black marble. Many would say that Liz is justified in believing that she is holding a black marble. However, this verdict is incompatible with infallibilism since, the probability that she is holding a black marble, given her evidence, is .99 instead of the required 1. However, because the infallibilist might reasonably complain that she is being accused of holding her own view, I will not pursue the issue any further.
According to Williamson (2000), if one knows that p, then p is part of one’s evidence. This means that p has probability 1 given S’s evidence whenever S knows that p. So, for Williamson, knowledge-level justification is infallible.
Dretske allows for misleading evidence to undermine knowledge; however, for him, misleading evidence leads to the loss of knowledge because it undermines belief, not because it undermines justification. According to him, ‘... if a person really does believe that [q (where q is incompatible with p)], aside from the question of whether or not this belief is reasonable, he surely fails to have the kind of belief requisite to knowing [that p]. He certainly doesn’t think he knows [that p]. I do not know exactly how to express the belief condition on knowledge, but it seems to me that anyone who believes (reasonably or not) that he might be wrong fails to meet it’ (Dretske 1981, p. 376). In the main body of the paper the focus is on infallibilist views, such as Williamsonian’s, that allow for the possibility of defeat of justification.
Williamson uses ‘evidence’ where I used ‘knowledge.’ The change is justified because the context in which this passage appears is one in which Williamson is defending the view that evidence is knowledge.
Many (for example, Brown 2018) claim that infallibilism is plagued with several other problems (e.g., skepticism). In that context, the dilemma I discuss here can be taken to be yet another stumbling block for the infallibilist.
Maria Lasonen–Aarnio calls knowledge held in the face of counterevidence ‘unreasonable knowledge’ in Lasonen-Aarnio (2010).
But some cases are not like the ones I describe here. In some cases the dogmatic stance seems rational. As Kripke noted (2011, p.49), most of us can rationally ignore any evidence suggesting that astrology, or necromancy amounts to an accurate description of reality. Kripke also notes that delineating when the dogmatic strategy is rational and when it is not is itself an epistemological problem. Nevertheless, the point in the body of text still stands—dogmatism cannot reasonably be applied to all cases where misleading evidence is a factor.
In Borges (2020b), I explore another way in which this problem might be epistemologically interesting: I discuss whether the diachronic threshold problem upsets views that accept different Lockean theses connecting credences and (full-blown) belief. I argue that it does. Here, however, I ignore the issue.
My thanks to Cesar Schirmer for raising this issue in conversation.
Again, if you find that one thousand tosses are not enough to move your intuitive needle, adjust accordingly. Also, as it should be obvious from the context of the case, I am assuming that the coin is in fact fair.
Luis Rosa posed this question in conversation.
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Acknowledgements
This paper owes much to the input and encouragement of others. Stephen Hetherington kindly sent me detailed comments on an earlier draft. I discussed different versions of this paper with my colleagues from the University of Florida in The Epistemology Working Group: John Biro, Greg Ray, Chris Dorst, Jim Gillespie, and James Simpson. I presented some of the material in this paper at the 2019 meeting of the Southeastern Epistemology Conference in Greenville, North Carolina. I am thankful to that audience for their feedback; especially Mike Veber, Ted Poston, Andrew Moon, Jonathan Matheson, Kevin McCain, Matthew Frise and Elijah Chudnoff. I also presented a draft of this paper to the brown bag meeting led by Luis Rosa at the University of Cologne. My thanks to those who came to that meeting, in particular to Luis Rosa, Cesar Schirmer, Eve Kitsik and Francesco Praolini. I am also thankful for the helpful suggestions I received from two referees for Philosophical Studies. Lastly, this paper and the research that lead to it has been deeply influenced by many fruitful conversations over many years with Peter D. Klein and Claudio de Almeida. I am deeply grateful for their advice and friendship. Needless to say, I am fully and uniquely responsible for any mistakes that might remain in this paper.
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Borges, R. The diachronic threshold problem. Philos Stud 179, 93–108 (2022). https://doi.org/10.1007/s11098-021-01652-x
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DOI: https://doi.org/10.1007/s11098-021-01652-x