3.1 The Argument from Reminding

Here then is a detailed version of the first argument to the conclusion that the bank will be assumed to be more likely to change its hours in the high standards case. Plausibly, when we don't think of an error-possibility, we tend to act as if we thought that its likelihood is zero even if we already know (in some sort of unconscious or tacit way) that the likelihood is not zero. For example, suppose that you know full well that robins and bluebirds are equally likely to be seen in your area. Suppose further that you see an orange-breasted bird that, for all you see, is either a robin or a bluebird. If you don't think of the possibility that the bird is a bluebird (maybe because it's been a while since you last saw a bluebird), you will presumably still say, “That's a robin!” This is so because you treat the likelihood of unthought-of possibilities as zero.Footnote ⁷ When subjects read the low standards case, they similarly don't think of the possibility that (normal) banks change their hours. Hence, given the previous observation, they will treat the likelihood of this possibility as zero. Given (NP), they will project this likelihood into the scenario. Thus, they will assume that the likelihood of the possibility that Hannah and Sarah's bank changes its hours is zero in the low standards case.

In the high standards case, the situation is different. It seems clear that once we are reminded of a known-to-be-likely possibility, we no longer treat its likelihood as zero even if we haven't been taking it into account before. For example, when I remind you, “It could also be a bluebird,” you'll immediately retract your original assertion of “That's a robin!” because you remember that this possibility is likely.Footnote ⁸ Similarly, when subjects read the high standards case, they are reminded of the possibility that (normal) banks change their hours because this possibility is mentioned in the scenarios. Hence, they also realize that its likelihood is, though maybe low, certainly not zero. Again, given (NP), they will project this assumption into the scenario and thus assume that it is likely at least to a certain degree that Hannah and Sarah's bank changes its hours. So, the assumed likelihood of this possibility will be higher in the high than in the low standards case.Footnote ⁹

3.2 The Argument from Implicatures

Here is a detailed version of the second argument for this conclusion. It is based on the idea that, first, Sarah implicates that it is likely to a certain degree that the bank changes its hours and, second, that this implicature will be assumed to be true in the high standards case given (NP). Let's discuss these claims in turn.

Why should Sarah implicate that it is likely to a certain degree that the bank changes its hours? Here, we can draw on the work of Dougherty and Rysiew (Reference Dougherty and Rysiew2009). They pursue a project that is closely related to mine, namely, they try to explain, from an invariantist (intellectualist and fallibilist) point of view, why so-called “concessive knowledge attributions” sound odd (a concessive knowledge attribution being a claim of the form “I know that p, but it is possible that q” where q entails not-p). We need not bother about the details of their account here. All that is relevant is that, in the course of their discussion, they plausibly argue for the following claim: “In saying that p is possible one implies that there is some real chance that p” (2009: 130). (Dougherty and Rysiew do not say much about what a “real” chance is supposed to be. Still, they assume that, if there is a real chance of error, then this “may well be enough to prevent one from knowing.”) Following Dougherty and Rysiew, the above implicature can be derived as follows:Footnote ¹⁰ The mere existence of an error-possibility will not be relevant for the question of whether someone knows that a certain proposition is true. (Otherwise, we would presumably be wedded to a fairly strong form of skepticism.) So, when Sarah says, “Banks can always change their hours,” she will say something irrelevant to the extent that all she says is that this possibility exists. The irrelevance of her claim will thus trigger the search for an implicature. And this implicature plausibly is that the possibility that banks change their hours not only exists, but also is likely to a relevant degree.Footnote ^11, Footnote ¹²

Why should readers of the bank cases assume that this implicature is supposed to be true? We do not normally try to mislead people. So, given (NP), Sarah will have to be assumed to believe what she implicates (that there is a real chance that the bank changes its hours). Now, in the absence of misleading evidence, we normally hold true beliefs about our everyday concerns (such as the opening hours of our bank). So, given that no reason is given in the bank cases to think that Sarah should have been misled in any way, and given (NP), Sarah's belief will be considered true. Thus, we have a second argument for the conclusion that the possibility that the bank changes its hours will be assumed to be more likely in the high than in the low standards case.Footnote ¹³

3.3 The Argument from Normal Cognitive Processes

Here is a detailed version of the third argument for this conclusion. As Bach plausibly points out, if “our cognitive processes are operating well, generally the thought of a possibility contrary to something we're inclined to believe occurs to us only if it's a realistic possibility, not a far-fetched one” (Bach Reference Bach, Campbell, O'Rourke and Silverstein2010: 121). Thus, the possibility that the bank changed its hours should normally occur to Sarah only if it is likely to a certain degree. So, given that it does occur to Sarah in the high standards case, we have to assume that it is likely there in order to preserve normalcy. Hence, given (NP), we have a further argument for the claim that the possibility that the bank changes its hours will be assumed to be less likely in the low than in the high standards bank case.Footnote ¹⁴

Note that the presently described mechanism is importantly different from the implicature mechanism above. For example, the implicature mechanism arguably won't apply when we consider bank cases where the error-possibility is not mentioned in the high standards case, but only considered in thought by the knowledge-ascribing subject. After all, thoughts (as opposed to mentionings) plausibly don't have implicatures.Footnote ¹⁵ The present mechanism, however, straightforwardly does apply to these cases, for, to repeat, an error-possibility normally occurs to somebody (in thought or in speech) only if this possibility is likely.

To sum up, we have seen that there are three straightforward reasons to hold that the possibility that the bank changes its hours will be assumed to be less likely in the low than in the high standards bank case. Given that, the invariantist is free to say that Bill's epistemic position is good enough for knowledge only in the low standards case. Thus, she has a straightforward explanation of the Contextualist Data: the manifested intuitions are correct with regard to the bank cases as they are interpreted by their readers.Footnote ¹⁶

4.1 Skepticism

Here is the first objection to projective invariantism. Schaffer and Knobe (Reference Schaffer and Knobe2012: 27) object to a similar position that it would commit the invariantist to “the quasi-skeptical view that in fact Hannah [in our case, Bill] does not know that the bank will be open on Saturday” and suggest “that most invariantists will already reject the strategy at this point.”Footnote ¹⁷ Since projective invariantism also entails that Bill doesn't know that the bank will be open in the high standards case, they would presumably level the same objection against this view. The reasoning could go as follows: In ordinary conversations, we generally ascribe knowledge to subjects whose epistemic position is the same as, or even weaker than, Bill's in the high standards case. So, saying that Bill fails to know that the bank will be open in the high standards case commits one to the thesis that our ordinary practice of ascribing knowledge is generally mistaken. This result, however, looks like a form of skepticism that almost everybody wants to avoid.

To respond, I think that there is just no basis for the assumption that, in general, we ascribe knowledge to subjects whose epistemic position is the same as, or even weaker than, Bill's in the high standards case. The projective invariantist, at least, has reasons to reject this assumption: According to the Contextualist Data, we would intuitively judge that it is correct for Hannah in the high standards case to say, “Bill doesn't know that the bank will be open.” Thus, assuming invariantism, we have a straightforward reason to hold that, in general, we wouldn't ascribe knowledge to subjects whose epistemic position is the same as, or even weaker than, Bill's in the high standards case.

Of course, according to the Contextualist Data, we would also intuitively judge that it is correct for Hannah in the low standards case to say, “Bill knows that the bank will be open.” However, for the projective invariantist, this will show at best that we would ascribe knowledge to subjects whose epistemic position is the same as Bill's in the low standards case. And this result is compatible with the result from the previous paragraph that we wouldn't ascribe knowledge to subjects whose epistemic position is the same as Bill's in the high standards case.

4.2 Making the Likelihood Explicit

Here is a second potential objection to projective invariantism. Stanley alludes to this objection when he writes that “even when we have full knowledge of the likelihood of various counter-possibilities, it does not affect our judgments” (Stanley Reference Stanley2005: 101). Applied to projective invariantism, the objection could be developed as follows: Projective invariantism crucially relies on the idea that the bank cases are underspecified when it comes to how likely it is that the bank changes its hours. For this allows readers to fill in the low and the high standards case in different ways. Thus, if projective invariantism holds, the Contextualist Data should disappear once we explicitly stipulate how likely it is that the bank changes its hours in the bank cases. To make the Contextualist Data disappear, it should suffice, for example, to end the high standards case with a claim to the effect that the likelihood of the possibility that the bank changes its hours is zero. Stanley's quote above can be seen as the objection that this prediction is mistaken.

To respond, I think that Stanley is just wrong about this latter judgment. At the very least, the judgment is unfounded. It seems quite plausible that the Contextualist Data would disappear if the scenarios were specified in the mentioned respect. Suppose, for example, that we end the high standards case with claims along the following lines:

It seems not at all clear that, once we add the above paragraph, people would still agree that Bill fails to know that the bank will be open in the high standards case.Footnote ¹⁸

4.3 Making Sameness Explicit

Here is a slight variation on the previous objection. Projective invariantism no longer applies once we explicitly stipulate that Bill's epistemic position is the same in the low and the high standards case after having described these cases. (Similarly, the view no longer applies when we consider a single scenario containing the dialogues from both the low and the high standards case.Footnote ¹⁹) Even so, the Contextualist Data would not disappear. Thus, projective invariantism fails to explain all relevant data.

To see that this objection fails, we have to get clear on what exactly the Contextualist Data amount to. I grant that, even when the bank cases are presented in the just proposed way, the following pattern would emerge: While reading the low standards case (before we arrive at the high standards case and the stipulation that Bill's epistemic position is the same), we would judge that the knowledge ascription in the low standards case is true. Once we have read the high standards case and the stipulation, we would judge that the knowledge denial in the high standards case is true. This pattern, I think, is driving the Contextualist Data. And projective invariantism straightforwardly explains it: The projective invariantist can simply argue that we change our interpretation of the scenarios once we are reminded of the error-possibility in the high standards case.

Projective invariantism would be in trouble only if, even after having read the high standards case and the stipulation, we would still say that the knowledge ascription in the low standards case is true. It is very much unclear, however, whether this would be so. Even DeRose (Reference DeRose2009: 2) admits that to obtain the Contextualist Data we should consider the low standards case “without also thinking about” the high standards case (and vice versa). The point can be strengthened by the observation that most people would grant so-called “retraction data.”Footnote ²⁰ Most people would agree that, once epistemic standards go up, we do not only say that we don't know this or that proposition, we also reject our earlier claims to the effect that we do know the proposition. In the same way, it seems very plausible that, once we have read the high standards scenario, we will no longer say that the knowledge ascription in the low standards case is true.

4.4 Far-Fetched Alternatives

Here is another closely related objection. One could argue that we would obtain the Contextualist Data even if we let Sarah mention an alternative that we don't consider likely at all. For example, one could argue that the Contextualist Data would still be present if Sarah mentions the possibility, say, that a meteor destroys the bank before Saturday. This result would be problematic because projective invariantists explain the Contextualist Data at least partly on the grounds that we do consider the alternative in the high standards case likely (and are reminded of that once the possibility is mentioned).

Again, my response is just to deny the alleged data. In fact, I think the real data favor my proposal. Gerken seconds this response in the following passage:

If Gerken is correct, it is indeed a good thing that projective invariantism does not predict contextualist effects when very far-fetched alternatives are mentioned; there simply are no such effects.Footnote ²¹

4.5 Skeptical Arguments

The following is a further objection in the vicinity of the previous considerations. Suppose a skeptic, instead of merely making an error-possibility salient, presents arguments to the conclusion that we don't know that the error-possibility does not obtain and then appeals to epistemic closure to reach the skeptical conclusion that we don't know what we thought we know. Suppose, for example, that the skeptic points out that we don't know that we are not brains in a vat because our sensory experiences would be exactly the same as they are if we were brains in a vat. Suppose further that she now appeals to one or the other epistemic closure principle to conclude that we don't even know we have hands. One might be inclined to think that people tend to respond to such arguments by granting that they don't know they have hands. And it might further be held that projective invariantism is unsuited to explain this datum. In support of this latter contention, Nagel, for example, argues that, when

I fully agree with Nagel that projective invariantism cannot account for the fact (if it is fact) that we retract knowledge claims in the face of skeptical arguments, at least when these arguments involve far-fetched alternatives such as that of being a brain in a vat. For, as indicated by Nagel, none of the mechanisms posited above to account for the Contextualist Data applies to these reactions. First, we will not be reminded that it is likely to a relevant degree that we are brains in vats when this possibility is pointed out to us. After all, we presumably consider this alternative extremely unlikely. Relatedly, the skeptic may happily cancel any implicature to the effect that this possibility is likely without undermining her case. Finally, it seems clear that the skeptical error-possibility comes to the mind of the skeptic not because it is likely but because the skeptic has been engaging in philosophy.

But how problematic is the result that projective invariantism cannot explain our assumed reactions to skeptical arguments? I don't think it is very problematic. After all, it seems to be very much unclear that we do indeed tend to retract knowledge claims in the face of skeptical arguments. Many, if not most people are entirely unmoved by such considerations.Footnote ²² What does seem correct is only that some people become convinced by skeptical arguments (some philosophers, for example) and that, for most people, it is difficult to see where exactly skeptical arguments go awry (even if most people think that these arguments just have to go awry at some point or other). Admittedly, projective invariantism cannot explain these residual data either. But this result is problematic only if there are no plausible accounts of these data the projective invariantism could adopt. This is not the place to argue that there are such accounts. It seems clear, however, that the burden of proof is on those who want to say that there are none. For example, the projective invariantist could argue that skeptical arguments may seem convincing because they involve one or the other non-obvious argumentative fallacy.Footnote ²³

4.6 Mere Stakes Effects

The next and final worry has it that we would obtain the Contextualist Data even if we only changed the stakes between the low and the high standards case and not the mentioned error-possibilities.Footnote ²⁴ This might again seem to undermine my proposal, for if no error-possibility is mentioned, we arguably won't be reminded of an error-possibility, the relevant implicature will also not be present, and there will be no reason to think that an error-possibility occurred to any of the subjects involved in the bank cases.

Here are my responses to this objection. First, it is far from clear that mere stakes effects cannot be explained on the basis of projective invariantism. Drawing on results from psychology, Buckwalter and Schaffer (Reference Buckwalter and Schaffer2013: 22) argue that high stakes “can be expected to trigger anxiety in the participants [of the studies they were conducting] and thereby ‘to intensify the generation of alternative hypotheses’.” In this way, additional alternatives may come to mind when one reads cases where the stakes are high. Thus, readers may be reminded that these alternatives are not unlikely. As a result, they may be less prone to ascribe knowledge because the epistemic position of the relevant subject will be assumed to be weakened (see the argument from reminding above). Second, an explanation of the salience effect alone seems progress enough, so even if the above account of the stakes effect fails, this would not be a devastating result.