Gaps in Semantics of ‘Knows’

[Word Counts: Main text: 3330 words Footnotes: 581 words Abstract: 80 words] Abstract Keith DeRose has proposed that different participants in a conversation do not have different contextually determined standards for knowledge-ascriptions. Rather, there is one contextually determined standard for the whole conversation. On this ‘single scoreboard’ view, when different participants use different standards, the semantics for ‘knows’ have a truth-value gap. This essay discusses a variety of cases in which truth-value gaps will arise on single-scoreboard contextualist views. These gaps will be widespread, but that is not an argument against single-scoreboard contextualism.

Keith DeRose has argued extensively for contextualism about the word ‘knows’: that the standards for what counts as knowledge are determined by the context in which the knowledge ascription is made. But DeRose does not hold that the context-sensitivity of ‘knows’ means that both parties to an apparent dispute about knowledge can be right. Some contextually sensitive terms, such as ‘I’, can take on different semantic values in the course of a single exchange, so that one person’s utterance of “I am sitting” and another’s utterance of “I am not sitting” can both be true. DeRose (2004), however, argues that the standards for knowledge never vary within a single exchange in a way that could make true one person’s utterance of “S knows that p” and another’s utterance of “S doesn’t know that p.” In fact, DeRose argues that in such exchanges it may be that neither party’s utterance is true; “S knows that p” falls into a truth-value gap. This essay explores DeRose’s gap view and argues that on his view truth-value gaps must be fairly widespread. DeRose uses two different kinds of case to argue for contextualism about knowledge. In one kind of case, the standard for knowledge is raised when a skeptical possibility is mentioned and acknowledged. When I first said “I know that there is a zebra in that cage,” I spoke truly; after the possibility that it might be a painted mule was brought up and acknowledged, I can no longer truly say “I know.” (See especially DeRose 1995.) Another kind of case brings in the practical costs of false belief. If nothing much rides on whether I get my paycheck deposited before Monday, I can truly say “I know that the bank is open Saturday” because I saw that it was open three Saturdays ago. If depositing my paycheck is vitally important, I should consider the possibility that the bank has changed its hours, and I can truly say “I don’t know that the bank is open Saturday.” (See especially DeRose 1992.) In the painted mule case the standards for knowledge are determined by which possibilities are acknowledged. In a context in which a skeptical possibility has not been acknowledged, knowledge ascriptions do not have to meet skeptical standards; once the possibility has been acknowledged they do. In the Bank Cases, the standards for knowledge could be determined either by which possibilities are acknowledged or by the practical costs of false belief. When, in the high-stakes case, I say “I don’t know that the bank is open Saturday,” is my negative knowledge ascription made true by the high stakes or by my acknowledgment of the possibility that the bank might have changed its hours?[1] In recent writings DeRose takes the position that the truth of the knowledge ascription is determined by the standards that the speaker chooses, even if those standards are not appropriate given the practical stakes: “If [speakers] opt for unreasonable standards, I’m inclined to think the truth conditions of their claim then reflect those unreasonable standards they are indicating” (DeRose 2004, p. 13).[2] So standards are determined by which possibilities are acknowledged as relevant. If we think something is wrong when someone says “I know” in the high-stakes Bank Case, it is because the speaker is using an inappropriate standard, not because the ascription is false. This view of DeRose’s, however, can be detached from the rest of his contextualist framework. Accordingly, I will treat both his actual view, on which the standards for knowledge are whatever the speaker chooses, and an alternative view, on which the standards for knowledge are whatever standards are appropriate given the practical stakes. Call these Choice Contextualism and Stakes Contextualism, respectively.[3] On DeRose’s view, truth-value gaps arise when the parties to a conversation cannot agree on a standard for knowledge. If you say, “That might be a painted mule, so you don’t know it’s a zebra,” and I say, “Don’t be ridiculous, of course I know (who would paint a mule?),” then we are consciously each invoking different standards for knowledge ascriptions. DeRose (2004) argues against a “multiple scoreboards” view on which each participant in the conversation sets their own standard of knowledge for evaluating their own ascriptions. Rather, on the “single scoreboard” view there is one standard for knowledge for the entire conversation.[4] There is no principled reason to let the higher or lower of the standards in play prevail. Hence the gap view: If knowledge ascription would be true according to one of the standards in play and false according to another, it has no truth value.[5] I will argue that gaps will be widespread on both Choice Contextualism and Stakes Contextualism. On either view, there will be many cases in which two standards are in play, and there is no principled reason to choose between them. The argument is not intended as a reductio of any view, but merely meant to draw out their consequences. However, I will conclude by arguing that our semantics for ‘knows’ should in fact be gappy.

Two Subjects Considering first Stakes Contextualism, on which the standard is determined by practical stakes, note that the stakes at issue need not always be the speaker’s. DeRose points out that, when the conversation concerns practical decisions that a faraway subject is making, it is natural to use standards that depend on the subject’s stakes (DeRose 2005, p. 189). Indeed, there can be cases in which the only stakes that could possibly set the standard are the subject’s stakes. Consider Hyla, who is in a high-stakes Bank Case, and Clio, who later looks back on Hyla’s situation. Clio says, “Hyla didn’t know that the bank would be open Saturday.” The standards for Clio’s ascription can’t depend on what Clio has to lose if the bank wasn’t open. For her, nothing rides on this question; she has no practical decision to make with regard whether the bank was open.[6] Hyla’s stakes are the only stakes that can determine the standards for knowledge. Suppose now that Clio is looking back at two subjects in Bank Cases. Hyla and Lola had the same evidence that the bank was open on Saturday, but Hyla was in a high-stakes situation and Lola was in a low-stakes situation. Someone asks Clio, “Did Hyla and Lola know that the bank would be open Saturday?” Whose stakes determine the standards that apply to Clio’s knowledge ascription? As before, it must be the subject’s stakes. Yet there are two subjects with different stakes. If there is no principled reason to choose one subject’s stakes as determining the standard of Clio’s ascription, then it will fall into a truth-value gap. One thought might be that Clio should shift the standard mid-sentence, so she can truly say “Lola knew, but Hyla didn’t know.” Such mid-sentence context shifts can occur with other context-sensitive terms, as in “Now I’m sitting, but now I’m standing.” They can even occur with ‘know’ when there is a clearly marked shift between contextually obvious high and low standards; DeRose cites the student in an epistemology class who says, “I know that I’m sitting in a classroom, but I don’t KNOW it” (DeRose 1998, p. 71). In this case, however, there may be no contextual indicators of what the high and low standards are. No one in Clio’s conversation, not even Clio herself, need be aware that Hyla and Lola have different stakes and so that different standards might apply to them. So Clio would have no reason to mark a context shift, and it would not convey anything if she stressed one occurrence of ‘know’. This suggestion merely introduces two standards for knowledge into a single conversation in which the word ‘know’ seems to be using to ascribe the same thing each time it is used. There seems to be no principled reason to allow that this conversation involves more than one standard and stop short of the multiple scoreboards view. On the multiple scoreboards view there would even be some principled reason for assigning different standards to the different ascriptions, in that the different standards would apply to different speakers’ utterances. If the Gap View is correct, the Stakes Contextualist must acknowledge a gap here. In this case the Choice Contextualist need not acknowledge a gap. Whatever standard Clio chooses will govern her knowledge ascription. The next case, however, will create a gap for the Choice Contextualist as well as for the Stakes Contextualist, and will raise some doubt as to whether even in this case Clio’s choice of standard is well defined.

Two Participants Consider a case in which, as before, Hyla has high stakes and Lola has low stakes in the question of whether the bank is open Saturday, but in which neither has any evidence concerning the bank’s hours. Hyla says to Lola, “I need to get to the bank this weekend.” Lola says, “So do I” (not knowing that her need is not nearly as strong as Hyla’s). “Maybe Samantha knows its hours,” Hyla says. They approach Samantha. “Is the bank open Saturday?” Hyla asks. “Yes,” Samantha says; she (though she does not say this) was at the bank three Saturdays ago. “Do you know that?” Lola asks (perhaps she thinks that Samantha is likely to pass on ill-founded testimony). “Yes, I know that,” Samantha says. Does Samantha speak truly or falsely? The Stakes Contextualist analysis: Samantha has no direct practical stake in whether the bank is open. The only decision she faces is whether or not to assert that she knows. The purpose of the conversation is to inform the other two about the bank’s hours, so it is appropriate for her knowledge ascription to be governed by what the others have at stake in the bank’s being open. But Hyla’s and Lola’s stakes differ. So two different standards are in play in this conversation, and Samantha’s knowledge claim falls into a gap. We might say there is a principled reason to say that Samantha’s knowledge ascription should conform to the highest available standard. Samantha does face the decision whether to assert that she knows the bank is open, and it is plausible that she should not claim knowledge unless her evidence is good enough for every member of her audience, given their stakes.[7] Still, this reasoning does not close the truth-value gap. For there are still two standards in play in the conversation: the high standard appropriate to Hyla’s and Samantha’s decisions, and the low standard appropriate to Lola’s decision. If Samantha’s answer is governed by her (indirect) high stakes, then Lola’s question must be governed by her low stakes, and Samantha’s answer does not address Lola’s question. But this is just the multiple scoreboards view. If Lola and Samantha are not to talk past each other, we must reject the multiple scoreboards view; then the disparity between Lola’s and Samantha’s stakes will create a truth-value gap. On Choice Contextualism, Samantha’s knowledge ascription also seems to fall into a truth-value gap. Prima facie, Samantha does not choose any standard in particular. No standard is indicated in the course of the conversation, and we may suppose that she simply answers the question without thinking of one standard or another. This seems to mean that there may be no way for Choice Contextualists to resolve the question of exactly what Samantha means when she says ‘knows’. Choice Contextualists might respond that all speakers implicitly have something in mind when they say ‘knows’, and this inner (perhaps unconscious) choice determines the standard that applies to their knowledge ascriptions.[8] On this line, truth-value gaps would be extraordinarily frequent. They could occur whenever the participants in a conversation make different inner choices of standard rather than explicitly discussing the standard; even in outwardly harmonious conversations. This, I think, would be pernicious. In any case, this view will produce a truth-value gap in this case. Hyla and Lola certainly make different inner choices when they utter the word ‘knows’, and Samantha’s inner choice might be different yet. To avoid pernicious proliferation of gaps, Choice Contextualists might take the stakes-appropriate standard as the default and say that overt insistence on a standard can change the standard for the conversation away from the default. So when a participant raises or brushes aside a doubt, the scoreboard for the conversation shifts to accommodate the new standard (unless another participant overtly rejects this standard, leading to a gap). If no standard has been overtly invoked, the standard for the conversation is whatever is appropriate given the practical stakes involved. This seems like a reasonable way to flesh out Choice Contextualism.[9] If the participants are not overtly thinking of a standard, we can interpret them as meaning to fall in line with the purposes of the conversation, which means aligning their standard with the stakes. But it means that, where there is no overt standard, Choice Contextualism reduces to Stakes Contextualism. In particular, it produces a gap in this case: Samantha’s knowledge ascription will be truth-valueless because of the difference between Hyla’s and Lola’s stakes. The foregoing indicates why the Two Subjects case might lead to a gap on Choice Contextualism as well as on Stakes Contextualism. Clio may not have adverted to a specific standard for knowledge, even inwardly, when she ascribes knowledge to Hyla and Lola. If the standard for her knowledge ascription depends on some inward choice, the ascription may not have a well-defined truth-value. If, on the other hand, the standard depends on the stakes in the absence of an overt choice, then Clio’s ascription will fall into a gap. The relevant stakes are the subjects’, and the two subjects have different stakes.

Cross Purposes In the Two Participants case, Samantha’s knowledge ascription had a clear purpose: conveying information to the others. The gap arose because Hyla and Lola required different standards for their information. Gaps may also arise when an ascription lacks a single clear purpose. Suppose that Hyla has often tried to convince Samantha that Lola is too rash, and Samantha defended Lola. On an occasion when this hasn’t come up explicitly, Hyla says to Samantha, “I wonder if Lola knows what the bank’s hours are.” Samantha replies, “Lola needs to go to the bank, and I saw her pass it by this afternoon, so she must know that it’s open Saturday.” Samantha takes Hyla to be wondering about Lola’s rashness, so she intends her knowledge ascription to conform to the standards appropriate to Lola’s low-stakes situation. But unbeknownst to Samantha, Hyla is in a high-stakes situation and wants to know whether Lola would be a good source of information for her, and so requires high standards for knowledge. As observed earlier, when the conversation concerns a faraway subject’s practical situation, it is natural to use a standard that depends on the subject’s stakes. In this case, the conversation’s purpose could be to evaluate the prudence of the faraway subject’s decision; but it could also be to evaluate the subject as a potential informant for one of the participants. The conversation does not come with its purpose clearly marked. If, on Stakes Contextualism, which stakes are relevant is determined by the purpose of the conversation, then a conversation whose purpose has not been settled can bring two standards into play. Truth values of knowledge ascriptions in such conversations will be gappy. So in this case it is not clear whose stakes ought to determine the standard for knowledge. Samantha thinks of the conversation as an impractical inquiry into the rationality of the faraway subject Lola, in which case Lola’s stakes are relevant; Hyla thinks of it as a way to gather information for her practical decision, making her own stakes relevant. These different stakes create a gap. Nor will Choice Contextualism avoid the gap. Since Samantha intends her knowledge ascription to reflect on Lola’s prudence, she has inwardly chosen the low-stakes standard. Yet Hyla, who desires to know whether Lola would be a suitable informant for her purposes, has inwardly chosen the high-stakes standard. The gap arises as before. As DeRose (2004) points out, the strength of the gap view is that on it participants in a single conversation mean the same thing when they say ‘know’, in the absence of obvious context shifts. If we allow each use of ‘know’ to carry its own standards, then in many apparent disagreements, answers to questions, and follow-up utterances will be non sequiturs, because what ‘know’ means in one utterance is not what it means in the next. Yet in the examples we have discussed, the speakers do intend to disagree, answer the question, etc., and they seem to succeed in doing so. Gaps arise when the speakers nevertheless bring in different stakes or inward choices of standard.

Why Gaps? The truth-value gaps we have discussed can all be resolved if the participants in the conversation know what is going on. All they have to do is clarify the differences in the standards that the different participants are using, or that are appropriate to the different subjects’ practical purposes.[10] In Cross Purposes, a fully informed Samantha could truly say, “Lola must have secure enough evidence for her own purposes, but if I were you I’d check the bank’s hours myself.” In Two Subjects, Clio could say “Both had the same evidence that the bank was open Saturday, but that evidence wasn’t enough for Hyla to rely on, given what was at stake for her.” And so on. This brings out why, in my opinion, the proliferation of truth-value gaps is not a problem for contextualism. Truth-value gaps arise only when our use of ‘know’ comes under some strain. If a knowledge ascription meets the contextually set standard, that should mean that the subject that has evidence that is good enough for whatever purpose is relevant in the context. In the cases we have examined, ‘good enough for whatever purpose’ is not well defined, because the purpose is not well defined, or the purpose brings more than one standard into play. Accordingly, saying that a subject knows (or doesn’t) is not a good way of conveying how much evidence she has. The speaker must say which evidential standard the subject meets and which she doesn’t. Such considerations suggest that any account that captures all our uses of ‘know’ will have a gappy semantics. Conversations do not always have a clear single purpose, participants in the conversation do not always share a goal that provides a single standard for evidence, and participants in a conversation will not always have a clear intention to invoke a particular standard, not to mention that if they do they may not invoke the same one. So it will often be unclear exactly what standard is invoked by ‘know’ in a particular conversation, or there will be more than one standard that might be invoked. One way to deal with these cases might be to say that knowledge ascriptions cannot accomplish one of the purposes that are appropriate to the conversational context. We could avoid gaps by saying that knowledge ascriptions always depend on the subject’s practical stakes, regardless of the speaker’s interests in the knowledge ascription.[11] Then knowledge ascriptions will often be useless in certain conversations. For instance, in the Cross Purposes case, Samantha will be right to say that Lola knows, and Hyla will not be able to find out whether Lola’s information would be good enough for her by asking whether Lola knows.[12] The cost of avoiding gaps in this way is that knowledge becomes much less important than it seems. Often it will not be appropriate to care whether the subject has knowledge. To preserve the importance of knowledge, we must say that knowledge ascriptions can in principle accomplish all the purposes that might be appropriate in some conversational context. Then, when the context calls for two incompatible purposes, there are two potentially incompatible demands on the ascription. Truth-value gaps arise when each purpose demands an ascription with a different truth-value.

Works Cited DeRose, Keith (1992). “Contextualism and Knowledge Attributions.” Philosophy and Phenomenological Research 52, 913-929. DeRose, Keith (1995). “Solving the Skeptical Problem.” Philosophical Review 104, 1-52. DeRose, Keith (1998). “Simple ‘Might’s, Indicative Possibilities and the Open Future.” Philosophical Quarterly 48, 67-82. DeRose, Keith (2004). “Single Scoreboard Semantics.” Philosophical Studies 119, pp. 1-21. DeRose, Keith (2005). “The Ordinary Language Basis for Contextualism and the New Invariantism.” Philosophical Quarterly 55, pp. 172-198. Feldman, Richard (2004). “Comments on DeRose’s ‘Single Scoreboard Semantics.’” Philosophical Studies 119, pp. 23-33. Hawthorne, John (2004). Knowledge and Lotteries. (Oxford: Oxford University Press). Lewis, David (1979). “Scorekeeping in a Language-Game.” Journal of Philosophical Logic 8, 339-359. Ludlow, Peter (2005). “Contextualism and the New Linguistic Turn in Epistemology.” in Contextualism in Philosophy: Knowledge, Meaning, and Truth, ed. Gerhard Preyer and Georg Peter (Oxford: Oxford University Press), pp. 11-50. Stanley, Jason (2005). Knowledge and Practical Interests (Oxford: Oxford University Press).
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[1] In the presentation of the Bank Cases in (DeRose 1992), DeRose points out that both these factors vary; in the case with high practical stakes the relevant doubt is brought up and acknowledged as relevant. [2] Cf. (DeRose 2005, pp. 177-8): “I think that speakers are free to use standards even wildly inappropriate to the practical situations they face—for instance, to use low standards where they face an extremely high-stakes situation in which it would be much wiser for them to employ much higher standards.” [3] Stakes Contextualism is what DeRose refers to as the “pure reasonableness” view (DeRose 2004, p. 11). [4] The scoreboard metaphor comes from (Lewis 1979). DeRose points out that his use of ‘scoreboard’ is not quite identical to Lewis’s. For Lewis, each participant always has their own scoreboard, reflecting what they think the score is; the right score for the conversation can differ from these individual assessments of the score. DeRose uses ‘scoreboard’ so that the scoreboard always has the right score. (DeRose 2004, p. 19n3). I follow DeRose’s usage. [5] DeRose in fact only tentatively accepts the gap view when the standards in play are fairly close together. He is more confident about the “exploding scoreboard” view, that (as in skeptical cases) when the standards are very far apart no knowledge ascriptions have truth-values. This essay will take the gap view for granted. [6] Of course it is not always true that a fact about the past has no practical implications. Perhaps Clio is faced with a bet on whether the bank was open, or perhaps Clio needs to know whether the bank was open in order to check someone’s alibi in a grave police investigation. But often there will be no practical stakes. [7] This is somewhat complicated, because Samantha has no way of knowing that her evidence is not good enough for Hyla, given Hyla’s stakes. Still, there seems to be a sense in which Samantha’s decision should be governed by the stakes for her audience, even if she does not know what those stakes are. If there were no such reason, there would be no ground for the Stakes Contextualist to say that Samantha’s ascription should be governed by the higher standard. [8] It would be implausible to say that this standard is precise, but it is generally implausible to say that contextually determined standards for knowledge are precise. Feldman (2004, p. 26ff.) suggests that DeRose ought to allow that a speaker’s intentions and dispositions can determine the standard for knowledge that governs the speaker’s utterances. Ultimately Feldman argues that this means that contextualists ought to adopt the multiple scoreboards view. [9] Compare Lewis’s (1979) account of how the standard for vague terms shifts to accommodate assertions such as “France is hexagonal.” DeRose, on the weblog [suppressed for blind review], has suggested that ‘knows’ is like other context-sensitive terms in that we can get by with extremely vague uses that can be sharpened later on if the purposes of the conversation make it necessary. [10] DeRose suggests this as a way out of a different sort of problem case; see his discussion of the interrogation case in (DeRose 2005, p. 197). See also Ludlow (2005) on operators for making standards explicit. [11] See the Subject-Sensitive Invariantism discussed by Hawthorne (2004) and Stanley (2005). [12] I take it that one of DeRose’s criticisms of subject-sensitive invariantism is that it forecloses the possibility that knowledge ascriptions might be used in this way. See his discussion of third-person cases in section 6 of (DeRose 2005).