[Forthcoming (2011) in the Journal of Philosophical Research] RADICAL SCEPTICISM, CLOSURE AND ROBUST KNOWLEDGE J. Adam Carter University of Geneva ABSTRACT: The Neo-Moorean response to the radical skeptical challenge boldly maintains that we can know we're not the victims of radical skeptical hypotheses; accordingly, our everyday knowledge that would otherwise be threatened by our inability to rule out such hypotheses stands unthreatened. Given the leverage such an approach has against the sceptic from the very start, the Neo-Moorean line is an especially popular one; as well see, though, it faces several commonly overlooked problems. An initial problem is that this particular brand of anti-sceptical strategy is available only to a theory of knowledge that will compromise itself to especially weak epistemic standards-indeed, standards as weak as our epistemic grounds are for accepting the denials of skeptical hypotheses. And the grounds here are weak. After all, we can't support our claim to know the denials of skeptical hypotheses by appealing to any relevant discriminatory capacities, and nor is it at all clear that we can adduce any independent rational grounds that stand to favour the denial of any given skeptical hypothesis over its skeptical alternative. With this said, the aim here is to investigate whether the Neo-Moorean line could be advanced against the sceptic in a way that wouldn't require wholesale lowering of epistemic standards. Here it will be important to note that Sosa's (2007; 2009) recent virtuebased epistemology distinguishes between higher-grade and lower-grade knowledge, and for this reason, his view seems specially equipped to handle the problem of lowering epistemic standards-a problem that would otherwise seem to leave the Neo-Moorean line too pricey a gambit. Sosa, to put it plainly, could allowably grant us low-grade, animal knowledge of the denials of skeptical hypotheses and at the same time insist that not all knowledge (i.e. reflective knowledge) can be gained so cheaply. Voila! Unfortunately, as we'll see, Sosa's view as well the other two most plausible contender-views for maintaining a Neo-Moorean line-Greco's and Pritchard's-run (for similar reasons) into dead ends. What it turns out that none of these views could do effectively was to reconcile the Neo-Moorean commitment to knowing the denials of skeptical hypotheses with (i) the demand that we don't compromise the epistemic standards for knowing wholesale, and (ii) the thought that not just knowledge, but knowledge grade, gets preserved over closure. This special point about closure (and one rarely discussed) turns out to be especially devastating for what seemed like the most well-equipped strategies for taking up the Neo-Moorean line. Having set the scene as such, my final move in the paper is a positive one: to take up the task of reconciling Neo-Mooreanism with the epistemic standards worry as well as with the problem posed by closure for knowledge grade. The way out, I'll argue, is to take on board a unique variety of robust virtue epistemology according to which knowledge is thought to be situated a certain way within a gradient balance between ability and luck 1. RADICAL SCEPTICISM AND NEO-MOOREANISM What radical skeptical arguments aim to show is that we lack everyday knowledge, and that we do is supposed to be a direct consequence of the presumed fact that we lack knowledge of the denials of skeptical hypotheses- hypotheses (i.e. the brain-in-a-vat hypothesis) that, if true, would be incompatible with the truth of everyday 2 propositions we take ourselves to know. The brain-in-a-vat hypothesis is, for example, incompatible with my claim to know I have a hand given that, were the BIV hypothesis true, I wouldn't really have a hand (e.g. instead, I'd just be being deceived by what are really hand-like appearances). That said, here's how the radical skeptical argument typically runs: let E represent some item of everyday knowledge (i.e. knowledge that I have a hand). Let SH represent a skeptical hypothesis that would be incompatible with E (i.e. the hypothesis that I am a brain in a vat). Finally, let's make explicit a characteristic of radical skeptical hypotheses: they are such that, were they true, my experiences would seem to me just as they presently do.1 The template radical skeptical argument then runs like this: Radical skeptical argument (1) S does not know skeptical hypothesis SH is false. (2) If S does not know not: SH, then S does not know E. (3) S does not know E.2 The sceptic defends (1) by claiming-among other things-that SH is not something my discriminatory capacities nor any independent reasons I have for thinking I'm not in such a scenario can (even in principle) rule out. This point of the sceptic's is hard to refute, which might explain in part why (1) seems so compelling. More interesting at present, though, is (2); this premise of the argument relies on the truth of a general principle which will itself imply that S knows E only if she knows ~SH. Such a principle would be a closure principle-a principle that preserves (basically) that one knows what one knows to follow from something else she knows. Closure (Knowledge) (CK) If S knows that p, and S competently deduces q from p (thereby coming to believe q while retaining her knowledge that p), then S knows that q.3 CK implies that if I know I have a hand and competently deduce from this that I am not the victim of a skeptical hypothesis, then I know I am not the victim of a skeptical hypothesis. As Duncan Pritchard (2005; 2008) has argued, the most promising way to resist the sceptic's conclusion is to take what is called the Neo-Moorean line of response, a strategy by which we deny (1) in the argument and thus claim to know the denials of skeptical hypotheses, thereby resisting the radical sceptic's conclusion that we lack everyday knowledge. Unlike anti-skeptical strategies4 that deny (2), the neo-Moorean line is not forced to deny the intuitive closure principle (CK). Unsurprisingly, though, the neo-Moorean line does not preserve closure and avoid the skeptical conclusion without some cost5. As Pritchard says: ...A concession all Moorean anti-sceptical strategies make is to allow that agents are unable to distinguish between everyday experiences and the sort of sceptical experiences that would be generated by being the victim of a (relevant) sceptical hypothesis. (Pritchard 2008: 2) 3 Once this concession is made, the neo-Moorean's claim that we can know the denials of skeptical hypotheses looks tricky to defend. Indeed, it commits one to denying something like the following: (i) If S knows p, then S has the ability to discriminate between conditions under which p holds and conditions under which ~p holds. But the concession of the neo-Moorean is more than just this. Given that skeptical hypotheses call into question our evidence en masse6, we lack any independent rational support for thinking that we are not the victims of such hypotheses. And so the neo-Moorean must also deny something like: (ii) If S knows p, then S has independent rational grounds (i.e. independent from what his discriminative abilities tell him) for thinking she is not the victim of a skeptical hypothesis. These considerations tell us that the neo-Moorean strategy carries with it relatively low requirements for knowing the denials of skeptical hypotheses. Indeed, a theory of knowledge will be able to preserve that we know the denials of skeptical hypotheses only if the requirements for knowing are weak enough to count my belief I am not a victim of a skeptical hypothesis as knowledge, and this is a belief I lack adequate discriminatory capacities as well as any independent rational grounds for accepting. The neo-Moorean strategy, if it is to be successful against the radical sceptic, must not lose sight of something easily overlooked: a theory of knowledge aims to salvage against the skeptic not merely groundless true belief, but something worth calling knowledge. 2. ANIMAL KNOWLEDGE AND REFLECTIVE KNOWLEDGE Ernest Sosa (2007; 2009) distinguishes between what he calls animal knowledge and reflective knowledge, and this distinction would seem quite germane insofar as we want to maintain that (i) we know the denials of skeptical hypotheses; and yet (ii) other items of human knowledge aspire to something epistemically more robust. On Sosa's view, animal knowledge is essentially just apt belief: that is, belief that is accurate (true) because adroit (skillful). For one's belief to be apt, according to Sosa, one must 'believe correctly (with truth) through the exercise of a competence in its proper conditions'. (Sosa 2007: 33) Reflective knowledge, on the other hand, requires more; it is apt belief aptly noted: that is, apt belief that our first-order belief is apt.7 Sosa, having drawn a distinction between animal knowledge and reflective knowledge, looks to be offering the sort of resources that would be needed to vindicate a neo-Moorean response to radical skepticism: in particular, it might be argued that our knowledge of the denials of skeptical hypotheses is merely animal knowledge 4 whereas our knowledge of everyday propositions, by contrast, aspires to reflective knowledge. Prima facie, this would seem more plausible than it would be to set the bar for knowledge so low that knowledge picks out nothing more epistemically robust than those relatively groundless beliefs we have in the denials of skeptical hypotheses. One might press here a worry here arising from a point of Sosa's, which is that: If K represents animal knowledge and K+ reflective knowledge, then the basic idea may be represented thus: K + p ↔ KKp. (Sosa 2007: 32) Plausibly, (as the objection would have it) if you can know the denials of skeptical hypotheses, then you could at least in principle know that you know them. So why think that our knowledge of the denials of skeptical hypotheses would be merely animal knowledge and not at least sometimes reflective? Here it will be helpful to draw from Sosa's (2007) discussion of a kaleidoscope perceiver: You see a surface that looks red in ostensibly normal conditions. But it is a kaleidoscope surface controlled by a jokester who also controls the ambient light, and might as easily have presented you with a red-light+white-surface combination as with the actual white-light+red-surface combination. Do you then know the surface you see to be red when he presents you with that good combination, despite the fact that, even more easily, he might have presented you with the bad combination? (Sosa 2007: 31) Sosa grants that your belief here is apt8 and thus that the correctness of the belief is attributable to the agent's competence. He captures the conditions under which the correctness of a belief is attributable to a competence as follows: Attributibility Condition for Aptness For any correct belief that p, the correctness of that belief is attributable to a competence only if it: (i) derives from the exercise of that competence in appropriate conditions for its exercise, and that (ii) exercise in those conditions would not then too easily have issued a false belief.9 (Sosa 2007: 33) Because, Sosa says, we are in the case of the kaleidoscope perceiver exercising our color vision in normal (with respect to lighting, distance, etc.) conditions, and because exercising our color vision in such appropriate conditions wouldn't easily have issued a false belief, the correctness of the belief is attributable to the perceiver's visual competence, and so the belief is apt and thereby animal knowledge. Importantly, though, Sosa denies that the perceiver's belief in this case counts as reflective knowledge, and it will be important to see why this is. Bear in mind here that reflective knowledge requires the perceiver have an apt belief that his first-order color belief is itself apt. Here Sosa writes: Consider now the kaleidoscope perceiver's belief that he aptly believes the seen surface to be red. We are assuming that the competence exercised in that meta-belief is a default competence, one which, absent any specific indication to the contrary, takes it for granted that, for example, the lights are normal. Because of the jokester in control, however, the exercise of that competence might then too easily have issued a false belief that the lights are normal. Given principle C, therefore, we must deny that the truth of our perceiver's belief that he aptly believes the surface to be red is attributable to his relevant competence. (Sosa 2007: 33) Now, let's consider just why one's belief in the denial of a skeptical hypothesis fails to qualify as 5 reflective knowledge against the background of why it is the kaleidoscope perceiver's belief fails to qualify as reflective knowledge. We'll begin by considering why such beliefs would be apt, and then consider whether that they are apt is itself something that would be aptly believed. The kaleidoscope perceiver's belief was apt because the correctness of the belief was attributable to the perceiver's vision competence, a competence the exercise of which would, in those conditions, not easily have issued a false belief. The correctness of one's belief in the denial of a skeptical hypothesis (hereafter ~SH), if apt, would be attributable to what competence? Of course, this won't be a competence as simple as vision. Let's suppose it is the competence by which one assumes that, generally speaking, things are normal which leads her to suppose she is in a 'good' environment, and thus, not the victim of a skeptical hypothesis. Presumably that competence will not easily have issued a false belief that ~SH; after all, SH worlds are ones we take to be faraway worlds. This much is enough for apt belief, for Sosa, and let's for now grant him this. In order to assess whether the apt belief (and thus animal knowledge) one has here aspires to reflective knowledge, we must ask: Does S aptly believe that she aptly believes that ~SH, and so, we must ask whether S's belief that she aptly believes that ~SH is attributable to a relevant meta-competence. But the relevant meta-competence here can't simply be the first-order competence of taking things to be normal. It would have to be something like: the competence by which one takes for granted that what one takes for granted as normal is. Now, let's continue to assume that there are no nearby worlds where SH is true. Even if that is granted, it wouldn't follow that the meta-competence (that would be employed in determining whether one's belief in the denial of some skeptical hypothesis is apt) wouldn't have easily issued S a false belief about whether she aptly believes ~SH. This is because the conditions appropriate for the exercise of this meta-competence, which one exercises only when she is taking for granted that what she takes as normal is normal, are distinctively philosophical conditions, unlike the conditions appropriate for exercising the competence by which one is simply taking for granted that things are normal. You count as having the first-order competence so long as you reliably take it for granted that things are more or less normal. But the second-order competence is one you would have only if you are competent at judging that what you take to be normal is normal. The second-order competence is thus one you'd have only if you could, for example, discriminate between what you've taken for granted to be normal and what is normal (at least, to the extent that you wouldn't easily have been wrong). But you lack any such discriminative capacities, even though your first-order competence of taking things for granted was reliable. Further, you lack any independent grounds in support of your belief that what you took for granted as normal was normal. Such independent grounds would be available only if you had some rational grounds for believing that what you took for granted to be normal was not actually a skeptical scenario. But you lack any such independent rational grounds (e.g. as was said, skeptical hypotheses by their very nature call into question such grounds en masse.) Consequently, even if 6 your belief that ~SH is apt, it cannot aspire to reflective knowledge; your belief that you believe ~SH aptly could never be attributable to what we could rightly call a meta-competence. 3. A NEW CLOSURE PRINCIPLE: CPK+ Let's revisit now the radical skeptical argument, bringing to bear Sosa's distinction between animal knowledge and reflective knowledge. Let 'know+' represent distinctively reflective knowledge-the sort we're supposing we lack as regards the denials of skeptical hypotheses but achieve with respect to everyday propositions. Pritchard (2008:13) anticipates10 the following troubling argument, the first premise of which builds from the point developed in the previous section-that the animal knowledge we have of the denials of skeptical hypotheses does not aspire to reflective knowledge. The Template Radical Sceptical Argument Reformulated (S1+) S does not know+ not: SH. (S2+) If S does not know+ not: SH, then S does not know+ E. (SC+) S does not know+ E. If this argument goes through then we must be radical skeptics regarding reflective knowledge, and this means giving up on the initial promise Sosa's view offered qua a variety of neo-Moorean response to radical skepticism. Recall that the initial promise was that Sosa's view appeared capable of reconciling the thought that we know the denials of skeptical hypotheses-an implication of the closure principle-with the intuition that knowledge- insofar as we think it is distinctively valuable-requires a stronger epistemic position than that which is enjoyed by our beliefs in the denials of skeptical hypotheses. Troublingly, there are compelling reasons for thinking this familiar-looking argument would indeed go through. Just as (2) in the original template radical skeptical argument was implied by a highly-intuitive closure principle, so (S2+) would be implied by a modified closure principle that we'll see is itself quite compelling, one on which not just knowledge, but knowledge-grade (in this case, reflective knowledge), is closed over competent deduction. As far as I'm aware of, only Pritchard (2008) has noticed the plausibility of such a 'grade-sensitive' variation on closure. Though he supposed it to be compelling, his brief discussion11 of the idea drew out only a few of its interesting implications. Let's look at such a closure principle again here. Let 'know+' represent specifically reflective knowledge. The Closure Principle for Knowledge+ (CPK+) If S knows+ that p, and S competently deduces q from p (thereby coming to believe q while retaining her knowledge+ that p), then S knows+ that q. 7 If CPK+ is correct, then-as was said-S2+ in the modified radical skeptical argument is implied. Before investigating this variation on closure more carefully, let's back up for a moment in order to locate more sharply the role it would play (if correct) in the dialectic here more generally. To this end, consider that Sosa wants to preserve that our everyday knowledge does indeed aspire to reflective knowledge, and the skeptical argument considered in this section challenges this. For reasons discussed in the previous section, denying (1+) in the argument is off limits to Sosa because his view implies that we lack reflective knowledge of the denials of skeptical hypotheses.12 Sosa's only escape from the conclusion then will be to deny (2+), but (2+) is straightforwardly implied by the closure principle for knowledge+ (CPK+). And so Sosa saves reflective knowledge from the skeptic only if he is able to undercut (2+) via demonstrating that CPK+ is false. But that, I'll argue now, is easier said than done. This is because CPK+ captures an idea that, on the surface, seems hard to deny. For one thing, it's not at all intuitive to think that epistemic robustness of our knowledge should get 'demoted' across a known entailment. Pritchard suggests that, if anything, we'd be inclined to think the presence of a competent deduction would have an 'enhancing' effect13 (Pritchard 2008: 17) To get a better feel for this idea, let's consider an example: suppose that, after skillful and careful examination, you come to believe (correctly) that a certain play Sceptica widely attributed to Shakespeare was actually written by Ben Johnson. Let's suppose further that your belief is apt and that you aptly believe it to be such-and so you have reflective knowledge that Sceptica the work of Johnson, not Shakespeare. Now that said, consider what you're rationally entitled to competently deduce (given that you clearly know Shakespeare to be the author of Hamlet): that the author of Sceptica is not the author of Hamlet. Surely, this is something you know just as well. Accordingly, then, if you have reflective knowledge that Johnson wrote Sceptica and from this deduce that its author was not the author of Hamlet, your reflective knowledge would seem to lack any chance to be 'demoted to mere animal knowledge' over this deduction. Plausibly, then, you count as reflectively knowing what you competently deduce from what you reflectively know.14 This much suggests that both (1+) and (2+) are off limits to Sosa. This is bad news for Sosa-insofar has he wants to resist the radical skeptical conclusion in a way that upholds both animal and reflective knowledge within our cognitive economy-and likewise bad news more generally for the neo-Moorean response to skepticism, insofar as the neo-Moorean should hope to preserve that we know the denials of skeptical hypotheses, even though we think that much of our everyday knowledge is, comparatively, of an epistemically higher quality. Consider now that the reason we took Sosa's distinction between animal and reflective knowledge to be promising as a way to supplement a neo-Moorean reply to radical skepticism owed to the fact that the theory allows one kind of knowledge to be apposite to the knowledge we have in the denials of skeptical hypotheses, and another kind of knowledge to be apposite to the more robust sort of knowledge we take ourselves to have 8 when (for example) we actually do possess the relevant discriminatory capacities for telling that something is so, and have additionally independent reasons in support of such beliefs. Unfortunately, the promise of this strategy collapsed once it was shown that a cousin closure principle-one according to which knowledge-grade is closed over competent deduction-bolsters a skeptical argument against reflective knowledge. Might there be an improvement somewhere in the neighborhood-that is, some view that, like Sosa's, distinguishes between higherand lower-grade knowledge whilst not succumbing to the problems caused by CPK+? What is needed, more plainly, is a view that can preserve low-grade knowledge for the denials of skeptical hypotheses whilst not implying that we lack more robust knowledge of everyday propositions. 4. COGNITIVE ACHIEVEMENTS: GRECO, PRITCHARD AND CPK+ Sosa's brand of virtue epistemology requires for knowledge that cognitive success be because of cognitive ability, and this is a view that has been notably endorsed by John Greco (2006; 2010). Unlike Sosa, Greco makes no room for a distinction between animal and reflective knowledge, though a modification of Greco's view actually does allow for higherand lower-grade knowledge. I want to explore now how such a modification would work, and we'll see whether it dodges the skeptical problem raised by CPK+. Greco's recent proposal centers around the idea that knowledge consists in cognitive achievement on the part of the agent. Cognitive achievements require not only cognitive success and cognitive ability, but cognitive success that arises through such ability.15 That is, the agent's believing truly has to be something we can credit (primarily) to the cognitive abilities manifested by that agent. To put the idea more succinctly: Cognitive achievement (Greco): S's true belief that p constitutes a cognitive achievement for S just in case that S believes p truly is primarily creditable to S's own cognitive abilities.16 There are three corollary theses closely related to the cognitive achievement thesis and which are noteworthy here. The first corollary thesis extends to achievement in any domain of endeavour; the claim is that achievements-successes through ability-are finally valuable; that is, valuable for their own sake (noninstrumentally)17, and in a way that mere successes in the absence of ability, or successes compresent with but not because of ability, are not. We may grasp this idea by considering that an archer's successful shot is one deserving of admiration when an achievement creditable to his skillful efforts, though the admiration we extend to the archer's achievement would not also be extended to the archer's success, were it one he gained merely by luck. This is not to say that the lucky success is not valuable, only that a success, when creditable to one's 9 manifestation of skill or competence, is distinctively valuable-its value is not reducible to the value of the success alone. The second corollary thesis of Greco's proposal that will be relevant here concerns knowledge: Greco's claim is that knowledge is a type of achievement-a cognitive achievement consisting in a cognitive success attributable to the agent's cognitive abilities. What is implied by these first two corollary theses is what Pritchard (2008; forthcoming a) calls the final value thesis, a strong commitment of Greco's: Final value thesis: Knowledge (qua achievement) is valuable for its own sake; qua achievement, knowledge is distinctively valuable in a way that true beliefs that are not the products of cognitive achievement are not. A proponent of robust virtue epistemology, Greco maintains that knowledge and cognitive achievements are mutually entailing (and thus extensionally equivalent); for Greco, there is no knowledge in the absence of cognitive achievement, and vice-versa. Consequently, on Greco's view, all knowledge will inherit the final value of finally valuable cognitive achievements. Pritchard (forthcoming b) has recently endorsed the claim that cognitive achievements are finally valuable while, at the same time, denying the biconditional Greco defends en route to defending robust virtue epistemology.18 For Pritchard (forthcoming a; forthcoming b), only some knowledge will be of a distinctively valuable sort, and this is the knowledge we have when our getting to the truth constitutes a cognitive achievement. Other knowledge, including much of the knowledge we gain by testimony (for example), falls short of achievement (i.e. our reaching the truth isn't primarily creditable to our own efforts), and so lacks final value, but nonetheless meets reasonable standards for knowing. Let's call knowledge in the absence of cognitive achievement 'K' and knowledge consisting in cognitive achievement 'K+'. The neo-Moorean line against radical skepticism invites on board a theory that preserves that we know the denials of skeptical hypotheses and that our everyday knowledge aspires to more robustness. It looks like Pritchard's view, on which we can distinguish between K and K+, has what the neo-Moorean line requires. Let's bring in again the radical skeptical argument bolstered by CPK+ and see how Pritchard's view fares: The Template Radical Sceptical Argument Reformulated (S1+) S does not know+ not: SH. (S2+) If S does not know+ not: SH, then S does not know+ E. (SC+) S does not know+ E. Pritchard (2008; forthcoming a) does not try to dodge the conclusion here-that no knowledge is finally valuable-by rejecting S1+. Having considered in §1 the problems Sosa's view would have for vindicating 10 knowledge of the denials of skeptical hypotheses as reflective, it should not be surprising that such knowledge would not constitute the sort of cognitive success that we would rightly call an achievement. Here's Pritchard: So in order to exhibit a cognitive achievement, one must either appropriately exercise one's discriminative capacities or else be in a position to rationally adduce independent grounds in favour of what one believes in order to compensate for the lack of such discriminatory capacities. Since one is unable to meet either condition when it comes to one's belief that one is not the victim of a sceptical hypothesis, it follows that such a belief, when true, does not constitute a cognitive achievement. So even if the Moorean is right that one can know such propositions, it does not follow that one can have knowledge+ of them...(Pritchard 2008: 16) It follows then that Pritchard might avoid radical skepticism in the domain of knowledge qua cognitive achievement only if S2+ can be resisted. And so it must be resisted that if S doesn't know+ not: SH, then S does not know+ E. But to resist this, Pritchard would have to reject the principle that straightforwardly implies it, CPK+: The Closure Principle for Knowledge+ (CPK+) If S knows+ that p, and S competently deduces q from p (thereby coming to believe q while retaining her knowledge+ that p), then S knows+ that q. But here Pritchard demurs. He takes CPK+ to be an intuitive closure principle, one that is too plausible to simply give up. Consequently, Pritchard supposes that, even for views that would take the neo-Moorean line against standard radical skeptical arguments, there is nonetheless a worrisome variety of radical skepticism- motivated by CPK+--which threatens to rob us of the sort of knowledge that would be distinctively valuable to us-or at least, more valuable than the low-grade knowledge we take our selves to have of the denials of skeptical hypotheses. Pritchard points out that: ...While we might well have much of the knowledge that we typically suppose ourselves to have, the type of knowledge that we possess may not be of the specially valuable variety. (Pritchard 2008: 18) Several things might be concluded at this point. For one thing, if Pritchard is right that this kind of skepticism about knowledge with special value is something we may have to live with, then perhaps it would not be a problem for the neo-Moorean response to standard radical skepticism were it unable to offer us an explanation for how much of the knowledge we take ourselves to have is more epistemically robust than the knowledge we have that skeptical hypotheses are false. Alternatively, we might conclude that such epistemic value skepticism isn't inevitable, that some of our knowledge really is epistmically more robust than our knowledge of the denials of skeptical hypotheses, and that this is something the neo-Moorean must account for when claiming that we know the denials of skeptical hypotheses. 5. THE CLOSURE PRINCIPLE FOR KNOWLEDGE+ REVISITED 11 In what follows, I'll be defending the second of these two conclusions. I think there is a way to escape radical skepticism about distinctively valuable knowledge, and that the way to do it is to examine more closely the closure principle CPK+ that underpins the skeptical threat to knowledge+. Again, that principle claims: The Closure Principle for Knowledge+ (CPK+) If S knows+ that p, and S competently deduces q from p (thereby coming to believe q while retaining her knowledge+ that p), then S knows+ that q. When considering Sosa's view, we took knows+ to represent reflective knowledge because, on that view, reflective knowledge was thought to be that which is more robust epistemically than our knowledge of the denials of skeptical hypotheses. Similarly, when considering Pritchard's line, we took knows+ to stand for knowledge qua cognitive achievements because, on that view, we were thinking of cognitive achievements as the mark of our robust knowledge but not of our knowledge of the denials of skeptical hypotheses. The relevant role knows+ played seems then to have been a value-marking role, the role whereby 'knows+' is supposed to indicate knowledge of a higher epistemic quality than that which we have of the denials of skeptical hypotheses. Suppose, for simplicity's sake, that this specially valuable knowledge has a value of n+1, whereas our knowledge that ~SH has a value of n. We could then recast CPK+ to reflect more accurately the value-centered idea at play, and without presupposing anything about whether reflective knowledge, cognitive achievement or whatever else is requisite for actually generating n+1 value: The Closure Principle for (V) Knowledge If S knows that p such that V (Sp = n+1), and S competently deduces q from p (thereby coming to believe q while retaining her knowledge that p), then S knows that q such that (VSq =n+1) Following precedent here, we'll assume that the value at issue is not pragmatic value, but instead, epistemic value. That said, it's plausible to suppose that our purely cognitive or theoretical aims explain why some items of knowledge are more epistemically valuable than others19. For example, if for the sake of nothing but burning curiosity I want to know who killed Caesar, then the purely epistemic value of this knowledge exceeds that of some pointless truth of no interest to me. Let the epistemic value of my knowledge of who killed Caesar be n+1 and let the epistemic value of my knowing some pointless truth be n. According to the Closure Principle for V Knowledge, if I know who killed Caesar and competently deduce from this that Someone killed Caesar, then the value of my knowledge that Someone Killed Caesar (n+1) is equal to the value of my knowledge of who killed Caesar. But comparatively, knowing that Someone killed Caesar is of little epistemic importance to me. Though it is something I may competently deduce from my knowledge of who killed Caesar, I indeed already knew that someone killed Caesar, and so this deduction from epistemically significant knowledge it is epistemically worth very little. Consequently, as a principle whereby knows+ represents 'possesses knowledge valuable to a certain 12 extent', the Closure Principle for Knowledge fails. Not every item of knowledge is as epistemically valuable as that knowledge from which it was competently deduced. Strictly speaking, then, the closure principle for knowledge+ must be a principle whereby knows+ represents 'knows in virtue of meeting some epistemic criterion.' We saw that if that epistemic criterion is the criterion for reflective knowledge, and reflective knowledge is something that our knowledge of the denials of skeptical hypotheses is supposed to lack, then the inevitable result was radical skepticism about reflective knowledge. Similarly, we saw that if that epistemic criterion is cognitive achievement, and cognitive achievement is something that our knowledge of the denials of skeptical hypotheses is supposed to lack, what results is radical skepticism about knowledge qua cognitive achievement. What if the epistemic criterion (whatever it is, as specified by the closure principle for knowledge+) is something satisfied by our knowledge of the denials of skeptical hypotheses? 6. KNOWLEDGE, CLOSURE AND EPISTEMIC ROBUSTNESS The move just considered might seem a misguided one at best. After all, the original puzzle considered when discussing the neo-Moorean response to radical skepticism was centered round the tension between (i) the neoMoorean's affirmation that we know the denial of skeptical hypotheses, and (ii) the related thought that some of our knowledge is knowledge we possess in virtue of meeting criteria that are more epistemically robust. This is precisely why Sosa's distinction between animal and reflective knowledge looked so promising initially. And so a view according to which the criteria for the presumed robust knowledge we have is actually satisfied by our knowledge of the denials of skeptical hypotheses-even though such a view would not be pinned with the implication that we must be radical skeptics about knowledge satisfying that criteria-would presumably fail to reconcile the original puzzle arising from the neo-Moorean anti-skeptical strategy. On closer inspection, though, this need not be the case. There is argument space for a view according to which the epistemic criteria demanded by knowledge can be satisfied more or less robustly. Call this supposed epistemic criterion for knowing EC. On the type of view I'm exploring here, the idea would be that our knowledge of the denial of skeptical hypotheses satisfies EC, but does so less robustly than does the sort of knowledge we take to be epistemically richer than the knowledge we have of the denials of skeptical hypotheses. There are two important theoretical benefits to such a view. Firstly, it offers in principle a way out of the puzzle surrounding the neo-Moorean reply to radical skepticism; it could account for how it is that we know the denials of skeptical hypothesis and also for how it is that this low-grade knowledge falls short by measure of epistemic robustness to our well-supported, everyday knowledge. The second theoretical benefit of the view under consideration would be that it dodges entirely sort of 13 radical skepticism about high-grade knowledge that presented problems for those accounts previously considered. On this point, let's revisit the skeptical argument that posed this threat: The Template Radical Sceptical Argument Reformulated (S1+) S does not know+ not: SH. (S2+) If S does not know+ not: SH, then S does not know+ E. (SC+) S does not know+ E. Because, as we saw, S2+ of this argument gains support from the corresponding closure principle for knowledge+ only if knows+ picks out a certain epistemic criterion (the satisfaction of which will be of some value) rather than some particular epistemic value itself, we are reading know+ accordingly: as picking out knowledge that satisfies some designated criterion (and not as knowledge that has some particular epistemic value). On the view under discussion, that criterion will be one that can be satisfied more or less robustly. Though it will be satisfied less robustly in the case of our knowledge of the denials of skeptical hypotheses, it is nonetheless satisfied. And so, unlike the view advanced by Sosa and the view at least entertained by Pritchard, the view I'm espousing has the benefit of simply denying (in the neo-Moorean spirit, no less) S1+ of the argument. After all, the epistemic criterion satisfied by our best-grounded knowledge-the criteria for knowledge expressed by know+--is also a criteria that (on our view) our knowledge of the denials of skeptical hypotheses satisfies. Again, the view I'm advancing is one on which there is but one epistemic criteria for knowledge which itself can be satisfied more or less robustly, instead of multiple criteria for knowing, some which our knowledge of the denials of skeptical hypotheses satisfy, some which only our more robust knowledge satisfies. So what is this criterion I'm proposing, which can itself be satisfied more or less robustly? 7. VINDICATING THE NEO-MOOREAN: ROBUST VIRTUE EPISTEMOLOGY It is nothing other than the criterion for knowledge advanced by robust virtue epistemology20, which I'll defend now as a set of theses, beginning in claim (i) with the most general thesis: (i) S knows that p iff it is creditable to S's cognitive abilities that S's belief that p is true. Recall here Sosa's attributability conditions for aptness, which specified for Sosa the circumstances under which it is creditable to S's cognitive abilities that her belief that p is true: Attributibility Condition for Aptness For any correct belief that p, the correctness of that belief is attributable to a competence only if it: (i) derives from the exercise of that competence in appropriate conditions for its exercise, and that (ii) exercise in those conditions would not then too easily have issued a false belief.21 (Sosa 2007: 33) Even if Sosa were to eliminate reflective knowledge from his programme and try instead to preserve that aptness itself 14 could be satisfied more or less robustly, he'd not be able to maintain this given his attributability conditions; in particular, condition (ii) is one that, if satisfied, will be satisfied once a particular threshold is met. Past that threshold, there is no room for distinctly more robust ways to satisfy (ii). Sosa's attributability conditions, then, wouldn't work for our own purposes. The attributability conditions that are required here are ones that, if met, will guarantee that one's believing truly is attributable to her ability at least to the extent that would be needed to yield minimally robust knowledge. Further, the attributability conditions we require are ones that must allow the possibility that they be satisfied more robustly, in order that we may account for why some of our knowledge is knowledge we take to be of an epistemically better quality than the low-grade knowledge we have of the denials of skeptical hypotheses. The guiding idea that motivates the attributability conditions I offer is this22: that one's getting to the truth depends on one's ability and on luck in a way that is not rigid, but gradient. When determining whether one knows, we should not ask whether her getting to the truth depends on her ability rather than luck. Instead, the important question will be whether her getting to the truth is a matter that depends on her ability moreso than luck. If so, then her having a true belief is creditable to her abilities in a way that will be sufficient for knowing on the present view. And so, I supplement the claim that S knows that p iff it is creditable to S's cognitive abilities that S's belief that p is true, with the following attributability conditions, expressed in (ii): (ii) It is creditable to S's cognitive abilities that S's belief that p is true iff it depends on S's ability moreso than luck that S's belief that p is true. In order to clearly address the puzzle surrounding the neo-Moorean response to radical skepticism, we'll need to show that our knowledge of the denials of skeptical hypotheses owes to ability just marginally moreso than to luck-enough to count as knowledge on our view, though knowledge that will count (on the view) as less epistemically robust than knowledge whereby one's true belief depends on her ability much more so than it depends on luck. This claim could be defended only with the aid of some further equation, one that specifies the conditions under which it depends on S's abilities moreso than luck that S's belief that p is true. I offer a modal representation of such conditions, which I express now in (iii): (iii) It depends on S's ability moreso than luck that S's belief that p is true just in case worlds in which S's abilities employed in the actual world couldn't easily have led S to a false belief about whether or not p are closer to the actual world than worlds where, holding these abilities fixed, S forms a false belief about whether or not p. The modal account in (iii) offers a framework within which we can track items of knowledge on the basis how robustly they satisfy the requirement that a knower's getting to the truth must depend on her ability moreso than 15 luck. The most epistemically robust knowledge is represented on this model when worlds in which S's abilities employed in the actual world couldn't easily have led S to a false belief about whether or not p are very close to the actual world, and worlds where, holding these abilities fixed, S forms a false belief about whether or not p, are far off worlds. We get less epistemically robust knowledge when the two sets of worlds are closer to each other; that is, when former worlds are not as close to the actual world and the latter worlds not as far off, though even in instances of this less robust knowledge, worlds where S's abilities employed in the actual world couldn't easily have led S to a false belief about whether or not p must nonetheless be closer on the whole to the actual world than worlds where, holding these abilities fixed, S forms a false belief about whether or not p. 8. CONCLUDING REMARKS Although I've defended a variety of robust virtue epistemology as an able resolver of both (i) the puzzle surrounding the neo-Moorean anti-skeptical strategy, as well as (ii) what I showed to be related skeptical threats that arise from gradespecific closure principles for knowledge, I've not yet shown how our knowledge of the denials of skeptical hypotheses would be modally represented so as to preserve that such knowledge depends on ability moreso (though only somewhat moreso) than luck, which is the result I need to maintain both that (i) knowledge of the denials of skeptical hypotheses is bona fide knowledge; and (ii) it is nonetheless low grade knowledge. To do this, I'll need to show that worlds where the abilities I employ in the actual world couldn't easily have led to a false belief about whether or not ~SH are themselves closer (but not much closer) to the actual world than worlds where, holding fixed the abilities whereby I came to believe ~SH in the actual world, I form a false belief about whether or not SH. Let's say, as we did when discussing Sosa's view, that the competence one employs when believing skeptical hypotheses do not obtain is one we can describe as a default competence whereby we take conditions to be normal. Are worlds where this competence couldn't easily have led to a false belief about whether or not ~SH close to the actual world? Indeed; after all, worlds where you could, holding fixed your having exercised a competence whereby conditions are taken to be normal, 'easily' have believed falsely about whether or not ~SH are far-off worlds where (for example) demons imminently threaten. The actual world, we are supposing, is one where such threats are not immanent, and so nearby worlds will be worlds where the exercise of this competence couldn't easily have led to a false belief about whether or not ~SH. What about worlds where, holding fixed the abilities whereby I came to believe ~SH in the actual world, I form a false belief about whether or not SH? Are these far off worlds? If so, then this poses a problem: I'd have to concede that knowledge of the denials of skeptical hypotheses is quite robust, which would be an unwelcome result, given that we lack rational grounds for such beliefs or the capacity to discriminate between conditions under which skeptical scenarios would or wouldn't hold. One might suspect they would be far off given that we are assuming that the sceptical scenarios requisite to 16 make such beliefs false are themselves occupiers of far-off worlds. Granting all this, it remains that worlds reasonably close to the actual world will be ones where, holding fixed my exercising of a competence whereby I simply take things to be normal, I take skeptical hypotheses to fall within the bounds of what would be normal (due to drugs, poor estimation or perhaps just misguided philosophical insight). Such worlds will not be radical departures from the actual world, and so will be relatively close-certainly much closer than worlds where I actually am the victim of a skeptical scenario. These worlds, where the falsity of skeptical hypotheses is not part of what I take for granted when supposing things are normal, will nonetheless not be as close to the actual world as worlds where, holding fixed my exercising of this competence, I couldn't easily have been wrong about whether or not ~SH. After all, these will be worlds where what I take to be normal really is-worlds closer to the actual world than those reasonably close worlds where my conception of the normal and what can be assumed about it is skewed. Therefore, we see that knowledge of the denials of skeptical hypotheses counts as knowledge, but only of a modestly robust sort. Let's consider, finally, why it would be that well-grounded, everyday knowledge is ruled especially robust on the view I've offered. The example here will be an item of knowledge the truth of which we may suspect owes significantly moreso to my abilities than to luck: my knowledge that the lights have just gone off. The competence I exercise in the actual world will be my highly accurate visual competence for distinguishing light from darkness. Worlds where I couldn't easily have been mistaken about the lights having gone off are extremely close to the actual world; given that we're holding fixed that I exercise the highly accurate visual competence I employ in the actual world to determine that the lights are off, there are no nearby worlds where I could 'easily' be wrong about this; after all, only in worlds where I could easily be duped by black holograms might I 'easily' be mistaken about whether the lights went out-but these are indeed far off words. And, indeed, it will be these far off worlds where, given the skill through which I form the belief the lights went out in the actual world, I'm wrong about this. The truth of such beliefs, thus, depends on ability significantly moreso than luck, and the view I've offered here accounts for such robustness. REFERENCES Dretske, F. (1970). 'Epistemic Operators', The Journal of Philosophy 67, 1007-23. Greco, J. (2010). Achieving Knowledge, Cambridge University Press. Nozick, R. (1981) Philosophical Explanations, Harvard University Press. Pritchard, D. (forthcoming a) 'Knowledge and Final Value' in The Value of Knowledge, eds. A. Haddock, A. Millar & D.H. Pritchard (forthcoming). ______ (forthcoming b) 'Anti-Luck Virtue Epistemology' in The Value of Knowledge, eds. A. Haddock, A. Millar & D.H. Pritchard (forthcoming). 17 ______(2008) 'Radical Scepticism, Epistemic Luck and Epistemic Value', Proceedings and Addresses of the Aristotelian Society (suppl. vol.) 82 (2008), 19-41 ______(2007) 'How to be a Neo-Moorean', Internalism and Externalism in Semantics and Epistemology, (ed.) S. Goldberg, (Oxford UP, 2007). ______(2005) Epistemic Luck, Oxford: Oxford University Press. Sosa, E. (2007) A Virtue Epistemology: Apt Belief and Reflective Knowledge, Volume 1, Oxford University Press. ______(2009) Reflective Knowledge: Apt Belief and Reflective Knowledge, Volume 2, Oxford University Press. NOTES 1 Thanks to an anonymous referee for pointing out that the experiences at issue here won't necessarily be the same simply in virtue of being such that I couldn't perceptibly distinguish one from the other-this is a matter that could be taken up by those defending particular accounts of perceptual experience. For the present purposes, I'll remain uncommitted on this score given that the relevant epistemic point being made here doesn't depend on facts about what actually constitute sameness of experience. The relevant point I wanted to make about skeptical scenarios is simply that the all the experiences we would have were we their victims would be, for all our discriminatory capacities tell us, just like the experiences we're having now under circumstances where we hold them to be false. The point is thus epistemic, not metaphysical. 2 The formulation of the radical skeptical argument template I'm using here is one I'm borrowing from Pritchard (2008: 2). 3 Ibid. p. 2. 4 See here Dretzke (1970) and Nozick (1981). 5 For a variety of lines taken against the neo-Moorean line, see Pritchard (2007) "How to be a Neo-Moorean' 6 For discussion on this point, see Pritchard (2005) and also Pritchard (2008:2). 7 Sosa understands aptness in a way that permits (for example) Henry, while driving through barn façade county, to aptly believe there's a barn-and thus to have a true belief that counts as animal knowledge. What Henry lacks, on Sosa's view, is reflective knowledge, which 'requires the belief to be placed also in a perspective within which it may be seen as apt'. (Sosa 2007: 63) Henry thus knows there's a barn without further knowing that he knows this (which is what reflective knowledge requires). 8 He points out that here you 'exercise your faculty of color vision in normal conditions of lighting, distance, size of surface, etc., in conditions generally appropriate for the exercise of color vision.' (Sosa 2007: 31) 9 The breakdown of Sosa's condition C into (i) and (ii) is my own. 10 To note: Pritchard (2008) originally posed this argument in a way such that 'knows+' picked out knowledge qua cognitive achievement; here I've just recast the argument slightly so that 'knows+' picks out reflective knowledge instead. I go on in what follows to discuss the implication of this argument for views like Pritchards, which hold that knowledge qua cognitive achievement is distinctively valuable in a way that low-grade knowledge (such as the knowledge we have of the denials of skeptical hypotheses) is not. 11 Pritchard (2008) was concerned mostly with whether such a closure principle could motivate a skeptical argument that could threaten distinctively valuable knowledge. See here especially § 8 and §9 in his (2008). 12 This I take to be a consequence of Sosa's view (given my arguments in the previous section) even though, by Sosa's own pronouncement, his view can preserve that we have reflective knowledge of the denial of skeptical hypotheses specifically engendered by the problem of dream skepticism. I am setting aside in this discussion Sosa's treatment of specifically dream skepticism as this turns on distinctions between 'beliefs' and 'imaginings' that are (though themselves interesting) not germane to what's at issue as regards the sort of radical skeptical arguments that have been my focus. 18 13 I'm not endorsing this stronger claim-I present it only to lend credence to the plausibility that the epistemic robustness of the knowledge is not 'demoted' across entailment, as the CPK+ maintains. 14 Because CPK+ expresses a conditional claim, it's important to note (and I thank an anonymous referee on this point) that it can't be 'proven' true simply by citing an instance in which the antecedent and the consequent are both satisfied. To be clear, this wasn't my endeavour in the Shakespeare case. My aim was to lend credence to CPK+ by providing a case according to which affirming the antecedent and denying the consequent (of the conditional expressed by the CPK+ principle) would be problematic. Other cases could lend force similarly. For example, suppose I have reflective knowledge (K+) that only three people are on the dance floor. From this I competently deduce that The Jackson Five are not all on the dance floor. It would be quite a strange (and I take it, highly counterintuitive) result to suppose that (under any circumstances) your knowledge that The Jackson Five are not all on the dance floor is not something you reflectively know, whereas, Only three people are on the dance floor is something I do. After all, both items of knowledge mark truths I gained because of my manifestation of competences in virtue of which my belief Only three people are on the dance floor was reflectively known. 15 I draw from Pritchard (2008) here that Greco's final value thesis can be understood as a conjunction of two more basic theses. 16 Here Greco (2010) parts ways with Sosa who doesn't specify the 'primarily creditable' clause; Sosa (2007; 2009) relies instead on a more pre-theoretical notion of 'through.' 17 For a helpful discussion of final value and in particular the distinction between final value and instrumental value, see Rabinowicz and Ronnow-Rasmussen (1999). 19 Similarly, it's plausible to suppose that our practical aims explain why some items of knowledge are more practically valuable than others. For example, if I want to watch TV, knowing where the remote is is more practically valuable than knowing what color the ceiling is. Similarly, 20 Pritchard (forthcoming a; forthcoming b) has argued against the plausibility of robust virtue epistemology, though on grounds that presuppose that satisfying an ability condition on knowledge could not suffice for ensuring that the target belief is insulated from knowledge-undermining luck. This is why Pritchard, who takes both the ability and luck platitudes to capture something important about knowledge, opts for a 'dual-conditon' view, according to which knowledge is understood in terms of and ability condition and an anti-luck condition, neither of which is supposed to entail the other. If Pritchard's assumptions about the failure of an ability condition to exclude knowledge undermining luck were correct, then it would be a mistake to attempt to understand knowledge as the robust virtue epistemologist does. On the proposal I defend here, however, this worry does not arise. It's important to note that the view I'm advancing only purports to analyze knowledge exclusively in terms of an ability condition (and not an separate antiluck condition) because on the proposal I offer, there is an anti-luck condition that is built-in to the requirements outlined for a belief to qualify as a cognitive achievement. Note here especially the transition from (i) to (ii) to (iii). This said, we can see how the worries Pritchard (forthcoming a; forthcoming b) for RVE and the cognitive achievement thesis more generally are based on a weaker conception of cognitive achievement than what I appeal to in standing by my proposed construal of robust virtue epistemology. 21 The breakdown of Sosa's condition C into (i) and (ii) is my own. 22 I defend this idea elsewhere in Carter (2009) see esp. Ch. 11.