name=bookmark342>Vague Objects
While it would not be at all surprising that a theory of quantification and determinacy could be carried out rigorously in a linguistic theory, it is worth being upfront about the complexity of this sort of theory.
Note, by contrast, that from a purely formal perspective quantification into the scope of a determinacy operator is no more complicated than quantification into the scope of the negation operator. For the operator approach it is rather the metaphysical commitments that are problematic.One puzzle that has occupied philosophers concerns issues to do with vague parthood and vague objects. Presumably there are rocks and stones such that it is borderline whether they are part of Mt Everest. Let a be one of these rocks. On the other hand, there is also the total lump of rocks and stones—call it Lump—that make up Mt Everest: it is presumably not borderline whether a is a part of Lump, since there is nothing more to a lump of rock and stone than the rocks and stones that make it up. It follows by Leibniz's law that Mt Everest and the lump of rock and stone are different.
This conclusion should strike us as extremely perplexing: Mt Everest and Lump coincide in space and time, they have all the same mereological parts, they appear to stand in the same causal relations to things, and so on. Moreover, this puzzle rested on the adverbialist account ofborderlineness. The puzzle does not arise on a linguistic conception ofborderlineness: the fact that ‘a is a part of Mt Everest' is a borderline sentence, and the fact that ‘a is a part of Lump' is not a borderline sentence, do not together entail that any mountain is distinct from any lump of rock and stone. They at best entail that the names ‘Lump' and ‘Mt Everest' are different—one is a precise name for a particular lump of rock and stones, and the other is a vague name whose meaning is indeterminate between a range of different candidate lumps of rock and stone.
It is not the things made up of rocks and stone themselves that are vague or precise.How this puzzle relates to the issues of quantifying into determinacy contexts, however, is extremely vexed. According to one sort of approach, inspired by McGee [103], we can say things like its borderline whether a is a part of Mt Everest, but we cannot infer from that things like there’s an x and a ó such that it’s borderline whether x is apart ofy using existential generalization into a borderlineness context.[49] This is, in some sense, thought to curtail commitment to vague objects. It is unclear, however, to what extent our original puzzle really relied on this instance of existential generalization: the distinctness of Mt Everest from Lump was derived from Leibniz's law and the claim that a is a borderline part of Mt Everest but not Lump. The view also has some fairly surprising consequences: one might have naively thought that there is a certain mountain which is widely known to be the tallest mountain in the world, that was first climbed in 1953, and so on. Of course it is widely known that Mt Everest has these properties, but without existential generalization you cannot infer that there is something that is widely known to have these properties. Moreover, since nothing determinately has these properties according to the view in question,[50] we have positive reason to doubt that there is something which is widely known to have those properties, given the widely held view that one cannot know something unless it is determinate.
It is worth drawing further parallels with the case of modality here. Quine, for example, was suspicious of the adverbial view of modality because of the metaphysical implications. As we know, in this debate the adverbialist approach to modality now dominates, metaphysical puzzles and all.
A strikingly similar puzzle for the adverbialist account of modality is the problem of the statue and the lump of clay.
The lump of clay out of which the statue is constituted could have been deformed without being destroyed, whereas the statue couldn't; thus the statue, it is concluded, is not identical to the clay for they have different modal properties. If this conclusion is correct then it is not at all surprising that Mt Everest is not identical (even indeterminately) to a precise lump of rock, soil, and snow—this is a conclusion that is motivated by an already established response to the corresponding modal puzzle. Indeed there are many solutions to this puzzle in the modal case that can be applied fairly straightforwardly in the present case.[51]Yet another strategy, one that is much less attractive in the modal case, but perhaps defensible in the case of vagueness, is to reject Leibniz's law. It would then be possible to say that Mt Everest is identical to exactly one fusion of particles, although it is indeterminate which.[52]
Although this is not the place to defend a particular solution to this conundrum, the metaphysical puzzles that adverbialists find themselves faced with are puzzles that I think we are already committed to on independent grounds. I see no particularly pressing objection here to an adverbialist conception of vagueness that is not equally an objection to an adverbialist conception of modality.
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