Basic Knowledge and Contextualist “E = K”

Thought ISSN 2161-2234

O R I G I N A L A R T I C L E

Basic Knowledge and Contextualist ‘‘E = K’’

Jonathan Jenkins Ichikawa

University of British Columbia

Timothy Williamson (2000) makes a strong prima facie case for the identification of a subject’s

total evidence with the subject’s total knowledge (E = K). However, as Brian Weatherson (Ms)

has observed, there are intuitively problematic consequences of E = K. In this article, I’ll offer a

contextualist implementation of E = K that provides the resources to respond to Weatherson’s

argument; the result will be a novel approach to knowledge and evidence that is suggestive of an

unexplored contextualist approach to basic knowledge.

Keywords knowledge; evidence; contextualism; Timothy Williamson; epistemology; Brian

Weatherson; inductive knowledge

DOI:10.1002/tht3.100

1 Motivations for E = K

Timothy Williamson has made what is, in my view, a prima facie compelling case for theidentification of a subject’s total knowledge with her total evidence (E = K). The viewfocuses on the sense of ‘evidence’ according to which evidence comprises propositions.Other senses are surely available—things like footprints and shell casings are sometimesappropriately described as ‘evidence’—but it is pretty clear that there is at least onesense of ‘evidence’ according to which propositions are the right sorts of things to beevidence, and Williamson’s (2000, pp. 194–97) suggestion that it is most theoreticallyfundamental seems to me very plausible. I take it as an operating assumption.

If a subject’s evidence is propositional, which propositions are among her evidence?Williamson’s famous answer is that it is those proposition that she knows. In favour ofthe necessity of knowledge for evidence, Williamson suggests a case:

‘‘Suppose that balls are drawn from a bag, with replacement. . . . For a suitablenumber n, the following situation can arise. I have seen draws 1 to n; each was red(produced a red ball). I have not yet seen draw n+1. I reason probabilistically, andform a justified belief that draw n+1 was red too. My belief is in fact true. But I donot know that draw n+1 was red. Consider two false hypotheses:h: Draws 1 to n were red; draw n+1 was black.h*: Draw 1 was black; draws 2 to n+1 were red.It is natural to say that h is consistent with my evidence and that h* is not. Inparticular, it is consistent with my evidence that draw n+1 was black; it is not

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282 Thought 2 (2013) 282–292 © 2014 Wiley Periodicals, Inc and the Northern Institute of Philosophy

Jonathan Jenkins Ichikawa Basic Knowledge and Contextualist ‘‘E = K’’

consistent with my evidence that draw 1 was black. Thus my evidence does notinclude the proposition that draw n+1 was red. Why not? After all, by hypothesis Ihave a justified true belief that it was red. The obvious answer is that I do not knowthat draw n+1 was red; the unsatisfied necessary condition for evidence isknowledge.’’ (Williamson 2000, pp. 200–201)

The central point about this case for our purposes is that it is intuitively a casewhere the proposition ball n+1 is red is not part of the subject’s evidence, although itis a true belief that is probabilistically well-supported. The intuitive verdict, therefore,commits one to claiming that probabilistically well-supported true belief is insufficientfor evidence. Knowledge is a natural alternative suggestion for what is required.1

Williamson also suggests that knowledge is sufficient for evidence, but offers noparticular argument to this effect; instead, he argues against a few particular attempts torequire a stronger state than knowledge. Brian Weatherson (Ms) has offered a challengeto the sufficiency of knowledge for evidence. It is worthy of careful examination.2

2 Weatherson’s challenge

To set up the challenge to E = K, consider a case of inductive knowledge. Suppose thatS knows H inductively: i.e., on the basis of evidence E, where E does not entail H. Forexample, we may suppose that E is the fact that for some large number n, n emeraldshave been observed, and each was green; let H be the inductively known hypothesis thatall emeralds are green.

We may even adapt Williamson’s own ball case to be one of the sort we require, fora large enough n and the right sort of circumstances: if there are ten balls in the bag, andI’ve made 100 observations of red balls, I might well be able to know that all the balls inthe bag are red, and therefore that the 101st draw will be red.3

Weatherson complains that in cases like these, some but not all propositions thatare inconsistent with what is known are intuitively inconsistent with the evidence. Inparticular, (1) but not (2) below is intuitively consistent with the evidence:

1. E but not H2. H but not E

It is intuitively consistent with the evidence that the first n observed emeralds weregreen, but that not all emeralds are green. But by hypothesis, it is known that all emeraldsare green. So by E = K, (1) and (2) are both inconsistent with the evidence. Acceptingthe intuition that (1) is consistent with the evidence, Weatherson concludes that E = Kis false.4

While I can certainly feel the force of the intuitions that Weatherson is relyingupon here, I think that reflection on twentieth-century epistemology suggests reason toproceed cautiously. There is a strong parallel between Weatherson’s argument againstE = K and a familiar argument against epistemic closure (roughly: competent deductionfrom known premises yields knowledge). Take a case of ordinary knowledge O and asceptical scenario S inconsistent with it—O might be the proposition that I have hands,

Thought 2 (2013) 282–292 © 2014 Wiley Periodicals, Inc and the Northern Institute of Philosophy 283


and S the proposition that I am a handless brain in a vat; or, O might be the propositionthat I won’t be a millionaire next week, with S the proposition that my lottery ticket willwin. In such cases, O is intuitively known; but intuitively, I do not know, nor can I easilycome to know, that S is false. Since O obviously entails not-S, however, closure impliesthat if I know O, I do (or can easily) know not-S. Accepting the relevant intuitions, then,the argument enjoins us to reject epistemic closure.

Few contemporary epistemologists accept this argument. I think that considerationof the strategies one might use to retain the theoretically appealing principle of closurehave reasonably close analogues for retaining the theoretically appealing principle ofE = K. Here are four:

(1) Scepticism. Contrary to our ordinary knowledge intuitions, I don’t know O. Soclosure holds.

(2) Mooreanism. Contrary to our sceptical intuitions about S, since I know O, I canthereby come to know not-S on the basis of O. So closure holds.

(3) Shifty invariantism (So-called ‘‘subject-sensitive invariantism’’). Whether I knowO depends on whether I’m thinking about S. When I am, I don’t know O. WhenI’m not, I do. So we have no counterexample to closure.5

(4) Contextualism. ‘‘S knows O’’ and ‘‘S knows not-S’’ each express differentpropositions in different conversational contexts. In a sceptical context, bothare false; in a non-sceptical context, both are true. So closure holds of every ‘knows’relation. (Within a given context, ‘‘S knows P’’ expresses a proposition that, alongwith P entails Q, entails the truth of ‘‘S knows Q’’. (Modulo necessary modificationsfor ‘‘in a position’’ etc.)) The argument against closure equivocates.

Most epistemologists, I’d expect, will embrace one of these four options in defenceof closure against the argument above. (In Ichikawa (2011a), I embrace the contextualistoption.) Each corresponds to a potential avenue of resistance to Weatherson’s argumentagainst E = K:

(1) Scepticism. The case as Weatherson describes it is impossible; one can’t know H ifit’s not entailed by the evidence.6

(2) Mooreanism. Do the modus tollens on Weatherson’s argument; deny the ‘‘sceptical’’intuition that (1) is consistent with the evidence. H is known; E = K; so the evidencedoes rule out (1).

(3) Shifty invariantism. Thinking about the gap between the evidence and the hypothesisprevents the latter from being known, and from being evidence, alike. When itis ignored, it is evidence. In defence of the posit of such shiftiness, it is helpfulto note that sceptical intuitions about inductive knowledge as evidence are lessthan univocal. In cases in which inductive knowledge is used in support of otherhypotheses, unrelated to the original inductive base, the evidence ascription ismuch more natural. Suppose that I know inductively that all emeralds are green,and that I also know that Jiecheng hates green things. I learn that someone gaveher an emerald; I hypothesize that she is displeased. It is reasonably intuitive thatamong my evidence is that she received something green.



(4) Contextualism. ‘‘Evidence’’ and ‘‘knows’’ are both context-sensitive. In any givencontext, ‘‘S knows H’’ and ‘‘S’s evidence includes H’’ will have the same truthconditions. The Weatherson argument equivocates. Only in the nonscepticalcontext in which we began does ‘‘S knows H’’ express a truth; later, when wesay that ‘‘S’s evidence is consistent with not-H’’, we are in a more scepticalcontext, relative to which ‘‘S knows H’’ is false. So there is no counterexample toE = K, which we can understand to hold in metalinguistic generality (i.e., ‘‘E = K’’expresses a truth in every context). The contextualist can also accommodate theshifty intuitions about Jiecheng and green emeralds in the familiar way.

These are all defensive moves on behalf of E = K in resistance to the Weathersoncritique. None amounts to a reason to accept E = K. It is an assumption of this articlethat there is something appealing about E = K—that if a defence is available, it is worthtaking seriously. Although as I mentioned above, Williamson himself does not give anyspecific argument for the sufficiency direction of E = K, I take the broad theoreticalsuccess of Williamson’s framework to offer some holistic support to this conclusion.

All four of these options, I think, are worthy of exploration. In this remainder of thisarticle, I’ll explore the contextualist option.

3 ‘‘Knows’’ and ‘‘Evidence’’

My preferred approach to contextualism about ‘‘knows’’ is based on that of Lewis(1996). Lewis describes the truth conditions for knowledge attributions thus: ‘‘S knowsproposition P iff P holds in every possibility left uneliminated by S’s evidence.’’ (Lewis1996, p. 551) Here are three immediate notes: first, ‘‘S’s evidence’’ here is stipulated to bethe facts about S’s subjective experiences; Lewis’s own view is quite distant in both letterand spirit from E = K. Nevertheless, as will emerge below, the Lewisian framework iscompatible with E = K, and the result is interesting. Second, the ‘‘every’’ in the Lewisiantruth conditions is to be understood as a context-sensitive quantifier with a restricteddomain; as Lewis puts it, some possibilities are ‘‘properly ignored’’ in a given context.Third, the object-level statement above is intended to hold true in every context. ‘‘Sknows P’’ is true in C iff ‘‘S’s evidence eliminates every not-P possibility’’ is true in C,with ‘‘every’’ understood in Lewis’s particular way.

In my (2011a), I argued that Lewis’s statement of the truth conditions for ‘knows’ought to be modified to include a belief requirement and a basing requirement. There, Ioffered:

S knows that p just in case, for some evidence E, (i) S believes that p on the basis of E,and (ii) all the E cases are p cases.

Like Lewis’s own formulation, mine is intended to hold in metalinguistic generality,and the ‘all’ in clause (ii) is a context-sensitive restricted quantifier. I was neutral on howto understand ‘evidence’. In the remainder of this article, I’d like to consider the meritsof my previous view combined with the contextualist approach to E = K suggested in



the previous section. I begin with a consideration of two worries: one about extensionaladequacy, and one about circularity.

Here is the worry about circularity. Is it legitimate to characterize the truth conditionsfor ‘knows’ in terms of evidence, and to understand evidence in terms of knowledge?Well, I have no aspirations to reductive analysis. It is also worth noting that, given mymodification to the Lewisian truth conditions, no straightforward triviality result followsfrom E = K, the way it would on Lewis’s own view. If S knows p iff S’s evidence eliminatesthe not-p cases, and E = K, then S knows p iff S’s knowledge entails that p relative to theset of relevant worlds; this is all but trivial. My view, however, combined with E = K,requires S to believe that p on the basis of some knowledge, where that knowledge entailsp relative to the set of relevant worlds. It is natural to supplement this proposal withthe suggestion that some knowledge is basic in the sense that it is known on the basisof itself. It is, of course, a substantive epistemological question about just which beliefscan be appropriately based on their own contents. It is a substantive question whichknowledge can be basic. I’ll consider in a bit more detail just what sort of approach tobasic knowledge we should prefer in Section 4. Before doing so, however, let’s considerthe worry about extensional adequacy.

Here is the worry (with thanks to a referee). The view in question is that, as thesphere of relevant possibilities expands and contracts, the extensions of ‘S knows H’ and‘S has H among her total evidence’ will remain coextensive. But why should we thinkthat this is so? One could be a contextualist about ‘knows’ and a contextualist about‘evidence’, without subscribing to this identification. What guarantee is there that theywill, to use Lewis’s colourful language, ‘‘sway together’’?7

The flat-footed answer to this question is this: the view under consideration just is theview that ‘knows’ and ‘has as evidence’ are equivalent in all contexts. So if the question is,what makes it the case that they sway together on this view, the answer is: stipulation. It isimportant in this context to remember that the contextualist treatment of the Weathersonargument was offered as a defensive move in favour of an antecently-appealingapproach. The deeper question, of course, concerns what the view I’m defending has tocommend it.

One thing that I think this contextualist implementation of E = K has going for it isthat it is part of a generally appealing contextualist implementation of the ‘knowledgefirst’ programme. Establishing this claim is well beyond my scope in this short article, butit is the main subject of my further research in progress. (See the final section of this articlefor a few more remarks on this relation.) But there is also a smaller-scale observationthat can be made: as mentioned above, the kind of sceptical conversational pressure that,according to the contextualist about ‘knows’, makes it harder to satisfy that predicate alsomakes it intuitively harder to satisfy ‘is evidence’. Remember the case of Jiecheng andthe green emeralds; my inductively-supported true belief that Jiecheng has been givensomething green seems intuitively to count as ‘evidence’ in precisely those contexts inwhich it seems to count as ‘known’. Focus on the inductive basis undermines both alike.Similarly, to return to Weatherson’s case in a contextualist framework, mention of thepossibility that the next ball is black is just the sort of conversational move that can shift



‘‘S knows that next ball is red’’ and ‘‘S’s evidence includes that the next ball is red’’ fromintuitively true to intuitively false. Put simply, the particular contextualist approach onoffer seems to get the cases intuitively right.8

To summarize the view on offer: ‘knows’ and ‘evidence’ are each context-sensitive;in a given context, the following are all equivalent:

(1) ‘S knows p’(2) ‘p is among S’s total evidence’(3) ‘For some E that S has as evidence, S believes p on the basis of E, and all E

possibilities are p possibilities’9

This is, I think, an appealing contextualist implementation of E = K; as far as I cantell, it retains the advantages of Lewisian contextualism and of E = K, and avoids theWeatherson objection to the latter.10

4 Basic knowledge and basic evidence

As mentioned above, the view I’ve been sketching affords a central role to basicknowledge. So it should be supplemented with a story about what basic knowledge is.One obvious possibility is that basic knowledge consists in known propositions aboutone’s subjective experiences. That I am having such-and-such experiences right now isoften thought to be the sort of thing that might be known on the basis of itself. This isthe development of the view that is closest to Lewis’s own attitude. Although it embracesE = K, and so does not follow Lewis in identifying evidence with propositions aboutmental experiences, it does, like Lewis, afford such experiences a special epistemologicalrole. They provide, on this approach, the basic evidence.

On this view, as on Lewis’s own view, in a context in which BIV possibilities arerelevant, ‘‘S knows she has hands’’ will typically be false, since there is nothing ‘‘known’’in that context that rules out ‘‘all’’ no-hand worlds. However, ‘‘S knows she has hand-likeappearances’’ will typically be true, since the proposition ‘‘S has hand-like experiences’’satisfies ‘‘known’’ on the basis of itself; and of course, this proposition rules out ‘‘all’’no-hand-like-experience worlds.

There is room to question, however, whether this is the best implementation of basicknowledge in the Lewisian framework I have been sketching. Here, in brief outline, aretwo reasons that might tell against this approach. First, the assumption that perceptualknowledge proceeds via evidence concerning the subject’s own perceptual experiencesthreatens to make some rather sophisticated introspective conceptual machinery anecessary condition on perceptual knowledge. Arguably, young children and animalsmay lack the conceptual repertoire necessary for possession of evidence like I havesuch-and-such experience; since they clearly have some perceptual knowledge, a storythat bases perceptual knowledge on introspective evidence seems unappealing.11 Second,there is room to challenge the theoretical motivation behind Lewis’s privileged statusfor conscious mental experiences. If, for instance, it is motivated by the idea thatsuch experiences comprise a domain to which subjects have some kind of special



access—a ‘‘cognitive home’’ in Williamson’s (2000) sense—then arguably, Williamson’santi-luminosity argument undermines that motivation.

It is therefore worth at least considering the prospects for a development of theproposal that denies a special role for conscious experience. We could instead consider amore Moorean implementation, allowing that at least some perceptual knowledge of theexternal world might be basic in the sense described above. Suppose, for instance, thatmy perceptual contact with my own hands puts me into direct contact with my hands:we may allow that I have hands as basic knowledge, legitimately known on the basis ofitself.

On this view, even in sceptical contexts where BIV worlds are relevant, ‘‘S knows shehas hands’’ will typically express a truth. It requires that S believe that she have handson the basis of something satisfying ‘‘known’’ in that context, where that basis entails,relative to the set of relevant worlds, that S have hands. On the present suggestion, thatS has hands is available to play this role. Since it is a sceptical context, satisfaction of‘‘knows she has hands’’ requires S’s evidence to eliminate BIV possibilities, but this iseasily done: her evidence, which includes that she has hands, is logically incompatiblewith the handless-BIV worlds.

This development of the view will not vindicate all of the radical sceptical intuitionswith which Lewis himself was concerned. It could, however, be an appealing contextualistapproach that can account for the shiftiness about knowledge ascriptions among moremoderate cases. For example, it might account for otherwise puzzling patterns ofintuitions about lottery cases, induction, bank cases, or even ‘fake barn’ cases. It isperhaps worth noticing that the Moorean response to the closure puzzle discussed inSection 2 is much less plausible for lottery cases than it is for BIV cases.

A contextualist who develops the Lewisian view in the more Moorean way heredescribed can make use of strategies that have been pursued by invariantists to accountfor more radical sceptical intuitions in many cases. For example, if BIV worlds are salientto the subject, this might well undermine knowledge for that subject by destroying theconfidence that is necessary to satisfy the belief condition on knowledge. See Nagel(2010).

I am not ultimately sure what to think about this Moorean form of Lewisiancontextualism; however, in light of the worries about motivation to a more restrictedset of basic knowledge, it seems to me that a view in this area is very much worthy ofconsideration.

5 Basic Knowledge and ‘Knowledge First’

I close with some brief reflections on how the contextualist approach to E = K sketchedabove might fit into the broader ‘knowledge first’ framework that characterizesWilliamson (2000). Prima facie, ‘knows’ contextualism and the knowledge firstprogramme appear to stand in a degree of tension. Certainly, Williamson himselfhas little sympathy for contextualism.12 More generally, contextualism is sometimescharacterized as the view that there is no single knowledge relation, but rather many



relations that are sometimes picked out with the word ‘knows’; this fits ill with theidea that knowledge is an important property that plays central theoretical roles. Inthe particular case of my contextualist implementation of E = K, it appears that I amprivileging a notion of basic knowledge as playing a central, fundamental role. As areferee pointed out to me, one might perceive a threat of instability in the position I amdescribing: E = K is motivated by the knowledge first programme, which fits poorly withmy contextualism.

Although this is not the place to argue it, I think that contextualism and a knowledgefirst stance are a much better fit than is often appreciated; in work in progress, I amattempting to develop such a synthesis in detail. For now, let me just suggest ways inwhich the approaches could fit together. With respect to the general worry mentionedabove, although contextualism is sometimes described as a commitment to the view thatthere is no single knowledge relation, this is not mandatory. One can think that ‘knows’has a stable semantic value, which takes an implicit argument from the conversationalcontext.13 If a contextualist thinks that there is a relation knows—perhaps one that takesone more argument place than is generally recognized—she may think that it plays thecentral role emphasized by a ‘knowledge first’ stance.

As for the more specific worry that I offer a privileged place for basic knowledge, asopposed to knowledge generally, I think there is something to the idea that this countsto some degree against a ‘knowledge first’ stance. Whether it is strictly inconsistentdepends on just what is meant by ‘knowledge first’. As I interpret Williamson, whatit is to hold that knowledge is in the relevant sense ‘first’ is to hold that knowledge isrelatively fundamental—i.e., it is more fundamental than it’s been typically thought tobe. Williamson was concerned to reject the attempt, for example, to explain knowledgein terms of belief, and instead suggested that belief should be understood in termsof knowledge. It is not among Williamson’s commitments that everything is posteriorto knowledge; for example, knowledge is not claimed to be ‘first’ in a sense thatis inconsistent with the ultimate reduction of knowledge to subatomic particles. Sopositing a special category of basic knowledge as privileged needn’t be inconsistentwith a modest form of the ‘knowledge first’ attitude. One might wonder, once one hasdone so, wonder whether basic knowledge will ultimately be a better candidate thanknowledge for all of the roles Williamson emphasizes for knowledge; if so, the theoreticalsignificance of knowledge in general might be to a significant degree undermined. Whilethis is worth thinking through in detail, I doubt that basic knowledge is suitable to playall such roles; knowledge in general at least looks better situated than basic knowledgeto serve as the constitutive norms of assertion and belief. Exploring these ideas furthercomprises a promising research project.

Acknowledgments

Thanks to Andy Cullison, Carrie Ichikawa Jenkins, Federico Luzzi, Daniele Sgaravatti,and Brian Weatherson for thoughts on early versions of this material; thanks alsoto two anonymous Thought referees for detailed comments on a draft of this paper.



Earlier incarnations of this project were presented in the Arche Epistemology Seminarat the University of St Andrews in 2009, the Young Philosophers Lecture Series inSUNY Fredonia in 2013, and the Early Career Conference at the Northern Institute ofPhilosophy at the University of Aberdeen in 2013; thanks to all participants and audiencemembers there as well.

Notes1 Other weaker epistemic relations than knowledge are of course possible here as well; for

instance, Goldman (2009) suggests that noninferential justified belief —a nonfactive state—is

sufficient for evidence. Weatherson (Ms) also suggests a nonfactive view. I agree with

Williamson and with Littlejohn (2012), p. 101 that violating the factivity of evidence is a high

cost. More complicated factive views short of knowledge are also available; one might

reasonably, however, complain of many of these that they seem somewhat ad hoc. Knowledge

is a strong candidate to play the theoretical role needed.

2 Weatherson’s article also gives a separate argument against necessity; that argument is not my

present concern.

3 We may allow that other conditions, beyond those stipulated, may play important roles here,

too. For example, if there is a particular ball that (by surprising coincidence) I have never yet

seen, I might not know that all the balls are red. Intuitions seem to vary as to whether one can

know that the next ball will be red if one hasn’t seen all the balls, or if one doesn’t know that

they’re all red. We needn’t settle that now; if there is some version of the case that yields

inductive knowledge, that’s the version here being considered.

4 An argument to the same conclusion with a similar structure—so far as I know, developed

independently—has also been developed in unpublished work by Elia Zardini. He presented

this argument at a Basic Knowledge workshop at the Northern Institute of Philosophy in

Aberdeen in October, 2013. I believe that what I say in response to Weatherson’s argument

applies equally to Zardini’s version of the worry.

5 Whether this is so depends on one’s precise formulation of closure. You might still admit to

counterexamples to ‘‘if you know that p, and p obviously entails q, then you’re in a position

to know q’’. But you won’t have counterexamples to Hawthorne’s (2003) ‘‘if you know that p,

and competently deduce q from p, retaining knowledge of p throughout, then you know q’’.

6 This might, but needn’t, imply that ordinary knowledge attributions are in error. If the view

of Bird (2005) is correct, for instance, then the kinds of cases Weatherson describes will

typically be instances of knowledge, but they are not known on the basis of non-entailing

evidence; part of the evidence consists in tacitly known propositions strong enough to

provide deductive arguments from the evidence to the conclusion.

7 Lewis (1973, p. 92). (Lewis here is not talking about knowledge.) I take the application of this

language from Keith DeRose, who cites it often—e.g., DeRose (2009), p. 99.

8 Compare the parallel relationship between dual contextualist approaches to knowledge

attributions and counterfactuals in Ichikawa (2011b), pp. 299–300; as I see it, the connection

here is exactly similar.

9 Two referees ask two questions about the effect on context of the first quantifier here: ‘‘for

some E that S has as evidence . . . ’’. The first question concerns whether it itself introduces

new context-sensitivity. Ordinary English quantifiers in general are context sensitive, so we

might expect that different contexts can introduce different domains that are relevant here.



This is a complication that interferes with the precise statement of the view. The intended

reading is one in which relevant evidence is always quantified over.

The simplest way to think about this would be to stipulate that, in the theoretical principle

(3), the initial quantifier is stipulated in an invariantist way, taking an arbitrarily large

domain. So I do not allow a context where ‘S has E as evidence’’ is true but where ‘‘For

something S has as evidence’’ does not include E within the domain of the quantifier. The

second question concerns whether the context-sensitivity already posited might have sceptical

effects, given my framework, when it ought to have anti-sceptical ones. When the relevant

domain contracts into what should be a non-sceptical context, doesn’t this limit what

evidence I have, even as it also limits what I must rule out? If so, can I claim Lewis’s result that

smaller domains always yield less sceptical contexts? What if the domain shrinks so far as to

exclude propositions about my sensory experiences? Here is the short answer to that

challenge: the domain cannot shrink that far, because of constraints on the domain of

relevant worlds. Consider, for example, Lewis’s Rule of Actuality (Lewis 1996, p. 554), which

guarantees that the actual world is always included in the domain, regardless of the context.

Since the actual world is one in which S has the relevant experiences, if those experiences

establish basic evidence, that evidence will be present, regardless of the context. As I say in

Ichikawa (2011a), I do not embrace all of Lewis’s ‘Rules’, but I do retain this one.

10 In addition to his theory of evidence, Williamson endorses a Bayesian-inspired story about

the ‘evidence-for’ relation; evidence E is evidence for H iff P(H|E) > P(H). The contextualist

‘E = K’ theorist can endorse Williamson’s equivalence, or tell a different story. (My

preference is for the former.)

11 This is related to another of the arguments in Weatherson (Ms), in addition to the one that

was my main focus in Section 2. Thanks to a referee for drawing my attention to the relevance

of this point.

12 See e.g. Williamson (2005).

13 Jonathan Schaffer’s (2004) ‘contrastivism’ is a view of this type, although the example is

complicated by the fact that Schaffer, unlike me, sometimes reserves the term ‘contextualism’

for the view that ‘knows’ is an indexical; as I use the term, Schaffer’s contrastivism is a

contextualist view, because it has it that ‘S knows p’ can express different propositions in

different contexts.

ReferencesBird, Alexander. ‘‘Abductive Knowledge and Holmesian Inference,’’ in Oxford Studies in

Epistemology, edited by Tamar Szabo Gendler and John Hawthorne. Oxford: OxfordUniversity Press, 2005.

DeRose, Keith. The Case for Contextualism. Oxford: Oxford University Press, 2009.Goldman, Alvin. ‘‘Williamson on Knowledge and Evidence,’’ in Williamson on Knowledge,

edited by Patrick Greenough and Duncan Pritchard. Oxford: Oxford University Press,2009.

Hawthorne, John. Knowledge and Lotteries. Oxford: Oxford University Press, 2003.Ichikawa, Jonathan. ‘‘Quantifiers and Epsitemic Contextualism.’’ Philosophical Studies 155.3

(2011a): 383–98.. (‘‘Quantifiers, Knowledge, and Counterfactuals.’’ Philosophy and Phenomenological

Research 82.2 (2011b): 287–313.Lewis, David. Counterfactuals. Cambridge, MA: Harvard University Press, 1973.



. (‘‘Elusive Knowledge.’’ Australasian Journal of Philosophy 74.4 (1996): 549–67.

Littlejohn, Clayton. Justification and the Truth Connection. Cambridge: Cambridge University

Press, 2012.

Nagel, Jennifer. ‘‘Epistemic Anxiety and Adaptive Invariantism.’’ Philosophical Perspectives 24(2010): 407–35.

Schaffer, Jonathan. ‘‘From Contextualism to Contrastivism.’’ Philosophical Studies 119.1–2

(2004): 73–104.

Weatherson, Brian E�=K (MS). URL: http://brian.weatherson.org/EK.pdf (accessed 3

December, 2013).

Williamson, Timothy. Knowledge and Its Limits. Oxford: Oxford University Press, 2000.

. (‘‘Contextualism, Subject-Sensitive Invariantism and Knowledge of Knowledge.’’ The

Philosophical Quarterly 55.219 (2005): 213–35.


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Basic Knowledge and Contextualist “E = K”