Main authors discussed: Gareth Evans

Gareth Evans’ argument against the coherence of vague identity presents a well-known obstacle for theories of vague objects.  The main purpose of Williams’ paper is to sketch a new model of ontic vagueness on which Evans’ argument can be blocked. Evans’ argument runs as follows:

1. Assume: It is indeterminate whether a is identical with b.
2. Then:  a has the property of being indeterminately identical with b.
3. Clearly: It is not indeterminate whether b is identical with b.
4. Then: b does not have the property of being indeterminately identical with b.
5. Thus: a is not identical with b.

Williams starts by laying down and defending a series of constraints on a satisfactory defense of ontically vague identity against Evans’ argument, constraints that rule out many of the extant solutions. One of the constraints–namely, that a defense should recover ontically vague identity and not locate the source of the vagueness in either semantic indecision or our ignorance–appears to rule out any solution that tries to block Evans’ argument by appeal to referential indeterminacy, because referential indeterminacy is typically viewed as a matter of semantic indecision.

Williams sketches a model on which the referential indeterminacy is instead due to ontic indeterminacy. Start by distinguishing, in actualist fashion, between the concrete universe we inhabit–Williams calls it reality–and the possible worlds that constitute the maximal properties that reality might have instantiated. Assuming that reality is vague while the possible worlds are precise, it is indeterminate which possible world is instantiated by reality. Say that a world w corresponds to reality just in case w is not determinately uninstantiated and call a world that does correspond to reality in this sense an actuality. If reality is vague, then there is more than one actuality.  We say that a sentence is true (of reality) just in case it is true with respect to all actualities. We say that a sentence is indeterminate if it is true with respect to some actualities, false with respect to others. Williams does not specify a detailed semantics, nor does he need to given the purpose of his paper, but the reader is referred to forthcoming work by both Williams and Elizabeth Barnes.

Next, the model of ontic indeterminacy is applied to what looks like a paradigm case of vague identity. An amoeba, Sue, splits into two amoebas. One of which, Sally, goes off west, while the other, Sandy, goes off east. Williams’ model allows him to diagnose the situation as one in which it is indeterminate whether Sue is identical with Sandy, and the indeterminacy arises from referential indeterminacy that is induced by ontic vagueness. Here is how. There are two relevant actualities. In the first, Sue survives as Sally, and in the second Sue survives as Sandy. Since Sue survives in all actualities, it is true that Sue survives. Yet, it is indeterminate whether Sue is identical to Sandy, because ‘Sandy’ (as well as ‘Sally’) is referentially indeterminate. In the second (first) actuality, it picks out the surviving amoeba, in the first (second), the new amoeba that splits off. ‘Sue’, on the other hand, is referentially determinate, picking out the surviving amoeba in each actuality and thus picking out the surviving amoeba in reality. The important point is that the referential indeterminacy of ‘Sandy’ does not flow from any deficiency in the semantic convention that fixes the name’s reference: ‘Sandy’ refers to the amoeba that floats off eastward. What is indeterminate is whether that amoeba is identical with Sue–the unique amoeba that exists before and survives the split.

Williams goes on to argue that this case of vague identity is not ruled out by Evans’ argument because, putting ‘Sue’ for ‘a’ and ‘Sandy’ for ‘b’, the inference from 3 to 4 fails. In every actuality, “Sandy is identical with Sandy” is true and so it is not indeterminate whether Sandy is identical with Sandy. Yet ‘Sandy’ is referentially indeterminate in reality, and so there is no object that ‘Sandy’ picks out and to which 4 can deny the property of being indeterminately identical with Sandy. Thus, Evans’ argument is invalid.

Besides this novel defense of the coherence of ontically vague identity, the paper also includes some interesting discussion of the importance of ontic vagueness as well as of the relationship between vague identity and other instances of vagueness, such as vague existence and vague instantiation. Building on work by Elizabeth Barnes and Kathrine Hawley, Williams argues that, contrary to what many authors believe, vague existence and vague property instantiation give rise to vague identity, so that Evans’ argument, if successful, rules out more than meets the eye.

One small point of criticism: Williams takes possible worlds to be maximal precise world properties. It would seem that, on the assumption that reality is genuinely vague, it does not instantiate any maximal precise world property, either determinately or indeterminately. The world might have been precise and so could have instanced one of these properties but as things actually stand, it doesn’t. While many precise images may depict vague reality equally well, none of them depicts it correctly. Elizabeth Barnes, whose closely related work Williams refers to, takes it that the world is precise but that it is indeterminate which precise world property it instantiates. This move would get around the objection, but at the cost of locating worldly vagueness not in the world but in the world’s relationship to how it might be.

Reviewed by Iris Einheuser
Duke University

2 Comments

• By Robbie, May 5, 2009 @ 11:04 am

  Thanks for this review! Just on the thought in the last paragraph. For simplicity, let’s pretend there’s just one property at issue: say, the one thing that exists being charged. (some more below on whether this is legitimate). And suppose that in reality, it’s indeterminate whether the one thing that exists is charged.

  Now, on the model I sketch in the paper, there’ll be two actualities: one that is instantiated by reality iff the one thing that exists is charged; the other that is instantiated iff the one thing that exists isn’t charged.

  The thought in the review is that the property “containing exactly one thing that is charged” should be determinately uninstantiated by a reality where the one thing is indeterminately charged.

  I was thinking that you can’t say this and maintain the determinate truth of plausible disquotational-style principle for instantiation: that something instantiates the property F iff it is F. If that biconditional is true, then by the description of the situation, the RHS is indeterminate (not determinately true nor determinately false). Under minimal assumptions about the logic of “D” (something like the modal principle K), we’d be able to derive that the LHS should be indeterminate as well. But that’s incompatible with maintaining that the LHS is determinately false, i.e. that determinately, reality doesn’t instantiate the world-property. So I thought it was reasonable to say here that it’s indeterminate whether reality instantiates the “precise” world-properties.
  Options? We could deny the disquotation-style principle. Alternatively, we could point to features of “precise” world-properties that aren’t covered in the toy model above, to find some independent reason to be dissatisfied with the little picture just sketched.

  It’s noticeable that my toy model doesn’t take a stand either way on whether the world contains “exactly one thing that is determinately charged”. You might reasonably think this is the crucial issue. If the worlds are to be *maximal* world-properties, surely (the thought goes) they should either require that exactly one thing is charged, and this is determinately the case, or require that exactly one thing is charged, and this is not determinately the case. On the first option, an indeterminate reality won’t instantiate the world-property in question. On the second option, the supposedly “precise” worlds themselves represent reality as indeterminate—which didn’t seem to be at all what I was selling in the paper.

  In fact, the “world-building” language I have in mind won’t allow talk about determinacy at all (compare to issues in the philosophy of modality about whether the world-building language should itself contain modal vocabulary). So I avoid the dilemma just sketched by fiat: the maximal properties by themselves simply don’t take a stance over issues of determinacy or indeterminacy. This highlights something you mention: it’s crucial to the success of the overall project that we be clear on the metaphysical and model-theoretic details—what the worlds are, how exactly truth et al is defined. I’ve continued to work on these issues, but they’re not explicitly addressed in the paper.

  (By the way, this makes the picture sound *very* close to the view you attribute to Barnes. I think it is very close—in fact, we’ve been working jointly on some of this stuff recently. I’m not sure why her view (or the one just sketched) “locates vagueness in teh world’s relationship to how it might be”—the thought would be that it’s indeterminate whether Sparky is charged. Full Stop. Because of this, and because w represents that Sparky is charged, it’s indeterminate whether w represents the world correctly. Facts about determinacy and indeterminacy *induce* interesting relations between worlds and the reality they represent—the direction of explanation doesn’t go from reality-world relations to determinacy facts, but rather the reverse.)
• By Iris Einheuser, May 27, 2009 @ 6:02 pm

  > I thought it was reasonable to say here that it’s indeterminate
  > whether reality instantiates the “precise” world-properties.

  Looked at this way, that does seem quite reasonable. And yet, I have
  this strong sense that if the world is indeterminate and the
  possible worlds aren’t, then none of the possible worlds correctly
  represents the world. So what’s the source of that intution? Maybe
  this: Possible worlds just represent how things are, not how things
  are determinately. So we need to distinguish between, on the one
  hand, what is the case and what is determinately the case; and on
  the other hand, what is *represented* to be the case and what is
  represented to be *determinately* the case. If it is the case that
  p, then it is the case that determinately p. I took a
  *representation* that p to be a representation that determinately
  p. Give this up (as your comment suggests you do) and you can say:
  If it is indeterminate whether C(a) then it is indeterminate whether
  a representation that represents the world as one in which C(a)
  represents the world correctly. The source of my intuition must have
  been the thought that a representation that represents the world as
  one in which C(a) is one that represents it as one in which
  determinately C(a). *Such* a world does determinately not represent
  the world correctly. Can we give up the idea that when a
  representation represents that p then it represents that
  determinately p, without also giving up the idea when it is the case
  that p then it is the case that determinately p? I don’t have
  arguments up my sleeve either way but am inclined to think that we
  can, because what we take representations to represent is pretty
  much up to us, so unless there is an analytical connection between
  what is the case and what is determinately the case, we should be
  able to take them to be neutral with respect to determinacy issues.

  What you say about your “world-building language” is very
  interesting. One question here is what it means to say that a
  possible world is not *determinately uninstantiated* by the world
  when talk of determinacy and indeterminacy is interpreted in terms
  of the relationship between the world and the actualities (where the
  actualities are the non-determinately uninstantiated world
  properties). I don’t think that it would be all that bad if in the
  end you needed some talk of (in)determinacy in the metalanguage.
  Many actualists have given up on giving a reductive account of
  modality and acknowldege that to characterize a space of
  possibilities with respect to which modal discourse is interpreted
  we need to help ourselves to some modal notions. That doesn’t mean
  that the possible worlds framework isn’t helpful in illuminating the
  nature of modal discourse.

  (Re. Elizabeth Barnes’ position: Maybe I spoke too fast (I had just
  recently given Elizabeth’s paper `Ontic vagueness: A guide for the
  perplexed’ a quick read and may not have absorbed all the
  subtleties; so I apologize if I have misrepresented her view and
  would be glad to hear if I did!), but the reason I thought that on
  her model vagueness was not in the world but in the relationship
  between the world and the possible worlds is that she explicitly
  says that on her view, in order to do justice to the rejection of a
  “third category” conception of indeterminacy, the world is precise
  and it’s just indeterminate which precise way they are. If the world
  is precise and the possible worlds are precise, then what other
  source of indeterminacy is there but the relationship between the
  world and the possible worlds? Maybe I’m reading this wrong, but
  then how should it be read?)

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