Friday, January 2, 2015

Mereological universalism universalized some more

Mereological universalism says that every set A of objects has a fusion: an object wholly composed of parts in A. One motivation for mereological universalism is to make sure that ordinary language terms like "this chair", "that bump" and "those waves" have reference, while avoiding the ad hoc anthropocentrism of positing all but only all the objects that ordinary language describes. We don't want to be ad hoc, so we suppose a vast multitude of objects.

In order to make sense of commonsense objects that have exactly the same parts now—such as the statue and the lump of bronze—the above strategy is normally extended to be four-dimensional: any set of four-dimensional objects has a fusion. The lump of bronze includes temporal parts that pre-existed the statue. On the other hand, if a piece of the statue will tomorrow break off and be repaired with brass, that piece of brass is a part of the statue but not of the lump of bronze.

But we also have to make sense of commonsense objects that have exactly the same parts for all time. For instance, it could just so happen that the lump of bronze is produced simultaneously with the statue (e.g., by solidifying within a mould) and destroyed simultaneously with it (e.g., by instantaneous vaporization). To distinguish such objects, mereological universalism is generalized to allow for something like arbitrary fusions across possible worlds. Even if the lump coincides with the statue throughout its career, it doesn't coincide with it in other worlds, say ones where the statue is destroyed in a way that preserves the lump, say by squashing. I call this five-dimensional mereological universalism—the fifth "dimension" being that of worlds. We could formulate this by saying that there is an object corresponding to every modal profile, where a modal profile picks out a four-dimensional (assuming the world is one with time and 3D space; this may need further generalization) object in each world.

The above is a fairly familiar story. But I now want to complicate it some more. If we really are out to preserve commonsense language, we not only have to get an object for every commonsense object, which we can do by saying that every modal profile has an object but we have to get right the definiteness profile for that object. Consider, for instance, a statue made of copper. The statue fairly quickly acquires a copper oxide patina. That patina is definitely a part of the statue. But the patina is not a part of the lump of copper, since copper oxide is not copper. However, it is vague when an atom of copper comes to be an atom of copper oxide—just how tightly bound to an oxygen atom does it need to be? So there will be a temporal part of a copper atom which will only vaguely be a part of the lump of copper, but be definitely a part of the statue.

To avoid anthropocentric arbitrariness, if we take such vagueness seriously, then the same reasoning that led us to mereological universalism in the first place requires yet another generalization. Not only should every set of objects have a fusion, but it should have a fusion with parts whose vagueness matches any "coherent (five-dimensional!) definiteness profile".

This yields a new variety of bloated ontologies. Given three fundamental particles, ordinary mereological universalism gives us seven objects (x, y, z, x+y, x+z, y+z, x+y+z). Five-dimensional universalism gives us an infinity out of these (since there will be infinitely many modal profiles that yield one of the seven objects above). But the vagueness bloat will give a new multitude of objects. For simplicity, I will consider only the world-bound objects. Thus, there will be an object that definitely has x, y and z as its parts. We might call this the definite fusion of x, y and z. But there will also be an object that definitely has x and y as parts, and vaguely has z (and two other similar objects). And an object that definitely has x as a part and vaguely y and z (and two other similar objects). And there will be stranger objects yet, such as an object that definitely has x as a part, and definitely has exactly one of y and z as parts, but it's vague which of the two it is, and the object that definitely has two of the three particles as parts, but it's vague which two it is. And there will be infinite multiplication of such possibilities through higher level vagueness.

It's hard to say how much bloat is too much bloat. But I find it very plausible that this much is too much.

If one rejects this bloat, I think one has three non-exclusive options:

  1. Do not insist on there being objects corresponding to so much of ordinary language.
  2. Be anthropocentric.
  3. Don't take vagueness about parthood, diachronic identity or transworld identity seriously.
Personally, I don't mind accepting all the options.

I do want to say something about (3). One fairly standard way of doing (3) is to say that identity is vague, but parthood, diachronic identity and transworld identity are not. Thus, for any object shaped roughly like me it's definite whether some particle is a part of it. But it's vague which object shaped roughly like me I am. Allowing for an infinite multitude of objects where it's vague which of them is me goes against commonsense in a very serious way, though. The commonsense picture of me is that it's not vague who I am, but vague which exact particles (say, on the peripheries, or in food that's in the process of being digested) are a part of me.

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