The topic of this paper is whether there is metaphysical vagueness. It is shown that it is important to distinguish between the general phenomenon of indeterminacy and the more narrow phenomenon of vagueness (the phenomenon that paradigmatically rears its head in sorites reasoning). Relatedly, it is important to distinguish between metaphysical indeterminacy and metaphysical vagueness. One can wish to allow metaphysical indeterminacy but rule out metaphysical vagueness. As is discussed in the paper, central argument against metaphysical vagueness, like those of Gareth Evans and Mark Sainsbury, would if successful rule out metaphysical indeterminacy. One way to argue specifically against the possibility of metaphysical vagueness might be thought to be to argue for a specific theory of the nature of vagueness according to which vagueness is a semantic phenomenon. But it is shown that there are complications also pertaining to arguments with that structure. Toward the end of the paper, I discuss Trenton Merricks’ well-known argument against a semantic view on vagueness and for a metaphysical view.
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Note the formulation “paradigmatically rears its head”. This characterization of vagueness does not immediately entail that vagueness, understood as characterized, is always associated with sorites phenomena. (Although I happen myself to believe a version of this stronger claim.)
Arguably other representational items than expressions can be vague, and a more appropriate label for what I will here keep referring to as semantic indeterminacy would be representational indeterminacy. I will however stick with standard terminology and use “semantic” instead of “representational”.
To explain, briefly, Field’s point: Two central tenets of Newtonian mechanics are (a) that momentum equals mass times velocity and (b) that for any two frames of reference, mass is the same with respect to both frames. Relativity theory shows that it cannot be that both tenets are correct, for the momentum of a particle divided by its velocity has different values in different frames of reference. But this does not mean that any specific Newtonian tenet has been refuted. For relativity theory posits one thing that satisfies (a)—relativistic mass (total energy divided by the square of the speed of light)—and another thing that satisfies (b)—proper mass (nonkinetic energy divided by the square of the speed of light). Relativity theory would have refuted a specific tenet of Newtonian physics if Newton’s “mass” determinately referred to either relativistic mass or proper mass (or determinately referred to neither). But Field’s claim is that precisely because relativistic mass and proper mass approximately satisfy the claims Newton made about “mass”, Newton’s term “mass” is indeterminate in reference as between these two possible referents (see Field (1973), pp. 466–7.)
Modulo minor details, this example is from Fine (1975).
Williams (2012) argues that different kinds of indeterminacy are associated with different normative roles. Or, better, that is what I see as the natural upshot of what Williams says. For discussion, see Eklund (2013).
One awkwardness concerning how to speak of this (at least) is that on standard views the objects of cognitive attitudes are propositions, but on standard views on semantic indeterminacy, propositions are not indeterminate—only the linguistic expressions we use are. In the main text, I adopt the expedient of speaking of the attitudes as directed toward sentences. Of course, that is not in the end a satisfactory solution. Some may be inclined to think this problem shows that there is something amiss with the idea of semantic indeterminacy. My own view is that there surely is some sense in which I can believe that 14 is nice and that what I believe is indeterminate, even if the indeterminacy at issue is semantic. But discussing how it can be so will have to await another occasion.
The example is from Weatherson (2010), p. 80.
Here, it matters that vagueness was characterized as the phenomenon that paradigmatically rears its head in sorites reasoning. Given a characterization linking vagueness to soriticality more tightly, this kind of purported counterexamples would be ruled out by definition.
Morreau (2002) takes this line, saying “The main problem with the argument from definite identities is just that there is no reason to think that things with fuzzy boundaries must have indefinite identities. Strangely, Evans did not even try to show that they must; perhaps it did not occur to him that having a fuzzy boundary and having an indefinite identity might be different things” (p. 338).
Morreau (2002) discusses a problem similar to this one. His proposed way out—applied to this case—is this. Suppose at the earlier time, object a is (determinately) F; but at the later time a is such that it is indeterminate whether it is F. Then S*, a’s state at the later time is indeterminate, but S, its state at the earlier time, is (we may assume) determinate. But then S and S* are determinately distinct for one has a property the other lacks.
I discuss the issue mentioned here also in Eklund (2008). To see that “few” and “many” are vague, consider the following sorites arguments:
If someone has exactly one hair on her scalp, then she has few hairs on her scalp.
For all n, if someone with exactly n hairs on her scalp has few hairs on her scalp, then someone with exactly n + 1 hairs on her scalp has few hairs on her scalp.
So, for all n > 0, someone with exactly n hairs on her scalp has few hairs on her scalp.
If someone has exactly one billion hairs on her scalp, then she has many hairs on her scalp.
For all n, if someone with exactly n hairs on her scalp has many hairs on her scalp, then someone with exactly n - 1 hairs on her scalp has many hairs on her scalp.
So, for all n less than a billion, someone with exactly n hairs on her scalp has many hairs on her scalp.
Williamson (2005), p. 705.
See, e.g., Barnes (2010), p. 612.
See Lewis, e.g. (1997).
See Fine (1975).
Merricks (2001), p. 149.
Compare here also
(2) “Harry is bald” is true.
One thing the supervaluationist can say about (2) is that it is plainly false. This is what she should say if she holds on to the view, traditionally associated with use of supervaluationist machinery, that truth simpliciter is truth under all precisifications. And then she ought presumably to say this also about (1). But if she says that it is equivalent to (0), which is another natural thing to say, then the same questions arise as those Merricks raises in the case of (1).
Merricks keeps speaking of “describes” as expressing many different relations on the supervaluationist view—but he notes that it may be preferable to describe the situation as one where it is indeterminate what “describes” expresses. He rightly sets aside the issue as irrelevant to his main point.
Merricks (2001), p. 150.
Merricks (2001), p. 150.
Merricks (2001), p. 150f.
Merricks (2001), p. 151.
Merricks (2001), p. 151. This is a good place to compare an intuitive challenge to the idea that vagueness or indeterminacy is merely semantic and not metaphysical: linguistic expressions are part of the world, so is saying that they are vague or indeterminate not a way of saying that the world is vague or indeterminate? A first remark on this intuitive challenge is: how would this not work also for ambiguity or context sensitivity? And since metaphysical ambiguity or context sensitivity is out, something must have gone wrong with the intuitive challenge. And secondly, the natural thing for the semantic theorist to say is that what she predicates of a linguistic expression when saying that it is “vague” is different from what she refuses to predicate of any worldly item when she says no such item is “vague”. In effect, it is this second train of thought that Merricks explores.
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Thanks to an audience at the GAP 8 in Konstanz, September 2012, as well as to Elizabeth Barnes, Ross Cameron and Robbie Williams, for helpful feedback.
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Eklund, M. Metaphysical Vagueness and Metaphysical Indeterminacy. Int Ontology Metaphysics 14, 165–179 (2013). https://doi.org/10.1007/s12133-013-0119-0
- Metaphysical indeterminacy
- Metaphysical vagueness
- Meaning-inconsistency view
- Gareth Evans
- Mark Sainsbury
- Trenton Merricks