Abstract
This paper is about an anti-expertise paradox that arises because of self-referential sentences like: (*) = I do not believe that (*) is true. The first aim is to motivate, develop, and defend a novel view of epistemic rationality according to which there can be genuine rational indeterminacy, i.e., it can be indeterminate which doxastic states an agent is rationally permitted or required to have. The second aim is to show how this view can provide a solution to this paradox while also avoiding the problems that plague its rivals.
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Notes
A terminological note: I will use “doxastic state” and “doxastic attitude” interchangeably, and when I talk about an agent’s doxastic states and doxastic attitudes, I mean to encompass both the attitudes that the agent has, as well as the ones they lack, e.g., later on I will talk about an agent who has, or rather is in, the doxastic state of failing to believe p. I am also going to talk about suspending judgment as having a doxastic attitude as opposed to lacking one. All of this is purely for the sake of convenience. Thanks to an anonymous referee for helping me clarify this.
There is an alternative version of the anti-expertise paradox that does not involve self-referential sentences like (*). Instead, the paradox involves an agent who receives testimony that they are anti-reliable at determining whether some proposition is true, e.g., a doctor tells Alpha that because of some mind-altering drugs, she is currently anti-reliable at determining which direction to drive. See, e.g., Conee (1982, 1987), Richter (1990), and Sorensen (1987). For reasons of space, I will not discuss this paradox in detail. However, as will become clear in Fn. 8, even if the solutions offered by Conee, Sorensen and Richter can resolve this alternative version of the paradox, they are incapable of resolving the puzzle discussed here.
Two points of clarification are in order. First, recall that an agent’s doxastic states encompass both the attitudes they have as well as those they lack. Thus, Introspection says that if you have extraordinarily good reasons to think that you lack a belief in p, then you should believe that you lack this belief. Second, notice that Introspection is a weak principle. For it does not say that if you have a doxastic state, then you must believe that you have it. Rather, Introspection just says that insofar as you have really good reasons to think that you have a particular doxastic state, then you should not ignore what your introspective powers clearly reveal as being true. Thanks to an anonymous referee for pointing out the need for these clarificatory points.
My presentation of this paradox draws heavily on Caie’s (2012). But see Fn. 7 for one important difference between the two.
Assume that “Alpha” has a first-person mode of presentation for Alpha.
Caie (2012), Turri (2012), Lasonen-Aarnio (2014) and Schoenfield (2014) have given compelling arguments for versions of this principle. I have also argued for it in Leonard (2020). There is, of course, a large literature about the possibility of dilemmas in general, and there are those who endorse the possibility of epistemic dilemmas in particular (e.g., Priest (2002), Ross (2010), Brouwer (2014), Hughes (2017) and, on some interpretations, Christensen (2007, 2010)). Because engaging with this literature in a satisfactory way would take us too far afield, I am going to assume that No Dilemmas is true for our purposes here.
While my presentation of this paradox is inspired by Caie’s (2012), it differs in one crucial respect. Caie sets up one version of the puzzle in which Alpha is psychologically constituted such that, whenever she has a doxastic state, d, she always believes that she has d. Caie argues that so long as Alpha is hardwired in this way, a paradox arises because it is impossible for Alpha to even satisfy Consistency; that is, Caie argues that we can generate an alternative version of the paradox by just maintaining that (a) Consistency is true (b) No Dilemmas is true and (c) regardless of whether Introspection is true, Alpha just so happens to correctly believe that she has d whenever she really does have it.
I do not think that the paradox can be whittled down this far. For if Introspection does not require Alpha to always believe that she has the doxastic states that she does, then it would be permissible for her to have d but fail to believe that she did. This is because if Introspection does not require Alpha to believe that she has d, then she would not be violating any rational requirements by failing to do so.
But—and here is the key—our puzzle only arises if it is the principles of rationality that are responsible for Alpha being doomed to have an impermissible doxastic state. This is because there is nothing paradoxical about an agent who, for reasons that have nothing to do with the rational requirements themselves, is forced to have an attitude that is impermissible. For example, suppose that Alpha is psychologically constituted such that whenever her evidence entails p, she believes p and she also believes not-p. Thus, for reasons having nothing to do with the principles of rationality themselves, Alpha is doomed to violate Consistency. It is hard to see what epistemically interesting conclusions can be drawn from cases like this, since the mere fact that Alpha is hardwired in this way does not reveal that there is anything problematic with Consistency itself. Thus, I think the best we can do is pare things down to a conflict between Consistency and Introspection, since both principles are needed to generate a case in which Alpha seems doomed to have an impermissible doxastic state for epistemically interesting reasons.
Recall from Fn. 2 that Conee (1982, 1987), Richter (1990), and Sorensen (1987) offer solutions to an anti-expertise paradox that crucially involves your doctor testifying to you that you are anti-reliable at determining which way to drive, e.g., you should turn left if, and only if, you do not believe it. On the one hand, Sorensen argues that we can resolve this puzzle because you should refuse to accept the doctor’s testimony in the first place. But this solution will not carry over to our puzzle, since the paradox discussed here does not crucially involve Alpha receiving testimony from anyone. On the other hand, Conee and Richter argue that the puzzle can be resolved because you should suspend judgment about which way to drive and refuse to believe what you know your evidence supports, i.e., you should suspend judgment about whether you should turn left, and you should believe that if you suspend judgment, then you should turn left, but you should refuse to believe that you should actually go that way. But this solution will not carry over to our puzzle either, since as we saw above (i.e., (10)-(13)), insofar as Introspection is true (which Conee and Richter accept), then Alpha cannot suspend on (*). Thus, the solutions offered by Sorensen, Conee, and Richter will not resolve the puzzle discussed here.
For reasons of space I will not flesh out the exact details, but as will hopefully become clear below, the solution I offer to our puzzle can be generalized to provide a solution to this alternative version of the anti-expertise paradox too.
It is important to note that according to DOXASTIC INDETERMINACY, the law of excluded middle fails such that having an indeterminate belief just is to possess a particular kind of attitude, i.e., an attitude that is neither belief nor failure of belief. Thus, whatever state Alpha is in such that they neither believe nor fail to believe (*) just is the state of having an indeterminate belief. See Caie (2012, Sect. 4) for more about the psychological possibility of having this attitude.
Instead of appealing to indeterminate beliefs, one might try to deny (14) by maintaining that Alpha ought to reject both (*) and not-(*). But Caie (2012) has convincingly shown that appealing to the attitude of rejection will not work here. For if Alpha rejects (*), then they are not believing it. And if they are not believing it, then they cannot satisfy Introspection, i.e., (11)-(13).
Compare: according to some supervaluational treatments of vagueness, the law of excluded middle holds such that Patchy the color swatch is either red or not-red, it is just that it is indeterminate which. That is, while some precisificaitons say it is true that Patchy is red, and while others say that it is true that Patchy is not-red, the law of excluded middle is preserved because all precisfications say that it is true that Patchy is either red or not-red.
This style of objection is explored in Brouwer (2014). As will become clear below, I am going to push this line of thought in a new direction.
Perhaps proponents of doxastic indeterminacy could respond by questioning just how costly it is to posit infinitely many of these indeterminate mental state types. After all, nobody balks at the idea of accepting an infinite number of credences, i.e., once we admit that there are some credences between 0 and 1, we should just admit that there are infinitely many. Similarly, then, insofar as we posit indeterminate beliefs, perhaps we should just admit that there are indeterminate indeterminate beliefs, indeterminate indeterminate indeterminate beliefs, and so on. Thus, insofar as the reason for unproblematically positing infinitely many credences also licenses us to unproblematically posit infinitely many of these indeterminate mental state types, once we pay the initial cost of accepting indeterminate beliefs, we can get all of the other indeterminate mental state types on the cheap.
While this strikes me as a line of thought worth exploring, the burden lies on the opponent to develop the motivation for unproblematically positing infinitely many mental state types in more detail, i.e., insofar as the ontological cost of accepting these various mental state types really is similar to the ontological cost of accepting infinitely many credences, the proponent of this reply owes an explanation of why this is the case (after all, insofar as credences and indeterminate beliefs are different types of attitudes, it is not obvious that the reason for positing infinitely many credences will also motivate the claim that it is not all that costly to posit infinitely many types of these indeterminate beliefs). Moreover, insofar as there is an initial cost of accepting indeterminate beliefs, proponents of DOXASTIC INDETERMINACY are still forced to pay a price that proponents of other views are not.
DOXASTIC INDETERMINACY does not have this problem. For if Alpha indeterminately believes (*), her doxastic state is neither false nor unsupported by the evidence. Thus, because Alpha is not in a position to tell that her attitude is either false or unsupported by the evidence, there would be nothing for her to be rationally perplexed about.
Recall: an agent’s doxastic attitudes include the attitudes they have as well as the ones they lack. Thus, some resolved sets will include beliefs about certain propositions as well as the lack of belief in others. Thanks to an anonymous referee for suggesting this reminder.
Insofar as Alpha has good reason to think that she believes that she believes (*), then Introspection will require her to believe that she has this belief as well. And this pattern will repeat itself until Alpha is unaware that she has one of the beliefs in question. But since nothing hangs on this for our purposes, I will ignore these additional iterations for the sake of simplicity.
See Fn. 16.
While I am going to put things in terms of classical supervaluationism (e.g., McGee and McLaughlin (1995), Barnes and Cameron (2009), Barnes and Williams (2011), and Cariani and Santorio (2018)), things could be easily reformulated in terms of standard supervaluationism too (e.g., Fine (1975) and Keefe (2000)).
It will also be indeterminate whether Alpha is permitted or required to have the other attitudes contained on some but not all of these resolutions, i.e., Ba(Ba(*)), Ba(Ba(*)), Ba(*), Ba((*)).
See, e.g., the references in Fn. 18.
It is worth noting that supervaluationism has some seemingly counterintuitive consequences of its own, e.g., the proposition “p or not-p” can be true even if neither of its disjuncts are. See Keefe (2000, 2008) for a nice discussion of these odd features, as well as what strike me as compelling responses. Thanks to an anonymous referee for a helpful discussion here.
But Alpha is not doomed to have a determinately impermissible attitude about (*) either. This is why RATIONAL INDETERMINACY preserves No Determinate Dilemmas.
I am grateful to Amy Flowerree, Michael Caie, Michael Glanzberg, Sandy Goldberg, the anonymous referees at Synthese, and the participants at the 2019 Formal Epistemology Workshop and the 2019 meeting of the Society for Exact Philosophy for very helpful comments. I am also grateful to Baron Reed and Jennifer Lackey for a fun conversation that resulted in most of the arguments in Sect. 3. Finally, I owe a special thanks to David Christensen and Fabrizio Cariani for providing feedback and guidance on many, many, many earlier versions of this paper.
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Leonard, N. Belief and rational indeterminacy. Synthese 199, 13523–13542 (2021). https://doi.org/10.1007/s11229-021-03386-z
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DOI: https://doi.org/10.1007/s11229-021-03386-z