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3. The Problem of Easy Knowledge: Towards a Solution

© 2017 Mark McBride, CC BY 4.0 https://doi.org/10.11647/OBP.0104.05

I develop my own solution to the problem of easy knowledge, criticising and improving on a proposal by Davies (2004). My solution is available to the dogmatist. Thus, so far, the prospects look good for a defense of dogmatism, immediate justification, and basic knowledge against the pattern of objection.

0.1 In Chapter Two, I introduced Stewart Cohen’s (2002, 2005) problem of easy knowledge (in sections 0.1–0.4 of that chapter), and then offered an extended commentary on José Zalabardo’s response to the problem. In this chapter, I take some steps towards a solution to the problem of easy knowledge.

1. Responses to (EK)-reasoning

1.1 One could accept KR (and thereby face a version of the problem of the criterion):1

KR A potential knowledge source K can yield knowledge for S, only if S knows K is reliable. (Cohen 2002: 309)

This principle would block basic knowledge, and so the problem of generating easy knowledge from basic knowledge by (EK)-reasoning wouldn’t arise. But I want to consider responses to the problem of easy knowledge which don’t accept KR2 (and thereby avoid the problem of the criterion). My focus is on a response which can be attributed to Martin Davies (2004, 2009). Davies’s response is promising, but my claim is that it is incomplete. In section 2 I introduce Cohen’s important modification of his original case. And in section 3 I identify, and make a positive move to remedy, the incompleteness of Davies’s response. First, though, I need to delineate Davies’s response.

1.2 Some preliminaries: first, Davies (2004: 229–31) endorses — at least for the sake of the argument — James Pryor’s (2000: 519–20) dogmatist epistemology, which licenses an immediate, though defeasible, transition from the experience described in (WARRANT FOR 1) to basic knowledge of (1). To the extent that Davies is a dogmatist we can conclude he doesn’t accept KR.

Second, Davies distinguishes between two epistemic projects: the epistemic project of deciding what to believe, and the epistemic project of settling a question.3 Here is Davies (2009: 361) on the epistemic project of deciding what to believe (call it the D-project):

If you review some of your beliefs, P1,…, Pn, and notice a valid argument from those premisses to Q then you should4 adopt the belief Q or, if other considerations argue against Q, then you should reconsider your beliefs P1,…, Pn.

Note a feature of this project: it’s deciding what to believe, Q, on the basis of noticing a valid argument from a set of premises, P1,…,Pn, to Q. The type of D-project of particular interest here is reasoning with an argument to come to know its conclusion.5

And here is Davies (2009: 364–65) on the epistemic project of settling a question (call it the S-project):

The project of settling the question whether or not Q is true […] begin[s] by taking the question to be open pro tempore […] I suppose, for the purposes of the question-settling project, that I have reasons to think that Q is, or may very well be, false. This suppositional doubt then governs my conduct of the project.6

Suppose that I have a warranted belief P and that my project is to deploy my warrant to believe P, and my appreciation of the valid argument from P to Q, in order to settle the question whether or not Q is true in favour of the positive. My conduct of the question-settling project is governed by suppositional doubt about Q. In some cases, my suppositional doubt about Q may prevent me from rationally availing myself of my warrant to believe P within the project that is governed by that suppositional doubt. In such cases, although I do have a warrant to believe P and there is an obviously valid argument from P to Q, I cannot deploy that warrant to settle the question in favour of Q.7

Note, as before, that undertaking an S-project doesn’t threaten many plausible knowledge-closure principles: while an (EK)-reasoner has warrant for (1), it’s left open that he has warrant for (3) other than by means of (EK)-reasoning within the scope of suppositional doubt.8 The type of S-project of particular interest here is reasoning with an argument to come to know its conclusion.

1.3 So, by Davies’s lights, when one undertakes a D-project in (EK)-reasoning a subject can put together antecedent warranted beliefs in (1) and (2) to come to know (3). But when one undertakes an S-project in (EK)-reasoning one suppositionally doubts (3). Now (WARRANT FOR 1) cannot be rationally deployed to settle the question in favour of (3). Thus no warrant for, and so no knowledge of, (3) is acquired by (EK)-reasoning within the S-project.9 Davies offers a like diagnosis of reasoning with Moore’s ‘Proof’ of (knowledge of)10 the existence of an external world.11

2. Cohen’s Modified Case

2.1 Cohen (2005: 420) considers a modification of his original case — a case designed to “eliminate entirely any dialectical context” from (EK)-reasoning:

Suppose my son is not worried about the possibility that the table is deceptively illuminated. He accepts that I know that the table is red and not white with red lights shining on it. He is just curious about how I know it. I respond in just the same way. “Oh that’s easy. It looks red, so it is red, so it is not white with red lights shining on it.” By my lights there is something unsatisfactory about my response.

Two responses are available. First, one might dispute Cohen’s intuition about this case. Maybe Cohen has been misled by considering a case in which, even though a dialectical context has been eliminated, there are still two parties involved — two parties, we can assume, sharing background assumptions. Perhaps the involvement of two parties — Cohen and his son — has misled Cohen into finding something unsatisfactory about a genuinely satisfactory response. That is, maybe Cohen has unconsciously imported differing background assumptions onto the parties in the case; such an importation rendering a satisfactory response ostensibly unsatisfactory. This first response would be hasty. I share Cohen’s intuition about the unsatisfactoriness of the father’s response in the modified case, but reliance on bare intuitions is philosophically unsatisfying. So I want — the second response — to give a philosophically satisfying account of this intuition.12 Doing this will reveal the incompleteness of Davies’s response to the problem of easy knowledge.

(Perhaps, though, we can, even at this stage, do slightly better than reliance on a bare intuition. It seems that the question, ‘How do you know?” is rather different from the question, ‘Why do you believe?’. One natural answer to the second question is: (a) I believe that the table is red; so, on that basis, (b) I believe that the table is not white; and so (c) I believe that the table is not both white and lit with red lights. If I do well in believing (a) then it seems that I also do well in believing (c). Dogmatism says that there is no epistemic circularity here. On one view, the intuitions about ‘know’ owe something to an intuition about sensitivity — a condition explored in Chapter Seven. However, I try to show that that latter intuition seems to be limited in some way. Sometimes sensitivity is unachievable in principle. In sum: the ‘How do you know?’ question seems more demanding, more challenging.)

2.2 By eliminating the dialectical context, Cohen removes any possibility of the dialectical phenomenon of begging the question entering the picture. Cohen’s son is prepared to grant Cohen that he does indeed know (3) and wants to be told how Cohen achieved the feat of coming to know (3). What Cohen’s case illustrates is that we find the answer intuitively inadequate if all it does is to spell out how Cohen did well in the D-project. This suggests that the son’s request calls for, but does not receive, an account of how Cohen settled the question whether or not (3) is true. So it’s not that eliminating the dialectical context removes the S-project from consideration, leaving only the D-project. Rather, the son’s question, ‘How do you know?’ — cf. ‘How did you find out?’, ‘How could you tell?’, ‘How did you rule out relevant alternatives to (3)?’ — asks for an account of Cohen’s conduct of the S-project. The son wants to know what evidence Cohen was able rationally to deploy in the context of a project that began by his suppositionally regarding the question whether or not (3) is true as a genuinely open one. And the son is unsatisfied by an account merely of Cohen’s conduct of the D-project.

3. Identifying and Remedying the Incompleteness of Davies’s Response

3.1 Consider the following variant on (EK), (EK*):

(WARRANT FOR 1) The table looks red.

(EK*)

(1) The table is red.

(2) If the table is red, then I’m not a BIV13 being deceived into falsely believing the table is red.

(3) I’m not a BIV being deceived into falsely believing the table is red.

This is just (EK) but with a different consequent in (2) and, resultantly, a different conclusion. And (EK*), predictably, can be explained in much the same way as (EK): we have a piece of basic knowledge, a bridging conditional that is knowable a priori, and an anti-sceptical conclusion. What’s the purpose of setting out (EK*), and considering (EK) and (EK*) side-by-side? The problem of easy knowledge, recall, is that particular arguments (beginning from a premise of which we have basic knowledge) seem to offer a ‘too-easy’ route to knowledge of a conclusion. But (EK) and (EK*) elicit very different intuitions about the legitimacy of the argument as a route to knowledge: (EK*)-reasoning seems much less unsatisfactory as a route to knowledge of its conclusion than (EK)-reasoning. However, both (EK)-reasoning and (EK*)-reasoning do well by the standards of the D-project and neither does well by the standards of the S-project.14 On these two projects, (EK)-reasoning and (EK*)-reasoning are matched. Given that the only theoretical considerations on which Davies can draw in determining whether a thinker knows a conclusion is whether that thinker does well in the D- and S-projects, if the question is whether to say that a thinker knows the conclusions of (EK) and (EK*), then Davies apparently has to (counterintuitively) give the same answer for this pair of examples matched on their performances in the D- and S-projects. Thus the incompleteness of Davies’s response.15

3.2 Now consider the following intuition of Cohen’s (2002: 313):

I think [(EK*)-reasoning] may look plausible only because it is obscure in general how we know global sceptical alternatives do not obtain, e.g., how we know we’re not brains-in-a-vat. And insofar as we are inclined to say we do know such things, this can seem like a reasonable hypothesis about how we know.

But the problem is that we cannot limit the knowledge we acquire in this way to denying global sceptical alternatives […] Presumably, I cannot know that it’s not the case that the table is white but illuminated by red lights, on the basis of the table’s looking red.

As before, two responses are available: we might reject Cohen’s intuition or we might try to give a philosophical underpinning to it. As before, I prefer the second response. Cohen admits to an intuition that (EK*)-reasoning is less unsatisfactory than (EK)-reasoning, although the two examples have the same structure (“the knowledge we acquire in this way […]” (my emphasis)). He seems to conjecture that the difference is that the conclusion of (EK*) denies a global sceptical hypothesis, while the conclusion of (EK) denies a more local sceptical hypothesis. He also enters a conjecture about why this difference should make a difference; namely, that “it is obscure” how we know global sceptical hypotheses to be false. I take it that the reason that this “is obscure” is that, in general, it is not plausible that we know they are false on account of sensory or perceptual evidence that counts against them. So, if we want to say that we do know that they are false then maybe “[(EK*)-reasoning] can seem like a reasonable hypothesis about how we know”. So, is the global/local distinction important here? Is the global/local distinction what’s driving Cohen’s intuition?

Where (EK*) and (EK) differ, then, is in (EK*) concluding with the falsity of a global sceptical hypothesis, whereas (EK) merely concludes with the falsity of a local sceptical hypothesis. The truth of a global sceptical hypothesis is incompatible with our knowing — but not necessarily with the truth of — any of the things we ordinarily take ourselves to be able to know by means of sense perception. The truth of a local sceptical hypothesis is incompatible with our knowing — but not necessarily with the truth of — a proper subset of the things we ordinarily take ourselves to be able to know by means of sense perception. Local sceptical hypotheses come in varying degrees of strength. The conclusion of (EK), for example, is the falsity of a fairly weak local sceptical hypothesis.16

3.3 Let’s now stipulate the following argument template:

(EK)-style argument: A valid argument with a first premise establishing a piece of basic knowledge, a second conditional premise knowable a priori, and a conclusion — reachable by a modus ponens inference — delivering (knowledge of) the falsity of a sceptical hypothesis (global or local).17

Notably, Moore’s ‘Proof’ is an (EK)-style argument. Call reasoning with an (EK)-style argument (EK)-style reasoning. While such arguments and reasoning are my focus from here on, my final proposal purports to have application to knowledge and reasoning in general (within the scope of our two epistemic projects).

Moreover, let us stipulate that the three instances of (EK)-style arguments encountered thus far — viz. (EK), Moore’s ‘Proof’, and (EK*) — are central cases of (EK)-style arguments in the following sense: each has a first premise establishing a piece of basic knowledge of an everyday proposition which is not the negation of a sceptical hypothesis. ‘Everyday proposition’ is not a perfectly precise term; moreover nor is ‘sceptical hypothesis’ — cf. n. 16. However, ‘I have hands’ and ‘The table is red’ serve as clear exemplars of everyday propositions which are not the negations of sceptical hypotheses. It is a characteristic of central cases of (EK)-style reasoning (but not only of such central cases) that they do badly in the S-project.

Finally, we can stipulate that (EK)-style arguments which are not central cases thereof — by virtue of not having a first premise establishing a piece of basic knowledge of an everyday proposition that is not the negation of a sceptical hypothesis — are peripheral cases. I think that this central/peripheral distinction is an important and natural one to draw. Indeed it captures the differing degrees of attention lavished by contemporary epistemologists on the two types of (EK)-style arguments, and on reasoning therewith. And, though we’ll encounter peripheral cases in what follows (see nn. 24–25 infra), our focus — following contemporary epistemologists — will be on central cases.

Now let’s ask the following two questions:

(Local Necessary?) Is the delivery of (knowledge of) the falsity of a (merely) local — and not global — sceptical hypothesis in (EK)-style-reasoning necessary to generate intuitions of unsatisfactoriness to (roughly) the level generated by (EK)-reasoning (even in a non-dialectical context)?

(Local Sufficient?) Is the delivery of (knowledge of) the falsity of a (merely) local — and not global — sceptical hypothesis in (EK)-style-reasoning sufficient to generate intuitions of unsatisfactoriness to (roughly) the level generated by (EK)-reasoning (even in a non-dialectical context)?18

(A key point is that, compatibly with a piece of reasoning not generating intuitions of unsatisfactoriness to (roughly) the level generated by (EK)-reasoning, something could still seem — and be — unsatisfactory about a piece of reasoning in question. Indeed my coming analysis of (EK*)-reasoning, and, by analogy, (MOORE)-reasoning, bears out this compatibility. (EK*)-reasoning is less unsatisfactory than (EK)-reasoning, yet suffers from an epistemic limitation: it cannot be used in the epistemic project of settling the question. Albeit this limitation, I’ll claim, is not such as to preclude knowledge.) It turns out that the answer to both questions is: ‘no’. We’ll discover this by means of two thought experiments. This will support the proposal that the global/local distinction isn’t driving Cohen’s intuition. In fact the two thought experiments lead us to the real distinction — a distinction cross-cutting the global/local distinction — that drives Cohen’s intuition.19

3.4 Thought experiment one — why the answer to (Local Necessary?) is ‘no’. We need a piece of (EK)-style-reasoning which seems as unsatisfactory as (EK)-reasoning, but which delivers (knowledge of) the falsity of a global — and not (merely) local — sceptical hypothesis. To get this we need to draw the following distinction:

Weak BIV: One is a Weak BIV iff one is a BIV with the availability of knowledge-conferring evidence that one is a BIV.

Strong BIV: One is a Strong BIV iff one is a BIV with no availability of knowledge-conferring evidence that one is a BIV.20

So Weak BIV and Strong BIV exhaustively and exclusively partition the set of BIVs. What might be some examples of evidence that one is a BIV? Pryor (2000: 537–38) suggests the following:

[A] ticker tape appears at the bottom of your visual field with the words: “You are a brain in a vat…”

[S]tatistical evidence, such as evidence that 7 out of 10 subjects are brains in vats, or evidence that you are a brain in a vat 7 mornings out of 10.

Pryor introduces these examples as cases of positive evidence that one is a BIV, which thus form evidence potentially undermining any warrant one might have that one is not a BIV. Pryor (537–38) categorises the ticker tape example as a case of “positive empirical evidence” that one is a BIV (and doesn’t explicitly categorise the statistical evidence example). I take the ticker tape — and the statistical evidence — example as a case of pseudo-perceptual evidence. Finally, why is one’s being a Weak BIV a global — and not merely local — sceptical hypothesis? Because a Weak BIV cannot — as local sceptical hypotheses permit — come to know anything by means of sense perception. That which it can come to know — that it is a BIV — is not, ex hypothesi, knowable by sense perception. BIVs have no such faculties; they’re limited to pseudo-perception.

With this distinction drawn, and examples explained, we can construct our argument:

(WARRANT FOR 1) The table looks red.

(Local Necessary? No)

(1) The table is red.

(2) If the table is red, then I’m not a Weak BIV being deceived into falsely believing the table is red.

(3) I’m not a Weak BIV being deceived into falsely believing the table is red.

Why does such (EK)-style reasoning dictate that the answer to (Local Necessary?) is ‘no’? As with — and to the level of — (EK), something is unsatisfactory with coming to know that one is not such a Weak BIV in such a manner. But (Local Necessary? No) has delivered a conclusion — unlike as with (EK) — falsifying a global sceptical hypothesis. Could the characteristic shared by (Local Necessary? No) and (EK) that explains our like dissatisfaction with reasoning therewith be the following: that there is (ex hypothesi) other reliable evidence available — other, that is, than evidence acquired by (EK)-style reasoning — for coming to know their conclusions?21

With respect to (Local Necessary? No) such evidence would be the absence of ticker-tapes, statistical evidence etc. informing you that you are a Weak BIV.22 What background knowledge a subject must have to exploit such evidence is something I don’t explore. Just assume that whatever background knowledge is required, our subject has it. I’m supposing our subject could, at a certain point, engage in the following non-(EK)-style modus tollens reasoning:

(Weak BIV)

(1) If I am a Weak BIV, then I will have received evidence that I am a Weak BIV by now.

(2) I haven’t received evidence that I’m a Weak BIV.

(3) I’m not a Weak BIV.

Note that (3) leaves open that one is a Strong BIV. Now suppose, as a result of (Weak BIV)-reasoning, our subject acquires reliable evidence for (3). (This supposition is not uncontroversial: in general, it is not clear how much weight in favour of Not-Weak-BIV is provided by the absence of evidence for Weak BIV.) Our subject can then deploy such evidence to come to know, by non-(EK)-style reasoning, the conclusion of (Local Necessary? No).23 Such evidence can be evidence directly for the conclusion of (Local Necessary? No), and thus deployment of it needn’t proceed by way of (EK)-style reasoning.24 Before — as I shall — conclusively answering affirmatively to the question whether the availability of other reliable evidence is the key to explaining our intuitions, let’s press on to thought experiment two and our negative answer to (Local Sufficient?).

3.5 Thought experiment two — why the answer to (Local Sufficient?) is ‘no’. We need a piece of (EK)-style reasoning which doesn’t seem as unsatisfactory as (EK)-reasoning, but which delivers (knowledge of) the falsity of a (merely) local sceptical hypothesis. We need (EK) again, but with an accompanying stipulation:

(WARRANT FOR 1) The table looks red.

(Local Sufficient? No)

(1) The table is red.

(2) If the table is red, then it is not white with red lights shining on it.

(3) The table is not white with red lights shining on it.

Accompanying stipulation: Unlike with (EK), there’s no other (inductive) knowledge-conferring evidence available against the possibility that there are red lights shining on the table.

Such — ex hypothesi proscribed — (inductive) evidence could be perceptual, memorial, or testimonial. Such evidence can be evidence directly for the conclusion of (Local Sufficient? No), and thus deployment of it needn’t proceed by way of (EK)-style reasoning.25 (Note that this is merely a thought experiment designed to prise apart conceptually the real distinction driving Cohen’s intuition from the (cross-cutting) global/local distinction. There is thus no need to demonstrate that the accompanying stipulation is commonly true. Indeed, as a matter of fact, it will commonly be false. We are countenancing a scenario in which there is no other way of gaining evidence one way or the other about red lights, other than following through the (EK)-reasoning. One thing is clear, however: in order to keep the sceptical hypothesis relevantly local, the scenario cannot be one in which an evil demon is going to prevent our discovery of the red lights by providing experiences as of there not being red lights.)

So, why does (Local Sufficient? No)-reasoning dictate that the answer to (Local Sufficient?) is ‘no’? As with (EK*), (Local Sufficient? No)-reasoning has not generated intuitions of unsatisfactoriness to the level generated by (EK)-reasoning. But, in contrast with (EK*), it’s delivered (knowledge of) the falsity of a (merely) local sceptical hypothesis. I suggest the characteristic shared by (Local Sufficient? No) and (EK*), which explains our similar level of satisfaction with reasoning therewith, is that there’s (ex hypothesi) no other reliable evidence available — other, that is, than evidence acquired by (EK)-style reasoning — for coming to know, respectively, that there aren’t red lights shining on the table, and that I’m not a BIV.26 Consider the following dilemma apropos of (Local Sufficient? No): Either one doesn’t know the conclusion at all — in which case (local) scepticism is true — or, in the absence of alternative satisfactory routes to knowledge of (3), one does know the conclusion by means of (EK)-style reasoning such as (Local Sufficient? No)-reasoning. Given we — I assume — don’t want to cave in to scepticism by taking the first horn, we must — however reluctantly — grasp the second horn. (As the accompanying stipulation will commonly be false, circumstances in which one would need to employ (Local Sufficient? No)-reasoning in order to acquire knowledge of (3) will be vanishingly small. But the moral to be drawn from this thought experiment is not that (Local Sufficient? No)-reasoning is a vital form of anti-sceptical reasoning. We are simply using this thought experiment to try to identify the correct basis on which (EK*)-reasoning — a (putatively) vital form of anti-sceptical reasoning — is less unsatisfactory than (EK)-reasoning.)

Quite apart from the question whether the two thought experiments are ultimately dialectically effective, there seems to be something intuitive about the main idea. On the whole — and especially when we are doing science, for example — we prefer evidence that retains its evidential status even if we begin by doubting the hypothesis that the evidence is supposed to support. We are not keen to allow that evidence that lacks this property provides a route to knowledge, if evidence that has the property is available. But if we do well doxastically in a case where there is no possibility of evidence with the preferred property, then we are inclined to allow that this might be sufficient for knowledge. (We might also think that there is a distinction to be made between knowledge that meets the additional condition and knowledge that does not, because it cannot, meet it.)

3.6 In sum: there is something to be said for the idea that doing well in the D-project yields knowledge. But there is also something to be said for the idea that knowledge requires doing well in the S-project. When someone does not do well in the S-project — say, in (EK), by not being able to settle the question whether (3) is true — it is natural to say that he has not come to know (3), because there is a higher standard that the person could meet. This generates conflicting pressures on our use of ‘knows’, since there are some cases where one does well in the (less demanding) D-project, but not in the (more demanding) S-project.27 One of those pressures is towards saying that knowledge requires doing well, not only in the D-project but also in the S-project. So, when Cohen’s son asks: ‘How do you know?’, he is (usually) looking for an answer to the question how Cohen did well in the S-project. That is, how did Cohen deploy evidence to settle the question whether (3) is true?28 The answer that Cohen gives his son in the case of (EK) is unsatisfying. It says nothing, for example, about evidence that shifts the balance of probability in favour of proposition (1), ‘The table is red’, and against the sceptical hypothesis ~(3). But now we see that this is equally true in the case of (EK*). Yet, in this case, it is less clear that the account is unsatisfying, and it is less clear that we want to conclude that Cohen really does not know.

What all this suggests is that there is pressure towards saying that knowledge requires doing well in the S-project except in cases where it is not possible to use evidence — no other reliable evidence is available — to settle the question whether the proposition in question is true or not.29 The foregoing, and related, modals are left uninterpreted.30, 31 Perhaps the pressure towards saying that knowledge requires doing well in the S-project reduces as the operative notion of possibility (and availability) becomes more difficult to meet (and vice-versa). In the case of (EK) it is possible to use evidence — other reliable evidence is available — to settle the question whether or not (3) is true: deploying inductive evidence, for example (though not the evidence of a table looking red).32 So, in the case of (EK), Cohen has failed to measure up to a standard that he could have measured up to — doing well in the project of settling the question whether or not (3) is true. The question-settling warrant provided by the evidence described in (WARRANT FOR 1) cannot be redeployed as a question-settling warrant for (3), but other evidence, we’ve noted, could have been used in an S-project for (3). In the case of (EK*), in contrast, Cohen has failed to measure up to a standard that he could not have measured up to. It is not just that the evidence described in (WARRANT FOR 1) cannot be redeployed to settle the question whether or not (3) is true. There is no evidence that could be deployed to settle that question. Both (EK)-reasoning and (EK*)-reasoning count as examples of doing badly in the S-project.33 But in the case of (EK*), this failure does not exert as much pressure towards saying that the reasoning is not a route to knowledge.34


1 See Cohen (2002: 309–10) on the problem of the criterion.

2 And, indeed, don’t accept WR: A potential knowledge source K can yield knowledge for S, only if S has warrant to accept that K is reliable.

3 This epistemological distinction parallels, respectively, Frank Jackson’s (1987: ch.6) dialectical distinction between the teasing out and the convincing purposes of arguing.

4 ‘[M]ay’ is preferable to avoid the project mandating the adoption of countless time-consuming and pointless beliefs.

5 Although Davies (2009: 363) does not speak explicitly about knowledge (in connection with either of his two epistemic projects), but only about “three progressively less demanding norms for the project of deciding what to believe”.

6 Davies also adds elsewhere (2009: 369): “[A] fuller treatment of the project of settling the question would have to allow for the case where I begin by supposing that it is as likely as not that Q is false”. This suggests that principled or mandated agnosticism (see Wright 2007) about Q — in which one assigns a credence of 0.5 to both Q and its negation — is, for Davies, a form of suppositional doubt about Q, but caution is in order. It may be that a Bayesian will describe a state of open-mindedness as a state in which probability 0.5 is assigned to a proposition and its negation. Those may also be the probabilities that are suppositionally assigned in suppositional doubt, but the fact that the Bayesian assigns the same probabilities in these two conditions does not show that the two conditions are epistemically equivalent. (In any case, it’s clear that Davies would not want to say that mere open-mindedness makes it impossible to make rational use of one’s warrant for (1) in the project of deciding what to believe.)

7 The extension of the S-project to multi-premise arguments is straightforward.

8 It will usually be that the thinker has a warrant to believe (3). But the project of settling the question is more demanding than the project of deciding what to believe and the set-up of the more demanding project may prevent the thinker from rationally deploying his warrant to believe (1) within the scope of the demanding project.

9 Though Davies does not explicitly say this in his 2009 paper (cf. n. 5 supra), his earlier discussion of the problem of armchair knowledge (2000, 2003) suggests this way of speaking. (In terms of warrant: the thinker does have a warrant to believe (3) and may well have a warranted belief in (3). But the warrant to believe (1) cannot be (re-)deployed within the context of suppositional doubt in order to settle the question whether or not (3) is true.) Given the distinction between two epistemic projects, it seems he should say that, if the thinker undertakes the more demanding project then he cannot arrive at knowledge of (3), but that he can arrive at knowledge of the very same proposition ((3)) by undertaking the less demanding project (cf. epistemic contextualism — see Rysiew 2007). This sounds a bit paradoxical, however. It may be we tend to run together two standards for knowledge — the standard of doing well in deciding what to believe and the standard of doing well in settling the question. Perhaps we tend to impose the more demanding standard — unless there is no possibility of meeting that standard, in which case we might shift to the less demanding standard. More on this later.

10 I use this parenthetical device throughout to signal that the key issue up for debate is whether such knowledge is indeed delivered.

11 Davies (2009) uses notions of defeat and transmission failure to explain how suppositional doubt can limit the rational deployment of warrant (in (EK)-reasoning, with respect to both (1) and (3)). Rather than explore this explanation further, I leave the explanandum intuitive, with (EK)-reasoning and Moore’s ‘Proof’ serving as putative exemplars thereof.

12 This is the first of several points in this chapter where, concededly, I use a contestable intuition (here: Cohen’s) as a stimulus to providing a theoretical underpinning thereof.

13 BIV = Brain-in-a-Vat, being fed pseudo-perceptual-experiences (by an evil scientist). One’s being a BIV is compatible with there being an external world — just not with one coming to know (any features) thereof. I leave open that a BIV can engage in competent intellectual functioning, cf. Wright (1991: 104).

14 Davies (2009) has two notions of transmission failure — one for each of the D- and S-projects — which, if met, result in a failure of transmission of epistemic warrant from premises to conclusion. Reasoning fails to do well in the relevant epistemic project iff that project’s transmission failure condition is met.

15 I’ve raised an ‘incompleteness’ problem for Davies. But, additionally, it seems (at least some) epistemic contextualist and subject-sensitive invariantist responses will inherit such a problem. On these analyses, so long as — as, suppose (cf. Lewis 1996), in Cohen’s modified case — the possibility that the table is deceptively illuminated is not raised, there is no way of diagnosing anything unsatisfactory about responding with (EK)-reasoning. I leave open how other analyses of knowledge will handle Cohen’s modified case.

16 For interesting remarks on conditions on being a sceptical hypothesis, see Beebe (2010).

17 Wright (2007: sections II and IV) presents a series of “justificational triads” which — with a little modification — can be fitted into my (EK)-style argument template, concluding with the falsity of sceptical hypotheses concerning the external world, testimony, other minds etc. In Wright’s triads the conditional does not function as a premise. My final proposal can go through operating with Wright’s formulations.

18 I omit the parenthetical ‘even in a non-dialectical context’ from here on in, simply to keep things less cumbersome. Our focus, though, is on both dialectical and non-dialectical contexts.

19 Cohen (2002: 313) hints at the real distinction to which my thought experiments lead. I therefore take any disagreement with Cohen to be one of emphasis rather than substance.

20 Cf. Cohen’s (1999: 69) ‘Brain-in-a-vat*’.

21 It’s a presupposition of the availability of other reliable evidence that the relevant subject is able to recognise and exploit such evidence as evidence for the hypothesis in question (cf. n. 30 infra).

22 Cf. Cohen (1999: 69).

23 I concede, given that a global sceptical hypothesis undermines all perceptual warrants, that (Weak BIV)-reasoning (which presupposes some form of externalism about perceptual evidence) is not clear-cut. I think my final proposal may go through without reliance on (Weak BIV)-reasoning, however (i.e. with reliance instead on the coming thought experiment two).

24 Two related points. (1) Of course, there is inference involved in obtaining the evidence, viz. (Weak BIV)-reasoning. The ‘directness’ point (here and, mutatis mutandis, later in the chapter) is simply that once this evidence is obtained, no further inference — and certainly not (EK)-style reasoning — need be involved: a non-inferential transition can instead occur. (2) Needn’t so proceed; but can. Consider:

(WARRANT FOR 1) (Weak BIV)-reasoning, concluding with reliable evidence for its conclusion.

(1) I’m not a Weak BIV

(2) If I’m not a Weak BIV, then I’m not a Weak BIV being deceived into falsely believing the table is red.

(3) I’m not a Weak BIV being deceived into falsely believing the table is red.

In principle this is a live candidate for being a case of (EK)-style reasoning. Indeed, let us grant that (1) is a piece of basic knowledge (bracketing the difficult question of identifying the operative knowledge source). We can note that, not only is (1) not an everyday proposition, but, moreover, it is the falsity of a sceptical hypothesis. It is thus a peripheral case of (EK)-style reasoning. Notably, reasoning with this argument — unlike central cases of (EK)-style reasoning — does well in the S-project. And this is so because (WARRANT FOR 1) can be evidence directly for (3).

25 Needn’t so proceed; but can. Consider:

(WARRANT FOR 1) Inductive evidence that there aren’t red lights shining on the table.

(1) There aren’t red lights shining on the table.

(2) If there aren’t red light shining on the table, then the table is not white with red lights shining on it.

(3) The table is not white with red lights shining on it.

Again (cf. n. 24), in principle this is a live candidate for being a case of (EK)-style reasoning. Indeed, let us grant that (1) is a piece of basic inductive knowledge. This time, however (cf. n. 24), we can note that, while (1) is, plausibly, an everyday proposition, it is also the negation of a sceptical hypothesis. It is thus a peripheral case of (EK)-style reasoning. Notably, reasoning with this argument — unlike central cases of (EK)-style reasoning — does well in the S-project. And this is so because (WARRANT FOR 1) can be evidence directly for (3).

26 There is, however, a salient difference between (Local Sufficient? No) and (EK*) in this regard: in the former, such evidence is stipulated to be de facto unavailable, whereas in the latter, such evidence is in principle unavailable. Considering further possible implications of this difference is a good exercise.

27 There may be additional conflicting tendencies generated by the S-project itself. Consider a case — say (EK) — in which the thinker did well in deciding to believe (1) and also in settling the question whether (1), but is not able to settle the question whether, say, (3): On the one hand, the thinker did settle the question whether (1) was true, so we might say that he did come to know that (1) is true (even by the demanding standard of doing well in the S-project). On the other hand, a plausible closure principle, plus the fact that the thinker is unable to settle the question whether (3) is true, may add up to a reason for saying that he does not know (by the demanding standard of doing well in the S-project) that (1) is true after all. So there may be conflict between the two standards and there may be additional conflicts within the use of the more demanding standard.

28 This would have to be evidence that one could rationally deploy even while suppositionally regarding the question as open pro tem.

29 Quotidian extensions of knowledge by competent deduction or inference — in which there is often other reliable evidence available for the conclusion — are correctly permitted: such deductions or inferences do well in the S-project.

30 Clearly, in one sense — the sense that such uninterpretedness leaves some degree of indeterminacy about application of my proposal — this is regrettable (cf. n. 21 supra). However, in another sense, such uninterpretedness is welcome. My proposal, though abstract, is still assessable. And there is a sense in which it can be considered a merit of an abstract proposal such as this that it can be assessed independently from, and in advance of, committing on how to interpret the modals in question. Finally, we can note that in the case of (EK*), however these modals are cashed out, there is no (reliable) evidence (available) to settle the question whether or not (3) is true.

31 Relatedly, it is possible — though I have not done so here — explicitly to prise apart two notions in the area of ‘evidence (un)availability’: (1) there is a kind of evidence such that, if one were to experience it, then one would have some support for X; (2) there is a kind of investigation that one can undertake, which has some prospect of uncovering evidence that would provide some support for X. It may be that ~(1) is a more natural understanding of ‘unavailability’ when considering the Weak/Strong BIV distinction and ~(2) is more natural when considering ‘red-table’ cases. Be that as it may, I’m confident my proposal — perhaps, once the two notions are explicitly prised apart, provided we do not flit unreflectively between them — survives such an observation.

32 The evidence described in (WARRANT FOR 1) does, however, normally count as settling the question whether the table is red or blue, for example.

33 By dint of suffering transmission failure. Davies (2009) uses two notions of transmission failure. The kind of transmission failure that he discerns in easy knowledge arguments is not, however, the kind that is closely related to epistemic circularity. (On a dogmatist conception of the situation, there is, of course, no epistemic circularity in these examples.)

34 Objection: consider the following kind of (direct) inference: The table is red; therefore, either I am not a BIV being deceived into falsely believing that the table is red, or there is not a zebra standing behind me right now. This disjunction is presumably one that a subject could come to know by other reliable means (by knowing the second disjunct via, say, perception or testimony). Given this, my proposal, given such reasoning does badly in the S-project, thereby classifies such reasoning as defective. But — objection — the reasoning is, intuitively, not clearly defective. Reply: we explain this intuition by noting that the conclusion can be reached non-defectively in two discrete steps: I (step 1) infer the first disjunct by satisfactory (EK*)-reasoning; I then (step 2) reach the conclusion by disjunction introduction.