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6. Conclusive Reasons

© 2017 Mark McBride, CC BY 4.0 https://doi.org/10.11647/OBP.0104.10

I explain Dretske’s challenge to knowledge-closure, based on his conclusive reasons condition on knowledge. I argue that his (1971) account of conclusive reasons can be supplemented so that his challenge to closure remains unmet.

0.1 Take the following principle (or schema)1 as the focus of the ensuing discussion (‘P’ and ‘Q’ are placeholders for propositions):2

(Closure) If one knows P and competently deduces Q from P, thereby coming to believe Q, while retaining one’s knowledge that P, one comes to know that Q. (Hawthorne 2005: 29)3

0.2 Some remarks about (Closure). First, it is defensible. Many closure principles are not worth defending. Consider, for example, the following:

(Closure’) If one knows P and, necessarily, P entails Q, then one knows Q.

This schema is not defensible. If P’s entailing Q is not known to the relevant subject, it is readily conceivable that the subject could know P without knowing Q.4

Second, to challenge (Closure) is not to challenge a fundamental rule of inference, modus ponens. Here is what Fred Dretske (2005a: 13) has written on the matter:

Closure is stronger [than modus ponens]. Modus ponens says that if P is true, and if P implies Q, then Q must be true. Closure tells us that when S knows that P is true, and also knows that P implies Q, then not only must Q be true (modus ponens gets you this much), S must know it is true.

Third, (Closure) respects Timothy Williamson’s view — endorsed by Hawthorne (2004: 33)5 — on the source of epistemic closure intuitions, namely that “deduction is a way of extending one’s knowledge” (Williamson, 2000: 117). Fourth, (Closure) is restricted to single premise inferences. (For remarks about closure principles involving multiple premises — in which issues concerning aggregation of risk become salient — see Hawthorne 2004: 46–50.)

Finally, what sense of entailment is in play in (Closure)? ((Closure) involves competent deduction of Q from P. I take it one can do this only if P entails Q — in some sense or other.) Closure principles are generally formulated in a way that requires the entailment to be strictly logical, but James Pryor (2012) notes:

[I]n practice epistemologists are pretty relaxed about what they count as “logical” […] [S]ay that a premise [P] implies for you a premise [Q] whenever you’re in a position to be reasonably certain that [PQ], regardless of whether there’s really any strictly logical entailment.

I will follow Pryor’s lead in taking ‘implies for you’ to be a sufficient ‘entailment’ relation for closure principles.

1. The Challenge to (Closure)

1.1 My strategy in outline: first, I want to set out Dretske’s classic challenge to (Closure) — a challenge which began in 1970–1971. Then I want to consider a specific counter-challenge to Dretske’s challenge to (Closure) mounted by John Hawthorne (2005), and to defend Dretske’s challenge from Hawthorne’s counter-challenge. Doing this is not to invalidate (Closure). In this regard my conclusions are modest: Dretske’s challenge to (Closure) is — or, better: can be made — sophisticated and, so far, unmet.

1.2 Dretske (1970: 1007) draws our attention to “sentential operators”; that is, terms or phrases which operate on a sentence or statement to give another sentence or statement. A focus on ‘S regrets’ and ‘S knows’ (where ‘S’ is a placeholder for a subject) will be useful. First, consider the following argument:

(R)

S regrets P

S knows P implies Q

Therefore, S regrets Q

Is (R) valid? No. Consider a subject, Sam, who regrets that he drank ten beers last night, and who also knows that drinking ten beers entails drinking some alcohol. It does not thereby follow that Sam regrets drinking some alcohol last night.

Consider, more germanely to our present discussion, the following argument:

(K)

S knows P

S knows P implies Q

Therefore, S knows Q

Is (K) valid? (K) is Dretske’s original (1970–1971) target, and he there concludes (K) is not valid.6 (K), while similar to (Closure), is distinct from (Closure) in a number of respects. Most notably (Closure), but not (K), requires the performance of a competent deduction. (Equally, (K), but not (Closure), explicitly requires that S knows that P implies Q.) In his (2005) debate with Hawthorne, Dretske shifts his focus squarely to attacking (Closure).

1.3 To understand Dretske’s attack on (Closure) (and (K)) we need to introduce three interrelated pieces of (Dretskean) terminology: conclusive reasons, relevant alternatives, and heavyweight implications.

Let’s introduce these concepts in one go by means of consideration of two closely related arguments (assume a subject marshalling these arguments claims knowledge of premises and conclusion):

(HANDS1) I have hands

(HANDS2) If I have hands then I have a hand

Therefore:

(HANDS3) I have a hand

(BIV1) I have hands

(BIV2) If I have hands then I’m not a handless BIV7

Therefore:

(BIV3) I’m not a handless BIV

Suppose, in line with Dretske, that one’s evidence for the first premise of both (HANDS) and (BIV) is an experience as of having hands: an experience neutral between veridical and non-veridical cases.8

1.4 Here is Dretske’s (2005a: 19) definition of a conclusive reason (where ‘P’, again, is a placeholder for a proposition):

R is a conclusive reason for P = dfR would not be true unless P were true

Dretske’s original (extensionally equivalent — cf. n. 9) formulation of a conclusive reason (1971: 1) better brings out the modal character of conclusive reasons:

R is a conclusive reason for P if and only if, given R, ~◊~P (or, alternatively, ~◊ (R.~P))9

Dretske makes clear later that the appropriate modality is empirical “possibility as it exists in relation to one’s evidence or grounds for believing P” (1971: 14). However, as the debate between Dretske and Hawthorne, which we will be entering here, centres on the former (2005a)-definition, it is that former definition on which we will focus. This (2005a)-definition (a close relative of the sensitivity condition to be encountered in the ensuing chapter) essentially asks whether, in (all) nearby possible worlds where P is false, is R also false? Iff this is so, R is a conclusive reason for P.

How does this piece of terminology map onto analysis of (HANDS) and (BIV)? Well the subject’s perceptual experience as of having hands is a conclusive reason for (HANDS1). The relevant alternative10 to having hands in the context of (HANDS1), is the subject having a stump in place of one hand, or a hand amputated, etc., and it is clear that the subject would not11 have an experience as of having hands were he to have a stump in place of one hand or be a hand-amputee. The subject’s evidence is, then, a conclusive reason for (HANDS1). The idea, then, is that a conclusive reason just is one that rules out all relevant alternatives. And a piece of evidence (described by a proposition, R) rules out all relevant alternatives to a proposition, P, iff in (all) nearby possible worlds where P is false, R would also be false.

And, moving on to (HANDS3) — (HANDS2) is knowable a priori — the relevant alternative to having a hand in the context of (HANDS3) is the subject being handless, perhaps through having both his hands cut off. It is clear that our subject’s experience as of having hands would not persist were he to become handless. The subject’s evidence is, then, also a conclusive reason for (HANDS3). We thus have, with (HANDS), an instance of closure of knowledge under known entailment.

1.5 But that there are instances of closure here and there is not good enough for closure supporters: closure must hold across the board if (Closure) is to be valid. This is where we must consider (BIV) and Dretske’s concept of heavyweight implications. As with (HANDS1), the subject’s perceptual experience as of having hands provides him with a conclusive reason for (BIV1). Likewise, the second premise of (BIV) is knowable a priori. The difference in the two arguments is brought out in the conclusion: in (BIV) — unlike with (HANDS) — the subject’s experiential evidence is not a conclusive reason for (BIV 3). The relevant alternative is different. Were our subject not not a handless BIV he would straightforwardly be a handless BIV. And, by hypothesis, our subject would still have an experience as of having hands were he a handless BIV. So, by Dretske’s lights, (BIV) is an instance of a counterexample to (Closure). (Closure) is thereby, for Dretske, invalidated.12

1.6 The final piece of the jigsaw is the concept of a heavyweight implication. Dretske wants to say something about when we will have instances of (Closure), and when we will have counterexamples. Dretske’s answer is that we will have counterexamples to (Closure) if there is a heavyweight implication as our conclusion. Clearly (BIV3) must count as a ‘heavyweight implication’. But can Dretske give an account of this concept without merely pointing to paradigms thereof when it suits his purposes?

Dretske is content simply to point to paradigms of heavyweight implications — for example, that there is a material world; that humans are not mindless zombies; that there was a yesterday — and to assert that “[t]here are some known implications of what we know […] that we do not have to know to be true in order to know to be true what implies them” (2005a: 23). It would be somewhat unsatisfactory to leave things there, so let’s invoke Hawthorne’s (2005: 33) take on what he calls a “heavyweight proposition”:13

Let P be a “heavyweight proposition” just in case we all have some strong inclination to think that P is not the sort of thing that one can know by the exercise of reason alone and also that P is not the sort of thing that one can know by the use of one’s perceptual faculties (even aided by reason).

In sum, Dretske views the denial of (Closure) as the only way to preserve ordinary knowledge — we do not have to know the heavyweight implications of (quotidian proposition) P to know P.

2. Hawthorne’s ‘Heavyweight Conjunct’ Counter-Challenge

2.1 First, an overview of Hawthorne’s (2005) strategy. His counter-challenge to Dreske’s challenge has two strands. First, he aims to show how we can have conclusive reasons for heavyweight propositions — but in such cases, as we have seen from our analysis of Dretske in section 1, Dretske’s machinery gives us no account of how knowledge of such propositions is blocked. (Although on the face of it Dretske is simply offering conclusive reasons as a necessary condition on knowledge, the first strand challenge makes sense when we see that Dretske accepts the challenge of explaining why we don’t know heavyweight propositions.) Secondly, he aims to show how we can “all too often lack conclusive reasons for a priori consequences of known propositions, even though those consequences are not [heavyweight implications]” (Hawthorne 2005: 35). That is, he aims to show that there are propositions for which we lack conclusive reasons (according to Dretske’s account of conclusive reasons) — in consequence, propositions that Dretske is bound to say we do not know — but which are not heavyweight propositions. (More on the dialectical efficacy of the second strand later in this chapter.)14

2.2 Our principal focus will be on the first strand: putative cases in which conclusive reasons are present for heavyweight implications. Hawthorne has three imaginative cases putatively exemplifying this property. I want to focus (initially) on Case 1: what I will call the case of the ‘heavyweight conjunct’. Here is case 1 (Hawthorne, 2005: 35–36):

[W]hile I might lack conclusive reasons for the proposition ~I am a brain in a vat, I will (supposing I have a headache) have conclusive reasons for I have a headache and ~I am a brain in a vat. My reason for that conjunction include my headache. Were the conjunction false I would not, then, have had my reasons.

So let’s consider this step by step. First a contrast proposition is set out: a heavyweight proposition — ~I am a brain in a vat — is asserted to lack the backing of conclusive reasons. The proposition in question — ~I am a brain in a vat — is a proposition for which we do not have conclusive reasons: the relevant alternative is that I am a brain in a vat, and it difficult to produce evidence that excludes that alternative.

Next a closely related proposition — I have a headache and ~I am a brain in a vat — is considered for which one does have conclusive reasons, in part, here, one’s headache. Why is the headache a conclusive reason for this proposition? Well, to use possible worlds discourse, the closest worlds where the conjunction is false are worlds in which one does not have a headache.15 Crucially, such worlds are not as outré as BIV-worlds: they are standard non-BIV-worlds.16 So my reasons for the conjunction are conclusive, but Hawthorne (2005: 36) contends that:

[T]he [conjunction] is every bit as apt to raise inner alarm bells as the proposition that ~I am a [BIV] and will thus come out as […] heavyweight.

2.3 What are we to make of case 1? An appealing response to Hawthorne is to deny one has conclusive reasons for the conjunction. This response will involve patching up Dretske’s definition (see 1.4) of a conclusive reason. (In this sense, Hawthorne is not criticisable for offering case 1 as a counterexample to Dretske’s challenge.)

2.4 To answer Hawthorne on behalf of Dretske, we need, I’ll contend, to supplement Dretske’s definition of a conclusive reason with a further (necessary) thesis for being a conclusive reason:

(SUPP) If P is a conjunctive proposition, R would not be true unless each of the conjuncts of P, taken separately, were true.

That is, R must be a conclusive reason for each of the conjuncts, taken separately, of a conjunctive proposition. What is the force of the italicised ‘taken separately’? In essence, the point is that (SUPP) comes into play when we are faced with a conjunctive proposition, and requires the relevant modal relation to hold between R and each of P’s conjuncts (and not just instead, as in the original formulation of conclusive reasons, between R and P itself).17 More specifically, suppose that proposition, P, is a conjunction: (P1 & P2). Alternatives to P are possibilities in which P is false. Conclusive reasons do not need to exclude all possible alternatives to P. However, by (SUPP), when P is conjunctive, conclusive reasons need to do more than exclude the most nearby alternatives to P. The nearby alternatives might be possibilities in which P1 is false. But, by (SUPP), conclusive reasons need to exclude nearby possibilities in which P1 is false and also the nearest possibilities in which P2 is false. That is, by (SUPP), both ~P1 and also ~P2 are relevant alternatives to P. What needs to be shown is (1) that in the nearest ~P1 worlds, R is false and also (2) that in the nearest ~P2 worlds, R is false.

With all this said: first I need to explain how this supplementation will solve case 1 for Dretske; then I need to defend the supplementation from a charge of being ad-hoc.

2.5 The first, explanatory part is straightforward. While having a headache is a conclusive reason for having a headache (first conjunct), I might well still have a headache were I a BIV (second conjunct), and this counterfactual precludes one’s having a headache from being a conclusive reason for one’s not being a BIV.18

2.6 More trickily, how do I justify appeal to (SUPP)? (I take it Hawthorne is committed – even if only: arguendo — to the denial of this supplementation as a necessary condition for a conclusive reason. So much is clear from Hawthorne’s treatment of case 1: with (SUPP) in place the headache is no longer, as Hawthorne requires, a conclusive reason for the conjunction.) I want to generate a reductio for this undeveloped Dretskean view of conclusive reasons, leading to justification of a Dretskean appeal to (SUPP).19 Consider the following case: suppose I have a headache. It seems, absent supplementation by (SUPP), that that experience can be a conclusive reason for the following proposition, (P): I have a headache and I have all my limbs. Without supplementation by (SUPP) this experience will count as a conclusive reason for this conjunction. After all, worlds in which I fail to have a headache are palpably closer than worlds in which I lose a limb. (Multiple like examples can be constructed. The form of such examples is developed in more detail in the next chapter. It is the case’s generalisability which makes it so pressing.)

Intuitively, however, the idea that this experience counts as a conclusive reason for this conjunction is nonsense (insofar as conclusive reasons in some sense justify belief in propositions for subjects).20 (SUPP) tells us why. (SUPP) rules out this result, as I might very well still have a headache were (P)’s second conjunct false. (Note that the second conjunct of (P) does not count as heavyweight by our definition of 1.6. This distinguishes my reductio from case-1-type examples: it is much more dialectically effective, in motivating a modification to Dretske’s account, to appeal to quotidian propositions, on account of their generalisability. The fact that the second conjunct of (P) is not heavyweight is developed in 3.1—3.3.)

My supplementary account of a conclusive reason hence provides a non-ad-hoc solution to case 1. I have not, as Hawthorne (2005: 34) scoffs: “scurr[ied] back to the epistemological laboratory to contrive an account which delivers the welcome result while avoiding the embarrassing one”. Rather my supplementation is necessary to avoid the absurdity into which an undeveloped Dretskean account leads us.

2.7 Hawthorne has two more imaginative cases involving propositions supposedly exemplifying the property of being heavyweight propositions for which we have conclusive reasons. I believe a (supplemented) Dretskean notion of conclusive reasons has the resources to accommodate them. Let’s quickly deal with them here.

Case 2: Suppose at the zoo I have experiences as of a bird flying around in a cage; and suppose that experience is my reason for thinking I am not looking at a cleverly disguised inanimate object in the cage. Suppose finally that it is much easier to make an inanimate object look like an animate object by making it turtle-like than by making it bird-like. Now Hawthorne posits that, while the proposition that I am not looking at an inanimate object cleverly disguised to look like an animate object is manifestly heavyweight, I have conclusive reasons for it: the ‘closest worlds’ where there is an inanimate object in the cage are worlds in which I fail to have a bird-like experience. In sum, there are two points that Hawthorne needs to make (here, and in the coming case 3). One is that, intuitively, reason plus perception cannot tell me that P is true; that is, that I am not looking at an inanimate object cleverly disguised to look like an animate object. Thus, by Hawthorne’s account of heavyweight propositions, the proposition (P) that I am not looking at an inanimate object cleverly disguised to look like an animate object, is heavyweight. The other point Hawthorne needs to make is that, when I have an experience as of a bird, this (R) counts as a conclusive reason for the proposition P. As noted, this second claim seems correct on Dretske’s account of conclusive reasons. In the nearest worlds in which P is false, I am looking at an inanimate object cleverly disguised to look like a turtle. So I do not have an experience as of a bird.21

Answer: Taken at face value, Hawthorne’s case 2 fails to set out a genuinely manifestly heavyweight proposition (and so is not ripe to be a counterexample to Dretske). Why not? If, as a matter of fact, the possibility of bird-like inanimate objects is as remote as Hawthorne stipulates, then I can (and do) know the proposition in question on the basis of my perceptual experience. (Whether I know that I know the proposition in question will depend on my knowledge of the germane objective facts about the circumstance of evaluation.) The possibility of bird-like inanimate objects in the cage is, by stipulation, too remote to be relevant, and it is of no matter that my evidence cannot discount such a counter-possibility. It is only if we — counter to how the case is set up — countenance bird-like inanimate objects in the cage as relevant alternatives that we fail to know the proposition in question. But on this supposition the proposition in question is manifestly heavyweight, and now Dretske’s conclusive reasons machinery gives the welcome result that we fail to know the proposition in question on the basis of our perceptual evidence. The basic point is that this supposition, contrary to Hawthorne’s dialectical aims, brings Hawthorne’s case 2 in line with standard Drestkean cases.

Case 3: I see a cookie. Suppose I have an experience as of a cookie five feet in front of me and, on this basis, form the belief that there is a mind-independent object roughly five feet in front of me. Again, Hawthorne opines, we have a (“highfalutin”) manifestly heavyweight proposition. On this first point, it must be conceded that there is some strong inclination to think that reason plus perception does not suffice for knowledge that there is a mind-independent object roughly five feet in front of me. Reason plus perception does not exclude the possibility that the causes of my perceptual experience are mind-dependent. And, moreover — the second point — Hawthorne shows it is a proposition for which we have conclusive reasons: the ‘closest worlds’ in which there isn’t a mind-independent object roughly five feet in front of me are worlds with laws like the actual world in which there is no physical object at all in front of me (and not worlds where “some bizarre metaphysics holds”). Therefore, on this analysis, in such close possible worlds I will fail to have an experience as of a cookie five feet in front of me. Put differently, in the nearest possible worlds in which there is not a mind-independent object roughly five feet in front of me, I do not have the same kind of perceptual experience as of a cookie roughly five feet in front of me.

Answer: My strategy, in a nutshell, is to side with Hawthorne on the second ‘conclusive reasons’ point, but to depart on the first ‘heavyweight proposition’ point. More specifically: as with case 2 I just do not see that we have a genuinely manifestly heavyweight proposition here.22 And on the intuitively plausible view of what counts as the closest possible world in this context of inquiry, we do indeed — as the Dretskean machinery predicts — have a conclusive reason for the proposition in question. The closest world in which there fails to be a mind-independent object roughly five feet in front of me is surely the world in which there is a mind-independent object failing to count as roughly five feet in front of me (and not either the world Hawthorne posits or worlds in which some bizarre metaphysics holds). Let’s suppose the cookie has been moved from its position; it is still in front of me, but not roughly five feet in front of me. Now I will not have an experience as of a cookie five feet in front of me when there is a mind-independent object failing to count as roughly five feet in front of me. And so I have a conclusive reason for this non-heavyweight proposition.23 The genuinely manifestly heavyweight proposition in this neighbourhood — indeed an entailment of Hawthorne’s proposition — is: there is a mind-independent object. Now the relevant alternative is a world in which there is no mind-independent object. (We are in the ‘bizarre metaphysics’ world, or some equally distant world.) And now I straightforwardly fail to have a conclusive reason for the heavyweight proposition in question.24

Assuming I am right on all this, the dialectical situation is as follows: Dretske’s conclusive reasons machinery, supplemented by (SUPP),25 can explain failures of closure satisfactorily by establishing the lack of conclusive reasons for heavyweight propositions.

3. Hawthorne’s Second Strand

3.1 In section 2.1, I mentioned the second strand to Hawthorne’s counter-challenge to Dretske. Hawthorne maintains we “all too often lack conclusive reasons for a priori consequences of known propositions, even though those consequences are not [heavyweight implications]” (2005: 35). He proceeds to construct two fun cases putatively establishing this point (36—7).26 Even if Hawthorne is granted this, insofar as he presents these cases as counterexamples to (better: problematic or challenging cases for) Dretske he commits an ignoratio elenchi.27 Of the following three theses, Dretske is — as pointed out at 1.6 — (and should be) committed to neither (I) nor (II), but only to (III):

(I) One lacks conclusive reasons for a proposition, p, iff the proposition is heavyweight.

(II) One lacks conclusive reasons for a proposition, p, only if the proposition is heavyweight.

(III) One lacks conclusive reasons for a proposition, p, if the proposition is heavyweight.28

3.2 Now Hawthorne has already — in the first strand — offered putative counterexamples to (III), and I have attempted to parry those counterexamples. In the second strand he goes on to argue that heavyweight propositions are neither necessary nor sufficient for failure of closure on Dretske’s account. Unfortunately for Hawthorne, however, these second strand cases count only against theses (I) and (II) — theses to which Dretske is not committed. In fact, these second strand cases provide the basis for further counterexamples to (Closure): grist to Dretske’s mill, one might think. Indeed, my reductio of the undeveloped Dretskean account in 2.6 is a further example of the phenomenon exemplified by these second strand cases (provided, of course, Dretske’s definition of conclusive reasons is supplemented with (SUPP)).

3.3 It would be better still for the Dretskean ‘anti-(Closure)’ project if Dretske could give an account of when non-heavyweight implications will lack conclusive reasons, but the project is hardly vitiated by the absence of any such account.29

4. Conclusion

4.1 My project is complete: (Closure) has certainly not been invalidated, but a sophisticated (suitably supplemented) Dretskean challenge thereto remains unmet. Deduction — pace Hawthorne (and Williamson) — may not always be a way of extending one’s knowledge.


1 As a schema it is assessable as valid/invalid (and not true/false).

2 And are so used throughout this chapter.

3 Precisely stating (Closure)’s relationship with transmission principles is a difficult thing to do. One way into this is to say that (Closure) is to be distinguished from transmission principles which, in addition to (Closure), require that one’s deduction furnishes one with — in a sense left intuitive here — a first-time warrant for Q. But, of course, (Closure) doesn’t explicitly mention warrant, so even this effort at a broad-brush statement may be too rough and ready to be particularly serviceable. Another way into this (anticipating the Conclusion’s discussion of Smith (2009)) is to distinguish between knowledge-closure (preservation) and knowledge-transmission: to reach our knowledge-transmission principle, perhaps we could simply say at the end of the principle: ‘one comes to know for the first time that Q’. (Quaere: does ‘comes to know’ already include that it is for the first time?)

4 (Closure) is defended by Stalnaker (1984), but Stalnaker’s conception of belief is unorthodox.

5 Hawthorne (2004) (tentatively) defends a position he calls sensitive moderate invariantism (and is often referred to as subject-sensitive invariantism) about knowledge on the back of consideration of a series of lottery puzzles. These puzzles “derive their force from the idea that […] some sort of closure principle holds for knowledge” (Hawthorne 2004: 31).

6 Nozick (1981: 240–42) also denies (K)’s (and (Closure)’s) validity. In the next chapter we come to engage directly with Nozick.

7 BIV = as before, Brain-in-a-Vat being fed pseudo-perceptual experiences by an evil scientist.

8 Klein (1995) gives an analysis of closure principles sensitive to different conceptions of evidential warrant. Note also — as a dialectical matter — Hawthorne (2005) does not contest this Dretskean conception of evidential warrant (notwithstanding it would not be his independently favoured way of viewing the matter).

9 The ‘~’ sign, here and elsewhere in this chapter, refers to negation. Although these formulations are both Dretske’s, one might, at first blush, think that they seem importantly different. One might think: the first formulation is naturally interpreted as saying that, in (all) nearby possible worlds where R is true, P is also true; but the second formulation (particularly the part in brackets) is more naturally interpreted as saying that, in all possible worlds where R is true, P is also true. Now it was not Dretske’s intention that these two formulations should be interpreted differently. Thus, one might ask: which formulation or interpretation would he have wanted? And — more on this later in this chapter — Dretske’s idea was that in (all) nearby possible worlds in which the proposition P is not true, the evidence proposition, R, is also not true.

10 What counts as a relevant alternative (strictly: a set of relevant alternatives), in this or that context, is an intuitive datum. There is no set of severally necessary and jointly sufficient criteria for relevance. We can say, though, if an alternative is a genuine objective possibility (a vague notion), it counts as relevant. (Heller (1999) defends Dretske’s notion and use of ‘relevant alternatives’ from attacks from Stine (1976), Cohen (1988), DeRose (1995) and Lewis (1996).) Finally, it is because only relevant (and not far-fetched) alternatives, for Dretske, need be ‘ruled out’ in order for a subject to have knowledge, that Dretske can be classed an infallibilist about knowledge.

11 In the relevant sense of empirical possibility. (Read this modal claim in, where appropriate, in subsequent counterfactuals.)

12 Note, for the (standard) contextualist, (Closure) is valid in all fixed contexts.

13 A heavyweight implication just is, I take it, a heavyweight proposition which is entailed by a quotidian proposition. To link this back to Chapter Two, it is not clear whether the notion of ‘heavyweight implication’ will distinguish between the conclusions of (EK)- and (EK*)-reasoning. One view would be that in both cases, the conclusion is not the sort of thing that one can know by perception and reasoning alone; but the difference is that in one case, and not in the other case, there is the possibility of gathering evidence that would favour the conclusion over its negation.

14 Dretske’s (2005b: 43–44) irenic reply to Hawthorne is, essentially, ‘confession and avoidance’.

15 So there is a crucial difference between this case and the (BIV) case. (BIV3) is ‘I am not a handless BIV’, which is equivalent to a disjunction: ‘Either I have hands or ~I am a brain in a vat’. Hawthorne’s example is a conjunction: ‘I have a headache and ~I am a brain in a vat’.

16 As we are not debating with the sceptic, we can join Dretske and Hawthorne in making the assumption that we are not presently in a BIV-world.

17 This is why (SUPP) is a genuine supplementation of the original conclusive reasons account. On the original account, and where P is a conjunctive proposition, the relevant modal relation must hold between R and P, and when P is true, each of P’s conjuncts is true; however it doesn’t follow that the relevant modal relation must hold between R and each of P’s conjuncts (and this is because it isn’t the case that whenever P is false, each of P’s conjuncts is false).

18 As the headache is internal to the BIV, I take it Putnam’s (1981: ch.1) objections to the capacity of a BIV to refer to external things are not germane.

19 In the next chapter I develop a like case against Nozick’s sensitivity condition. There I consider in detail a possible response to the case extractable from Peacocke (1986). Though Peacocke’s response is relevant here, I reserve treatment of the response until Chapter Seven.

20 This parenthetical claim is not explicit in Dretske’s account of conclusive reasons. However, insofar as Dretske affirms “knowledge is belief based on […] conclusive reasons” (2005a: 19), we might take the parenthetical claim to be in keeping with a Dretskean account of knowledge.

21 Before coming to my answer, there is a possible extrapolation from case 1. Arguably, P can be taken as equivalent to (P1 & P2), where P1: I am not looking at an inanimate object cleverly disguised to look like an animate turtle, and P2: I am not looking at an inanimate object cleverly disguised to look like an animate bird. Now, by parity with my treatment of case 1, we allow that, if P1 were false then I should not have evidence R. But we also point out that if P2 were false then I should still have evidence R. Thus, as before, R does not exclude relevant alternatives to P2, although it does exclude relevant alternatives to P1. My reason for not pursuing this answer lies in my doubts over whether P is indeed equivalent to (P1 & P2).

22 To anticipate my reasoning, and speaking metaphorically: the ‘highfalutin’ stain Hawthorne detects in the proposition in question, brought about by reference to a “mind-independent object”, is removed by the down-to-earth reference to “roughly five feet in front of me”. Everything turns on my rejecting Hawthorne’s claim that the proposition P meets the definition of a heavyweight proposition. It is important here that, in order not to beg the question against Hawthorne and in favour of Dretske, we must not take the fact that we have a conclusive reason for P to show that P is not heavyweight (that is, is not heavyweight by Hawthorne’s criterion).

23 There are delicate issues here about the fine-grainedness of perceptual experiences and judgments (see Schaffer 2003). But to reject my analysis here is to allow that one fails to have conclusive reasons for quotidian perceptual judgments, such as: there is a cookie roughly five feet in front of me.

24 It has been put to me that, in light of cases 2 and 3, Hawthorne perhaps ought to be operating with an account of heavyweight propositions (cf. 1.6 supra) relativised to perceptual reasons or to empirical investigations. In advance of any such account being developed further, however, I prescind from further comment thereon.

25 (SUPP) enters the picture only for Hawthorne’s case 1 (but cf. n. 21 supra).

26 For why Kripke’s (2011) ‘red barn’ case is not a candidate to be a ‘second-strand’ case, see Dretske (2005a: n. 4).

27 As I grant Hawthorne his point here — viz. Dretske allows for non-heavyweight implications not backed by conclusive reasons — I do not set out his intricate cases.

28 In fact, (Closure) would be denied with the weaker still:

(IV) Some heavyweight propositions lack conclusive reasons.

Without more by way of explanation, however, any such denial might seem unprincipled. Equally unmotivated would be the following (Closure)-denying principle which Hawthorne (2005: 37) considers:

If one knows P and deduces Q from P then one knows Q, unless Q is a manifestly heavyweight proposition.

Without being told what feature of manifestly heavyweight propositions allows them to fulfil this role, any such principle must seem ad hoc.

29 It must be conceded that Hawthorne seems to read Dretske as offering a kind of explanation of when, and only when, these failures of (Closure) arise, viz. they arise when, and only when, the implied proposition is heavyweight. An implied proposition’s being heavyweight is not, however, what failure of closure consists in. Rather, on Dretske’s account, what failure of closure consists in is that the implied proposition does not meet the conclusive reasons criterion for being known. It is hard to see the idea of a heavyweight proposition being at the heart of an explanation of failures of closure if there are plenty of examples of failures of closure that do not involve heavyweight propositions. Again, though, it must be conceded that Hawthorne will take himself to have argued already that there is something wrong with Dretske’s account because examples that seem to be relevantly similar (e.g. both seem to involve heavyweight propositions) can receive different verdicts from the conclusive reasons test.