Friday, July 27, 2007

Simples and "Occupation"

Two of the main competing views of simples are occupation accounts. These two competing views are the Pointy View (PV) and MaxCon. Each of these views was originally formulated by Ned Markosian in his paper "Simples". Kris McDanial has argued, however, that occupation accounts are false on the grounds that there can be fusions of co-located individuals. This, in combination with the fact that non-occupation accounts of simples are false, suggests a brutal view of simples. I am inclined to think that McDaniel's arguments are sound. My inclination is as strong as my inclination toward accepting co-location. But, if it should turn out that co-location is impossible, then I think that these occupation accounts of simples are the strongest views thus far discussed. However, I think that there is a serious worry for PV and MaxCon that has not yet been addressed. In this post, I wish to spell out this worry and suggest alternative occupation accounts of simples.

I will take the pointy view as my main example. But, notice that everything I say about the pointy view can be said (with very slight modification) about MaxCon. Thus, the problem that I pose is a problem for both views. According to the pointy view,

Necessarily: for any x: x is a simple (at t) iff x is a pointy object (at t).

x is a pointy object (at t) =df the region occupied by x (at t) contains exactly one point.

This seems clear enough. However, there are some terms that we have been using that has not been fully defined. These terms are are related to the verb 'to occupy'. Markosian borrows from van Inwagen the following definition (I have added subscripts for help in later disambiguations):

O occupies1 R (at t) =df R is the set containing all and only those points that lie within O (at t).

Here are some comments that I would like to make at this point. First, this definition puts the burden of understanding this view of simples squarely on the primitive 'lie within'. I think I have an intuitive grasp of this primitive. However, there is some room for confusion. For example, one might believe that for one thing to lie within another it must be a part of the other. But, this is not the correct sense of 'lie within' for van Inwagen's definition. Another way that one object might lie within another is when the first is completely surrounded by the second. For example, a ring might lie within a box. But, again, this is not the correct sense of 'lie within'. For the record, even though I think I understand how van Inwagen is trying to use 'lie within' I am inclined to think that it is a deviant use of the phrase. If it is not a deviant use of the phrase, then it is certainly a restricted use and the restriction should be made explcit by ruling out the kinds of examples I suggested above.

The more important worry that I wish to address is the following. This definition seems to suggest that the relation picked out by 'occupies1' is functional. That is, every material object occupies1 exactly one region. This suggests that the definition of ' O occupies1 R' is equivalent to Parson's definition of 'O is exactly located at R' (correct me if I am mistaken here). This fact makes it clear why Markosian uses the definite article in his formulation of PV. But, there is a problem with this assumption.

Here is a case. Suppose that there is a single point sized object that persits for an hour. After an hour of its life has passed by, it appears as if another point sized particle appears along side the first. Then it seems like these two particles persist together until the first particle dissappears. One seemingly metaphysically possible event that fits this discription is a case of time travel. It could be that a single particle persists for a while until it materializes alongside itself. This materialization is the result of the particle time traveling from the future. It seems appropriate to say that his particle is a mereological simple. After all, it doesn't seem like an object can gain parts simply by time traveling in the way that this particle did. But, under PV, this particle is not a simple (during the time when it sits alongside itself). This is because the particles occupies a region that contains two points during those times. This suggests that the pointy view is false. (this example should also show that MaxCon is false since a region containing exactly two points cannot be continuous).

It is not enough to modify the pointy view by getting rid of the definite article. This is because 'occupies1' picks out a relation that is functional. So, eleminating the definite article will not solve the problem. We must also reinterpret the word 'occupies'. McDaniel (and independantly our very own Rock*) has suggested that there is a primitive occupation relation. This occupation relation is not functional. Let's use 'occupies2' to pick out this new relation and use 'might' in some kind of epistemic sense. When an object occupies2 a region it might also occupy2 another region. Moreover, when it occupies2 two regions, it need not occupy2 the union of those two regions. Finally, when we say that one thing occupies2 a region it might be that that thing or parts of that thing occupy2 subregions of that region and it might not. This is not entirely clear, but I think that we get the idea.

Now, we can simply reinterpret PV with 'occupies2'. But, this will not solve the problem. The definite article has to go. Here is one variant of the pointy view which turns out to be inadequate.

PV*: Necessarily: for any x: x is a simple (at t) iff a region occupied2 by x (at t) contains exactly one point.

Here is why this account is inadequate. Suppose we accept DAUP and the Liberal View of Recepticles. Suppose also that there is an object that occupies a pointy region and also occupies an extended region. Then, by the combination of DAUP and the Liberal View of Recepticles, this object has parts. It will have parts that occupy each of the subregions of the extended region it occupies. However, according to PV* it is a simple since one of the regions it occupies contains exactly one point.

Here, I think, is the best reformulation of the pointy view:

PV**: Necessarily: for any x: x is a simple (at t) iff x occupies2 (at t) a region and every region occupied2 by x (at t) contains exactly one point.

There is a similar reformulation of MaxCon that avoids the time travel counterexample given above. However, I worry about cases of time travel where a MaxCon simple comes into contact with itself. But, I have not thought through that example yet.


Blogger rock* said...

There are a few things I would like to note about the issues addressed by Joshua in his post. These points are not meant to be objections to the substance of his post, however, since I agree with the main points he makes.

First, notice that the van Inwagen/Markosian definition of "occupies" presupposes that regions are sets of points. This is a flaw of the definition that Joshua does not address. But it is, I think, a flaw.

Second, the van Inwagen/Markosian definition of "occupies" can be modified so that it does not presuppose this. Suppose that we introduce the technical term "region-fusion" so that x is a region-fusion of yys iff each of yys is a subregion of x and every subregion of x has a subregion in common with at least one of yys. Then we can modify the van Inwagen/Markosian definition as follows:
O occupies1* R (at t) =df R is a region-fusion of all and only those points that lie within O (at t).

Third, plausible principles concerning region-fusions will guarantee that there is a unique region occupied by each object, thus securing the functionality of occupation1*. Thus, occupation1* will be subject to the same sorts of worries concerning time travel that Joshua mentions.

Fourth, there is a different problem with occupation1 and occupation1* that Joshua does not mention. In particular, if one believes that spatial regions need not wholly decompose into points (as would be the case if some spatial regions were gunky or if some were made up of extended simple regions), then one is likely to be unhappy with occupation1 and occupation1*. (I should note that this is one place where the van Inwagen/Markosian definition of "occupies" and Parsons' definition of "is exactly located at" diverge. Parsons makes no assumptions concerning the possible structure of space.)

Anyway, thes are just some thoughts concerning issues related to Joshua's post.

7:46 PM  

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