Abstract
It is argued, on the basis of new counterexamples, that neither knowledge nor epistemic justification (or “epistemic rationality”) can reasonably be thought to be closed under logical implication. The argument includes an attempt to reconcile the fundamental intuitions of the opposing parties in the debate.
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Notes
I confess that I find it downright uncomfortable to speak, as most in the literature have done, of a principle that is not an explicit directive. So, I’ll take the liberty to speak of closure claims or theses.
The authors associated with the following theses are only some of those who have discussed these theses, occasionally remaining non-committal about those with which they are associated in what follows. The reference is not meant to indicate endorsement of a given thesis by a given author. Also, the association is only a good approximation to the author’s actual choice of words. Some of the theses are not found verbatim in these references. The author whose name appears first is the one who is quoted.
In his 2005 paper, Dretske writes: “[I]f S knows that P is true and knows that P implies Q, then, evidentially speaking, this is enough for S to know that Q is true” (emphasis added). Internal evidence suggests that he should be associated with this claim discussed in Stewart Cohen (1988) — even though he has also subscribed to claim (e), below, in his 2005 reply to John Hawthorne.
Russell’s paradox is the most stunning of all the paradoxes involving deductive reasoning that I know. To my mind, the other logical paradoxes give us more wiggle room to reject (or suspend judgment on) one of the premises. But I’m giving you a recipe here: Take your favorite paradox involving valid deductive reasoning and it should look to you like a reason for withholding belief in epistemic closure claims.
It is, of course, awkward to speak of a “knowable proposition”, and of “knowing a proposition”, but this is well-established philosophical clumsiness that allows us to avoid painful circumlocution. I follow standard usage.
Granted, some will feel inclined to hold that this anti-closure move is paradoxical. I will give you reason to reconsider this optimistic view of the intuitive content of closure claims in Sect. 3 below.
In his 1986 paper, Priest explicitly suggests that Russell’s paradoxical argument is sound and that the argument is his basis for saying that “I, for example, believe that the Russell set is both a member of itself and not a member of itself”.
“Closure denial” is something of a misnomer here. My case from Russell’s paradox is a case for justified suspension of judgment. It is, however, tempting to avoid deviating from the established terminology of the debate as much as possible. This is still a case against closure, though not exactly a case for closure denial. It will, however, turn into a case for closure denial in Sects. 5 and 6 below.
I thank Anthony Brueckner, Stewart Cohen, Patrick Greenough, and Doris Olin for discussion leading to this point.
Again, for the fate of those who have argued against acceptance of the Russellian premises, I’ll refer you to Priest (2006).
It is noteworthy that, if we were to adopt Crispin Wright’s distinction between closure and transmission (Wright 2003), and if, as I have argued, we must acknowledge the dilemma posed by a paradox like Russell’s (again, the dilemma whose first horn is disbelieving the paradoxical premises and whose second horn is embracing dialetheism) as providing us with a reason for withholding belief in epistemic closure claims, we should notice that the paradox may be a genuine counterexample to closure (as characterized by Wright). It cannot be only a counterexample to transmission (as characterized by Wright) because it should seem absurd to think that warrant for believing the paradoxical premises may in any way depend on our having a warrant for believing the Russellian contradiction. The case does not obviously conform to his information-dependence template for transmission failure. (As he sees it, every case of closure failure is a case of transmission failure but not conversely. And every case of transmission failure is characterized by him as a case of epistemic circularity — though he makes no use of the term “epistemic circularity”.) This is noted in passing. The philosophical worth of Wright’s views on closure cannot be gauged here.
On the Carrollian perils of reflection on one’s reasons for belief, the reader is referred to my 2005.
I anticipate this objection: “Suppose you take it on good authority that p but fail to notice that p implies that not-p. Surely, it is an objective fact that you shouldn’t believe that p.” Isn’t this ultimately motivated by some form of justification-closure dogmatism? I just can’t see that such a far-reaching condemnation of inferential near-sightedness is philosophically warranted by a tenable theory of epistemic rationality. I suppose we don’t want to count such a common form of “stupidity”, of inferential mediocrity as a case of irrationality. Clearly, there is something undesirable in the cognitive life of such an agent. He can’t know that p. But, assuming fallibilism, I can’t see a charge of irrationality that will stick. Maybe the objection rests on a confusion between synchronic and diachronic desiderata of epistemic rationality. I will not pursue the matter here. For important admonition in this regard, see Richard Foley (2001).
As Jonathan Kvanvig (2005) notes, the literature on so-called “closure principles” has stretched the terminology to breaking point. Strictly speaking, some of these claims are not really closure claims, since the property referred to in the antecedent of these conditionals is not the property referred to in the consequent. So, “closure” has really become a metaphor of sorts in the literature. I share in Kvanvig’s point about this kind of excessive terminological permissiveness, but I’ll be willing to play along and call a “closure claim” anything in the neighborhood of closure.
Granted, the thought that intuitive appeal comes in degrees is not obviously false, but that is cold comfort for Hawthorne. It does seem that any such hesitation makes the talk of intuitive appeal self-refuting. We lose our grip on any useful notion of intuition.
In his 2005 paper, Dretske called “heavyweight implications” those propositions “we needn’t know even though we know our knowledge depends on their truth”. He hasn’t offered an explicit definition of the term “heavyweight implication”, but the concept is not hard to grasp (not hard for our purposes here anyway). According to some of his examples, one may know that there are cookies in the jar without knowing the heavyweight implication that there is a material world; one may know that there are zebras in the pen without knowing the heavyweight implication that the zebra-looking objects are not cleverly disguised mules. It is typically thought that the class of heavyweight propositions includes the negations of skeptical hypotheses.
For more criticism of Hawthorne’s case for closure, see Fred Adams and Julia Figurelly, forthcoming publication.
I’m not casual in speaking of the generation of knowledge or justification in episodes of reasoning where Robert Audi (2003), for one, would have preferred to speak simply of the transmission of epistemic status via reasoning. We must take account of inferential knowledge arising from benign falsehoods. My 2006 offers an introduction to the matter and references for further reading.
I adhere to the terminology put forward in Klein (1981) in speaking of “overriders”. If you prefer “defeaters”, notice that these must be internal defeaters.
I thank Peter Klein and Roy Sorensen for discussing this case of apparent closure failure with me in 1998.
Commenting on a draft of this passage in correspondence, Williams adds: “Here’s another reason: If you know (iii) then you know its second conjunct, but since whatever you know is true, you lack the belief that your father loves you, which is a necessary condition of knowing that he loves you.” Thank you, John!
If I’m not mistaken, this thesis was first introduced in the literature in Klein 1981 (though I phrase it differently and give it a label here).
Although this is certainly very close to the surface in the literature and tacitly assumed by many, I can’t recall any statement of it. (EC) is a partial explanation of the concept of counterevidence.
I thank Doris Olin for calling my attention to the need to discuss this objection, though she may not approve of the way I have fleshed out her sketch of the objection.
It’s certainly uncontroversial that every reasonable fallibilist must feel some measure of attraction to David Lewis’ (1996) claim that fallibilism is a form of madness. Discussing that fundamental tension is outside the scope of this paper. We’re merely exploring a fallibilist alternative to the present difficulties.
Robert Audi (1991) suggests that a weaker principle might be defensible: “[I]f S has reason to believe p, and S can understand both q and the proposition that it is entailed by p, then S has reason to believe q”. This is most significantly different from (h) for not concerning knowledge-grade evidence.
In the case of the paradoxical counterexamples, the non-overridden overrider may be as simple as this: “But that’s absurd!” The overriders in the other cases are given in the text. It should also be noted that, for the Dretskean counterexamples (the cases involving “heavyweight” implications), the non-overridden overriders are the conjunctions encompassing every claim in a skeptical argument – or maybe just the conclusion of the argument – of which the believer is aware but is rationally unable to deny.
Count Mark Sainsbury (2001, pp. 11–12) among those who have explicitly subscribed to the traditional view of implying reasons as conclusive reasons.
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Acknowledgments
I have benefited from insightful comments on earlier drafts of the paper generously offered by Fred Adams, Jonathan E. Adler, Rodrigo Borges, Anthony Brueckner, Stewart Cohen, Rogel de Oliveira, Fred Dretske, Patrick Greenough, Nicholas Griffin, Peter Klein, Jonathan Kvanvig, Nenad Miscevic, Ernest Sosa, Marcus Willaschek, and John N. Williams. I am most especially indebted to Doris Olin and Danilo Suster for much helpful discussion. A draft of the paper was presented at the 2007 Bled Conference on Contemporary Epistemology. I am grateful to my audience there.
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de Almeida, C. Closure, Defeasibility and Conclusive Reasons. Acta Anal 22, 301–319 (2007). https://doi.org/10.1007/s12136-007-0013-x
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DOI: https://doi.org/10.1007/s12136-007-0013-x