Abstract
Ginger Schultheis offers a novel and interesting argument against epistemic permissivism. While we think that her argument is ultimately uncompelling, we think its faults are instructive. We explore the relationship between epistemic permissivism, Margin-for-Error principles, and an epistemological version of Dominance reasoning.
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Notes
We note in passing that the author (who kindly read this paper) was happy with our reconstruction of her reasoning.
Such rational ranges can be either open or closed depending on whether \(c_1\) and \(c_2\) are rational.
Schultheis discusses some intrapersonal principles, but that discussion does not directly address this issue.
Perhaps even more carefully—for some agent at some time. We mean to screen off esoteric views according to which the credences licensed by an evidential state can vary across times even for particular agents.
The mathematically inclined may feel free to mentally rename this principle “Convexity”.
Any range contains uncountably infinitely many credences.
Schultheis slightly misstates her position. She writes, “To believe that the lower bound is roughly .3 is just to believe that it might be slightly higher or slightly lower than .3” (Schultheis 2018). But an agent who has no idea where the lower bound is believes that it might be slightly higher or slightly lower than .3, yet does not believe that the lower bound is roughly .3.
Epistemic uniqueness being the thesis that a total evidential state can rationally permit only one credence in a proposition.
Similarly, an agent might not know what her evidence is, and thus might not know which credences are rationalized by her evidence even if she knew which credences were rationalized by each possible evidential state.
Indeed (though not quite for the same reasons) Schultheis later falls back on a “can be” version of the argument later. This qualification also assuages the worry that a rational range extending either to 0 or 1 would pose problems. Even if an agent knows that the bounds for rational credences could not be a bit lower than 0 or a bit higher than 1, other cases will be more germane for Schultheis’ line of reasoning.
We stipulate that according to any notion of closeness, the close to relation is reflexive.
In the familiar case regarding the height of a tree, the set is that of propositions about the tree’s height, the property is that of falsity, and the notion of closeness is that of having the tree’s height be within an inch. If the tree is x inches tall, then it’s not false that the tree is x inches tall, and so an agent subject to Margin-for-Error cannot know that it’s false that the tree is \(x + 1\) inches tall. For alternate views of this case and related cases see Weatherson (2004), Greco (2014), and Goodman and Salow (2018).
Note that this principle is weaker than the principle Schultheis states in her paper. Let us call that principle (appropriately generalized) S-Dominance. A set satisfies S-Dominance relative to a property just in case it is such that if the property is known to hold for \(e_2\) only if it also holds for \(e_1\) and is not known to hold for \(e_1\) only if it holds for \(e_2\), then that property does not hold for \(e_2\). But Dominance is all that is needed for the simplified argument, and indeed Schultheis herself does not use the additional strength of S-Dominance.
Instead of having Quotidian Context, Margin-for-Error, and Dominance apply to a set relative to a property and a notion of closeness, we could have Quotidian Context, Margin-for-Error, and Dominance apply monadically to triples of a set, a property, and a notion of closeness. Readers should feel free to mentally reformulate if they like.
For simplicity, hereafter we will take Quotidian Context, Margin-for-Error, and Dominance to refer to the propositions that Quotidian Context, Margin-for-Error, and Dominance hold for contextually specified properties in contextually specified sets given a contextually specified notion of closeness.
It’s convenient to rely on the factivity of knowledge, but unnecessary. The close to relation is reflexive, thus \(e_1\) is close to itself. Since the property is known to hold in \(e_1\), by Margin-for-Error it must hold in \(e_1\).
As we use the term, a property is luminous just in case it is known to obtain whenever it obtains. Here luminosity should be understood to be relativized to the set in question. We are aware that luminosity is sometimes defined in terms of being in a position to know rather than in terms of knowing, but depart from that here. See Williamson (2000) for more about luminosity.
Again, it’s convenient to rely on the factivity of knowledge, but unnecessary. The close to relation is reflexive, thus the element is close to itself. Since the property is known to obtain in the element, by Margin-for-Error it must obtain there.
The details of tininess don’t matter much. All that matters is that the notion of closeness be one according to which the set of possible credences obeys Connectedness.
Yet again, it’s convenient to rely on the factivity of knowledge, but unnecessary. The close to relation is reflexive, thus any credence is close to itself. So if some credence is known to be rational, by Margin-for-Error it must be rational.
Schultheis (2018).
Schultheis (2018).
Indeed, in Schultheis’ preferred framework of epistemic uniqueness, any setting in which Margin-for-Error holds will be one in which no credence can be known to be rational.
Modulo worries about vagueness.
We will revisit the plausibility of Margin-for-Error for this sort of case later.
Note that this result does not depend on you reasoning on the basis of the demonic declaration; it depends only on the demonic declaration being true. The case could have been framed to have the demon talking to himself, but it seemed more dramatic to have him tell you his fiendish intentions.
Note that these considerations suggest that Dominance applies to the normative property of OKness. Dominance would not be plausible at all regarding the non-normative property of being enough to nourish a particular malnourished baby.
Yet again—and for the same reasons—relying on factivity is convenient but unnecessary.
For example, Timothy Williamson considers safety to be a fruitful principle for evaluating knowledge in a wide variety of contexts. But others, notably Robert Stalnaker, deny the existence of a safety constraint on knowledge even in fairly mundane cases. For more, see Williamson (2000) and Stalnaker (2006).
The following case parallels the earlier case, Demonic Declaration. There we were taking Margin-for-Error for granted, here we don’t.
For convenience, we assume that Barack Obama knows that if he’s dead at some time then he’s dead at all future times.
Again, we will revisit what difference—if any—would be made by employing alternative epistemological notions.
Note that given the idealizing assumption of logical omniscience the argument could be simplified by assuming Known Closure
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Known Closure: \({\mathrm {K}}(p \supset q) \supset ({\mathrm {K}}p \supset {\mathrm {K}}q\))
from which both Liveness Closure and Combination follow given the other principles.
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The deduction does not involve (1), but it is helpful for stage-setting nonetheless.
Nor should stipulating the knowledge of correct epistemological principles make that pattern impossible.
Here’s a slightly different proof. Its structure is slightly more complex, but it doesn’t require that anything be known to be known to be rational: Let’s suppose that an agent knows that .3 is a rational credence and doesn’t know that .4 is a rational credence. But due to a lack of introspective access, the agent doesn’t know that she knows that .3 is a rational credence and doesn’t know that she doesn’t know that .4 is a rational credence. More formally, we have the following premises—
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\({\mathrm {(1): K}}rat_{.3}\)
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\({\mathrm {(2):}} \lnot {\mathrm {K}} rat_{.4}\)
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\({\mathrm {(3):}} \lnot {\mathrm {KK}} rat_{.3}\)
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\({\mathrm {(4):}} \lnot {\mathrm {K}} \lnot {\mathrm {K}} rat_{.4}\)
Let’s further suppose that the agent doesn’t know that it’s not the case both that she doesn’t know that .3 is rational and that she does know that .4 is rational. (Although there are cases in which an agent is guaranteed to know that a conjunction is false without knowing that either conjunct is false, there’s no reason to believe that such a dynamic is at stake here.) More formally, we have the further premise—
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(5): \(\lnot {\mathrm {K}}\lnot (\lnot {\mathrm {K}}rat_{.3} \wedge {\mathrm {K}}rat_{.4}\))
These seemingly innocuous premises (indeed, even premises (1) and (5) alone) lead to contradiction, as they license the following deduction—
\({\mathrm {(6): L}}(\lnot {\mathrm {K}}rat_{.3} \wedge {\mathrm {K}}rat_{.4})\)
by (5) and Duality
\({\mathrm {(7): L}} \lnot rat_{.3}\)
by (6), Known Dominance, and Liveness Closure
\({\mathrm {(8):}} \lnot {\mathrm {K}}rat_{.3}\)
by (7) and Duality
\({\mathrm {(9):}} \bot \)
by (1) and (8)
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Strictly speaking, the agent’s knowledge that no probabilistically incoherent credal state is rational is not needed for this argument. All that is needed is the fact that no probabilistically incoherent credal state is rational.
Note that the result is not that in the agent’s case there is no rational credal state. The result is that the suppositions of the case are impossible.
Propositions constitute a partition when they are mutually exclusive and jointly exhaustive.
This number is assumed to be finite.
In essence, the problems with blindspots discussed above are caused by a failure of Agglomeration.
The requirement of probabilistic coherence is only one example of a non-local constraint; there are other potential sources of non-locality. For example, it might be rationally required to give p and q equal probability despite there being latitude about what probability to assign each proposition. Suppose you know that a political leader was deposed in a military coup and convicted of crimes against the state. It might be rational to have high credence that the trial was corrupt and high credence that the leader was innocent and it might also be rational to have low credence that the trial was corrupt and low credence that the leader was innocent. Nonetheless, it might well be irrational to have high credence that the trial was corrupt and low credence that the leader was innocent or to have low credence that the trial was corrupt and high credence that the leader was innocent.
In conversation with the author we explored a reconstruction of her reasoning that involved both rational certainty and knowledge. The idea was to put Margin-for-Error in terms of knowledge and Dominance in terms of rational certainty. The argument would then unfold by saying that (i) if you know that you don’t know that p then it is not rational to be certain that p and (ii) it is rational to be certain that the credences in the middle of the rational range are rational. (Known) margin for error for knowledge is meant to play a role in underwriting (i).
We agreed, however, that this argument adds extra liabilities and complexity with insufficient compensating gain. In particular, it is not so easy to show using Margin-for-Error that if \(c_1\) is an endpoint of the rational range then one knowns one doesn’t know that \(c_1\) is rational. Of course, given (known) Margin-for-Error one knows that if \(c_1\) is an endpoint of the rational range then one doesn’t know that \(c_1\) is rational. But the latter does not secure the former. It is also harder to motivate the idea that some middle points of the rational range are such that it is rational to be certain they are rational than it is to motivate the the idea that some middle points of the rational range are such that one knows them to be rational.
In particular, the inconsistency does not depend on the factivity of knowledge. See footnotes 17, 19, 21 and 29 for more.
References
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Goodman, J., & Salow, B. (2018). Taking a chance on KK. Philosophical Studies, 175(1), 183–196.
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Acknowledgements
As this article represents the equal contributions of both authors, any praise and/or blame for what follows should be distributed equally. We would also like to thank Juhani Yli-Vakkuri, Andrew Bacon, and Ginger Schultheis for their generous assistance.
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Appendix
Appendix
We framed our presentation of Schultheis’ reasoning in terms of knowledge. In fact, she employed a multiplicity of epistemological ideologies including—but not limited to—knowledge, certainty, and what one ought to believe. What difference—if any—does choice of epistemological ideology make?
Schultheis herself wavers between alternate ideologies. For example, her treatment of Dominance in light of epistemic permissivism begins with a discussion of the limits of knowledge, switches to a discussion of what one should be certain of, and then switches again to a discussion of what one ought to believe. This is unfortunate. For example, Schultheis asserts that an agent shouldn’t be certain of the lower bound of the rational range. She then asserts that an agent should believe that the bounds of the rational range are roughly where they actually are. But one is left guessing about whether an agent should be certain that the bounds of the rational range are roughly where they actually are. The changes in ideology make the reasoning seem modest: denying certainty is more modest than denying that one ought to believe, and affirming that one ought to believe is more modest than affirming certainty. But absent a sustained treatment of the issues taken up it is unclear how the topic at hand, knowledge, certainty, and what one ought to believe interact.
Note that a profusion of epistemological ideologies is especially problematic for those of Schultheis’ sensibilities. Suppose one wants to have knowledge about what is and is not rational, but have Dominance deal with what is and is not certain to be rational. More formally, we have the following principles—
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Factivity: K\(p \supset p\)
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C-Dominance: \({\mathrm {(C}}rat_{p} \wedge \lnot {\mathrm {C}}rat_{q}) \supset \lnot rat_{q}\)
For these purposes, we make the standard assumption that there is no logical connection between knowledge and subjective certainty. Let us suppose that an agent knows that .3 is a rational credence and does not know that .4 is a rational credence. Let us also suppose that the agent is certain that .4 is a rational credence and is not certain that .3 is a rational credence. More formally, we have the following premises—
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(1): \(\hbox {K}rat_{.3}\)
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(2): \(\lnot {\mathrm {K}} rat_{.4}\)
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(3): \(\hbox {C}rat_{.3}\)
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(4): \(\lnot {\mathrm {C}} rat_{.4}\)
These seemingly innocuous premises lead to contradiction, as they license the following deduction—
\({\mathrm {(5): }} rat_{.3}\) | by (1) and Factivity |
\({\mathrm {(6): C}} rat_{.4} \wedge \lnot {\mathrm {C}} rat_{.3}\) | by (3) and (4) |
\({\mathrm {(7):}} \lnot rat_{.3}\) | by (6) and C-Dominance |
\({\mathrm {(8):}} \bot \) | by (5) and (7) |
In order to get a viable argument against epistemic permissivism, some measure of uniformity is needed. If there are some premises about knowledge, other premises about certainty, other premises about belief, and so on, then (absent stipulated relationships between knowledge, certainty, belief, and so on) it will be very hard to combine those premises together into a cogent argument.Footnote 44
Moreover, any uniform treatment of Schultheis’ reasoning is liable to be helpfully clarified by our simplified argument. While we employed the ideology of knowledge, the inconsistency between Quotidian Context, Margin-for-Error, and Dominance does not depend on any distinctive features about knowledge.Footnote 45 The import of our simplified argument is therefore not limited by our choice of ideology.
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Hawthorne, J., Isaacs, Y. Permissivism, Margin-for-Error, and Dominance. Philos Stud 178, 515–532 (2021). https://doi.org/10.1007/s11098-020-01443-w
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DOI: https://doi.org/10.1007/s11098-020-01443-w