Abstract
There are few indulgences academics can crave more than to have their work considered and addressed by leading researchers in their field. We have been fortunate to have two outstanding philosophers from whose work we have learned a great deal give ours their thoughtful attention. Grappling with Stephen Yablo’s, and Juan Comesaña’s comments and criticisms has helped us gain a better understanding of our ideas as well as their shortcomings. We are extremely grateful to them for the attentiveness and seriousness with which they have considered our arguments and to philosophical studies for giving us this opportunity. Given the substantive difference between the two response papers, there is not much beyond sincere gratitude that we can covey to them jointly. We will therefore address them in turn.
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Notes
We also have no objection and nothing substantial to add to his exceptional discussion of Hempel and related issues in the appendix to his paper.
We could slightly change (ED) so that Yablo’s case wouldn’t apply: (ED*) If A does not know at time t0 that q, and the evidence she acquires between t0 and t1 counts against q only, then A does not know q at t1 either. Since Alma gains some evidence against q but some evidence in favor of q, (ED*) wouldn’t apply. The problem, however, with this type of claim is that it rules out many instances where some of the evidence counts in favor of q even though as a whole it counts against q. This is the case in many instances where it is clear that one gains no knowledge. See our comments below regarding Black winning the silver medal.
In footnote 8 Yablo says: “Another way to see the problem with (ED). Evidence e that refutes b surely also refutes a hypothesis c that strictly entails b. (ED) cannot allow this when c = e&b; e as a consequence of b&e cannot lower its probability. It seems like double-counting for e’s recurrence in a hypothesis to be what spares the hypothesis from refutation by e. The principle that suggests itself, letting p–q be what remains when q is extricated from p, is this.
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(1)
e is evidence for (against) p iff e makes p–e likelier (less likely).
Call that the remainder principle. Putting e&¬h for p,
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(2)
e is evidence for (against) e&¬h iff e raises (lowers) the probability of (e&¬h)–e.
Putting ¬h for (e&¬h)–e,
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(3)
e is evidence for (against) e&¬h iff e raises (lowers) the probability of ¬h.”
It’s hard to see why Yablo thinks that e surely refutes c if it refutes b that logically follows from c. If refutation of p is the confirmation of ¬p, this is a restatement of evidence closure (that he claims has been surrendered long ago). Even viewed as a principle, (ED) is about knowledge and its relation to evidence, (ED) is silent on the conception of the evidence-for relation. But even if we do engage with the suggestion that there is some double counting in his example, as we’ve shown, all that is required for refuting a probabilistic closed evidence principle is evidence that raises the probability of ¬(e&¬p), we need not have e itself as evidence. Vogel’s car being stolen from a certain place is more probable if memory of it being last parked there is his evidence. Yet it entails that the car is not where he last parked it.
The suggested principle is hard to evaluate. Suppose e is that the die landed on an even number and p is that it landed on 4. Now e is evidence for p, iff e supports p–e. But what is it to extract from 4 its being an equal number? We are not clear about the remainder principle, is the point.
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(1)
What we had in mind, and what we think makes (ED) hold in many cases, regards a comparison between what is sometimes called in Bayesian parlance Ur-Prior—the as-if confidence one has in a proposition without any evidence or background empirical knowledge—and the posterior probability. The first thing to note about Ur-Priors is that they are often understood as subjective prior guesses, or at least nothing like known propositions (even within a more objective framework). Second, the “as-ifness” allows us to disregard the “ups and downs” of confidence one has in a proposition due to biographical evidence-profiles that may include misleading evidence, undermining/undercutting evidence, etc. Some differences in biography can be abstracted away for the purpose of evaluating cases like those of Alma and her friends John and Brown. One way of seeing that these differences should not matter is checking to see if reversal of the time order of evidence Alma receives will make any difference. We will leave the excise of this comparison for another opportunity. We turn now to our second point.
The problem Yablo notes about “for all Alma knows, p” (Yablo, Sect. 4) as opposed to “for all Alma knows ¬(p&q)” is a problem for knowledge failure of equivalence just as it is for closure generally. And this is true regardless of whether one has made inferences or drawn equivalences or is even in a position to do so (e.g., for all Alma knows the axiom of choice might be false has no worlds witnessing this possibility). A world witnessing Vogel’s car being in the driveway is a world witnessing it's being there and not towed away. The point is, the possible world framework is ill fitted to capture any view regarding epistemic possibility that rejects “multi-premise closure” that in the present fallibilist framework is agreed to be invalid. It is hard to see how normal modal logic can be used even locally for any one proposition for a view that is fallible. Such a logic will entail inaccessible relations to possibilities that one has no evidence to rule out (and that are not ruled out a priori).
Relatedly see John Hawthorne’s argument along these lines in his (2004) against Herman and Sherman’s denial of an epistemic equivalence principle (2004). The problem is worse for a deniers of evidence equivalence principles, e.g., because there isn’t any foreseeable way of avoiding straightforward synchronic Dutch-Book situations (as there is by severing the tie between decision and knowledge).
Intuitively, it seems that one cannot have evidence for p&q without having evidence for either p or for q. But arguments of the kind presented by Carnap and others show that this is unavoidable, as we elaborated in our paper.
Thanks here to Yablo for correcting a mistake we made.
We thank Yablo for helping us clarify that our commitment to closure under equivalence entails a commitment to knowledge of general propositions of the type evidence against p is evidence against a truth, while rejecting knowledge of some particular propositions, such as Doug’s report is misleading. This is another instance of closure-failure of the kind we argue for.
What we mean by Fred-like cases is cases in which one’s evidence is not conclusive (i.e. does not entail the proposition it supports) and when one does not have prior knowledge of the relevant entailments of what one comes to know on the basis of the evidence. We are not wedded to any of the examples we use to demonstrate these features, only to the existence of such possibilities on any fallibilist account of knowledge, which can be proved as we show in our article (footnote 43). Our argument, then, is structural, not one that is based on cases. That the cases in the literature also fit the structural features of knowledge we highlight—in particular Yablo’s ION’s—gives added support to our conclusion.
Jonathan Vogel defends (in an unpublished paper) an evidence-for relation based view that is precisely the kind of non-probabilistic view aimed at preserving evidence closure that our argument was meant to address.
Comesaña also thinks that our argument that we claimed does not appeal to (CS) tacitly appeals to his (Entailment) principle. Here is his presentation of our argument:
Sharon and Spectre suggest at one point that they can do without anything like Entailment. I reconstruct their argument as follows. Suppose that our evidence is given by an atomic proposition a and that it supports two alternative theories: (a∧b) and (a∧¬b) (where b is another atomic proposition). Then, by Closure, a also supports the following proposition: [(a∧b)∨¬(a∧¬b)]. But that proposition is logically equivalent to its second disjunct: ¬(a∧¬b), which in turn is logically equivalent to ¬a∨b. Therefore, assuming that logically equivalent propositions are supported by the same evidence, a supports ¬a∨b. But that last claim, Sharon and Spectre say, is “absurd.” Now, why would it be absurd to say that a supports ¬a∨b? It is, of course, incompatible with Entailment, but if we are not assuming Entailment or anything like it, I do not see how Sharon and Spectre’s argument goes through (Comensaña, Sect. 2).
Comesaña is correct that without further principles we cannot derive a contradiction. The reductio argument, however, was meant to show an absurd conclusion from (EC). The absurdity does not stem from the claim that the evidence is entailed by the hypothesis a∧b and a∧¬b and hence should not support their negations ¬(a∧¬b) and ¬(a∧b). The absurdity stems from two things: (1) that a and b are atomic propositions, and (2) that a is silent with respect to b. The absurdity is that, if evidence is deductively closed, a supports ¬a∨b although it is silent on b.
The only way out seems to be ascribing to scientists conclusive evidence that maybe theory T is correct, that it is highly probable that T is correct, or something of this sort. However, this would require showing that they have evidence that entails these kinds of propositions. But this is highly doubtful for the same reasons that conclusive evidence is doubtful in the first place.
See Hawthorne (2005).
If all the “gap-fillers” are known, then the conditional probability of each entailed proposition will be 1 (see Sect. 1.4). For an additional argument against the a priori account see footnote 54 in our paper.
Another possibility, highlighted by Cohen, is to deny that we need justification for believing that our perceptual faculties are reliable in order to be justified in believing their deliverances.
This is what holds when we think about the standard role of a priori knowledge in conditional probability. As far as we know, there isn't any worked out theory regarding such matters. The challenge in developing such an account and remain within fallibilists is to say, first, why the entire "evidential gap" is to be filled by a priori knowledge, and, if so, how is it different from other a priori knowledge (regarding its probability, its role in conditionalization etc.) that allows the probability of known propositions to be <1.
References
Cohen, S. (2010). Bootstrapping, defeasible reasoning, and a priori justification. Philosophical Perspectives, 24(1), 141–159.
Cohen, S., & Comesaña, J. (2013a). Williamson on Gettier cases and epistemic logic. Inquiry, 56(1), 15–29.
Cohen, S., & Comesaña, J. (2013b). Williamson on Gettier cases in epistemic logic and the knowledge norm for rational belief: A reply to a reply to a reply. Inquiry, 56(4), 400–415.
Harman, G., & Sherman, B. (2004). Knowledge, assumptions, lotteries. Philosophical Issues, 14(1), 492–500.
Hawthorne, J. (2004). Replies to Harman, Sherman, Vogel, Cohen. Noûs, 38, 510–523.
Hawthorne, J. (2005). The case against closure. In M. Steup & E. Sosa (Eds.), Contemporary debates in epistemology. Malden, Ma: Blackwell.
Sharon, A., & Spectre, L. (2013). Epistemic closure under deductive inference: What is it and can we afford it? Synthese, 190(14), 2731–2748.
Sorensen, R. A. (1988). Dogmatism, junk knowledge, and conditionals. Philosophical Quarterly, 38(153), 433–454.
Wedgwood, R. (2013). A priori bootstrapping. In A. Casullo & J. Thurow (Eds.), The a priori in philosophy (pp. 226–246). Oxford: Oxford University Press.
White, R. (2006). Problems for dogmatism. Philosophical Studies, 131(3), 525–557.
Williamson, T. (2000). Knowledge and its limits. Oxford: Oxford University Press.
Yablo, S. (2014). Aboutness. Princeton: Princeton University Press.
Acknowledgments
Levi Spectre’s research was supported by the Israel Science Foundation (grant no. 463/12).
