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