Arguments from Coincidence

Arguments from Coincidence

The material constitution puzzles from §2.3 can be repurposed as arguments against two forms of permissivism: universalism and the doctrine of arbitrary undetached parts (DAUP). The basic idea behind both arguments is that permissivists end up committed to objects that are distinct and yet share all of their parts, which is impossible.[70]
Here is a coincidence argument against universalism. Let the ks be the atoms that presently compose my kitchen table, K, and let us suppose that there is some time, t, long before the table itself was made, at which the ks all existed.

(CU1)If universalism is true, then there is some object, F, that the ks composed at t.
(CU2)If the ks composed F at t, then F exists now.
(CU3)If F exists now, then F = K.
(CU4)If F = K, then K existed at t.
(CU5)K did not exist at t.
(CU6)So, universalism is false.

CU1 looks to be a consequence of universalism, given our assumption that the ks all existed at t. The idea behind CU2 is that there would seem to be only two nonarbitrary accounts of the persistence conditions of the widely scattered fusion F: (i) that F exists for as long as the ks are in precisely the arrangement that they enjoy at t or (ii) that F exists for as long as the ks exist. Option (i) imposes an implausibly severe constraint on the sorts of changes an object can survive, which leaves us with option (ii)—from which it follows that, since the ks exist now, so does F. The idea behind CU3 is that there cannot be distinct objects which (like F and K) have exactly the same parts and exactly the same location. CU4 is a straightforward consequence of Leibniz’s Law: F by hypothesis existed at t, so if F = K then K must also have existed at t. As for CU5, tables plausibly are essentially tables, in which case K could not have existed before the table was made.
Here are some options for resisting the argument (some mirroring responses to the puzzles of material constitution). One can deny CU2 on the grounds that table is the “dominant kind”, and once K comes into existence, it takes F’s place and F is annihilated. Constitutional pluralists can deny CU3 and affirm that F ≠ K, perhaps granting that distinct objects can have exactly the same parts and location, or insisting that F and K have different (e.g., temporal) parts. Or one can deny CU5, insisting that K is only contingently a table and (like F) was once a scattered fusion.[71]
Now for the coincidence argument against DAUP. Take the example of Woodrow and Woodrow-minus from §2.8. At t1, Molly the cellulose molecule is a part of Woodrow and at t2 Molly is removed and destroyed. Let Woodrow1 be that (if anything) which ‘Woodrow’ picks out at t1; Woodrow2, that (if anything) which ‘Woodrow’ picks out at t2; and mutatis mutandis for Woodrow-minus1 and Woodrow-minus2. Here is the argument:

(CD1)If DAUP is true, then Woodrow-minus1 exists.
(CD2)If Woodrow-minus1 exists, then Woodrow-minus2 exists.
(CD3)If Woodrow-minus2 exists, then Woodrow-minus2 = Woodrow2.
(CD4)If Woodrow-minus2 = Woodrow2, then Woodrow-minus1 = Woodrow1.
(CD5)Woodrow-minus1 ≠ Woodrow1.
(CD6)So, DAUP is false.

CD1 looks trivial: DAUP guarantees that there is an arbitrary undetached part of Woodrow composed of all of its parts other than Molly. The idea behind CD2 is that Woodrow-minus doesn’t undergo any change between t1 and t2 that could threaten its existence; all that happens is that it is separated from something (Molly) that was not even a part of it. CD3, like CU3, is motivated by the intuition that objects with the same parts and same location must be identical. CD4 is an application of the transitivity of identity: Woodrow-minus1 = Woodrow-minus2, so if Woodrow-minus2 = Woodrow2, then (by transitivity) Woodrow-minus1 = Woodrow2; and since Woodrow2 = Woodrow1, it follows (by transitivity) that Woodrow-minus1 = Woodrow1. Finally, CD5 is a straightforward consequence of Leibniz’s Law: Woodrow-minus1 and Woodrow1 have different parts and thus cannot be identical.
As with the argument against universalism, one can resist this argument by denying CD2 and insisting that once Molly is removed, Woodrow-minus is “dominated” by Woodrow and ceases to exist. Or one can deny CD3 and insist that Woodrow and Woodrow-minus are distinct at t2despite having all the same material parts at t2. Or one can deny CD4 by insisting that Woodrow has all of its parts essentially, in which case Woodrow1 ≠ Woodrow2.[72]

3.5 Arguments from Gunk and Junk

A “gunky” object is a composite object all of whose parts themselves have parts. The mere possibility of gunky objects underwrites an argument against the nihilist thesis that (actually) there are no composite objects.

(GK1)It is possible for there to be gunky objects.
(GK2)If gunky objects are possible, then nihilism isn’t necessarily true.
(GK3)If nihilism isn’t necessarily true, then nihilism isn’t actually true.
(GK4)So, nihilism is false.

GK1 is plausible. It seems easy enough to imagine gunky objects, for instance by imagining an object with a right and left half, each of which itself has a right and left half, which themselves have right and left halves … “all the way down”, and never terminating in simple parts. Moreover, it may even be that actually all objects are gunky. GK2 is trivial: if there are gunky objects in world w, then there is something with parts in w, in which case there are composites in w and nihilism is false in w. GK3 is plausible as well: the actual world contains what would seem to be paradigm cases of composites (trees, etc.), so if composition occurs anywhere, it surely occurs here. Moreover, nihilism is meant to be an answer to the special composition question, and one would expect such an answer to be giving necessary and sufficient conditions for composition—in which case one would expect proponents of nihilism to regard it as a necessary truth.[73]
Some will deny GK1. What does seem obviously possible (and easily imaginable) for there to be certain kinds of infinite descent. But infinite descent need not be mereological. For instance, it does seem possible for there to be objects that can be divided into two halves, and whose halves can in turn be divided into two halves, and so on. But it is controversial whether the fact that o canbe divided into two halves, h1 and h2, entails that o is not simple. One might deny that h1 and h2exist at all before the division: they are brought into existence when o is divided and, a fortiori, are not parts of o prior to division. Or one might concede that, prior to division, h1 and h2 exist and are partially colocated with o, but deny that they are thereby parts of o.[74]
One might instead reject GK3 on the grounds that it runs afoul of “Hume’s Dictum”, according to which there can be no necessary connections among distinct existences. There is some controversy about how best to understand Hume’s Dictum and, in particular, whether it prohibits necessary connections even between overlapping items (which typically are thought not to be “distinct” in the relevant sense). But assuming that it does, then it will rule out any principle of composition according to which simples in certain arrangements cannot fail to compose something—for this would be to impose a necessary connection between simples being in that arrangement and the existence of a (numerically distinct) whole that they compose. And if we cannot in general expect theories of composition to be necessary if true, we should not expect nihilism to be necessary if true.[75]
Just as the possibility of infinite descent can be wielded against nihilism, the possibility of infinite ascent can be wielded against universalism. Let us say that there is “junk” iff every object is a part of some further object.

(JK1)It is possible for there to be junk.
(JK2)If junk is possible, then universalism isn’t necessarily true.
(JK3)If universalism isn’t necessarily true, then universalism isn’t actually true.
(JK4)So, universalism is false.

The idea behind JK1 is that an infinite ascent of wholes is no less imaginable than an infinite descent of parts. The idea behind JK2 runs as follows. According to universalism, every plurality of objects has a fusion, and, in particular, the plurality consisting of all things has a fusion. But there can be no fusion of all things in a junky world. For that fusion would have to be a part of something (since the world is junky); but if it already has everything as a part, there is nothing left for it to be a part of. JK3 can be motivated in much the same way as GK3: universalism is meant to be an answer to the special composition question, and thus will presumably be necessary if true. The strategies considered above for resisting the gunk argument seem to apply equally to the junk argument—one can, for instance, deny that we are imagining what we think we are, or one can invoke Hume’s Dictum and deny that universalism is necessary if true

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Arguments from Coincidence

Arguments from Coincidence

3.5 Arguments from Gunk and Junk

Arguments from Coincidence :: تعاليق

Arguments from Coincidence

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