As is often the case in philosophy, competing philosophical theories, purportedly about the same subject matter, can be couched in very different vocabulary.
In such cases it is often quite hard to state, in a neutral way, exactly what the disagreement is— choice of ideology can sometimes contain assumptions of its own.
Sometimes it is not even clear whether two theories are in competition or whether they are just talking about two different things.As a case in point, consider the two distinctions that will be the focus of this chapter:
Sentential Bqrderlineness: Some sentences exhibit features that are correlated, in some way or other, with the presence of vagueness: call this feature ‘sentential borderlineness’. Examples of English sentences that are sententially borderline include ‘if a glass is two thirds full it is pretty full’, ‘France is hexagonal’, and ‘Janet is rich’, where Janet is someone of moderate wealth. Examples that are not sententially borderline include the sentences ‘there are electrons’, ‘there are at most three bald people on the planet Earth’, and ‘the smallest tall person is tall’.
Prqpqsitiqnal Bqrderlineness: Some propositions exhibit features that are correlated, in some way or other, with the presence of vagueness: call this feature ‘propositional borderlineness’. Examples of propositions that are propositionally borderline include ‘if a glass is two thirds full it is pretty full’, ‘France is hexagonal’, and ‘Janet is rich’. Examples that are not propositionally borderline include the propositions ‘there are at most three bald people on the planet Earth’ and ‘the smallest tall person is tall’.
Related to these distinctions are parallel distinctions between vague propositions and sentences.
The sentence ‘there are at most three bald people on Earth’ is sententially vague; but it is not sententially borderline because it is determinately true. Similarly, if there are any vague propositions at all, presumably the proposition that there are at most three people on Earth is propositionally vague, even though it is similarly not propositionally borderline. Throughout this chapter when I talk about giving ‘an account of vagueness’ whether sentential or propositional, I shall generally mean the project of giving an account of both vagueness and borderlineness. The difference between giving an account of vagueness and giving an account of borderlineness may actually be more subtle than it might first appear, but we will defer that discussion until chapter 12 and treat them as if they stand or fall together for the moment.I take it to be Uncontentious that the first of these distinctions draws a non-trivial line: there are sentences which are sententially borderline and sentences which are not sententially borderline. There is, for instance, a distinctive reason not to assert the sentence ‘Janet is rich' when you know that Janet falls within the borderline region, and it clearly has something to do with vagueness. And there are other sentences, like ‘Janet has $200,000' for which there is no distinctive obstacle to appropriate assertion.
size=1 color=black face=Cambria>The non-triviality of the second distinction, however, is a bit more contentious. On the face of it, it might seem obvious that there's a principled distinction to be drawn between, say, the proposition that Janet is rich, and the proposition that Janet has at least $200,000. For example the truth of the former proposition seems not to be amenable to investigation, whereas the truth of the latter is. However, some philosophers maintain that this apparent difference is an illusion and that these seemingly distinct propositions might even be identical, for all we know.
By analogy, one might note that there is no fundamental difference between the largest small number, whichever it might be, and the number 5—they are both precise entities. There is no vague number—the largest small number—in addition to the numbers 1,2,3, and so on; there is just vagueness concerning the relation between these precise entities and the vague description ‘the largest small number'. Perhaps the entities denoted by ‘the proposition that Janet is rich' and by ‘the proposition that Janet has at least $200,000 dollars' are similarly just as precise as one another, although the relation between the former expression and the proposition it picks out is more complex than it seems. There is one important disanalogy between numbers and propositions, however: for each n the proposition that Janet has at least $n is something we appear to be in a position to know, whereas the proposition that Janet is rich doesn't seem to be like this, blocking a straightforward identification of the latter proposition with one of the former precise propositions.In chapter 5, I shall argue that the best way to make sense of our ignorance is to accept both sorts of distinction: the distinction between sentences and the distinction between propositions, or the objects of thought whatever they may. For someone who accepts the existence of both distinctions, however, it is natural to wonder what the dispute between the linguistic and propositional approaches to vagueness and borderlineness amount to. Are both sides not just giving an account of different things?
The answer, I take it, is that those espousing one or the other of these approaches typically take themselves to be doing more than just exploring a side effect of vagueness, whatever it may be. They take their project to be that of giving an explication of what vagueness is, and providing the means to address the fundamental problems of vagueness.
Thus I take it that the issue at stake concerns the following two hypotheses:1. Hypothesis one: it is sentential borderlineness (or, perhaps, a related property of some other linguistic category) which is at the root of, and will feature in the explanations of all the fundamental puzzles associated with vagueness.
2. Hypothesis two: it is propositional borderlineness that is at the root of, and will feature in the explanations of all the fundamental puzzles associated with vagueness.
The fundamental puzzles of vagueness, I take it, include at least the sorites paradox, and the problem of explaining the puzzling kind of ignorance that comes along with vagueness. Given the first hypothesis, our theoretical investigations ought to be focused around a metalinguistic relation to languages: ‘sentence S is vague in language L,, or something similar. Propositional vagueness should be reduced to and explained in terms of sentential vagueness. According to the latter hypothesis it is rather a notion of propositional vagueness that plays a more basic role in explaining the relevant puzzles and we should instead theorize about this monadic property of propositions, which we might express using a predicate taking a that clause, or more commonly, an operator taking a sentence. Sentential vagueness and the phenomena associated with it should be explained in terms of propositional vagueness.
The linguistic approach to vagueness, characterized by its preoccupation with the aforementioned relation between sentences, utterances, or more generally linguistic items, is pervasive within the philosophy of vagueness. The following prominent theories, for example, all appear to subscribe to something like the first hypothesis:1
• Semantic indecision (Dorr [34], Keefe [78], Lewis [92], McGee and McLaughlin [104], Rayo [117])
• Semantic plasticity (Williamson [156])
• The inconsistency theory (Eklund [40])
• Contextualism (GraffFara [45], Raffman [115], Shapiro [131])
• lang=EN-US>Ambiguity (Braun and Sider [20])
• Use theories of meaning (Horwich [71])
• Nihilism about vague language (Unger [144]).
Although not complete, I take it that this list is fairly representative of the state of the literature on vagueness at present.
Proponents of propositional vagueness are by contrast less abundant but include, among others, Salmon [125] and Schiffer [127].[38] [39]An analogy with a related debate might be illuminating here. Historically, linguistic accounts of modality were quite pervasive. According to that view the fundamental issues surrounding contingency and necessity were to be best understood by looking at the way we use language, and it was common to theorize about modality by drawing a distinction between certain sentences.[40] Although that view is held by hardly anybody today, it is also surely true that nobody denies the difference between the sentence ‘Hesperus is Phosphorus' and ‘Hesperus is bright'. The modern view is not that it was a mistake to draw this distinction between sentences, but that it is a mistake to think that an account of this distinction exhausts all there is to be said about modality. By contrast, once we have an adequate account of propositional necessity, either a theory of a propositional necessity predicate, or (as is more common) of a necessity operator, the distinction between sentences can be explained in terms of the distinction between propositions: in the above example the former sentence expresses a necessary proposition whereas the latter expresses a contingent proposition.
Critical to the failure of the linguistic approach was the fact that the converse reduction does not seem to be possible: one cannot explain propositional necessity in terms of sentential necessity. Contingency concerning the brightness of Venus itself is a contingency Venus would have had even if there hadn't been any language users, and it looks on the face of it as though no linguistic account of necessity could account for this.
The situation is similar in the case of vagueness. I of course acknowledge the existence of sentential borderlineness, but think that it is not a theoretically central notion: sententially borderline sentences merely express borderline propositions, and it is in elucidating the latter notion that the action lies.
Accounts that theorize purely in terms of sentential borderlineness, I will argue, do not have the resources to explain propositional borderlineness and are therefore, at best, incomplete.Indeed, the analogy between the two debates is much closer than I have suggested above. Much like the linguistic account of modality, linguistic accounts of borderlineness are subject to a number of technical difficulties that need to be worked out before we can compare them. The purpose of this chapter is to describe the best version of each kind of formalism, so that we will have a more precise target in the later chapters.
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