Sensitivity-based tracking accounts of knowledge have faced three principal sources of intense resistance ever since their most well-known elaboration and defense in Nozick (Reference Nozick1981). The first and perhaps most notorious problem is that sensitivity, construed as a necessary condition for knowing, implies, absent further remedial conditions, that knowledge is not closed under known entailment. A second problem is that Nozickean sensitivity generates incorrect implications concerning inductive knowledge. The third problem is that sensitivity also generates incorrect implications regarding higher-level knowledge – specifically, knowledge that one does not believe falsely. Early articulations of this problem claim that Nozickean sensitivity is simply incompatible with higher-level knowledge. This is the core problem about (/objection to sensitivity and) higher-level knowledge. Later articulations claim that, even if (properly construed) sensitivity is compatible with some cases of higher-level knowledge, it is implausibly incompatible with others. Worse still, sensitivity is counterintuitively compatible with knowledge of strong but not weak higher-level propositions. This is the heterogeneity problem (Melchior, Reference Melchior2014, Reference Melchior2015, Reference Melchior2017).
Here I aim to resolve the problems that higher-level knowledge presents for sensitivity.Footnote 1 The key, following Dretske (Reference Dretske1971), is to shift focus from the questions of whether S’s belief is sensitive or whether S’s method of forming belief is sensitive to the question of whether S’s reasons are sensitive. A common dialectic has emerged with regard to all three of the problems mentioned. First, it is argued that belief sensitivity generates a problem. Second, the response is that closer attention to belief-forming methods is key to answering the problem. Third, the rejoinder is that the cure is as bad as or worse than the disease.Footnote 2 In addition, once the pandora’s box of belief-forming methods is flung open, broader problems emerge.Footnote 3 A better approach is to ask whether one’s actual reasons are sensitive to the truth that p, regardless of whether, if p were false, one’s belief would be based on those reasons, or one would believe that p, or one would have used their actual belief-forming method.
In §I, I set out the core and heterogeneity problems for sensitivity with regard to higher-level knowledge. I then develop Dretskean sensitivity (§II), which requires taking a stand on at least two key issues left unresolved in Dretske’s presentation. I then explain how Dretskean sensitivity can handle the higher-level knowledge problems (§III).
1. Higher-level knowledge problems for sensitivity
Nozick first sets down sensitivity of belief as a necessary condition for knowing. S knows that p only if, were p false, S would not believe that p (1981, 172ff. for development).Footnote 4
Belief sensitivity generates the core objection (Sosa Reference Sosa1999, 145; Vogel Reference Vogel2000, 610-11). Suppose that S knows that q. Surely, then, S sometimes knows p: that [S’s] belief that q is not false. However, if p were false, S would have a false belief that q. But because S would believe that q, S would believe that they do not have a false belief that q, violating sensitivity. The core objection is that belief sensitivity is logically incompatible with higher-level knowledge. I pause to emphasize that, obviously, there is logically no way out of this problem, formulated this way, for belief sensitivity.
In a footnote, Vogel points out that the problem involves closure failure, since q entails that the belief that q is not false. (Vogel puts it like this (substituting my “q” for his “X”): q entails (
$\neg $
(B(q) &
$\neg $
q) (Reference Vogel2000, n. 15).) As mentioned above, many sensitivity theorists accept closure failure – a point whose relevance to these proceedings is addressed further below, §III – but even for those willing to countenance closure failures, the logical incompatibility of belief sensitivity and higher-level knowledge is surely unacceptable. That is, it is one thing to deny closure and say that one is not always in a position to know that q, based on one’s knowledge that p and that p entails q; it’s another to say that knowing that q, for a specific class of q, is logically incompatible with knowing that p and that p entails q.
Becker (Reference Becker2006) and Salerno (Reference Salerno, Campbell, O’Rourke and Silverstein2010) respond by pointing out that belief sensitivity is compatible with higher-level knowledge, construed in a different way. Again, suppose that S knows that q. S can know p* that they have a true belief that q. How? If it were false that S has a true belief that q, either (a) S would not believe that q or (b) q would be false. On (b): Given that S knows that q, S would not believe that q if it were false. Either way, (a) or (b), S would not believe that q, and so S would not believe p* that they have a true belief that q.
One concern is that, even if the response reconciles belief sensitivity with some kinds of higher-level knowledge, it remains deeply problematic that one could never know that they do not have a false belief – as in the original formulations of the core problem. Melchior (Reference Melchior2014, Reference Melchior2015) rubs this in a little. He points out that to know that one has a true belief is to know the conjunction c: B(p) & p. Not knowing that one’s belief is not false is failing to know the disjunction d:
$\neg $
(B(p) &
$\neg $
p), i.e.
$\neg $
B(p) v p. Whereas Becker (Reference Becker2006) and Salerno (Reference Salerno, Campbell, O’Rourke and Silverstein2010) suggest that the former is a more faithful rendering of the relevant higher-level knowledge because it alone correctly implies that S (actually) believes that p, Melchior points out that the result is still embarrassing because disjunctions are weaker propositions and ought to be easier to know. Melchior labels this sort of problem “heterogeneity” not only because of the mixed implications, but also because the implications are counterintuitively mixed.Footnote
5
Just a few pages after laying out belief sensitivity, however, Nozick presents the following well-known example to show that the method by which one comes to believe must be taken into account. A grandmother sees that her grandson is well when he comes to visit. But if he were ill, his parents would tell her that he is at home and doing fine, so she would believe that her grandson is well even if he weren’t. The problem is that, while surely grandma knows that her grandson is well, her belief is insensitive – she would believe he is well even if he were ill.
Nozick responds to the problem by claiming that, in assessing whether a belief is sensitive, we must hold the believer’s actual belief-forming method constant. If it were false that the grandson is fine, grandma would not believe that he is fine via her actual method of seeing his healthy-looking visage. Wallbridge (Reference Wallbridge2016) argues that taking methods into account is key to reconciling sensitivity and higher-level knowledge and, later (Reference Wallbridge2017), that the approach can also resolve the heterogeneity problem. Melchior claims that the heterogeneity only gets worse on Wallbridge’s method-relative belief sensitivity approach.
Let us begin to investigate this dialectic with a revised Nozickean sensitivity condition:
RNS: S knows that p only if, were p false, S would not believe that p via [S’s actual belief-forming method] M.
Wallbridge argues that RNS is compatible even with knowing the weaker, disjunctive higher-level proposition that it is not the case that one has a false belief. He returns to Vogel’s (Reference Vogel2000, 609) original example, where S sees Omar, “a perfectly decent and straightforward sort of person,” wearing shiny white shoes, and Omar tells S that he has new shoes. S knows that Omar has new shoes, but, Vogel argues (as we have already seen), S does not know that they do not have a false belief. Wallbridge contests this conclusion in the following way. S believes that Omar has new shoes on the basis that Omar says so and they look new. This is then also part of the basis for their higher-level belief that they do not believe falsely. Given that Omar is trustworthy, it follows that “it would not easily have been the case that Omar lied to you or was otherwise mistaken” (Wallbridge Reference Wallbridge2016, 168). Therefore, if S were to believe falsely that Omar has new shoes, “this would have been on some other, less reliable, basis” (ibid.). Otherwise put, the claim is that worlds where S believes falsely by some other method are closer than those where S believes falsely by their actual method. In that case, even though S would falsely believe that their belief is not false, their higher-level belief would not be formed from their actual method, hence would not violate sensitivity, construed in a method-relative way. Wallbridge (Reference Wallbridge2017) then uses this strategy to argue that Melchior (Reference Melchior2014, Reference Melchior2015) is wrong to say that sensitivity has a heterogeneity problem with higher-level knowledge.
Melchior responds by formulating “Wallbridge’s condition” and arguing that it still implies unwanted heterogeneity.
Wallbridge’s condition: S’s belief that she does not falsely believe that p formed via method M is sensitive iff…W is fulfilled. W: Possible worlds where S falsely believes that p via some other method M* are closer than the nearest possible worlds where S false believes that p via M. (Melchior Reference Melchior2017, 5).
Melchior constructs cases where another method M* is available to S only in worlds that are further out than those where S uses M and forms a false belief. The recipe is simply to construct examples where any other method would be hard to come by. Melchior (ibid, 3-4) reimagines Omar as Robinson Crusoe stranded on an island alone with Freitag, playing the role of S, such that Freitag has no other way to know that Crusoe has new shoes except through Crusoe’s testimony. The upshot is that some higher-level beliefs in the “weaker” disjunctions are sensitive and some are not, even though, “Epistemically, there is no crucial difference between [the] cases” (ibid., 5). This only exacerbates the heterogeneity problem.
To sum up this section, Becker’s and Salerno’s approach makes logical space for sensitive higher-level belief (that one has a true belief) in response to the core problem, and Wallbridge’s approach responds both to the core and to the original heterogeneity objections by showing how higher-level beliefs (that one does not have a false belief) can be sensitive on a method-relative belief sensitivity account (RNS), assuming that, if one’s belief were false, one would not have formed it by one’s actual method. Melchior effectively says, “But that’s not always true,” and on that basis reissues the heterogeneity concern. A more satisfying dissolution of this updated version of the heterogeneity problem – which essentially asks why it should be that S can achieve higher-level knowledge that p if one’s first-level belief that q would have been formed from a different method if p were false, but not otherwise – would explain how one can have higher-level knowledge that p even if one were to use the same method if p were false. It would, of course, also answer the core objection.Footnote 6
A bit of reflection on the preceding reveals that, in pursuit of this kind of response, construing the sensitivity condition either in terms of belief or of method-relative belief is a dead end. However, when the question of sensitivity shifts from whether, if p were false, one would believe that p, or one would believe that p via one’s actual method, to whether one’s reason for believing that p would be the case, a more plausible and satisfying sensitivity-based account of higher-level knowledge emerges. I turn to that account now and then show how it solves the problem(s) of higher-level knowledge.
2. Reasons-based Dretskean sensitivity
We begin with Dretske’s initial presentation of a conclusive reason R:
-
1) S knows that P and he knows this on the basis (simply) of R entails
-
2) R would not be the case unless P were the case (Dretske Reference Dretske1971, 1).
We set aside the question of whether having such a reason is also sufficient for knowing. Dretske discusses this in detail and concludes with a qualified “yes” (ibid., 16ff.). We shall treat such reasons only as necessary for knowing, since that is the source of the higher-level knowledge problem.
For the remainder of this section, I will draw on Dretske’s own words to develop an account of reasons-based sensitivity, though I do not claim that I am interpreting Dretske as he intended. I aim to be clear but relatively brief, since I have presented a fuller explication of Dretskean reasons-based sensitivity in another paper (Becker Reference BeckerMS).
There is an ambiguity in Dretske’s initial statement of the nature of conclusive reasons (2) and his first gloss on them: “For if (2) is true, we are entitled…to deny that…given R…not-P might be the case” (ibid., 1). A fairly straightforward reading construes this as a safety condition on knowing: If R were true, p would be true. But later, in his treatment of the lottery problem, where one does not know that one’s ticket will lose, even given its enormous likelihood, Dretske characterizes a conclusive reason as one that is sensitive: “Adjusting the word order…to suit the example we have…If S were going to win the lottery [if it were false that S will lose], his chances of winning would not be 1/m (m being the number of tickets sold)” (ibid., 4). This is false, which is why S does not know that they will lose the lottery. Here is the sensitivity interpretation of a conclusive reason: If it were not the case that p, R would not be the case.
From here on, I take the liberty of construing Dretske’s notion of a conclusion reason as one that is sensitive. I do not claim this was clearly his intention. Rather, my aim is to show that doing so positions us to see how Dretskean sensitivity, or at least my development of it, generates acceptable implications regarding higher-level knowledge where RNS does not.Footnote 7
Interpreting conclusive reasons as sensitive only tells us something about what makes them conclusive, not what they are qua reasons or how they contribute to S’s knowing that p. To these ends, Dretske elaborates:
-
S has conclusive reasons, R, for believing P if and only if:
-
A. R is a conclusive reason for P [R would not be the case unless p],
-
B. S believes without doubt, reservation, or question that P is the case, and he believes this on the basis of R,
-
C.
(i) S knows that R is the case or
-
(ii) R is some experimental [sic] state of S… (ibid., 12-13)
-
Two small points. First, on (C)(ii), the overall context of the discussion suggests that it should read “experiential” rather than experimental. Second, since our main interest is in sensitive reasons as a necessary condition for knowledge, we set aside any question about Dretske’s characterization of the strength of S’s belief (B), though S must believe that p on the basis of R.
What kind of thing is R? R is either a proposition (C)(i) or an experiential state (C)(ii) which, when conclusive, stands in a specific modal relation to some known proposition – perhaps p, perhaps some other reason in the inferential chain leading to p. (I’ll come back to this, which is important.) To have a conclusive reason R to believe that p is for R to be the causal basis of one’s belief that p, for example when either S believes that R (occurrently or dispositionally) or when R is “the way things look” (ibid., 15) on the basis of which S believes that p (clause (B)).Footnote 8 When R is S’s reason for p, S may not “be in a position to give R as his reason…He may find it difficult or impossible to give verbal expression to R. He may have forgotten R” (ibid., 14). Whatever the explanation, R need not be cognitively accessible to S. Distinguishing the questions whether R is a conclusive reason (A) for p – that is, whether R is sensitive to or tracks p – and whether S would believe that p on the basis of R if p were false is important for understanding the advantages of Dretskean sensitivity over RNS. We are not concerned with whether S would have R if p were false, but if R would be the case.
Another interesting question arises from the two subclauses under (C). To the concern that the appearance of “know” in (C)(i) is circular, Dretske says the circularity “can be eliminated by recursive applications of the three conditions until (C) (ii) is reached” (ibid., 13). Dretske requires that, whatever one’s reasons, they are ultimately grounded in experience. One’s basic reasons, then, are like Nozick’s methods – dependent on “upshot in experience” – whether or not one is consciously aware of that upshot.
Importantly, however, the structure of Dretske’s account of conclusive reasons can be exploited to solve problems that afflict Nozickean methods. Dretske’s characterization of having conclusive reasons is recursive with a “foundationalist” structure, of which experience forms the base. This allows that one’s belief that p can be based on R1, that R1 can be based on R2,…, that Rn-1 can be based on Rn, and (finally) Rn on an experiential reason Re. This in turn opens the possibility that one knows that p on the basis of R1, knows that R1 on the basis of R2, R2 on the basis… of Re, such that each reason is sensitive to (or simply “tracks”) what it is a reason for, without its being the case that R e is sensitive to, tracks, p. This is another ambiguity in Dretske’s account, which again I will exploit for my purposes. One can read Dretske as saying that knowledge that p requires one’s basic experience to track p. However, not doing so is also consistent with his text, and it opens a promising avenue for sensitivity theorists.
I mentioned at the outset that focusing the question of sensitivity on reasons rather than beliefs and dismissing the question of whether S would have (conclusive) reasons R in a counterfactual situation in favor (simply) of whether R would be the case constitute the two central advances of Dretskean sensitivity over Nozickean sensitivity (even in the latter’s best higher-level-knowledge-friendly version, RNS). The final key move is to resolve the aforementioned second ambiguity in our favor and explicitly unpack the structure of reasons underlying a single higher-level belief conclusion to reveal the possibility that S can achieve higher-level knowledge that p (that they do not have a false belief) without S’s actual experience tracking p, which is anticipated neither in Nozick, nor, from what I can see, among his defenders.Footnote 9 In the following section, I illustrate how reasons-based Dretskean sensitivity (hereafter RDS) handles the core problem and the heterogeneity problem.Footnote 10
3. RDS’s more satisfying account of higher-level knowledge
To set the stage, recall first that Becker and Salerno have already shown how one can have higher-level knowledge in cases where, if it were false that one has a true belief that p, one would not believe that p. But this does not reconcile sensitivity with knowing that it is not the case that one has a false belief, which is the core problem and, together with the Becker and Salerno approach, raises the original heterogeneity problem. Recall second that Wallbridge has shown how to reconcile RNS sensitivity with knowing that it is not the case that one has a false belief, provided that in the closest worlds where one does have a false belief, one uses a different belief-forming method, raising another heterogeneity problem.
An adequate response to the core problem will also alleviate Melchior’s concerns about heterogeneity. If it can be shown how one can have a sensitive higher-level reason for believing that one’s belief that p is not false, both when one’s method of believing p would be the same if p were false and when it would not be the same, then the concern that appealing to alternative methods in counterfactual worlds (in order to rescue sensitivity) generates further heterogeneity does not arise.
3.1. What is the core problem again?Footnote 11
I take the core problem to be that sensitivity is logically incompatible with knowing that one’s belief is not false, explained how Becker and Salerno do not address this problem specifically, and explained Melchior’s criticism that Wallbridge’s solution to the core problem leads to heterogeneity. I noted early in §I, however, that Vogel sees the core problem as (also?) involving a violation of closure, because p itself, which S knows, entails that S’s belief that p is not false.
If one takes closure violation to be the central issue, the RDS approach may offer relief. S knows that Omar has new shoes because, if that were false, S’s reason (Omar said so) would not be the case. S knows that their belief that Omar has new shoes is not false because, if it were false and S did have a false belief, S’s known, higher-level reason (Omar has new shoes) would not be the case, even though in that counterfactual world S would believe Omar has new shoes, perhaps even because Omar said so!
Sensitivity theorists may be reluctant to accept the offering, however, because it may smack of Moorean insouciance (or worse still, begging the question). “How do you know that Omar has new shoes [/that you have hands]?” Because he said so [Because look!]. “But how do you know that your belief is not false [/that you’re not being deceived by how things look]?” Because what I believe is true! Most sensitivity theorists notoriously reject closure, and I submit that this is because they think that the epistemic requirements on knowing q, even when one knows that it follows from p, are sometimes stronger than knowing that p. According to this line of thinking, knowing that one is not a BIV takes more than knowing that one has hands. Achieving higher-level knowledge sometimes takes more than first-level knowledge that entails it. In the RDS idiom, it takes further reasons. In the remainder of this section, I articulate an alternative RDS account that coheres with these commitments.Footnote 12
3.2. RDS treatment (A): preliminaries
Preliminaries (1): S has first-order knowledge. Assume that S knows that q: Omar has new shoes. (Note that I am back to using “q” for the first-level proposition here, because the central question is how and whether S knows that p: that their belief that q is not false.) S’s reason for believing that q, Rq, is that Omar said he has new shoes and the shoes Omar is wearing look new. If q were false, Rq would not be the case. This much is granted even by opponents of sensitivity. For S to know that q, it must also be true that Omar is not lying or mistaken, but S need not know that.
Preliminaries (2): stronger requirements on higher-level knowledge. Does S know that their belief that q is not false? Because it is a condition on knowing that q that Omar is not lying or mistaken, for S to achieve higher-level knowledge that their belief is not false, arguably, S must know that the condition is satisfied – or so I think many sensitivity theorists would agree, as explained in the previous subsection. The question – But how do you know your belief is not false? – can be understood as generating the implicature that maybe Omar is lying or mistaken, to which the reply “Because Omar has new shoes” will ring hollow. Extant responses to the higher-level knowledge do not try to account for this. Becker’s and Salerno’s reconciliations of sensitivity with higher-level knowledge do not depend on one’s being in an epistemic position any stronger than what is required for first-order knowledge, for example that q: Omar has new shoes. Their view is that, if S’s belief that they had a true belief that q were false, S would either not believe that q anyway, or q would be false, but in the latter case, because, ex hypothesi, S actually knows that q, S would not believe that q. Either way, S would not believe that q and so would not believe that they believe that q. Wallbridge’s response to the core problem is, essentially, “Maybe S doesn’t know that Omar is not lying or mistaken, for if Omar were lying or mistaken, S would still believe him, but that world is further away than one where S uses a different method.” Sensitivity theorists who countenance closure failures in cases where requirements on knowing that q are stronger than those on knowing that p and that p entails q should welcome the incorporation of this thought in their response to the higher-level knowledge problems.
3.3. RDS treatment (B): application of RDS
What is S’s (Dretskean) reason for believing p? Let’s ask S: You believe Omar has new shoes because he said so, but how do you know your belief is not false? S gives their reason, Rp: Omar is not lying or mistaken. (1) If p were false, Omar would be lying or mistaken. Rp is sensitive to, or tracks, p. Crucially, I am not claiming (and RDS does not imply) that if p were false, S would not believe Rp or would have some other basis for belief. That would be just another version of Nozickean sensitivity. Applying RDS as developed above, I am only pointing out that Rp tracks p. Still, for Rp to be a Dretskean conclusive reason for p, and to deliver the advertised more compelling response to critics, S must know Rp.Footnote 13
Does S know that Rp, that Omar is not lying or mistaken? Let us ask S: What is your reason for believing Rp (that Omar is not lying or mistaken)? S replies with RRp: Omar is trustworthy. (2) If Rp were false, RRp would not be the case. RRp tracks Rp. If Omar were lying or mistaken, it would be false that Omar is trustworthy. Here again, S may still believe that Omar is trustworthy if Omar were lying or mistaken, but S’s actual reason RRp tracks Rp. The closest worldsFootnote 14 where Omar is lying are worlds where Omar is not trustworthy. Does this not contradict the previous paragraph? No. The worlds relevant to assessing the counterfactual “If S’s belief that p were false,” are not those relevant to assessing “If Omar were lying or mistaken.” This is an important and potentially controversial point. I will come back to it after rounding off the RDS treatment.Footnote 15
Which takes us, finally, to the question: Does S know RRp, that Omar is trustworthy? S believes Omar is trustworthy based on Re, experience with Omar asserting truths. (3) If RRp were false, Re would not be the case. Re tracks RRp. ((3) is true if S knows RRp. It could otherwise be false. When (3) is false, it just shows that S does not know that Omar is trustworthy, and therefore does not know that Omar is not lying or mistaken, and therefore does not know that their belief is not false.)
Now for a summary to make the results explicit. S knows that p (they do not have a false belief that Omar has new shoes) on the basis of Rp (Omar is not lying or mistaken). That is, (1) if p were false, Omar would be lying or mistaken. Rp tracks p. S knows that Rp (Omar is not lying or mistaken) on the basis of RRp (Omar is trustworthy). That is, (2) if Rp were false, RRp would not be the case. RRp tracks Rp. S knows that RRp (Omar is trustworthy) on the basis of Re (experience with Omar asserting truths). That is, (3) if RRp were false, Re would not be the case. Re tracks RRp. And yet, it could easily be the case that (4): if p were false, Re would still be the case and that S would believe that it is not the case that p is false. Indeed, it could even be that if Rp were false – if Omar were lying or mistaken – Re would still be the case. What matters is that each reason in the chain of reasons tracks that for which it is the immediate reason, not that one’s actual experience tracks the truth.Footnote 16 It is not required that S would not have believed that p, or would have had a different method or different set of experiences, if p were false. The recursive structure of conclusive reasons and focus on the sensitivity of the reasons themselves allow the RDS account to succeed where belief sensitivity and RNS fail to reconcile sensitivity and higher-level knowledge.
3.4. RDS treatment (C): explication and clarification
The RDS response now complete, I turn to two concerns that spring to mind with the RDS treatment of higher-level knowledge. The most prominent is a question about the evaluation of the counterfactuals. The other concern is whether achieving higher-level knowledge requires such an elaborate structure of reasons. I’ll take the second concern first.
One might wonder why there should be so many layers of reasons in a typical case of higher-level knowledge. The first thing to note is that higher-level knowledge is conceived here as a greater epistemic achievement than simply knowing that p. The second thing is that, while perhaps not all cases of higher-level knowledge require as many layers of reasons, in the case illustrated, a compelling response to both the core problem and heterogeneity problem requires that S knows that Omar is not lying or mistaken (or can know it – keep in mind that sensitivity, even as construed as RDS, is a necessary but not sufficient condition). S must have some reason for believing this, and simply having had a set of past experiences, or observations, by itself does not constitute a reason. Typically, S must generalize in some way, for example, infer that Omar is trustworthy, and use it as a reason for believing that Omar is not lying or mistaken. The case under consideration has the structure of an inductive inference (conscious or otherwise) to a particular conclusion: observation→generalization→application to particular instance. In short, that there should be a somewhat sophisticated structure of reasons for what is a fairly sophisticated epistemic achievement should not, on final consideration, be surprising.
I imagine two separate but perhaps related questions concerning the evaluation of the counterfactuals. The first is this: How can Rp track p, RRp track Rp, and Re track RRp, while Re does not track p? (A similar question can be raised with regard to the potentially closure-saving strategy briefly articulated near the beginning of this section.) The basis of the answer is that counterfactuals are widely regarded as not transitive. (See Haze Reference Haze2023 and Brogard and Salerno Reference Brogard and Salerno2008 for possible explanations.) A simple example: (a) If I were a fireman, I would wear red suspenders. (b) If I were to wear red suspenders, my outfit would look funny. (c) If I were a fireman, my outfit would look funny. (a) and (b) are (or can be) true compatibly with (c) being false.Footnote 17 When the set of worlds relevant to assessing the conclusion in a hypothetical syllogism (e.g. worlds where I am a fireman) is not a subset of the set of worlds relevant to assessing one or more premises (e.g. worlds where I am not a fireman, but I wear my typical clothes, as in (b)), it can turn out that the syllogism is not valid (Haze Reference Haze2023, 241).
As applied to the Omar case, worlds relevant to (4), where p is false (S does believe falsely that q), may not be among the set of worlds relevant to (3), where Omar is untrustworthy. In the closest worlds where p is false, somehow, what Omar said was incorrect. Period. (Omar is nevertheless trustworthy and S has their actual experience with Omar’s truthfulness, which explains why S comes to believe what Omar says, albeit falsely.) But in worlds where Omar is untrustworthy, S doesn’t have their experience with Omar’s truthfulness.
The explanation of lack of transitivity just adumbrated is somewhat brief, perhaps too abstract, and arguably also ducks the second, more pressing question, which has more to do with (2) than (3). That is, the explanation implies (and relies upon) the claims that (1) if S had a false belief that q, Omar would have lied or been mistaken but would still have been trustworthy (and S would have had their experiences with Omar’s truthfulness), whereas (2) if Omar would have lied or been mistaken, he would not have been trustworthy (and S would not have had their experiences with Omar’s truthfulness). Some will find this contentious. Because the fireman example is less contentious, perhaps we can gain insight from it.
In the not-so-distant worlds where I wear red suspenders, my outfit looks funny. The explanation is that my actual clothes don’t go with red suspenders. But in the more distant worlds where I am a fireman, I wear red suspenders and my outfit would not look funny. The explanation is that in such faraway worlds I also wear fireman gear. In the not-so-distant worlds wear Omar speaks falsely (about plain facts in relation to which he is in excellent epistemic position), he is untrustworthy. The explanation is that trustworthy people do not utter falsities (about plain facts in relation to which they are in excellent epistemic position). But worlds where S believes falsely that Omar has new shoes are more distant, and in them Omar lies or is mistaken and is trustworthy. S believes falsely because Omar is trustworthy.
Consider the illustration below. In the actual world: my outfit does not look funny (a matter of controversy I suppose, but let it stand) and I don’t wear red suspenders; Omar tells the truth and is trustworthy. As one moves out from the actual world, my outfit’s looking funny naturally “comes with” the red suspenders; Omar’s untrustworthiness naturally “comes with” his lying or being mistaken. But as we move further out still, something else is different: I am a fireman, which naturally “comes with” red suspenders so my outfit no longer looks funny; S has a false belief, where S’s believing Omar’s false utterance naturally “comes with” or is explained by Omar’s being trustworthy (at least not being untrustworthy).Footnote 18
Illustration
I am a Fireman/S has a False Belief that their belief is not false, F/FB
I wear Red Suspenders/Omar Lies or is Mistaken, R/OLM
My outfit Looks Funny/Omar is Untrustworthy, LF/OU
I do not claim that my reading of the counterfactuals is unquestionably true, but I do claim that it is defensible, that other cases of intransitivity of counterfactual conditionals support it, and that the explanations of intransitivity are analogous.
4. Concluding remarks
Sifting through all the details, the main objective of this paper is to provide a framework for answering the various criticisms that sensitivity makes a mess of higher-level knowledge. Taking the bull by the horns, I grant, in accord with Melchior and in deference to the spirit of the core objection, that whether or not one achieves higher-level knowledge should not depend on whether they would have used a different method in coming to a first-order belief if their higher-level belief were false. The more specific goal then is to show how sensitivity is compatible with higher-level knowledge even though the closest worlds where one falsely believes that their belief is not false are worlds where their first-order belief has the same basis as in the actual world.
The goal is achieved through two Dretske-inspired moves. The first is the shift in focus from the sensitivity of either belief or method-relative belief to the sensitivity of reasons. The second involves unpacking the recursive structure of reasons. Putting these ideas together, I have shown how S can know p (that their belief is not false), when they have a reason Rp that tracks p, can know Rp when they have experiences that track Rp, even when their experiences (and methods and beliefs) do not track p. The very possibility derives in general from the intransitivity of counterfactuals. At the end of the previous section, I offered an explanation of how intransitivity applies to cases of higher-level knowledge.Footnote 19
Open access
