Abstract
Can identity itself be vague? Can there be vague objects? Does a positive answer to either question entail a positive answer to the other? In this chapter, we answer these questions as follows: no, no, and yes. First, we discuss Evans’s famous 1978 argument and argue that the main lesson that it imparts is that identity itself cannot be vague. We defend the argument from objections and endorse this conclusion. We acknowledge, however, that the argument does not by itself establish either that there cannot be vague objects or that there cannot be identity statements that are indeterminate for ontic reasons. And we further acknowledge that it does not by itself establish that there cannot be identity statements that are indeterminate in virtue of the existence of vague objects. We then go on to argue that, despite this, one who believes in vague objects cannot endorse Evans’s argument. To establish this we offer supplementary arguments that show that if vague objects exist then identity is vague, and that if identity is vague then vague objects exist. Finally we draw attention to an argument parallel to that of Evans’s, but safer, which can be employed against the putative ontic indeterminacy in identity of vague objects which can be differentiated by identity-free properties.
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- 1.
To give just a few examples, the responses to Evans’s argument given in each of the following rely, in one way or another, on the rejection of one of the conditions A to D and are thus immediately ruled out as admissible responses on our view: Broome (1984), Cook (1986), Johnsen (1989), Garrett (1991), Parsons and Woodruff (1995), Copeland (1997), Parsons (1987, 2000), Lowe (2005), French and Krause (1995, 2003, 2006), van Inwagen (1988, 1990, 2009), and Cowles and White (1991) (the response given in this last paper is explicitly directed at Pelletier (1989) but is also applicable to Evans’s argument). (See also fn. 7 for additional comments on French and Krause (1995, 2003, 2006).)
- 2.
See Heck (1998, pp. 282–283) for precisely how to derive ∼∇(a = b) from ∇(a = b).
- 3.
See also fn. 7 below for more on this.
- 4.
Some of the papers cited in fn. 1 above do also reject one or both of the abstraction steps in Evans’s argument. But where they do so, they do so not for independent reasons, but on the basis of one of the other rejected ways of rejecting Evans’s argument. For example, Parsons (2000, ch. 4) argues that the abstraction step from (1) to (2) fails because there is no property of ‘being indeterminately identical with a’ (see pp. 50–52). Lowe and Barnes, by contrast, offer independent reasons for rejecting the abstraction steps that (at least prima facie) do not rely upon a prior commitment to one of the other rejected ways of rejecting Evans’s argument.
- 5.
Again, nothing hangs on the fact that the example is quantum mechanical. Lowe does not think this reply appropriate only with respect to employment of the non-identity-involving property style of argument in quantum mechanical examples. He would give the same reply to Hawley.
- 6.
Lowe again returns to the topic of vague identity in his 2005 ‘Identity, Vagueness, and Modality’, developing earlier material (from his 1982), though he does not specifically discuss the variant of Evans’s argument which appeals only to non-identity-involving properties. His main claim in this paper is that the Evans argument, like the Barcan-Kripke argument for the necessity of identity, involves a transition (in the Evans argument in the move from (3) to (4)) from an ascription to an object a of the property of being determinately/necessarily self-identical to an ascription to a of the property of being necessarily identical to a, but that this transition is illegitimate since these are different properties (everything has the first, only a has the second). The flaw in Evans’s argument (and mutatis mutandis in the Barcan-Kripke argument) which he thinks this reveals is that (3) and (in the Barcan-Kripke argument) ‘□(a = a)’ are ambiguous between two modally non-equivalent readings, one ascribing to a the property of being determinately/necessarily self-identical and the other ascribing to a the property of being determinately/necessarily identical to a. (As he notes, he has to make this ambiguity claim since he must deny the validity of the ‘stripped down’ Evans argument which omits steps (2) and (4) and the original Kripkean formulation of the Barcan-Kripke argument (2005, p. 305).) Despite the obvious non-identity of the properties, the supposed non-equivalence seems difficult to defend. Suppose a possesses the property of being determinately/necessarily self-identical. Then it is a determinate/necessary truth that a possesses the property of being self-identical. But if a has the property of being self-identical, then a has the property of being identical to a. That is also a determinate/necessary truth. Whence we can conclude that it is a necessary truth that a has the property of being identical to a (not just the distinct property of being self-identical, which everything has). So a has the property of being necessarily identical to a. Whatever may be said about this argument, the response to Evans in Lowe’s 2005 paper is different from the one presently under discussion in this section and, in fact, is a version of way (i) of responding to Evans listed above (i.e. not accepting the determinate truth of (3)) which is why we list Lowe’s 2005 paper in fn. 1 above.
The other development in Lowe’s 2005 paper is that he now denies that the names ‘a’ and ‘b’ in the electron example make determinately identifying reference. But he insists that these terms could not be made determinate by precisification. If he is right, then this is another example of what we emphasise the possibility in Sect. 15.5 below – singular terms which are referentially indeterminate but not on account of semantic indecision. But as Williams (2008) explains, the possibility of such cases (of ‘ontically induced’) referential indeterminacy is no objection to Evans.
- 7.
French and Krause have, in various places (e.g. 1995, 2003, 2006), defended the view that in quantum mechanical cases such as the one that Lowe describes, it is indeterminate whether the particles involved are identical. Unlike Lowe, however, they explicitly endorse the view that such quantum particles are non-identical with themselves (they refer to particles with such a characteristic as ‘non-individuals’) (1995, p. 24; 2003, p. 109; 2006, p. 143). This does allow them to respond to Evans’s argument, but in a way that we have explicitly rejected (i.e. way (i) – by rejecting premise (3)). Above we said that it is dialectically inappropriate to deny premise (3) purely in order to reject Evans’s argument. But French and Krause take themselves to have independent reasons for rejecting premise (3) with regard to quantum particles – that is, they think that considerations from quantum mechanics itself strongly support the view that quantum particles are non-individuals. To consider French and Krause’s arguments for this claim in any detail would take us beyond the scope of the current essay. But briefly, we do not think French and Krause are right about this. French and Krause’s main argument for the conclusion that quantum particles are non-individuals, and so indeterminately identical with each other and non-identical with themselves, is in effect that such particles are absolutely indistinguishable (i.e. that they share all of their non-identity-involving properties) (2003, p. 99; 2006, ch. 4). But we simply do not see why we are supposed to conclude that two entities are indeterminately identical, and so non-identical with themselves, from the fact that they are indistinguishable. And even prescinding from this, we have further worries about French and Krause’s view. For one, it is difficult to see how it is possible to secure determinate reference to a non-individual in the first place. And secondly, if it is true that for some quantum particle a, that it is not the case that a = a, then how can it be indeterminate, for some quantum particle b, whether a = b (for surely, if it is not the case that a = a, then it should also be that it is not the case that a = b). But whether or not these latter worries amount to anything, we do reject the view that anything can fail to be self-identical, and can see no reason to revise our opinion based on quantum mechanical considerations. So we reject French and Krause’s response to Evans’s argument along with all other responses that deny premise (3).
- 8.
For those who do not, see Gibbard (1975) for a classic introduction.
- 9.
That this is so is by no means a new insight. Noonan (1991) makes just this point. Incidentally, in that paper it is also argued that one cannot respond to Evans’s argument in a counterpart-theoretic manner (see p. 191).
- 10.
Vague objects, if such there be, must be weird. But Table is very weird indeed. An example due originally to Hawley (2002) provides us with a (comparatively) less weird example:
-
Example: Hawley’s Mouse
Algernon and Socrates are two mice in a cage. Whilst Socrates is a perfectly precise mouse, Algernon is a vague object. Algernon’s vagueness consists in indeterminacy in whether his tail, which is hanging by a thread, is a part of him. It may then be that ‘the largest mouse in the cage’ is indeterminate in reference between Algernon and his more fortunate companion Socrates with an intact, but shorter, tail. So, the identity statement ‘the largest mouse in the cage = Socrates’ is indeterminate in truth-value.
-
- 11.
This is assuming, of course, that such a defender does not wish to reject the classical mereological inference from identity of parts to identity.
- 12.
Whether it is right so to picture mountains and clouds, of course, depends on whether they have minimal extended parts – a mountain-sized heap of footballs does not have a fuzzy boundary in the sense in use here.
- 13.
Other examples of the same type are Edgington’s landmass which is either two mountains divided by a valley or one twin-peaked mountain and van Inwagen’s example of two places connected by a narrow and frequently inundated isthmus that is not definitely land or sea (Edgington 2000, p. 40; van Inwagen 1990, p. 243).
- 14.
If only because if ‘a = b’ is true ‘∃x(Ax&Bx)’ is true in which the predicates ‘A’ and ‘B’ relate to ‘a’ and ‘b’ as ‘Socratizes’ relates to ‘Socrates’.
- 15.
Though it is definitely true that there is a man, just one, in Room 100 before and definitely true that there is a man – just one – in Room 101 afterwards.
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Curtis, B.L., Noonan, H.W. (2014). Castles Built on Clouds: Vague Identity and Vague Objects. In: Akiba, K., Abasnezhad, A. (eds) Vague Objects and Vague Identity. Logic, Epistemology, and the Unity of Science, vol 33. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7978-5_15
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