Abstract
This paper is about the ‘threshold problem’ for knowledge, namely, how do we determine what fixes the level of justification required for knowledge in a non-arbitrary way? One popular strategy for solving this problem is impurism, which is the view that the required level of justification is partly fixed by one’s practical reasoning situation. However, this strategy has been the target of several recent objections. My goal is to propose a new version of impurism that solves the threshold problem without succumbing to these criticisms.
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Notes
Standard formulations of fallibilism include: (a) one can know that p even though one’s justification for p is less than conclusive (BonJour 2010: 57); (b) the level of justification requisite for knowing that p is compatible with p being false (Reed 2002: 144); and (c) one can know that p on the basis of evidence that does not guarantee the truth of one’s belief that p (Brown 2014: 179). Although it is controversial how to formulate fallibilism precisely (see Reed 2002), these standard formulations all give rise to the threshold problem on which I focus.
This debate presupposes that the concept of justification is conceptually prior to the concept of knowledge and can be understood independently. For a contrary view, see Williamson (2000).
To keep things simple, I’ll speak in terms of the level of justification required for knowledge, rather than in terms of evidence, probability, warrant, or supporting grounds. I do not deny that these terms can fruitfully be given distinct senses, but these distinctions do not matter for my purposes. I use ‘justification’ generically, encompassing both internalist and externalist conceptions.
Is the threshold problem merely rehearsing the familiar problem of vagueness? Both problems have a similar structure. For example, it is plausible that there is no precise point at which a person goes from being not-bald to bald (the property ‘bald’ is vague); similarly, it is reasonable to suppose that a small increase in probability (e.g. 0.01) can never make the difference between not-knowing and knowing (the property ‘know’ is vague). Thus, an inability to locate a precise boundary between not-knowing and knowing would not be a sufficient reason to doubt that some boundary exists. However, it is surely not good enough for fallibilists to say the level of justification required for knowledge is “high” or “strong” or makes one “highly likely” to be right. While an adequate answer to the threshold problem shouldn’t demand more precision than is achievable (or necessary), fallibilists must provide a reasonable degree of approximation. They have not met this challenge, and so I take the threshold problem seriously.
More specifically, Hetherington says mere true belief is a conceptual end point within the graded category that is knowledge: there are a whole lot of potential grades of knowing that p, so there is no threshold problem on his view.
Hetherington (2006) tries to solve the threshold problem in a different way, but there are at least three problems with his solution. First, on his view we can know where the threshold for knowledge is set, but only vaguely and on the basis of very weak justification. In particular, he says that even if we know full well (perfectly or conclusively) that any evidence which probilifies my belief to degree 0.9 would be good enough for knowledge, and even if we know full well that a probilification of merely 0.3 is not good enough for knowledge, then all we can know is that the justificatory boundary for knowledge falls within that 0.6 span of justificatory support. This is pretty vague and surely not precise enough to meet the challenge of providing a reasonable degree of precision (see fn. 4). Second, if we subtract 0.6 from the maximum 1, we would know that knowledge has a justificatory boundary with only 0.4 strength. But can knowledge of a fact be so poor—so weak? See Hetherington (2001) for a full defense of this idea. Third, Hetherington acknowledges that his solution goes against his own theory of knowledge, as defended in his 2001 book (Hetherington 2006: 45).
‘Impurism’ may be understood more broadly as the view that whether some true belief is knowledge does not only depend on truth-conducive factors. My focus is on the more specific view that concentrates on stakes, or how important it is to S that p be true.
Fantl and McGrath (2009: 66) write, “If you know that p, then p is warranted enough to justify you in Φing, for any Φ.” This formulation imposes no restriction that the proposition p should be relevant to the action in question. Thus, for Fantl and McGrath, the strength of epistemic position required for a subject to know any proposition at a given time is fixed by a privileged practical reasoning situation facing a subject at that time (i.e. the unity approach). In contrast, Hawthorne and Stanley (2008: 578) write, “Where one’s choice is p-dependent, it is appropriate to treat the proposition that p as a reason for acting if and only if you know that p.” This formulation allows that the strength of epistemic position required for a subject to know one proposition at a given time may differ from the strength of epistemic position required for her to know a distinct proposition at that time (i.e. the relevance approach).
Brown isn’t claiming that the unity approach entails that we know nothing at all. A subject might happen to face no high-stakes situation at a time.
See Russell and Doris (2008) for a similar objection.
I will speak in terms of the purpose (role, function) of the concept of knowledge for expository convenience, but I do not assume that there is only one role played this concept. Rather, I claim this is a central (common, important) role. This hypothesis has been endorsed by Dogramaci (2015), Fricker (2008), Greco (2008), Grimm (2015), Hannon (2014), Henderson (2009), McKenna (2013), Neta (2006), Pritchard (2012), and others.
One important way in which our views differ is that I do not posit a fictional ‘state of nature’, which is perhaps the weakest and most problematic aspect of Craig’s genealogical account. Indeed, I am not providing a genealogy at all. Rather, I claim that the concept of knowledge is the outcome of very general facts about the human situation, especially our need for information from reliable sources to guide our actions.
A true belief becomes knowledge when enough justification supports it, but it is still possible that further justification will make one’s knowledge better. We needn’t insist, as Dretske (1981: 363) does, that somewhere along the spectrum of justification is a point beyond which one’s knowledge cannot be further improved by more justification. I merely insist that when a certain amount of justification is acquired, knowledge is achieved and non-knowledge is left behind.
This might plausibly include some non-actual people, as Henderson (2009) argues. Moreover, there are arguably some actual skeptical epistemologists who imagine that deceiving demons are relevant to every contingent proposition; thus, it must also be true that the interests of some actual people will not affect the communal standard.
Austin (1946) has a similar view, and Lawlor develops this idea in chapter 5 of her (2014) book. Some experimental epistemologists doubt that there is sufficiently wide cross-cultural agreement to say that “we” have an idea of what normally counts as having done enough to establish the propriety of a knowledge claim (e.g. Weinberg et al. 2001). However, these findings have been disputed by Boyd and Nagel (2014), Hannon (2015), Machery et al. (2015), Nagel et al. (2013), and Turri (2013).
Another way in which my view goes beyond Craig’s is that his own description of a reliable informant is not sufficiently detailed to resolve the threshold problem. Craig says that a knower is “someone with a very high degree of reliability, someone who is very likely to be right—for he must be acceptable even to a very demanding inquirer” (1990: 91, my emphasis). But, as BonJour says, “it is surely not good enough to say merely, as is commonly said, that the level of justification in question is “strong” or “high” or “adequate” or enough to make it “highly likely” that the belief in question is true, for nothing this vague is enough to specify a definite level of justification and a corresponding definite concept of knowledge” (2010: 60). My relevant alternatives account is more precise than Craig’s view, but not more precise than the subject matter allows (as Aristotle would say).
You might wonder whether the community-wide epistemic standard is the same across all propositions or whether it depends on the proposition (or perhaps the topic) in question. According to the former view, there would be something like an average amount of reliability or justification that is expected for any proposition. I prefer the later view, however, which says the amount of reliability or justification required for knowledge will depend on the relevant proposition (or topic). Although I will not provide a detailed argument for this view here, I will motivate it with an example. In the case of lottery propositions (e.g. ‘I won’t win the lottery’), it is implausible to think that we know this even if we have overwhelming statistical evidence to support this judgment. However, if the level of reliability needed to know this proposition were the same for all propositions, then either we would know that we’ll lose the lottery or we would know almost nothing (depending on how high you set the general standard). Both results are counterintuitive. Thus, it is more plausible to think that the community-wide standard will depend on the proposition (or topic) in question.
Elsewhere I have called the communal standard the ‘default’ standard to indicate that it can be overridden when elevated stakes are involved (Hannon 2013).
This standard cannot be too high because that would make knowledge less than widely available, which would prevent knowledge from playing its role in practical reasoning.
The idea of a communal (or default) threshold might be compatible with insensitive invariantism. According to the insensitive invariantist, what counts as being in a sufficiently good epistemic position to know some proposition does not vary—is not sensitive to—any individual’s stakes or practical interests at the time in question, whether it be those of the subject, the attributor, or the evaluator of a knowledge claim. An insensitive invariantist might argue that the communal threshold for knowledge firmly settles at a level high enough to satisfy the function of identifying good informants to the community, and the alleged context-sensitivity of our knowledge ascriptions might be dealt with at the level of pragmatics (see Rysiew 2001; Brown 2006; Gerken 2011). I see no reason to rule out the possibility of such a view. However, my aim in this paper is not to settle the issue of whether we should endorse insensitive invariantism or some rival view. Rather, my aim is to defend a new version of impurism that (a) is motivated by plausible assumptions about the purpose of the concept of knowledge, (b) does not succumb to Brown’s incisive objections against standard formulations of impurism, and (c) offers a plausible solution to the threshold problem.
It is theoretically possible for an entire community to be in a high-stakes reasoning situation with respect to some proposition, but that would only make it difficult for the community to know the truth of that proposition.
I am not suggesting that seeking the truth is always motivated by practical concerns: we may want to know something simply because it satisfies our curiosity. Nevertheless, it is unlikely that anyone would (or should) be interested in the number of grains of sand merely for its own sake.
See Hannon (2015) for a detailed defense of this view.
Given how expansive the epistemic community is, one might prefer a label other than ‘community’. You might say we are all members of the same epistemic world [see Thomas (2008) for a similar idea].
That said, Grimm’s example of the 323rd number in the Wichita phone directory is problematic. Suppose the 323rd number is Kirstie Alley’s. While it is plausible that someone might want to look up her number, it is unlikely that anyone will want to look up the 323rd number (without caring whose number it might be). Grimm interprets this case in the former way, but I think the latter interpretation is the one Alvin Goldman intended when he originally presented this case. On the latter reading, this example doesn’t support Grimm’s argument.
In the passage quoted above, Grimm does not explicitly say that the story one might tell must be reasonable, but he is committed to this idea. As mentioned in Sect. 3, Grimm claims the threshold for knowledge will reach a level high enough to respect the “typical” or “normal” stakes of people in the epistemic community (and not stakes that are merely logically possible but unlikely or unreasonable).
This is similar to a standard way of arguing in ethics, namely, if we should do X in circumstances C1, and circumstances C2 are just like C1, then we should do X in C2.
The policy of treating like cases alike might threaten to leach to absolutely all cases via the transitivity of “x-is-similar-to-y.” However, we can resist this by proposing a two-tiered policy: only add those cases that are similar to a base case (i.e. to a case captured by the original communal impurist principles).
The heap of sand must be ‘similarly sized’ because it becomes more difficult to count grains of sand as the number goes up. When counting, I would be more certain there are three grains before me than 200.
See Dogramaci (2012) for a similar approach to rationality.
It is for similar reasons that I reject Henderson’s view (2009). Although we agree that knowledge ascriptions certify people as reliable informants to members of their epistemic community, Henderson maintains that “the community in question may be […] composed of just the attributor and the interlocutor” (2009: 123). If this were correct, however, and if neither the informant nor her interlocutor had practical stake in the matter, then The Problem of Easy Knowledge would easily resurface. Thus, an implausible consequence of Henderson’s view is that the standard for knowledge may be set too low.
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Acknowledgments
Thanks to Nathan Ballantyne, Sinan Dogramaci, Elizabeth Edenberg, Mikkel Gerken, Stephen Grimm, Nick Hughes, Andy Mueller, Coran Stewart, and Emily Sullivan for comments on an earlier draft. This paper was presented at the Young Philosophers Lecture Series, and I am grateful to the audience there for feedback.
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Hannon, M. A solution to knowledge’s threshold problem. Philos Stud 174, 607–629 (2017). https://doi.org/10.1007/s11098-016-0700-9
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DOI: https://doi.org/10.1007/s11098-016-0700-9