Weatherson, Brian

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Review of “Vagueness andContradiction”BrianWeatherson2003Review of Roy Sorensen, “Vagueness and Contradiction”. Cambridge: Cam-bridge University Press, 2000.Like all epistemicists, Roy Sorensen holds that vagueness poses no threat to classicallogic, and that appearances to the contrary are the result of mistakenly assigning se-mantic force to certain barriers to inquiry. We may not be able to know whether 932seconds after noon is still noonish, but there is a fact of the matter about whether itis. Hence the sentence 932 seconds after noon is noonish is either true or false, just asadherents of classical logic presuppose, and the threat from vagueness to classical logicdissolves.But Sorensen is not an orthodox epistemicist. He does not hold that these barriersto inquiry rise because of our limited powers of discrimination. That would imply thata more discerning observer, say God, could know where the boundary is. Sorensenholds that vagueness is an absolute barrier to inquiry. No one can know whether 932seconds after noon is noonish, even God. This is because competently using the vaguepredicate ‘noonish’ requires believing a particular analytic falsehood involving it, andhaving this belief prevents knowing the truth about a borderline case. Much of thisbook is dedicated to defending these surprising claims. The first half of the book arguesthat this is the right thing to say about vague cases, and the second half provides moregeneral arguments that we can and should believe analytic falsehoods.It’s illuminating to compare Sorensen’s epistemicism with that of TimothyWilliamson. A core feature of Williamson’s position is neatly summarised in thisquote, which Sorensen cites: “for the epistemicist, definiteness is truth under allsharp interpretations of the language indiscriminable from the right one.” (“Onthe Structure of Higher Order Vagueness” Mind 108 (1999): 127‑43.) Sorensendisagrees with the Williamson’s position in four ways. Two of these disagreements areimmediate, and two are with deeper presuppositions of Williamson’s.First, Sorensen thinks that Williamson here ignores the need for ‘completeness’.Williamson holds that p is definite iff, roughly, it is true on all interpretations wecannot know to be incorrect. Call these the admissible interpretations. Sorensen2 BrianWeathersonclaims that is not enough for p to be knowable, and hence definitely true. It must alsobe knowable that these are all the admissible interpretations.Secondly, indiscriminability is always indiscriminability by something, so onWilliamson’s account definiteness is only defined relative to a discriminator. Sorensenwants there to be absolute borderline cases, and absolute indefiniteness, so he cannotrest with this definition. Sorensen thinks that unless we accept absolute borderlinecases, we do not properly respect the sense in which vagueness is an absolute barrier toinquiry. The two other innovations in Sorensen’s theory guarantee that his theory hasplace for absolute indefiniteness.Consider a normal Sorites conditional, say If 932 seconds after noon is noonish, so is933 seconds. Sorensen holds that being a competent user of ‘noonish’ requires that onebelieve every such conditional involving ‘noonish’. Someone who failed to believe itwould not be competent in the language. Although Sorensen always puts this in termsof linguistic competence, he also says that one who didn’t believe this couldn’t havebeliefs about the extension of our predicates. The most natural conclusion to drawis that from Sorensen’s perspective, one who doesn’t believe the Sorites conditionallacks the concept NOONISH. Sorensen talks about predicates rather than concepts,so he doesn’t put it quite this way, but it succinctly summarises the picture he sketches.Moreover, beliefs in such Sorites conditionals are a priori, despite the fact that one ofthem is analytically false. These are distinctive views, and they need good arguments.A bad argument would be, “It is always irrational to deny a Sorites conditional, soit is always rational to believe it.” This ignores the possibility that agnosticism aboutthe conditional is always possible, and sometimes desirable. Sorensen does not endorsethis argument, though he does note it shows that Sorites conditionals satisfy a ‘negativeconception’ of the a priori: no empirical evidence can make us believe they are false.Sorensen’s argument seems to be that believing every Sorites conditional gives usmany true beliefs at the cost of only one false belief. He thinks that cost is worth thebenefit. But this is at best a reason why we should believe Sorites conditionals, not whyGod should. And it doesn’t implymuch aboutwhyGod needs to believe this falsehoodif He is to have the concept NOONISH. If we think subjectivism about language im-plies that God can’t know more about our language than we do, that may draw Godinto our dilemma. But it should seem very implausible, especially to an epistemicist,that God can’t know more about our language than we do. So even if it is good adviceto believe every Sorites conditional, it does not follow that those who spurn this advicelack any concepts, or lack linguistic competence.In any case, there are other costs to adopting Sorensen’s advice and believing a bunchof Sorites conditionals that we know includes a falsehood. For example, we can nolonger safely believe the logical consequences of some things we believe. Sorensen hap-pily accepts that consequence. He holds p and q can both be a priori even though theirconjunction is not a priori. In chapter 6 Sorensen replies to several arguments againstthis, including a purported proof that a priority agglomerates across conjunction. Theproof assumes that all logical truths are a priori. Sorensen says this is false because thereare logical truths that are too complex for us to believe, a priori or otherwise. Since theReview of “Vagueness and Contradiction” 3only logical truth needed in the proof was p → (q → (p & q)), this is not obviously asound response.Sorensen has a more speculative reason for thinking there is absolute vagueness.(This is the final way in which Sorensen’s position differs fromWilliamson.) Considera card that has The sentence on the other side of this card is false written on each side. Ifthe sentences have truth values, then one is true and the other false. Whichever is trueis a truth without a truthmaker, for any truthmaker would do just as well at making theother true. So Sorensen concludes that here we have a truth without a truthmaker, andthe truthmaker principle is false. If there are some truths without truthmakers, therecould be several. Sorensen holds that a is F is such a truth whenever a is an F which is aborderline F. Assume further that only truths with truthmakers are knowable, becauseknowability goes via knowing truthmakers, and we conclude that no one could knowof a borderline F whether it is F. This is quite an interesting line of thought, and itdeserves further attention. (Sorensen is quite upfront about how speculative it is.)Two immediate issues spring to mind. First, it is not clear how this is still a versionof epistemicism, for vagueness is now at base a metaphysical phenomenon. There areepistemic consequences, but vagueness is constituted by the fact that there are truthswithout truthmakes, not by the unknowability of these. Secondly, and relatedly, itis no longer clear how higher order vagueness will be incorporated into the model.The most obvious thought is that there will be no truthmaker for the claim that someparticular truth has a truthmaker. But whether some object is a truthmaker for sometruth is not contingent, and it is notoriously difficult to apply truthmaker theory tonecessary truths. Since every proposition entails any necessary truth, it is plausible thatany object is a truthmaker for a necessary truth.Sorensen argues that we should believe all Sorites conditionals, including ones thatare analytically false. He notes this requires an argument that we can, and should, be-lieve some analytic falsehoods. (He calls these impossibilities ‘contradictions’, a termsome may think should be reserved for sentences of the form p & ¬p.) His argumentthatwe can is fairly quick. Assume, for reductio, the philosophical thesis thatwe cannotbelieve analytic falsehoods. As a philosophical thesis, this is analytically true if true at all.But Sorensen believes its negation. So it is possible for someone to believe an analyticfalsehood. The weakest premise here is that if we cannot believe analytic falsehoods,then it is analytic that we cannot. If it turns out that only creatures with a language ofthought can believe analytic falsehoods, and it is a contingent feature of us that we lacka language of thought, Sorensen’s premise is false.The argument that we should believe some analytic falsehoods uses a version of thepreface paradox. If we can believe analytic falsehoods, we should take apparent occur-rences of this (aswhenwemake arithmetic errors) at face value. That is, reasondemandswe believe that we believe an analytic falsehood. But this implies it is provable that ourbeliefs are not collectively true. So if we follow the dictates of reason, it is provable webelieve something provably false. This argument is obviously useful for removing a par-ticular barrier to accepting Sorensen’s account of vagueness, that it seems absurd thatreason could require we believe an analytic falsehood. But even if we reject Sorensen’s4 BrianWeathersontheory of vagueness, they are independently interesting contributions to the theory ofbelief.Sorensen makes two distinctive contributions to the theory of vagueness here. First,he argues that linguistic competence demands that we believe Sorites conditionals. Sec-ondly, he links the existence of vagueness to the failure of the truthmaker principle.As those familiar with Sorensen’s work will suspect, he makes these contributions in alively and entertaining way. Anyone working on vagueness, and especially anyone in-terested in investigating the range of theories of vagueness that preserve classical logic,should pay it close attention.Published in Australasian Journal of Philosophy, 2003, pp. 290-292.

Vagueness and contradiction

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Vagueness and contradiction

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