Vague Simples

Vague Simples

Neil McKinnon

Abstract: Gareth Evans has argued influentially against vague identities. David Lewis and Theodore Sider have argued against vague parthood. Much of the distaste among philosophers for metaphysical vagueness is sourced in these arguments. I argue that even if the considerations adduced by Evans, Lewis and Sider are conclusive, metaphysical boundary vagueness remains possible.

1. Background

Here is a simplified account of Gareth Evans' influential argument against metaphysical vagueness (1978). Suppose we have a putative vague object, such as the Dead Sea. There are various precise objects, differing only slightly at their peripheries, that we might describe as being equally good candidates to be identical to the Dead Sea. Yet, from the assumption that the Dead Sea is a vague object we can derive a contradiction. If the Dead Sea is really a vague object then it is indeterminately identical to each of the precise candidates. But this cannot be the case. Consider one of the candidates, a. Although a is indeterminately identical to the Dead Sea, it is determinately identical to a. However, the Dead Sea is not determinately identical to a. The Dead Sea and a therefore differ with respect to the property of being identical to a. And thus, by the Indiscernibility of Identicals, we can infer that the Dead Sea is not identical to a.

Timothy Williamson, though not ultimately sympathetic to metaphysical vagueness, suggests that even if this argument is correct, it does not follow that there is no metaphysical vagueness:

…[F]uzzy boundaries do not in any obvious way require vague identity. Objects are identical only if their boundaries have exactly the same fuzziness (Williamson, 1994, p. 255).

Along these lines, one obvious response to Evans’ argument is to suggest that vagueness is located not in identity, but in parthood; parthood, but not identity, is vague (ibid., p. 256). On this view, there are xs for which it is indeterminate whether they are parts of the Dead Sea, but the Dead Sea is not indeterminately identical to anything.

There are, however, objections to vague parthood. If parthood is vague, then so is composition. If the Dead Sea has indeterminate parts, then there are pluralities of xs such that it is indeterminate whether they compose the Dead Sea. And perhaps, composition cannot be vague. As Lewis puts it:

The question whether composition takes place in a given case, whether a given class does or does not have a mereological sum, can be stated in a part of language where nothing is vague. Therefore it cannot have a vague answer (Lewis, 1986, p. 213).

Theodore Sider develops this argument by noting that if composition were vague, it would be indeterminate how many concrete objects exist. And since the question, ‘How many concrete objects exist?’ can be expressed in non-vague language, it must have a non-vague answer (Sider, 1997, pp. 221-22), contrary to what we would expect if composition were vague. Another worry about vague composition might flow from concerns that composition and identity are so tightly connected that indeterminate composition entails indeterminate identity. So Evans’ argument still has purchase.

I will not attempt to adjudicate any of these issues here. Instead, I will argue, even if we concede that there could not be vague identities (as opposed to vague identity statements), nor vagueness of composition, objects could nevertheless have vague boundaries.

2. Simples

Suppose that the world contains mereological simples; objects with no proper parts. Suppose, also, that these objects are not point-particles, but have spatial extension. The idea is that these simples could still have vague boundaries. Consider such a simple. There are spatial points and regions such that the simple is determinately located at those points and regions. Yet, there are also points and regions at which the simple is indeterminately located.

It might be objected that without recourse to vague parthood there is no good reason to say that the simple is determinately located at various points and regions but indeterminately located at others. Simples lack the structure required to ground such differences. However, I think no one who accepts that mereological simples could be spatially extended ought to find this argument congenial, since a closely analogous argument can be given to suggest that mereological simples could not have spatial extension. Moreover, as I will now urge, such arguments are mistaken.

Here is the analogous argument against spatially extended simples. If an object has spatial extension then it has a shape. An object's having spatial extension is consistent with its having all sorts of shapes. We can explain why different objects have different shapes if the objects have proper parts; the differing shapes are due to the different configurations of each object's proper parts. But differing shapes among simples cannot be accounted for in this way. Whatever shape a simple has, it has as a matter of brute fact. And this is unacceptable.

Should we find this argument persuasive? It would certainly be more than odd to say that objects with spatial proper parts have their shapes as a matter of brute fact. But I see no non-question-begging reason for denying that mereological simples have their shape as a matter of brute fact. If this is right, then the objector must say that the notion of brute shapes is blatantly incoherent. And it isn't.[1]^,[2] Just as there is no non-question-begging argument against brute shape, I doubt that a non-question-begging argument against brute boundary indeterminacy is available. If there were metaphysical boundary indeterminacy for mereologically complex objects, this indeterminacy would have to be accounted for in terms of vague composition.[3] But it is question-begging to draw conclusions from this about the boundary indeterminacy of extended simples. Again, the objector needs to say that such boundary indeterminacy is blatantly incoherent. And again, so it seems to me, it isn't.

3. Conclusion

It remains controversial whether Evans has succeeded in showing that there could not be vague identities. It is also contentious whether parthood could be vague. However, even if the notions of vague identities and vague parthood are incoherent, metaphysical boundary vagueness is not entirely vanquished. It could be the case that there are mereological simples with vague boundaries, and vague complexes composed of those simples.[4]

References

Evans, Gareth (1978), “Can There Be Vague Objects?”, Analysis, 38, p. 208.

Lewis, David, (1986), On the Plurality of Worlds, (Oxford: Blackwell).

Markosian, Ned, (1998), “Simples”, Australasian Journal of Philosophy, 76, pp. 213-228.

Sider, Theodore, (1997), “Four-Dimensionalism”, Philosophical Review, 106, pp. 197-231.

Williamson, Timothy, (1994), Vagueness, (London: Routledge).