Abstract
Does vagueness exclude knowledge? After arguing for an affirmative answer to this question, I consider a fascinating objection. Barnett (Philos Phenomenol Res 82:22–45, 2011) offers purported counterexamples to the following: Vagueness as to whether p entails that nobody knows whether p. These putative counterexamples, were they successful, would establish that standard accounts of vagueness are mistaken. I defend three central theses: First, whenever it is vague whether p (i) competent speakers would be ambivalent about whether p when considering whether p, and (ii) such ambivalence would exclude knowledge of whether p. Second, it is impossible for there to be vagueness regarding which of two polar opposite mental states obtains when only one of such states obtains. Finally, this type of impossibility constitutes evidence for dualism; i.e., the thesis that mental states are neither identical to physical states nor obtain in virtue of the obtaining of physical states.
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Notes
Barnett (2011).
See Sorensen (2010).
Raffman (2010) argues against the possibility of clear borderline cases. Raffman’s central argument assumes that failure to classify a case as borderline need not impugn the competence of speakers. Raffman writes: “Failure to classify an item as borderline \(\Psi \) cannot be mistaken or in any way improper or even questionable. (Intuitively, one is never required to classify something as borderline; a judgment of ‘borderline’ is always optional.)” (p. 513). In defense of this claim Raffman offers two remarks: First, “ordinary linguistic intuition” reveals that competent speakers do not apply ‘borderline’ when considering members of a Sorites series. Second, cases which can be competently judged to be borderline \(\Phi \) can also be competently classified as \(\Phi \) and as not-\(\Phi \). On Raffman’s view, no case mandates the classification of ‘borderline’, not even putative borderline cases.
What should we make of these considerations? First, given that English speakers would rarely use the term ‘borderline’, their failure to do so when considering a Sorites series isn’t suggestive. In my experience, speakers will use the terms ‘vague whether’ or ‘unclear whether’ or ‘is sort of \(\Phi \)’, i.e., if these expressions are made available to them prior to considering a candidate borderline case. Regarding cases like Harry’s, speakers often say he is “balding” as a first pass. Second, I reject the claim that a borderline \(\Phi \) can be competently classified as \(\Phi \). The right response to a borderline case is ambivalence, in which case a speaker, if competent, will be ambivalent about how to classify a borderline \(\Phi \). No doubt speakers might classify a borderline \(\Phi \) as both \(\Phi \) and as not-\(\Phi \) when ambivalent and when prompted to do so. This is because speakers typically aim to satisfy the requests of those asking for their classifications, as speakers tend to be cooperative, and classifying a case as either \(\Phi \) or not-\(\Phi \) will seem to be the only way to satisfy such requests cooperatively.
Wright (1992) argues against the possibility of clear borderline cases and assumes that vague predicates draw no “sharp” boundaries between their positive and negative instances. He writes: “When spelled out it goes, presumably, something like this. If F is vague, its very vagueness must entail that in a series of appropriately gradually changing objects, F at one end but not at the other, there will be no nth element which is F while the n + 1st is not; for if there were, the cut-off between F and not-F would be sharp, contrary to hypothesis. Accordingly, the vagueness of F over such a series must always be reflected in a truth of the form: (i) \( \lnot (\exists \hbox { x})(\hbox {Fx } \& -\hbox {Fx}')\), (where x\('\) is the immediate successor of x)” (p. 129). I reject the last contention. There can be a “sharp” boundary between x and its successor, where x is not F and x’ is F in a Sorites series; e.g., there can be a particular dollar amount such that someone that possesses just less than that amount is not rich, but someone that possesses just that amount is rich. So long as it is vague what that amount is, and thus, vague which induction step should be rejected, there is no objectionable sense in which putative “sharp” boundaries are problematically sharp. See Barnett (ibid.) for a careful and entirely convincing discussion of this point. For further examples of higher-order vagueness see Sorensen (ibid.). I should point out that Wright (1987) argues that all borderline cases are definite borderline cases. It’s unclear to me whether Wright (1992) agrees with his earlier self or whether he has a different conception of borderline cases in mind.
See Lopez de Sa (2010).
See Barnett (Ibid.).
A reviewer suggested that one view, namely a “degrees-of-truth” account of vagueness, does not entail Excluded Knowledge (see Smith 2008). I disagree. The truth-predicate employed here does not come in degrees (or to put my thesis in the mouth of a defender of degrees-of-truth, my thesis and supporting arguments only regard truth to degree 1, as would be advanced by all other accounts of vagueness except an account defended by a degrees-of-truth theorist). However, if we suppose that there is a coherent truth-predicate that comes in degrees, I can’t see how a theory which incorporates that predicate could fail to entail Excluded Knowledge. Suppose that Harry is a clear borderline case of baldness and that it is .5 degrees true that Harry is bald. A competent speaker would form the belief that it is .5 degrees, or near enough to .5 degrees, true that Harry is bald. This would not suffice for knowledge that Harry is bald; at best it could suffice for knowledge that it is .5 degrees true that Harry is bald. This proposition is not the proposition in question, which is that Harry is bald. Alternatively, one might claim that a competent speaker should be .5 degrees confident that Harry is bald if Harry is clearly borderline bald. If so, surely this degreed belief would not constitute knowledge that Harry is bald any more than a .5 degree confidence that a fair coin will land heads when tossed (just suppose it did, in fact, land heads) would constitute knowledge that the coin will land heads if tossed. For present purposes I will set to the side accounts of vagueness which incorporate putative degrees of truth. For related discussions see Weatherson (2010), Williamson (1994), and Smith (2010).
See Huemer (2005).
See Schiffer (2000).
According to the Oxford English Dictionary ‘ambivalence’ is “[t]he coexistence in one person, or one work, of contradictory emotions or attitudes towards the same object or situation.” I assume that among these attitudes are desires, beliefs, and seemings. The OED confirms the account of ambivalence presented here.
Schiffer (2010) writes: “Now Harry is standing before Jane, a rational non-philosopher, in circumstances that are optimal for her to determine whether or not he is bald. Her being in Quandry as regards whether or not Harry is bald reveals that she takes him to be borderline bald...Jane’s Quandary as regards whether or not Harry is bald is not, and is not thought by her to be, a state of ignorance or uncertainty. It is a state of ambivalence in which she is stymied to make any judgment at all as to whether or not Harry is bald, and this because of the way she finds his resemblance to men who she would say are bald to be in competition with his resemblance to men she would say are not bald” (p. 111). I wholeheartedly agree. Schiffer follows up this passage with an interesting footnote: “If she thinks Harry’s resemblance to men she would judge to be bald is counterbalanced by his resemblance to men she would judge not to be bald, then that counts her as locating Harry in the middle of the penumbra; if she thinks his resemblance to men she would judge to be bald is greater than his resemblance to men she would judge not to be bald, then counts her as locating him closer to the definitely bald men than to the definitely not bald men, and vice versa if the weights of the resemblances are reversed” (p. 111).
Thanks to anonymous reviewers for pressing this worry.
See Williamson (1994). Barnett provides a strong reason to reject this contention. More below.
We will see that Barnett argues that application conditions for some vague predicates are determined by competent speaker’s intuitions, and the intuitions these speakers would have over a range of cases. Though Barnett agrees that competent speaker’s would be ambivalent when considering clear borderline cases like Harry’s, Barnett does not consider the possibility that such ambivalence, understood to involve conflicting seemings, gives rise to vagueness in the first place.
An astute reader has likely noticed my emphasis on competent speaker’s intuitions. A natural question to ask is whether an incompetent speaker could acquire knowledge about whether Harry is bald? The answer is no. The reason is simply that by ‘competence’ I mean semantic competence and incompetent speakers do not mean by ‘Harry is bald’ what competent English speakers mean by ‘Harry is bald’. If there is any propositional-content for incompetent speaker’s beliefs about whether Harry is bald that content is not the target proposition under consideration. Fortunately, there isn’t near enough space here to discuss the nature of semantic competence. See Raffman (1994) for discussion of psychological factors that effect the application conditions for vague terms.
What of Barnett’s weak counterexample? Suppose that, as a matter of fact, it seems to Sophie that Harry is bald* and there is an absence of a seeming that Harry is not bald*. In this instance, is it true that (i) Sophie knows that Harry is bald* while (ii) it is vague whether Sophie knows that Harry is bald*, and (iii) it is vague whether Harry is bald*? Has Barnett established that Excluded Knowledge is not clearly true? The answer is yes, but only if we grant Barnett the claim that a mental state that is a borderline case of being a seeming that p and an absence of a seeming that p can justify a belief in a way that suffices for knowledge that p, and we reject the account of ambivalence I offered above. We should do neither.
Raffman (2005) seems to agree (in spirit if not letter). Raffman writes:
Now of course, even if all borderline cases can be defined in terms of an opposition between incompatible predicates (this has not yet been shown), not all pairs of incompatibles share borderline cases. ‘Rich’ and ‘destitute’ are incompatibles but nothing is borderline between being rich and being destitute; similarly ‘red’ and ‘green’. Just which pairs in a family of incompatibles share borderline cases seems an open question, and intuitions will diverge: does ‘large’ share borderline cases with ‘small’? ‘Red’ with ‘yellow’? ‘Tall’ with ‘short’? However one resolves these questions, the point is that in order to share borderline cases, two incompatibles must be related sufficiently closely within their family. Let us say that they must be proximate incompatibles (p. 8).
Raffman goes on to suggest that competent speakers would have (roughly) equal justification for applying proximate predicates, with respect to some particular borderline case, but that this is not so for non-proximate predicates. The rational is interesting: competent speakers could (reasonably) disagree when it comes to whether proximate predicates apply, but not so when non-proximate predicates apply. If what I’ve argued above is correct, Raffman is partly right and partly wrong. Borderline cases must be somehow proximate as Raffman argues; moreover, speakers would be equally justified in disagreeing about whether such proximate predicates apply in particular cases. But no competent speaker would apply proximate predicates when considering a borderline case, in the first instance; so such disagreement would not be reasonable (both speakers would be roughly equally unjustified in believing the proximate predicates apply).
My analogy is not perfect. Gray appears to be between black and white in a different way than, say, indifference appears to be between a strong positive and a strong negative seeming. But we can imagine a speaker looking at shades that transition from black to white and ask: Is the phenomenal state the speaker would enjoy, when observing a clear shade of gray, in between the phenomenal states they would enjoy when observing shades of black and white? The sense in which the answer to this question is yes is just the sense in which indifference lies between polar opposite seemings. Another sense is less metaphorical. If a speaker moves gradually, by small changes in confidence, from it’s seeming to the speaker that p to it’s seeming to the speaker that not p, the speaker will pass through some stage of indifference about whether p before reaching the latter stage.
See Barnett (2009) for discussion of a related point.
Clearly, seemings involve concepts. The view is not that any state that involves a concept cannot be fundamental since mental states, I think, are plausibly fundamental. My claim is that, intuitively, vagueness arises at the level of a concept’s application not at the level of a concept’s existence.
Many, many thanks to David Barnett.
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Lee, C.R. Excluded Knowledge. Synthese 193, 2427–2452 (2016). https://doi.org/10.1007/s11229-015-0858-2
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DOI: https://doi.org/10.1007/s11229-015-0858-2