According to a popular, plausible, but also controversial view about the nature of vagueness, vagueness is a matter of semantic indecision. In the words of one of its main defenders, David Lewis:
Likewise for other vague singular terms, like `Tibbles,' `Everest,' `Toronto,' and `I.' Donald Smith (2006) argues that if `I' is indeed vague, and the view of vagueness as semantic indecision is correct after all, then `I' cannot refer to a composite material object. But his considerations would, if sound, also establish that `Tibbles,' `Everest,' or `Toronto,' do not refer to composite material objects either--nor hence, presumably, to cats, mountains, or cities. And the considerations can be resisted, anyway. Or so I argue.
Smith observes that, according to the view of vagueness as semantic indecision, although it is definitely the case that there is something to which a vague singular term refers, nothing is such that it is definitely the case that it is what a vague singular term refers to--at least, on standard ways of characterizing what it is for something to satisfy a definiteness-involving matrix, see (McGee 1998). Therefore (Tibblesdd) and (Idd) are true, according to the view, but (Tibblesdr) and (Idr) are not:
|(Tibblesdd)||D∃x(Tibbles = x);|
|(Tibblesdr)||∃xD(Tibbles = x);|
|(Idd)||D∃x(I = x);|
|(Idr)||∃xD(I = x);|
(where `D' stands for the notion of definiteness, and assuming variables are precise).
Next Smith observes that (if one beliefs that one exists) rejecting (Idr) commits one to
odd I exist and for all x either the use of `I' in this sentence fails to refer to x or it is indefinite whether the use of `I' in this sentence refers to x.
Although he does not say, in a similar manner (if one beliefs that Tibbles exists) rejecting (Tibblesdr) commits one to
odd? Tibbles exists and for all x either the use of `Tibbles' in this sentence fails to refer to x or it is indefinite whether the use of `Tibbles' in this sentence refers to x.
According to Smith, odd is odd. The reason he gives, however, would also make odd? odd, which it is not.
And the consideration is flawed, anyway. Here it is, in a variant involving Tibbles:
Obviously, the problem lies with the very first conditional. If `Tibbles' is vague, and the view of vagueness as semantic indecision is correct, then, when I assert sentence containing it, I do no need to take myself to having successfully referred to any particular thing--if that is understood as definitely referring to something. Rather, I aim my statement to turn out true on any admissible way of making the semantic decisions that are not (and should not, and maybe cannot, be) made. But surely, on any admissible sharpening of `Tibbles,' `Tibbles exists' turns out to be true. Hence the first conjunct of odd? is true no matter what, and perfectly compatible with the vagueness of `Tibbles' in a way that also vindicates the second conjunct, according to the view of vagueness as semantic indecision. Mutatis mutatis, of course, for `I' and odd.
The other one consideration Smith offers seems more important, and concerns the problem of the many.Foot note 1 According to the view of vagueness as semantic indecision, nothing in the thoughts, experiences and practices of language users, nor in the way things are, determines any particular thing as the cat referred to by `Tibbles.' Rather there is a number of different candidates that are equally eligible candidate referents for `Tibbles.' Now, given that it is definitely the case that Tibbles is a cat, the different candidates seem to share those features that are relevant for something being a cat, and hence seem to have equal claim to be a cat. Hence the problem of the many: where it seemed to be one and just one cat, there turn out to be many candidates with equal claim to be the cat, and there is nothing in the vicinity with a better claim. So, instead of one cat, we seem to have many. Mutatis mutandis, again, regarding the different candidates to which `I' indeterminately refers, if it is vague and the view of vagueness as semantic indecision is correct: each seem to have equal claim to be a person.
One solution to the problem of the many accepts that the many are indeed cats (or people), and explain why this notwithstanding, the adequate response to the question `How many cats are there on the mat?' is (typically) `Just one.,' appealing to independently motivated facts about the pragmatics of counting, see (Lewis 1993). To the possibility that the many are people, Smith simply responds: «There simply is not, so it seems to me, this massive collection, pain-experiencing, action-performing entities.» One would certainly appreciate some reason for thinking that the Lewisian account of why it seemed to us that there simply is not a massive collection--even if strictly speaking there is one such--is faulty. For what it is worth, my own view is that, actually, one such «many» solution is the most promising one to the problem of the many, and certainly the solution that I think defenders of the view of vagueness as semantic indecision should ultimately adopt, see (López de Sa 2004).
But be this as it may, it is certainly not the only solution that defenders of the view of vagueness as semantic indecision can adopt--and have indeed adopted. One rival solution by disqualification is the so-called «supervaluationist» solution, mentioned also in (Lewis 1993), and more recently defended by (McGee & McLaughlin 2000), (Varzi 2001) and (Weatherson 2003). According to this alternative solution, each sharpening of `is a cat' or `is a person' selects just one of the many candidates--different ones in the different sharpenings, thus respecting the arbitrariness felt in denying that they all had an equal claim. `Tibbles is a cat' serves as a penumbral connection, guarantying that it is rendered inadmissible any sharpening that selects a different candidate as the referent of `Tibbles' from the one that is selected as belonging to the extension of `is a cat'--inasmuch as `If it is not red, then it is orange' serves to exclude sharpenings in which borderline rose Fifí is assigned both to the extension of `is red' and to that of `is orange.' Thus the many candidates are indeed equally eligible as referents of `Tibbles,' but it definitely the case that one and just one of them is a cat after all. Mutatis mutandis, once again, for me.
Thus the view that the many candidates are all indeed people (or cats), «very substantive and wildly implausible» as it might be, it is by no means «a metaphysical commitment incurred by anyone who accepts the negation of (Idr)» (or of (Tibblesdr) for that matter), against what Smith contends. On the contrary, any reason one could have for thinking that it is indeed implausible would be a reason for the defender of the view of vagueness as semantic indecision to adopt a so-called «supervaluationist» solution to the problem of the many.
I conclude that, even if `I' is vague and the view of vagueness as semantic indecision is correct, I could be a material composite object all the same.Foot note 2
Dan López de Sa
LOGOS--Grup de Recerca en Lògica, Llenguatge i Cognició
Universitat de Barcelona
Research Centre for the Philosophy of Logic, Language, Mathematics and Mind
University of St Andrews
dlopezdesa [at] ub [dot] edu
[Foot Note 1]
Strictly speaking, Smith also submits the following «Cartesian» consideration: «In order for me to believe that something is the case, I must definitely be around to belief it. And this requires there to be something that is definitely identical with me...» But this certainly does not require that: it suffices that it is definitely the case that I am around to belief it. In any event, Smith himself does not seem to put much weight in his «Cartesian» consideration.
[Foot Note 2]
For discussions on these topics, thanks to Robbie Williams. Research funded by project HUM2004-05609-C02-01 and a GenCat-Fulbright Postdoctoral Fellowship.