. The Argument From Skepticism

According to Dretske and Nozick, we can account for the appeal of skepticism and explain where it goes wrong if we accept their view of knowledge and reject K. Rejecting knowledge closure is therefore the key to resolving skepticism. Given the importance of insight into the problem of skepticism, they would seem to have a good case for denying closure. Let us consider the story they present, and some worries about its acceptability.

5.1 Skepticism and Antiskepticism

Dretske and Nozick focused on a form of skepticism that combines K with the assumption that we do not know that skeptical hypotheses are false. For example, I do not know not-biv: I am not a brain in a vat on a planet far from earth being deceiving by alien scientists. On the strength of these assumptions, skeptics argue that we do not know all sorts of commonsense claims that entail the falsity of skeptical hypotheses. For example, since not-biv is entailed by h, I am in San Antonio, skeptics may argue as follows:

(1)K is true; i.e., if, while knowing p, S believes q because S knows that p entails q, then Sknows q.
(2)h entails not-biv.
(3)So if I know h and I believe not-biv because I know it is entailed by h then I know not-biv.
(4)But I do not know not-biv.
(5)Hence I do not know h.

Dretske and Nozick were well aware that this argument can be turned on its head, as follows:

(1)K is true; i.e., if, while knowing p, S believes q because S knows that p entails q, then Sknows q.
(2)h entails not-biv.
(3)So if I know h and I believe not-biv because I know it is entailed by h then I know not-biv.
(4)′I do know h.
(5)′Hence I do know not-biv.

Turning tables on the skeptic in this way was roughly Moore's (1959) antiskeptical strategy. (Tendentiously, some writers now call this strategy dogmatism). However, instead of K, Moore presupposed the truth of a stronger principle:

اقتباس :: PK: If, while knowing p, S believes q because S knows that q is entailed by S's knowing p, then S knows q.

Unlike K, PK underwrites Moore's famous argument: Moore knows he is standing; his knowing that he is standing entails that he is not dreaming; therefore, he knows (or rather is in a position to know) that he is not dreaming.

5.2 Tracking and Skepticism

According to Dretske and Nozick, skepticism is appealing because skeptics are partially right. They are correct when they say that we do not know that skeptical hypotheses fail to hold. For I do not track not-biv: if biv were true, I would still have the experiences that lead me to believe that biv is false. Something similar can be said about antiskepticism: antiskeptics are correct when they say we know all sorts of commonsense claims that entail the falsity of skeptical hypotheses. Having gotten this far, however, skeptics appeal to K, and argue that since I would know not-biv if I knew h, then I must not know h after all, while Moore-style antiskeptics appeal to K in order to conclude that I do know not-biv. But this is precisely where skeptics and antiskeptics alike go wrong, for K is false. Consider the position skeptics are in. Having accepted the tracking view—as they do when they deny that we know skeptical hypotheses are false—skeptics cannot appeal to the principle of closure, which is false on the tracking theory. We track (hence know) the truth of ordinary knowledge claims yet fail to track (or know) the truth of things that follow, such as that incompatible skeptical hypotheses are false.
One shortcoming of this story is that it cannot come to terms with all types of skepticism. There are two main forms of skepticism (and various sub-categories): regress (or Pyrrhonian) skepticism, and indiscernability (Cartesian) skepticism. At best, Dretske and Nozick have provided a way of dealing with the latter.
Another worry about Dretske's and Nozick's response to Cartesian skepticism is that it forces us to give up K (as well as GK, and closure across instantiation and simplification). Given the intuitive appeal of these principles, some theorists have looked for alternative ways of explaining skepticism, which they then offer as superior in part on the grounds that they do no violence to K. Consider two possibilities, one offered by advocates of the safe indication theory, and one by contextualists.

5.3 Safe Indication and Skepticism

Advocates of the safe indication theory accept the gist of the tracking theorist explanation of the appeal of skepticism but retain the principle of closure. One reason skepticism tempts us is that we tend to confuse CR with SI (Sosa 1999, Luper 1984, 1987c, 2003a). After all, CR—if p were false, R would not hold—closely resembles SI—R would hold only if p were true. When we run the two together, we sometimes apply CR and conclude that we do not know that skeptical scenarios do not hold. Then we shift back to the safe indication account, and go along with skeptics when they appeal to the principle of entailment, which is sustained by the safe indication account, and conclude that ordinary knowledge claims are false. But, as Moore claimed, skeptics are wrong when they say we do not know that skeptical hypotheses are false. Roughly, we know skeptical possibilities do not hold since (given our circumstances) they are remote.
Skepticism might also result from the assumption that, if a belief formation method M were, in some situation, to yield a belief without enabling us to know the truth of that belief, then it cannot ever generate bona fide knowledge (of that sort of belief), no matter what circumstances it is used in. (M must be strengthened somehow, say with a supplemental method, or with evidence about the circumstances at hand, if knowledge is to be procured.) This assumption might rest on the idea that any belief M yields is, at best, accidentally correct, if in any circumstances M yields a false or an accidentally correct belief (Luper 1987b,c). On this assumption, we can rule out a method of belief formation M as a source of knowledge merely by sketching circumstances in which M yields a belief that is false or accidentally correct. Traditional skeptical scenarios suffice; so do Gettieresque situations. Externalist theorists reject the assumption, saying that Mcan generate knowledge when used in circumstances under which the belief it yields is not accidentally correct. In highly Gettierized circumstances M must put us in an especially strong epistemic position if M is to generate knowledge; in ordinary circumstances, less exacting methods can produce knowledge. The standards a method must meet to produce knowledge depend on the context in which it is used. This view, on which the requirements for a subject or agent S to know p vary with S's context (e.g., how exacting S's method of belief formation must be to yield knowledge depend on S's circumstances), might be called agent-centered (or subject)contextualism. Both tracking theorists and safe indication theorists defend agent-centered contextualism.

5.4 Contextualism and Skepticism

Theorists writing under the label “contextualism,” such as David Lewis (1979, 1996), Stewart Cohen (1988, 1999), and Keith DeRose (1995), offer a related way of explaining skepticism without denying closure. For clarity, we might call them speaker-centered (or attributor) contextualists since they contrast their view with agent-centered contextualism. According to (speaker-centered) contextualists, whether it is correct for a judge to attribute knowledge to someone depends on that judge's context, and the standards for knowledge differ from context to context. When the man on the street judges knowledge, the applicable standards are relatively modest. But an epistemologist takes all sorts of possibilities seriously that are ignored by ordinary folk, and so must apply quite stringent standards in order to reach correct assessments. What passes for knowledge in ordinary contexts does not qualify for knowledge in contexts where heightened criteria apply. Skepticism is explained by the fact that the contextual variation of epistemic standards is easily overlooked. Skeptics note that in the epistemic context it is inappropriate to grant anyone knowledge. However, skeptics assume—falsely—that what goes in the epistemic context goes in all contexts. They assume that since those who take skepticism seriously must deny anyone knowledge, then everyone, regardless of context, should deny anyone knowledge. Yet people in ordinary contexts are perfectly correct in claiming that they know all sorts of things.
Furthermore, the closure principle is correct, contextualists say, so long as it is understood to operate within given contexts, not across contexts. That is, so long as we stay within a given context, we know the things we deduce from other things we know. But if I am in an ordinary context, knowing I am in San Antonio, I cannot come to know, via deduction, that I am not a brain in a vat on a distant planet, since the moment I take that skeptical possibility seriously, I transform my context into one in which heightened epistemic standards apply. When I take the vat possibility seriously, I must wield demanding standards that rule out my knowing I am not a brain in a vat. By the same token, these standards preclude my knowing I am in San Antonio. Thinking seriously about knowledge undermines our knowledge.

6. Closure of Rational Belief

To say that justified belief is closed under entailment is to say that something like one of the following principles is correct (or that both are):

اقتباس :: J: If, while justifiably believing p, S believes q because S knows p entails q, then Sjustifiably believes q.

اقتباس :: GJ: If, while justifiably believing various propositions, S believes p because S knows that they entail p, then S justifiably believes p.

However, GJ generates paradoxes (Kyburg 1961). To see why, notice that if the chances of winning a lottery are sufficiently remote, I am justified in believing that my ticket, ticket 1, will lose. I am also justified in believing that ticket 2 will lose, and that 3 will lose, and so on. However, I am not justified in believing the conjunction of these propositions. If I were, I would justifiably believe that no ticket will win. If a proposition is justified when probable enough, lottery examples undermine GJ. No matter how great the probability that suffices for justification, unless that probability is 1, in some lotteries we will be justified in believing, of an arbitrary ticket, that it will lose, and thus, by GJ, we will be justified in believing that all of the tickets will lose.
Even if we reject GJ, it does not follow that we must reject GK, which concerns knowledgeclosure. Consider the lottery example again. How justified we are in believing that ticket 1 will lose depends on how probable its losing is. Now, the probability that ticket 2 will lose is equal to the probability that ticket 1 will lose. The same goes for each ticket. However, consider the conjunction, Ticket 1 will lose & ticket 2 will lose. The probability of this conjunctive proposition is less than the probability of either of its conjuncts. Suppose we continue to add conjuncts. For example, next in line will be: Ticket 1 will lose & ticket 2 will lose & ticket 3 will lose. Each time a conjunct is added, the probability of the resulting proposition is still lower. This illustrates the fact that we can begin with a collection of propositions each of which surpasses some threshold level of justification (let it be whatever is necessary for a belief to count as “justified” according to GJ) and, by conjoining them, we can end up with a proposition which falls below that threshold level of justification. We may “justifiably believe” each conjunct, but not the conjunction, so GJ fails. However, we need not reject GK on these grounds. Even if we grant that we justifiably believe that Ticket 1 will lose is true we might deny that we know that this proposition is true. We might take the position that if we believe some proposition p on the basis of its probability, nothing less than a probability of 1 will suffice to enable us to know that it is true. In that case GK will not succumb to our objection to GJ, for if the probability of two or more propositions is 1 then the probability of their conjunction is also 1.
We can reject GJ. Should we also reject J? The status of this principle is much more controversial. Some theorists argue against it using counterexamples like Dretske's own zebra case: because the zebra is in plain sight, you seem fully justified in believing zeb, but it is not so clear that you are justified in believing not-mule, even if you deduce this belief from zeb. Anyone who rejects K on the grounds that K sanctions the knowledge of limiting or heavyweight propositions (discussed earlier) is likely to reject J on similar grounds: justifiably believing that we have hands, it might seem, does not position us to justifiably believe that there are physical objects even if we see that the former entails the latter.
One response is that cases such as Dretske's do not count against J, but rather against the following principle (of the transmissibility of evidence):

اقتباس :: E: If e is evidence for p, and p entails q, then e is evidence for q.

Even if we reject this principle, it does not follow that justification is not closed under entailment, as Peter Klein (1981) pointed out. Arguably, for justification closure, all that is necessary is that when, given all of our relevant evidence e, we are justified in believing p, we also have sufficient justification for believing each of p's consequences. Our justification for p's consequences need not be e. Instead, it might be p itself, which is, after all, a justified belief. And since p entails its consequences, it is sufficient to justify them. Moreover, any good evidence we have against a consequence of p counts against p itself, preventing us from being justified in believing p in the first place, so if we are justified in believing p, considering all our evidence, pro and con, we will not have overwhelming evidence against propositions entailed by p. (A similar move could be defended against the tracking theorists when they deny the closure of knowledge: if we track p, and believe q by deducing it from p, then we track q if we take p as our basis for believing q.) Looked at in this way, J seems plausible. (There is a substantial literature on the transmissibility of evidence and its failure; see, for example, Crispin Wright (1985) and Martin Davies (1998).
Some final observations can be made using Roderick Firth's (1978) distinction between propositional and doxastic justification. Proposition p has propositional justification for S if and only if, given the grounds S possesses, p would count as rational. That p has propositional justification for S does not require that S actually base p on these grounds, or even that S believep. Whether S's belief has doxastic justification depends on S's actual grounds for believing p: if, on these grounds, p would count as rational, then p possesses doxastic justification. Consider the following principles:

اقتباس :: JD: If p is doxastically justified for S, and p entails q, then q is doxastically justified for S.
JP: If p is propositionally justified for S, and p entails q, then q is propositionally justified for S.

Clearly JD faces two fatal objections. First, we might fail to believe some of the things implied by our beliefs. Second, we may have perfectly respectable reasons for believing something p, yet, failing to see that p entails q, we might not be aware of any grounds for believing q, or, worse, we might believe q for bogus reasons. But neither difficulty threatens JP. First, propositional justification does not entail belief. Second, S might be propositionally justified in believing q on the basis of p whether or not S fails to see that p entails q, and even if S believes q for bogus reasons. As further support for JP, we might cite the fact that, if p entails q, whatever counts against q also counts against p.

. The Argument From Skepticism

5.1 Skepticism and Antiskepticism

5.2 Tracking and Skepticism

5.3 Safe Indication and Skepticism

5.4 Contextualism and Skepticism

6. Closure of Rational Belief

. The Argument From Skepticism :: تعاليق

. The Argument From Skepticism