Many Many Problems

Recently four different papers have suggested that the supervaluational solution to the Problem of the Many is flawed. Stephen Schiffer (1998, 2000a,b) has argued that the theory cannot account for reports of speech involving vague singular terms. Vann McGee and Brian McLaughlin (2000) say that theory cannot, yet, account for vague singular beliefs. Neil McKinnon (2002) has argued that we cannot provide a plausible theory of when precisifications are acceptable, which the supervaluational theory needs. And Roy Sorensen (2000) argues that supervaluationism is inconsistent with a directly referential theory of names. McGee and McLaughlin see the problem they raise as a cause for further research, but the other authors all take the problems they raise to provide sufficient reasons to jettison supervaluationism. I will argue that none of these problems provide such a reason, though the arguments are valuable critiques. In many cases, we must make some adjustments to the supervaluational theory to meet the posed challenges. The goal of this paper is to make those adjustments, and meet the challenges. 1 Schiffer’s Problem Stephen Schiffer suggests the following argument refutes supervaluationism. The central point is that, allegedly, the supervaluational theory of vague singular terms says false things about singular terms in speech reports. Pointing in a certain direction, Alice says to Bob, ‘There is where Harold and I first danced the rumba.’ Later that day, while pointing in the same direction, Bob says to Carla, ‘There is where Alice said she and Harold first danced the rumba.’ Now consider the following argument: (1) Bob’s utterance was true. (2) If the supervaluational semantics were correct, Bob’s utterance wouldn’t be true. (3) ∴ The supervaluational semantics isn’t correct. (Schiffer, 2000a, 321) Assuming Bob did point in pretty much the same direction as Alice, it seems implausible to deny (1). The argument is valid. So the issue is whether (2) is correct. Schiffer has a quick argument for (2), which I will paraphrase here. On supervaluational semantics, a sentence is true iff each of its acceptable precisifications is true. † Penultimate draft only. Please cite published version if possible. Final version published in Philosophical Quarterly 53 (2003): 481-501. Many Many Problems 2 In this case, this means that if Bob’s utterance is true then it must be true however we precisify ‘there’. Each precisification of ‘there’ will be a (precise) place, and since ‘there’ is rather vague, many of these precisifications will be acceptable. For Bob’s utterance to be true, then, Alice must have said of every one of those places that it was the place where Harold and her first danced the rumba. But Alice couldn’t have said all those things, so (2) is true. Schiffer suggests that one way out of this problem would be to accept the existence of a vague object: the place where Harold and Alice first danced the rumba. I will note in section four several reasons for thinking the cost of this move is excessive. Fortunately, there is a cheaper way home. Schiffer underestimates the scope of supervaluationism. On Schiffer’s vision of the theory, a precisification assigns a precise content to a word, and hence to a sentence, then the world determines whether that content is satisfied, and hence whether the sentence is true on that precisification. This is hardly an unorthodox view of how supervaluationism works, it seems for instance to be exactly the view defended in Keefe (2000), but it is neither the only way, nor the best way, forward. We could say, rather, that a precisification assigns content to every linguistic token in the world, and the truth conditions of every one of these tokens is then determined relative to that global assignment of content. So if a precisification P assigns a place x to Bob’s word ‘there’, Bob’s utterance is true according to that precisification iff P also assigns x to Alice’s utterance of ‘there’. That is, Bob’s utterance is true according to P iff the precisification of his words by P just is what Alice said according to P.1 It is a dramatic widening of the scope of precisifications to claim that they assign content to every linguistic token in the world, rather than just words in the sentence under consideration, but it can be justified.2 Consider how we would react if later in the day, pointing in the crucial direction, Alice said, ‘Harold and I never danced the rumba there.’ We would think that Alice had contradicted herself – that between her two statements she must have said something false. A standard supervaluationist account, where sentences are precisified one at a time, cannot deliver this result. On such a view, it might be that each of Alice’s utterances are true on some precisifications, so they are both neither true nor false. On my theory, each precisification applies to both of Alice’s utterances (as well as every other utterance ever made) and since on each precisification one or other of the utterances is false, it turns out supertrue that Alice said something false, as desired. The current view allows for penumbral connections between sentences, as well as penumbral connections within sentences. Just as someone who says, “That is red and orange” says something false, my theory decrees that someone who says, “That is red. That is orange,” while pointing at the same thing says something false, even if the object is in the vague area ‘between’ red and orange. It is crucial for this response to work that on every precisification, Alice and Bob’s demonstratives are co–referential. It does not seem like a particular expansion of supervaluational theory to posit this as a penumbral connection between the two 1Following Schiffer, we ignore the vagueness in ‘is where Harold and I first danced the rumba.’ This phrase is vague, but its vagueness raises no extra issues of philosophical importance. 2Thanks to John Hawthorne for the following argument. Many Many Problems 3 words. At least, it seems plausible enough to do this if Alice and Bob really are pointing in a similar direction. If their demonstrations are only roughly co-directional, then on some precisifications they may well pick out different objects. This will definitely happen if some admissible precisification of Alice’s ‘there’ is not an admissible precisification of Bob’s ‘there’. In such a case, the theory here predicts that Bob’s utterance will be indeterminate in truth value. But if Alice and Bob only vaguely pointed in the same direction this is the correct prediction. 2 Natural Properties Schiffer’s problem seems to have been solved with a minimum of fuss, but there is still a little work to do. Above I posited a penumbral connection between Alice’s and Bob’s words without explaining how such a connection could arise. This connection can be explained by some general considerations about content, considerations closely tied to the view of vagueness as semantic indecision that provides the best motivation for supervaluationism. As a few writers have pointed out (Quine, 1960; Putnam, 1980; Kripke, 1982), there is not enough in our dispositions to use words to fix a precise content all terms in our lexicon. This does not immediately imply a thorough-going content scepticism because, as a few writers have also pointed out (Putnam, 1973; Kripke, 1980; Lewis, 1983, 1984), meanings ain’t (entirely) in the head. Sometimes our words refer to a particular property or object rather than another not because our dispositions make this so, but because of some particular feature of that property or object. David Lewis calls this extra feature ‘naturalness’: some properties and objects are more natural than others, and when our verbal dispositions do not discriminate between different possible contents, naturalness steps in to finish the job and the more natural property or object gets to be the content. Well, that’s what happens when things go well. Vagueness happens when things don’t go well. Sometimes our verbal dispositions are indiscriminate between several different contents, and no one of these is more natural than all the rest. In these cases there will be many unnatural contents not eliminated by our dispositions that naturalness does manage to eliminate, but there will be still be many contents left uneliminated. Consider, for example, all the possible properties we might denote by ‘tall woman’. As far as our usage dispositions go, it might denote any one of the following properties: woman taller than 1680mm, woman taller than 1681mm, woman taller than 1680.719mm, etc. And it does not seem that any of these properties are more natural than any other. Hence there is no precise fact about what the phrase denotes. Hence it is vague. In sum, our dispositions are never enough to settle the content of a term. In some cases, such as ‘water’, ‘rabbit’, ‘plus’, ‘brain’ and ‘vat’, nature is kind enough to, more or less, finish the job. In others it is not, and vagueness is the result. (The above reasoning has a surprising consequence. Perhaps our verbal dispositions are consistent with the predicate Tall X denoting the property of being in the top quartile of Xs by height. Unlike each of the properties mentioned in the text, this is a more natural property than many of its competitors. So if this kind of approach to vagueness is right, there might not be quite as much vagueness as we expected.) Many Many Problems 4 If this is how vagueness is created, then there is a natural way to understand how precisifications remove vagueness. Vagueness arises because more natural than is a partial order on putative contents, and hence there might be no most natural content consistent with our verbal dispositions. If this relation only defined a strict ordering, so whatever the candidate meanings were, one of them would be most natural, vagueness might be defeated. Well, that isn’t true in reality, but it is true on each precisification. Every precisification is a completion of the ‘naturalness’ partial order. That is, each precisification P defines a strict order, more natural-P than, on possible contents of terms such that o1 is more natural-P than o2 if (but not only if) o1 is more natural than o2. The particular contents of terms according to P is then defined by using the more natural-P than relation where the more natural than relation is used in the real theory of content. This conjecture meshes nicely with my theory of the role of precisifications. First, it explains why precisifications apply to the whole of language. Since a precisification does not just remedy a defect in a particular word, but a defect in the content generation mechanism, precisifications are most naturally applied not just to a single word, but to every contentful entity. Secondly, it explains why we have the particular penumbral connections we actually have. Recall that it was left a little unexplained above why Alice’s and Bob’s use of ‘there’ denoted the same precise place. On the current conjecture, Alice’s term refers to a particular place x according to P because x is more natural–P than all the other places to which Alice might have referred. If this is so, then x will be more natural–P than all the other places to which Bob might have referred, so it will also be the referent according to P of Bob’s there. Hence according to every precisification, Bob’s utterance will be true, as Schiffer required. We can also explain some other unexplained penumbral connections by appeal to naturalness. Consider the sentence David Chalmers is conscious. Unless this is supertrue, supervaluationism is in trouble. It is vague just which object is denoted by David Chalmers. On every precisification, there are other objects that massively overlap David Chalmers. Indeed, these very objects are denoted by ‘David Chalmers’ on other precisifications. These objects are not conscious, since if one did there would be two conscious objects where, intuitively, there is just one. But each of these rogue objects must be in the extension of ‘conscious’ on the precisifications where it is the denotation of ‘David Chalmers’. So ‘conscious’ must be vague in slightly unexpected ways, and there must be a penumbral connection between it and ‘David Chalmers’: on every precisification, whatever object is denoted by that name is in the extension of ‘conscious’, while no other potential denotata of ‘David Chalmers’ is in the extension. How is this penumbral connection to be explained? Not by appeal to the meanings of the terms! Even if ‘David Chalmers’ has descriptive content, it is highly implausible that this includes being conscious. (After all, unless medicine improves a bit in a thousand years Chalmers will not be conscious.) Rather, this penumbral connection is explained by the fact that the very same thing, naturalness, is used in resolving the vagueness in the terms ‘conscious’ and ‘David Chalmers’. If the precisification makes one particular possible precisification of ‘David Chalmers’, say d1, more natural than another, d2, then it will make properties satisfied by d1­ more Many Many Problems 5 natural than those satisfied by d2, so every precisification will make the denotation of ‘David Chalmers’ fall into the extension of ‘conscious’. We can say the same thing about Alice’s original statement: That is where Harold and I first danced the rumba. Since one can’t first dance the rumba with Harold in two different places, it seems Alice’s statement can’t be true relative to more than one precisification of ‘That’. But really the phrase after ‘is’ is also vague, and there is a penumbral connection (via naturalness) between it and the demonstrative. Hence we can say Alice’s statement is supertrue without appealing to any mysterious penumbral connections. 3 McGee and McLaughlin’s Challenge Vann McGee and Brian McLaughlin (2000) raise a challenge for supervlauational approaches to the Problem of the Many that uses belief reports in much the way that Schiffer’s problem uses speech reports. They fear that without further development, the supervaluational theory cannot distinguish between the de re and de dicto readings of (4). (4) Ralph believes that there is a snow-capped mountain within sight of the equator. They claim, correctly, that (4) should have both a de dicto reading and a de re reading, where in the latter case it is a belief about Kilimanjaro. The problem with the latter case is unclear how Ralph’s belief can be about Kilimanjaro itself. To press the point, they consider an atom at or around the base of Kilimanjaro, called Sparky, and define “Kilimanjaro(+) to be the body of land constituted . . . by the atoms that make up Kilimanjaro together with Sparky [and] Kilimanjaro(-) [to] be the body of land constituted . . . by the atoms that make up Kilimanjaro other than Sparky.” (129) The problem with taking (4) to be true on a de re reading is that “there isn’t anything, either in his mental state or in his neural state or in his causal relations with his environment that would make one of Kilimanjaro(+) and Kilimanjaro(-), rather than the other, the thing that Ralph’s belief is about.” (146) So if the truth of (4) on a de re reading requires that Ralph believes a singular, or object-dependent, proposition, about one of Kilimanjaro(+) and Kilimanjaro(-), then (4) cannot be true. Even worse, if the truth of (4) requires that Ralph both that Ralph believes a singular proposition about Kilimanjaro(+), that it is a snow-capped mountain within sight of the equator, and the same proposition about Kilimanjaro(-), then given some knowledge about mountains on Ralph’s part, (4) cannot be true, because that would require Ralph to mistakenly believe there are two mountains located roughly where Kilimanjaro is located. We should not be so easily dissuaded. It is hard to identify exactly which features of Ralph’s “mental state or neural state or causal relations with his environment” that make it the case that he believes that two plus two equals four, but does not believe that two quus two equals four. (I assume Ralph is no philosopher, so lacks the concept QUUS.) I doubt, for example, that the concept PLUS has some causal Many Many Problems 6 influence over Ralph that the concept QUUS lacks. But Ralph does have the belief involving PLUS, and not the belief involving QUUS. He has this belief not merely in virtue of his mental or neural states, or his causal interactions with his environment, but in virtue of the fact that PLUS is a more natural concept than QUUS, and hence is more eligible to be a constituent of his belief. So if Kilimanjaro(+) is more natural than Kilimanjaro(-), it will be a constituent of Ralph’s belief, despite the fact that there is no other reason to say his belief is about one rather than the other. Now, in reality Kilimanjaro(+) is no more natural than Kilimanjaro(-). But according to any precisification, one of them will be more natural than the other, for precisifications determine content by determining relative naturalness. Hence if Ralph has a belief with the right structure, in particular a belief with a place for an object (roughly, Kilimanjaro) and the property being within sight of the equator, then on every precisification he has a singular belief that a Kilimanjaro-like mountain is within sight of the equator. And notice that since naturalness determines both mental content and verbal content, on every precisification the constituent of that belief will be the referent of ‘Kilimanjaro’. So even on a de re reading, (4) will be true. Schiffer’s problem showed that we should not take precisifications to be defined merely over single sentences. McGee and McLaughlin’s problem shows that we should take precisifications to set the content not just of sentences, but of mental states as well. Precisifications do not just assign precise content to every contentful linguistic token, but to every contentful entity in the world, including beliefs. This makes the issue of penumbral connections that we discussed in section two rather pressing. We already noted the need to establish penumbral connections between separate uses of demonstratives. Now we must establish penumbral connections between words and beliefs. The idea that precisifications determine content by determining relative naturalness establishes these connections. To sum up, McGee and McLaughlin raise three related problems concerning de re belief. Two of these concern belief reports. First, how can we distinguish between de re and de dicto reports? If I am right, we can distinguish between these just the way Russell suggested, by specifying the scope of the quantifiers. McGee and McLaughlin suspect this will not work because in general we cannot argue from (5) to (6), given the vagueness of ‘Kilimanjaro’. (5) Kilimanjaro is such that Ralph believes it to be within sight of the equator. (6) There is a mountain such that Ralph believes it to be within sight of the equa-