Abstract
Recently, Levinstein (Philos Phenomenol Res, 2015) has offered two interesting arguments concerning epistemic norms and epistemic peer disagreement. In his first argument, Levinstein claims that a tension between Permissivism and steadfast attitudes in the face of epistemic peer disagreement generally leads us to conciliatory attitudes; in his second argument, he argues that, given an ‘extremely weak version of a deference principle,’ Permissivism collapses into Uniqueness. However, in this paper, I show that when we clearly distinguish among several types of Permissivism (what I call Permissivism \(_{1}\), Permissivism \(_{2}\), and Permissivism \(_{3}\)), we can see that any type of Permissivism fits well with steadfast attitudes. Further, even though Levinstein’s ‘extremely weak version of a deference principle’ does rule out a possibility for some types of Permissivism (Permissivism \(_{1}\) and Permissivism \(_{2}\)), it is still compatible with the other type of Permissivism (Permissivism \(_{3}\)), so we may regard at least that version of a deference principle as a viable position in connection with that particular type of permissive rationality.
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Notes
I am following Christensen (2009) in the use of Steadfast (and Conciliationism).
I am following Levinstein (2015) in the use of Deference.
Levinstein (2015, p. 3). The bracket is mine.
There could be other versions of Uniqueness (and Permissivism). For my purposes in this paper, other versions of Uniqueness (and Permissivism) could be allowed—so long as there are counterparts of Agent Uniqueness and Permission Parity, respectively, for those versions. For recent discussions of Uniqueness/Permissivism, see Ballantyne and Coffman (2011), Christensen (2007), Feldman (2007), Kelly (2014), Meacham (2014), Schoenfield (2014), and White (2005, (2014).
For the proof of the equivalence, see Meacham (2014, p. 1188).
The distinction between two permissive intuitions is from Meacham (2014, p. 1190).
The distinction between interpersonal import and intrapersonal import is from Kelly (2014).
Intrapersonal Permissivism has interpersonal import as well because it appeals to both Permissive Intuition 1 and 2, but, in this paper, Interpersonal Permissivism refers only to Permissivism \(_{3}\) while Intrapersonal Permissivism refers to Permissivism \(_{1}\) or Permissivism \(_{2}\).
Among the various types of Permissivism, Levinstein seems to be implicitly assuming Intrapersonal Permissivism (Permissivism \(_{2}\)). For instance, he (p. 2) says “Many writers think that if Permissive is true, conciliationism is wrong. If Alice has credence .3 that Hilary will win, and she discovers Bob has credence .25, it seems Alice can retain her opinion even if she’s aware that Bob is rational too. When asked why, she can appeal to the fact that .3 is perfectly rational, and .3 just struck her as the most attractive credence to have out of the set of rational credences.” (The italic is mine.)
For instance, any conservative updating policy such as Bayesian Conditionalization is generally incompatible with Intrapersonal Permissivism.
Here I restrict my discussion to a version of Steadfast that is motivated by permissive rationality as described above. Of course, there are other motivations for Steadfast. For instance, Wedgwood (2010, p. 238) asserts that one should give special treatment to her own current beliefs, experiences, memories, and intuitions, because they can guide her directly in a way that beliefs, experiences, memories, and intuitions of others cannot. Wedgwood takes such an epistemic partiality towards one’s own current mental states to motivate Steadfast. It is worth investigating in detail how well this sort of motivations justifies Steadfast, but that would go beyond the scope of this paper.
Note that, after t\(_{0}\), if Alice actually updates her credences by Conditionalization, there is a uniquely rational credence function for Alice. Why? When Alice updates her credences by Conditionalization, her prior credence function and her new evidence suffice to determine a uniquely rational credence function for her at a relevant time after t\(_{0}\). However, note that Alice can be sure that she will update her credences by Conditionalization even if she is not obliged to do so. Thus, (2) and (3) are compatible on the assumption of any type of Permissivism at t\(_{0}\), and even after t\(_{0}\), given that she does not actually update her credences by Conditionalization after t\(_{0}\). Thanks to an anonymous referee for this point.
Why does Levinstein take the Reflection principle for granted here? Levinstein assumes that (3) Alice will update her credences by Bayesian Conditionalization, and seems to take it for granted that Bayesian Conditionalization implies the Reflection principle. But it is at least not uncontroversial whether Bayesian Conditionalization implies the Reflection principle. For instance, see Weisberg (2007) and Park (2012). However, let’s set aside this issue for now.
C3 says that, according to \(a_{0}\), p and \(b_{1}(p)=y\) are conditionally (probabilistically) independent given \(a_{1}(p)=x\). Conditional (probabilistic) independence is symmetric. That is, for any propositions p, q, and r, and probability function pr, according to pr, p and q are conditionally independent given r (i.e., pr(\(p{\vert }q, r\)) = pr(\(p{\vert }{\sim }q, r\))) if and only if q and r are conditionally independent given r (i.e., pr(\(q{\vert }p, r\)) = pr(\(q{\vert }{\sim }p, r\))). Thus it follows from C3 that \(b_{1}(p)=y \) and p are also conditionally independent given \(a_{1}(p)=x,\) and that is exactly what C4 says.
Levinstein seems to think that (3) Bayesian Conditionalization and (5) Steadfast imply P2. He says that “Alice thinks that her future self will still be sensitive to whether p even conditional on Bob’s credence. Otherwise Alice couldn’t both be a steadfaster and be sure she’ll update by conditionalization.”(p. 12) However, Levinstein does not provide a proof for this. We can prove that Bayesian Conditionalization and Steadfast imply P2, given that, as Levinstein seems to think, Conditionalization implies the Reflection principle. (I owe this point to Ilho Park.)
Proof) Let’s assume, for reductio, that the denial of P2 holds: for all x and y, \(a_{0}(a_{1}(p)=x{\vert }p\), \(b_{1}(p)=y)=a_{0}(a_{1}(p)=x{\vert }{\sim }p\), \(b_{1}(p)=y)\). Then, by Steadfast, it follows that for all x, \(a_{0}(a_{1}(p)=x{\vert }p)\)=\(a_{0}(a_{1}(p)=x{\vert }{\sim }p)\), which is equivalent to \(a_{0}(p{\vert }a_{1}(p)=x)=a_{0}(p)\). Then, given that Conditionalization implies the Reflection principle, it follows that (\(\alpha \)) for all x, \(a_{0}(p{\vert }a_{1}(p)=x)=a_{0}(p)=x\) by the Reflection principle (given \(a_{0}(a_{1}(p)=x)>\) 0). However, (\(\alpha \)) is contradictory, given that \(a_{0}\) considers two different possible future credences in p. To see this, suppose that there are two real numbers \(x_{1}\) and \(x_{2}\) such that \(x_{1}\,{\ne }\,x_{2}\), \(a_{0}(a_{1}(p)=x_{1})>\) 0, and \(a_{0}(a_{1}(p)=x_{2}\) ) > 0. Then, by (\(\alpha \)), it immediately follows that \(x_{1}=x_{2}\), which is contradictory to the assumption that \(x_{1}\,{\ne }\,x_{2}\).
Of course, if \(a_{0}\) is sure that \(a_{1}\) will have one particular credence in p (i.e., \(a_{0}(a_{1}(p)=x_{1})\) =1), the proof does not work. However, note that such a case does not fit well with Alice’s case where \(a_{0}\) does not know her own future credence in p at t\(_{1}\).
Levinstein (2015, p. 7). The brackets are mine.
In his paper, Levinstein (p. 7) defines Basic Sensitivity as follows:
Basic Sensitivity: An agent \(s_{\mathrm{i}}\) is basically sensitive to whether p according to a credence function c if for some \(x, c(s_{\mathrm{i}}(p)=x{\vert } p)\,{\ne }\,c(s_{\mathrm{i}}(p)=x{\vert } {\sim }p)\).
However, he implicitly assumes the converse of it as well. For instance, he (p. 7) says that “Note that because Basic Sensitivity is subjective, it only tracks whether [c] thinks learning [\(s_{\mathrm{i}}\)]’s credence could be informative about whether p. If, for instance, [c] already knows whether p or already knows [\(s_{\mathrm{i}}\)]’s credence, then [\(s_{\mathrm{i}}\)] won’t count as basically sensitive according to Pr.” (The brackets are mine.) Here it is implicitly assumed that “if for all x, \(c(s_{\mathrm{i}}(p)=x{\vert } p)=c(s_{\mathrm{i}}(p)=x{\vert }{\sim }p)\), then c regards \(s_{\mathrm{i}}\) as being basically insensitive,” which is equivalent to “if c regards \(s_{\mathrm{i}}\) as being basically sensitive, then for some x, \(c(s_{\mathrm{i}}(p)=x{\vert } p)\,{\ne }\,c(s_{\mathrm{i}}(p)=x{\vert }{\sim }p)\). A similar point applies to Conditional Sensitivity as well.
Note that for all \(x, c(s_{\mathrm{i}}(p)=x{\vert } p)=c(s_{\mathrm{i}}(p)=x{\vert }{\sim }p)\) is equivalent to \(c(p{\vert } s_{\mathrm{i}}(p)=x)=c(p)\), where conditional credences are well defined.
Note that \(y(l(m)=x{\vert } m, e)=y(l(m)=x{\vert } {\sim }m, e)\) is equivalent to \(y(m{\vert }l(m)=x, e)=y(m{\vert } e)\).
We can also easily show that \(a_{0}(b_{1}(p)= y{\vert }{\sim }p)\) is determined by \(a_{0}(a_{1}(p)=x_{\mathrm{i}}{\vert }{\sim }p)\) and \(a_{0}(b_{1}(p)=y{\vert } a_{1}(p)=x_{\mathrm{i}})\).
Note that C4 is equivalent to (for all x and y) \(a_{0}(b_{1}(p) = y{\vert }p, a_{1}(p) = x)=a_{0}(b_{1}(p)=y{\vert }a_{1}(p)=x)\).
Levinstein (2015, p. 12). The bracket is mine.
Note that \(a_{0}(a_{1}(p)=x{\vert } p) = \sum _{\mathrm{i}} a_{0}(a_{1}(p)=x{\vert } p\), \(b_{1}(p)=y_{\mathrm{i}})\cdot a_{0}(b_{1}(p)=y_{\mathrm{i}}{\vert } p)\,{\ne }\,\sum _{\mathrm{i}} a_{0}(a_{1}(p)=x{\vert } b_{1}(p)=y_{\mathrm{i}})\cdot a_{0}(b_{1}(p)=y_{\mathrm{i}}{\vert } p)\).
Levinstein (2015, p. 12).
In discussing an intrapersonal permissivist’s response to Levinstein’s first argument, I will provide a case (The Double Epistemic Life of Véronique) in which an agent is a steadfaster from her purely practical perspective.
There are a number of different versions of Conciliationism. For instance, the Equal Weight View says that in disagreements with an epistemic peer, one should always split the difference (see Elga 2007; Christensen 2007); the Epistemic Value Maximization View says that in disagreements with an epistemic peer, one should always compromise by maximizing the average of the expected epistemic values that she and her epistemic peer give to their consensus credence function (see Moss 2011). Here Levinstein assumes a moderate version of Conciliationism that is weaker than the Equal Weight View and the Epistemic Value Maximization View: In contrast to the Equal Weight View and the Epistemic Value Maximization View, as Levinstein points out, the moderate version does not imply that disagreeing epistemic peers always end up with a same credence.
See also Ballantyne and Coffman (2012, pp. 663–664) and Christensen (2009, p. 764) for a similar point. The point can also apply to Levinstein’s second argument that will be discussed in Sect. 4. However, I agree with Levinstein (2015, p. 23) that “most permissivists want rationality to be permissive even when rational functions are aware of the alternative rational choices.”
See Christensen (2014) for more details. Levinstein appears to acknowledge this possibility as well. See his Max & Eve case and discussions about it (pp. 24–26).
Of course, Levinstein also acknowledges this point. He provides some additional reasons against “the move from moderate conciliationism to full agreement” (see p. 15). And that is why he does not regard the first argument as a real threat to Permissivism per se.
That is, there is a pressure to adopt D\(_{1}\) from purely practical point of view.
We can also regard Weronika as Véronique’s counterpart who is in a possible world where Véronique has \(D_{2}\) rather than \(D_{1}\). That is, Véronique can imagine herself in a counterfactual situation where she has \(D_{2}\) rather than \(D_{1}\) and compare her doxastic states in the actual situation and in the counterfactual.
Note that we cannot directly apply ES to The Double Epistemic Life of Véronique case since Véronique knows that she will be a steadfaster from her purely epistemic perspective. My question is about whether, without assuming ES, \(v_{2}(p)\) is epistemically better than \(w_{2}(p)\) in any good sense.
For instance, see Fantl and McGrath (2009).
In order to support his own view on a tension between Steadfast and Permissivism, Levinstein also claims that Steadfast and (Intrapersonal) Permissivism imply odd conclusions in some betting situations. To briefly examine this point, let’s begin by assuming that, as already described, Véronique is a (epistemically) rational steadfaster and Weronika is her epistemic doppelgänger who is as epistemically rational as Véronique is, shares total evidence with Véronique at every time, and adopts the same system of epistemic evaluation that Véronique adopts. Suppose further that there is (intrapersonal) permissive evidence for a proposition h, which allows Véronique and Weronika to have v(\(h) = 0.999999\) and w(\(h) = 0.000002\), respectively, even after they are fully aware of each other’s opinion about h. In such a case, Levinstein claims, “Even if [Véronique] and [Weronika] are extremely risk averse, they will still make large bets if their credences are close enough to 0 and 1. Nevertheless, they’re fully aware that rationality allows them to hold the opposite view, that only lucky rational agents will end up winning, and they have no special evidence for thinking they’re lucky.” (see p. 14. The brackets are mine.) For instance, according to Levinstein, Véronique would be willing to bet her life savings on h, while admitting that it would have been just as rational to have bet her life savings against h. Here Levinstein dramatizes a tension between Steadfast and (Intrapersonal) Permissivism by imaging Véronique (Weronika) would bet her life on (against) h while admitting permissive rationality allows her to do so in an opposite direction.
Note that this argument cannot apply to Interpersonal Permissivism since, according to Interpersonal Permissivism, no total evidence is permissive with respect to the range of rational beliefs open to any particular individual. But, I think, Levinstein’s argument based on some betting situations could be a real threat to intrapersonal permissivists. In order to fully evaluate the argument, however, we must figure out how beliefs and context in which we have them influence bets including ones at extreme stakes. In particular, we must examine whether, in the betting cases that Levinstein considers, credences could represent the permissive world in a way that is disconnected from corresponding preferences. However, I do not have space here to give a full account of how credences and preferences are related to each other in the betting cases. I will leave that for future research.
E does not contain any information about a membership of R.
Levinstein himself also provides and considers what he calls “permissivist’s best hope for escape” from his second argument: “There’s an important evidential difference between rational priors considered as abstract objects and rational priors realized in a particular agent’s cognitive architecture.” (p. 3) Even though it seems to be an interesting idea, it is unclear how it works and why Levinstein takes it as “permissivist’s best hope for escape”. Here and below, I provide another response, which, at least in some respects, may be better than Levinstein’s response.
This is similar with what Meacham (2014) calls Permission Parity.
Here’s the proof. Suppose that your permissible credence functions (that are members of R) and Daisy’s permissible credence functions (that are members of \({\varvec{R}}^{\prime }\)) have a common element r. Then for any \(r_{1}\in {\varvec{R}}\), \(r_{1}(\cdot {\vert }E\), \(r_{1}, r \in {\varvec{R}})\) = \(r(\cdot {\vert }E, r, r_{1}\in {\varvec{R}})\). Therefore, for any \(r_{1}\in {\varvec{R}}\), \(r_{1}=r\). And, for any \(r_{3}\in {\varvec{R}}^{\prime }\), \(r_{3}(\cdot {\vert }E, r_{3}, r\in {\varvec{R}}^{\prime })\) = \(r(\cdot {\vert }E, r, r_{3}\in {\varvec{R}}^{\prime })\). Therefore, for any \(r_{3}\in {\varvec{R}}^{\prime }\), \(r_{3}=r\). Thus, for any \(r_{1}\in {\varvec{R}}\), for any \(r_{3}\in {\varvec{R}}^{\prime }\), \(r_{1}=r_{3}=r\).
Thanks to Ilho Park for suggesting this point.
Levinstein also takes it for granted that there is at least one non-maximally rational probability function. (See p. 21)
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Acknowledgments
Many thanks to Inkyo Chung, Ángel Pinillos, Douglas Portmore, the logic group at Korea University, and an anonymous referee from Synthese for their helpful comments and suggestions. I am especially grateful to Brad Armendt and Ilho Park for all their help on this project.
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Jung, J. Steadfastness, deference, and permissive rationality. Synthese 194, 5093–5112 (2017). https://doi.org/10.1007/s11229-016-1197-7
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DOI: https://doi.org/10.1007/s11229-016-1197-7