An Account of Semantic Indecision

Each of the examples mentioned looks as though it ought to be amenable to an analysis in terms of semantic indecision. Semantic indecision, unlike my account of vagueness, is something that only makes sense when it is attributed to a linguistic item, such as a sentence or a predicate.

Let us consider how we might apply this to the word ‘bald'. According to the proposal, we are to suppose that there is no property—or ‘condition' in McGee and McLaughlin's lingo—which is determined by the linguistic practices of the speakers to be the meaning of‘bald’. Despite this, there might well be several properties that are candidate meanings for the word bald: a property which is not determined to be not meant by the word ‘bald’ by the linguistic practices of English speakers. With this in place, McGee and McLaughlin go on to develop a broadly supervaluationist account of semantic indecision.

style='font-size:9.0pt;line-height:122%'>But what exactly is the notion of ‘determining’ that is being invoked here? Perhaps it can be spelt out in terms of metaphysical necessity by some kind of supervenience thesis. P is determined by present linguistic practices to be the meaning of the word ‘bald’ if and only if it’s necessary that when the linguistic practices of English are as they in fact are, the word ‘bald’ means P.

This account of ‘determining’ will not do, for McGee and McLaughlin want their theory to be consistent with the supervenience of meaning on use, yet such a supervenience thesis would ensure that the meaning of‘bald’ was always determined by the usage facts. Moreover, even if meaning does not supervene purely on use— perhaps the existence of reference magnetism, or something similar, prevents this— it would not be in the spirit of their view to think that the precise meanings of vague predicates are determined once you add these extra facts to the supervenience base. Presumably, meaning ought to supervene on the totality of physical facts, for example, but in the relevant sense of ‘determine’ the extension of the ‘bald’ is surely not determined by the totality of physical facts for, otherwise, its extension would be determined by completely precise matters.

Perhaps the notion of determining at hand is an epistemic one. Although the linguistic usage facts necessarily imply that the word ‘bald’ means what it means, and thus ‘determines’ in this same sense what its cutoff point is at each world, neither the cutoff nor the necessary implication between the usage facts and meaning facts are knowable to us. The sense in which the meaning of ‘bald’ is undetermined thus might be an epistemic one: there are several properties that, for all we know, are the meanings of the word ‘bald’. We don’t know which because, although the meaning of ‘bald’ supervenes on its use, we do not know how the meaning of ‘bald’ supervenes on its use—thus we are just as ignorant about what ‘bald’ means as we are about how this meaning gets fixed by usage.

This is, of course, just a version of the epistemic theory of vagueness—a theory that McGee and McLaughlin, and other sympathetic writers, take care to distinguish from semantic indecision.^[193] If we are to explicate the notion of semantic indecision in terms of how linguistic practices fail to determine meanings of vague words, we need a non- epistemic account of this ‘determining’ relation.

Luckily, if we accept the theory of vagueness that I have been endorsing so far, then there is a perfectly suited non-linguistic notion of borderlineness, which is neither contingency nor ignorance, that can be used to explicate the sense in which the usage facts can fail to determine the meanings of certain words: when the usage facts leave it indeterminate or borderline what a word means.

On this account, the linguistic facts determine that F means P when it is necessar­ily determinate that if the linguistic facts are as they in fact are, F means that P.^[194] The linguistic facts leave it open whether F means that P iff it's possibly not determinate that ‘F means something else while the linguistic facts are as they in fact are.

Assuming the supervenience of meaning on use, the ‘possibly's and ‘necessary's can be eliminated from these definitions. Thus we can give simple definitions of semantic definiteness and undecidedness: say that a sentence is semantically definite iff every proposition it doesn't determinately not express is true, and semantically undecided if neither it nor its negation is semantically definite. Given fairly uncontroversial assumptions, a sentence is semantically undecided if there's both a true and a false proposition it doesn't determinately not express.^[195]

Two things about this account are worth pointing out at this juncture. Firstly, this account of semantic indecision clearly cannot be accepted by someone who does not already accept the ideology of a non-linguistic determinacy operator.

Of course, it is controversial whether the examples I listed in section 7.1 are semantically undecided according to this account of semantic indecision. Nonethe­less, semantic indecision so defined undoubtedly exists—semantic properties and relations, like most non-fundamental properties and relations, are vague. In particular the linguistic meaning relation is vague and has borderline cases. To see this note that words clearly change their meanings over time. For example, the phrase ‘a kleenex' went from meaning a particular brand of tissue to being a general term for a tissue: presumably there was a time at which it was borderline which of the two things this phrase meant. Here is an example from the philosophical literature, which we will appeal to later: consider a sorites in which a person's use of ‘water' switches from referring to H₂O to another water-like substance, XYZ: perhaps I have moved to twin earth and my uses of the word ‘water' are slowly changing their meaning to refer to the local colourless, odourless watery stuff. Istart off clearly referring to water, and end up clearly referring to XYZ, but presumably there will be some point in between where it's borderline whether my use of ‘water' refers to water or XYZ.

It is important to distinguish semantic indecision from linguistic borderlineness. As I argued in chapter 4, even if one accepts a non-linguistic account of vagueness there is quite clearly a distinction between sentences to be captured, even if it is not taken to be basic: the difference between the sentence ‘Harry is bald' and ‘Patrick Stewart is bald', for example. The former is linguistically borderline, I argued, because it expresses a borderline proposition, whereas the latter is not linguistically borderline, because it expresses a determinately false proposition.

Note, however, that a sentence can be linguistically borderline without being semantically undecided. Suppose that there is a proposition, P, which the sentence ‘Harry is bald' determinately expresses. Presumably P would be the proposition that Harry is bald, and since this is borderline, it follows that the sentence ‘Harry is bald' is linguistically borderline. However, it is not semantically undecided: if Harry is bald, then every proposition the sentence ‘Harry is bald' doesn't determinately not express is true—there's only one such proposition and that's the proposition that Harry is bald. If Harry is not bald, then by analogous reasoning there's a proposition the sentence ‘Harry is bald' determinately expresses and it's false: thus ‘Harry is bald' is either semantically definite, or its negation is semantically definite (although it is borderline which).

Conversely, a sentence can be semantically undecided without being linguistically borderline. For example, suppose that it is determinate that XYZ does not contain hydrogen as a chemical component. H₂O, on the other hand, determinately does con­tain hydrogen as a chemical component.

The concept I have introduced under the name ‘semantic indecision’, I think, does a good job of accounting for the examples introduced in this chapter. In section 17.2, I considered the suggestion that sentences involving the words ‘nice*’, ‘/’ and ‘mass’ often expressedvague propositions,and thatthis couldbeusedtoexplain theapparent indeterminacy of these examples. In other words’ I was suggesting that sentences like ‘15 is nice*’ are linguistically borderline: they express borderline propositions. However’ there are some puzzles for this view and I think a much more natural way to model the above examples would be in terms of semantic indecision.

Let us focus on the example involving incomplete definitions. According to this analysis, the word ‘nice*’ expresses either the property of being at most 14 or the property of being at most 15, although it is borderline which. Thus the sentence ‘15 is nice^*’ is semantically undecided: it doesn’t determinately fail to express the true proposition that 15 is at most 15, and it doesn’t determinate!/ fail to express the false proposition that 15 is at most 14. Note also that neither of the candidate propositions for ‘15 is nice*’ are borderline. Thus, even though this is sentence semantically undecided, it is not linguistically borderline. Presumably on this view there is also a penumbral connection between what ‘nice*’ refers to and what ‘nice*’ refers to, namely, the former refers to whichever property the latter doesn’t.

It is independently plausible that it is borderline which property the word ‘nice^* ’ picks out. If there was a sorites sequence starting with ways of introducing the word ‘nice*’ so that it refers to the property of being at most 15 and ending with ways of introducing the word ‘nice*’ so that it ends up referring to the property of being at most 14, you might expect the incomplete definition of‘nice* ’ given in section 17.1 to be one of the cases in the middle of the sorites sequences—one of the cases where it’s borderline which of the two properties it refers to.

Presumably, in this case, I can still talk about the property of being nicestyle='font-size:12.0pt;line-height:122%; font-family:"Arial",sans-serif'>*, but when I do I end up referring either to the property of being at most 15 or the property of being at most 14 (and it’s propositionally borderline which). That is to say, the expres­sion ‘the property of being nice*’ inherits semantic indecision from the subexpression ‘nice*’. The crucial thing about this view is that, although there is the property of being nice*, it is a precise property for it is either the property of being at most 15 or the property of being at most 14. Both of these properties are precise—the property of being nice^* isn’t a third vague property distinct from either of these two properties. This is the crucial difference between the semantic indecision account and the account in which ‘15 is nice*’ is linguistically borderline. There is therefore no problem of property multiplication to be levelled against this account in the way that there was according to the latter account.

A similar story can be told about the other two examples. According to the semantic indecision account, the pre-relativistic uses of ‘mass’ refer either to proper mass or relativistic mass. However, the practices of the people using the word ‘mass’ leave it borderline whether they meant proper mass or relativistic mass by it, for they never really had to apply the word in the cases where the meanings came apart. Again, one can justify the ascription of borderlineness in meaning by considering a sorites starting off with a community of people who are disposed, after learning about relativity, to apply the word ‘mass’ to the proper mass of objects, and ending with a community disposed to apply the word ‘mass’ to relativistic mass upon learning about relativity. One would assume that the way people actually were disposed to apply the word ‘mass’, once the special theory of relativity was discovered, is one where it’s pretty much borderline whether we would want to apply the word ‘mass’ to proper mass or relativistic mass.^[197] On this account, then, we do not need to posit this strange third quantity, ‘Newtonian mass’. It was simply borderline whether ‘mass’ as it was used then referred to proper mass or relativistic mass.

As for the example involving the two mathematical communities, the semantic indecision account would say that the sentence ‘i = /’ either expresses a necessarily false proposition saying of one of the square roots of —1 that it is identical to the other, or a necessarily true proposition saying of one of the square roots that it is identical to itself. Thatis to say, letting x andy be the square roots of — 1, the candidate propositions wouldbe the singular propositions that x = x, thaty = y, that x = y, and that y = x. There are thus between two and four candidate propositions depending on how finely we individuate, and they are all perfectly precise. Again, we can contrast this with the earlier view in which ‘i = /’ did not express a singular proposition at all. On that view the contribution of‘/’ and ‘i’ was roughly the same as a vague name such as ‘Everest’ to the sentence ‘Everest is Π,GGGTh (see chapter 4). The proposition that ‘i = /’ expressed was a borderline proposition due to names like ‘i’ and ‘/’ introducing vague individual concepts to the proposition.

The account of semantic indecision I have outlined here assumes that it is some­times borderline which proposition I have expressed with a particular sentence. There is, however, a contrary argument that it’s never borderline what proposition a sentence expresses which I therefore need to address. Taking the example of the sentence ‘15 is nice*’ the argument starts with a disquotational premise:

1.        It’s determinate that ‘15 is nice*’ expresses the proposition that 15 is nice* and nothing else.

2.        Therefore it’s not borderline what ‘15 is nice*’ expresses.

The argument is indeed valid, assuming existential generalization, and the conclusion excludes semantic indecision for the sentence ‘15 is nice*’

A little thought, however, demonstrates that this argument overgenerates quite radically. For if the above argument is fine, then one can argue quite generally that, given that ^,P^, determinately expresses the proposition that P and nothing else, it is not borderline what ‘P’ expresses. But this conclusion is absurd for arbitrary sentences, for it shows that the expressing relation has no borderline cases. The relation of semantic expressing is clearly as vague as any other non-fundamental relation, and therefore is just as prone to having borderline cases. It is a matter of routine to describe a sorites in which an expression begins with a particular meaning but over time changes its meaning as people begin to use it in incrementally different ways. As with any sorites, we should conclude that there will be borderline cases in the middle of this sequence.

The solution is to reject the determinacy of the disquotational principle we began with. The idea, in the present case, is that it is borderline whether ‘15 is nice*’ expresses the proposition that 15 is nice* or the proposition that 15 is nice*, but determinate that it expresses one of them. What, then, is to be made of our intuitions in favour of the determinacy of the disquotational principle? What is it that seems to be special about disquotational sentences like ‘“15 is nice*” expresses the proposition that 15 is nice*’?

In chapter 5, I cast some doubt on the determinacy of the disquotational prin­ciples in our discussion of Williamson’s metalinguistic safety account of vagueness. However, there is a status that they enjoy which could easily be taken to explain the intuitions we have in favour of them: they are determinately true. This point requires distinguishing sharply between the following two principles:

It’s determinate that ‘15 is nice*’ expresses the proposition that 15 is nice*.

The sentence ‘“15 is nice*” expresses the proposition that 15 is nice*’ is determin­ately true.

The former principle I am denying. The latter, however, is true, which can be reasoned out from the following principles.

1.        It’s determinate that either ‘15 is nice*’ expresses the proposition that 15 is nice* or the proposition that 15 is nice*.

2.       It’s determinate that the word ‘expresses’ expresses the expressing relation.

3.       The semantic principle of compositionality is determinate.

The first premise presents us with two cases to consider. Suppose that ‘15 is nice*’ expresses the proposition that 15 is nice*. Then the sentence ‘“15 is nice*” expresses the proposition that 15 is nice*’ expresses the proposition that [‘15 is nice*’ expresses the proposition that 15 is nice* ] by the second premise and compositionality (I am using square brackets here simply to indicate scope). The proposition expressed is true by hypothesis. For the second, non-disquotational, case suppose that ‘15 is nice*’ expresses the proposition that 15 is nice*. This time, the sentence ‘“15 is nice*” expresses the proposition that 15 is nice*’ expresses the proposition that [‘15 is nice*’ expresses the proposition that 15 is nice*] by the second premise and compositionality. Again, by the description of the case, this proposition is true. So either way the proposition ‘15 is nice*’ expresses is true. Since each of the premises of this argument is determinate, we can determinize our conclusion: ‘15 is nice*’ is determinately true.^[198]

What is interesting about this case is that the two propositions that the disquota­tional principle is associated with are both borderline. As I argued earlier, the propos­ition that [‘15 is nice*’ expresses the proposition that 15 is nice*] is borderline, as is the proposition that [‘15 is nice*’ expresses the proposition that 15 is nice*]. Nonetheless, the indices at which the disquotational principle expresses the former proposition happen to be indices at which that proposition is true, and similarly for the indices at which it expresses the latter proposition. There is a penumbral connection between what the sentence expresses and the truth value of the proposition it expresses. This is why it is possible for it to be determinate that the disquotational principle expresses some true proposition, even though everything it doesn’t determinately not express is borderline.

This situation might seem pathological, but can be constructed easily in other cases. Let’s suppose I stipulatively introduce a name, ‘Fred, for the tallest short person.^{[199] [200]} There is plausibly a penumbral connection between the individual ‘Fred’ refers to and the cutoff point for being short. The sentence ‘Fred is short’ is thus surely determinately true, since we know that whoever ‘Fred’ refers to, they’re going to be a short person (the tallest one, in fact). But all of these candidate referents of ‘Fred’ are people who are borderline short. Thus we can also be sure that whoever ‘Fred’ refers to, the proposition expressed by ‘Fred is short’ is borderline.

17.4