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1 Metaphysical Vagueness and Metaphysical Indeterminacy Matti Metaphysical Vagueness and Metaphysical Indeterminacy Matti Eklund [Published in Metaphysica 14 (2013)] 1. I will here discuss vagueness, specifically whether there is “metaphysical” vagueness, vagueness in the world. Let me start with an important preliminary concerning what the phenomenon under discussion, vagueness, is. The term tends to get used one way in ordinary parlance and one way in philosophy. If I reply to a question about where Holger is by saying “he is in some bar”, I can fairly be said to have been ‘vague’ about Holger’s whereabouts. But that’s just a way of saying that I was unspecific about his whereabouts. Often in philosophy, ‘vague’ is used with a different meaning. Vagueness is that phenomenon, whatever it is, that paradigmatically rears its head in sorites reasoning.1 How we decide to use ‘vague’ is just a matter of terminology. The important point is that there is a distinction between what I call ‘vague’ and what I call ‘indeterminate’. Being careful about what the topic under discussion is, is especially important when we consider the possibility of metaphysical vagueness. Many authors freely go back and forth between considering metaphysical indeterminacy and metaphysical vagueness, but one may wish to render one verdict on the possibility of metaphysical indeterminacy and another on the possibility of metaphysical vagueness. The question I will deal with is whether vagueness is associated with semantic indeterminacy, metaphysical indeterminacy, or at best epistemic indeterminacy. Here are rough thumbnail sketches of these types of indeterminacy. (Some qualifications will be introduced later.) On the view that vagueness is associated with semantic indeterminacy it is indeterminate what the expression stands for.2 On the view that vagueness is 1 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 myself.) 2 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”. 1 associated with metaphysical indeterminacy, vague expressions stand for objects that are in and of themselves vague. On the view that vagueness is associated with epistemic indeterminacy, vague expressions have semantically determinate reference, and the objects they stand for are not in themselves vague: the only indeterminacy (if we can even call it that) associated with vagueness is epistemic: for principled reasons we cannot know the reference of vague expressions. In my discussion I will set the possibility of epistemic indeterminacy aside, and focus only on semantic and metaphysical indeterminacy. Throughout, I will speak of the indeterminacy with which vagueness is associated, or vagueness-related indeterminacy, rather that of the indeterminacy which vagueness is. The reason for the perhaps somewhat convoluted formulation is that I want to leave open the possibility that the relation between vagueness and the relevant kind of indeterminacy falls short of identity. My own favored view on vagueness and indeterminacy – briefly summarized and discussed in section 3 – is one on which the relation between vagueness and indeterminacy is less than straightforward, but I believe the talk of indeterminacy “associated with” vagueness is advisable even independently of my own favored view. 2. A fully unified account of indeterminacy is hardly a realistic goal. An account of the indeterminacy associated with vagueness is not necessarily an account of indeterminacy generally. Vagueness-related indeterminacy may be only one kind of the different kinds of indeterminacy, requiring different sorts of treatment, that there are. Already the seeming fact that some purported indeterminacy is semantic and other purported indeterminacy is metaphysical shows, if genuine, that indeterminacy is not a unified phenomenon. But I will also point to how there seem to be distinctions to be drawn between different instances of semantic indeterminacy and between different instances of metaphysical indeterminacy. Let me start by bringing up some rather different instances of semantic indeterminacy. First, consider Quinean indeterminacy. According to Quine, nothing in what determines what a speaker means by her words and symbols determine exact 2 reference – nothing determines that ‘rabbit’ in a given speaker’s mouth refers to rabbits and not e.g. undetached rabbit parts, timeslices of rabbits, etc. Given the holistic features of interpretation, there are other hypotheses about the reference of words that fit all the facts equally well. Second, consider an example made famous by Field (1973). We know from modern physics that nothing satisfies all the claims that Newtonian physics makes about ‘mass’. Instead there exist two different possible referents of Newtonian ‘mass’, proper mass and relativistic mass, both of which approximately satisfy the claims Newtonian physics makes about ‘mass’. It seems wrong to say that ‘mass’ as it occurs in Newtonian physics does not refer. Rather, ‘mass’ as used in Newton is indeterminate in reference as between proper mass and relativistic mass.3 Third, something for which we can use the label semantic indecision or the label incompleteness of meaning. (Both have been used. Maybe the former label is preferable since it carries less theoretical baggage.) 4 Consider a predicate ‘nice’ introduced by incomplete stipulations: n is nice iff n<13 n is nice iff n>15 The predicate ‘nice’ is partially defined. We have been somewhat semantically indecisive with regard to ‘nice’. Maybe it is right to say that its meaning is incomplete. Next, turn to different instances of metaphysical indeterminacy. First, there is the metaphysical indeterminacy that is sometimes said to be shown by quantum physics to obtain. Second, there is the open future. Third, there is indeterminacy as it comes up in certain realist/antirealist discussions. For example, some claims of set theory, 3 To explain, briefly, Field’s point: Two central tenets of Newtonian mechanics is (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 can’t 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.) 4 Modulo minor details, this example is from Fine (1975). 3 prominently the continuum hypothesis, are such that both they and their negations are consistent with the currently accepted axioms of set theory; and there are no obvious additions to the axioms that settle the continuum hypothesis, or so the standard account goes. One dividing line between realism and (prominent types of) antirealism about sets concerns whether the continuum hypothesis anyway has a determinate truth-value. The realist says yes, while the antirealist in one way or other demurs. The antirealist view is that this in one way or other is a matter of indeterminacy of mathematical reality. I find it natural, when considering the different instances of semantic and metaphysical indeterminacy, to say that there are different kinds of semantic indeterminacy and of metaphysical indeterminacy. Putting it this way immediately invites the question of what exactly it means to say that two instances of indeterminacy are, or are not, of different kinds. But for present purposes the important question is just whether there is reason to believe that the questions about indeterminacy raised in the literature are likely to have univocal answers. These are questions about, for example, the logic of indeterminacy and about the cognitive (or normative) role of indeterminacy – where the question of the cognitive role of indeterminacy is the question of what an agent’s attitude toward p ought to be when she takes it to be indeterminate whether p. First, consider the logic of indeterminacy. One popular view on vagueness – although not one I subscribe to myself – is that fuzzy logic is the logic of vagueness: the indeterminacy with which vagueness is associated is a matter of vague sentences taking truth-values on a continuum. But this idea seems like a non-starter in the case of some of the kinds of semantic indeterminacy listed. What we have here is one consideration given which vagueness-related indeterminacy would be a different kind of indeterminacy from the just listed kinds of semantic indeterminacy, even if vagueness-related indeterminacy is indeed semantic. This point about the logic of indeterminacy does nothing to distinguish between purported kinds of semantic indeterminacy distinct from vagueness. But consider then a second issue: the cognitive roles of the indeterminacies. One reasonable view on “14 is nice” is that this is simply to be rejected. But even if one holds this view one can think that “this object has mass ” is one we ought to have a more 4 ambivalent attitude toward, if this is true given one but not the other of the candidate 5 referents of mass. If so, these two types of indeterminacy have different cognitive roles.
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