Áreas de conservación especial

In the previous subsection, we finally made good on our promise to promote a semantic analysis explaining the necessary relationship between standard- sensitivity and the possibility of having borderline cases. We also inadvertently made good on our promise to offer some hypothesis regarding the “nature of vagueness.” Proposition 8.7 permits us to venture that vagueness simply is

standard-sensitive context dependency.

Now, the claim that vagueness is standard-sensitivity, or at least that vague- ness and standard-sensitivity have a deliciously sordid relationship, is one which has been made in the literature before13_{. In order for this accusation to stick,} however, it must be argued that standard-sensitive context dependency is both necessary and sufficient for the other two properties of vague predicates: the ability to have borderline cases and the susceptibility to sorites paradoxes. To my knowledge, no such arguments yet appear in the literature. In this chapter, however, we were able to argue, thanks to the added assistance of our theory of vague selections and our dichotomy between the classesvagueandprecise, that standard-sensitivity is necessary and sufficient for a predicate’s ability to have borderline cases. In the next chapter, we will argue that, moreover, our theory of vague selections is enough to guarantee us that standard-sensitive con- text dependency is necessary and sufficient for a predicate’s being susceptible to sorites paradoxes. This will complete our argument that the underlying na-

ture of vague predicates – that feature of theirs marking the source of all their characteristic properties – simply is standard-sensitive context dependency.

The key ingredient of this argument is, of course, the theory of vague se- lections. After all, standard-sensitivity does not by itself imply the ability to have borderline cases inallcontexts, nor the presence of higher-order vagueness, nor, as we shall see in the next chapter, the susceptibility to sorites paradoxes. Instead, standard-sensitive predicates take on all these properties precisely be- cause vague selections are so integral to their interpretation, and vague selec- tions happen to be saddled with a distinctive sort of “haziness”. In this sense, linguistic vagueness is metaphysically reduced to the “vagueness” of these selec- tions. By the end of the next chapter, we will have shown that the existence of borderline cases and the susceptibility to sorites paradoxes – perhaps the most recognized properties of vague predicates – are features of human language pre- cisely because vague selections have all those characteristic uncertainty orders and are used in the interpretation of so many natural language expressions. In a real sense, then, vague selections are the source of all vagueness in language, and it is in this sense that our theory offers a metaphysical reduction of linguistic vagueness to the “vagueness” of vague selections.

Chapter 4

The Heap

Vague Selections and the Sorites

4.1

Chapter Overview

We at last come to that subject with which most studies of vague predicates begin: the sorites paradox. The reader is warned that this final chapter contains the most speculative and unpolished material of the thesis. One might say that the road is rough, but the weather is nice. Even the lightest stroll through this chapter will still jarringly lead the reader over a great many lacunae, yet he will be continually cooled by a soft, pleasant breeze emanating from some olympic style hand-waving.

The goal of this chapter is to demonstrate that our dynamic semantics — and in particular, the second Vagueness Principle — provides an original resolution to the sorites paradox. Furthermore, when this perspective on the sorites is combined with our theory of predication from Section 3.8.3, one may deduce that predicates are sorites-susceptible if and only if they are standard-sensitive. The chapter begins in the next section with a defense of the fundamental assumptions regarding the sorites from which our analysis starts. Specifically, we defend the claims that the sorites argument does not reveal a genuine paradox, and that the proper response to the argument is to reject one of its premises, rather than to restrict one’s reasoning from those premises.

In Section 4.3, we ready ourselves for a formal attack upon the sorites by our dynamic semantics. The notions of “sorites susceptibility” and “sorites series” are retooled to interconnect more amenably with the technology of our formal theory in Chapter 3. This train of thought then abruptly breaks off in the following sections, as we introduce two important components of our analysis. Section 4.4 addresses the peculiarities of asserting the existence of precise boundaries within well orderings, while Section 4.5 discusses and then precisely formulates the notion that vague selections have a “minimal size.” This lower bound on the girth of vague selections is then argued to imply a

law further constraining the structure of contexts, one that will have a great importance in our theory of the sorites.

Section 4.6 unveils our analysis of the sorites. In a soundbite: the size restriction on vague selections implies a minimum degree of difference between two objects which can be identified in a context as lying on opposite sides of the extension of a vague predicate. This is argued to provide a resolution to the paradox somewhat akin to that found in Graff 2000. Section 4.7 generalizes this analysis to the “higher order” versions of the sorites. Finally, in Section 4.8, we argue that a slightly revised version of the analysis may be combined with our theory of predication from Section 3.8 to predict that predicates are sorites susceptible if and only if they are standard-sensitive.

Then, the thesis is over.