Tuesday, December 02, 2008

SCQ and the Brutality of Parthood

The Special Composition Question is often formulated as follows:

The Special Composition Question (SCQ): What necessary and jointly sufficient conditions must any xs satisfy in order for it to be the case that there is an object composed of xs?

And answers to the Special Composition Question often take the following form:

The Special Composition Schema (SCS): Necessarily, for any non-overlapping xxs, there is a y such that y is composed of xs iff ____________________.

Often, however, those who are concerned with SCQ take SCQ to be a question about what it is in virtue of which some things compose something. The formulations of SCQ and SCS given above do not make this clear.

I will not attempt to formulate more satisfactory versions of SCQ and SCS. Rather, I want to investigate whether we should expect there to be an answer to SCQ on the assumption that it is a question about what it is in virtue of which some things compose something.

Consider the simples that compose me. Call these simples 'ggs'. ggs compose something. We may now ask: In virtue of what is it the case that there is an x such that ggs compose x?

It seems to me that there is an obvious answer to this question: There is an x such that ggs compose x in virtue of the fact that ggs compose me. (Compare with this case. In virtue of what is it the case that there is someone to whom I am married? Answer: There is someone to whom I am married in virtue of the fact that I am married to Mary.)

If, then, SCQ is a question about what it is in virtue of which some things compose something else, it appears that the answer to SCQ will look something like this:

ggs compose something in virtue of the fact that ggs compose Greg, ees compose something in virtue of the fact that ees compose the Eiffel Tower, etc.

There is a further question that can be asked, however. Suppose that ggs compose something in virtue of the fact that ggs compose me. In virtue of what do ggs compose me? This is an interesting question as well.

Now to say that ggs compose me is to say that ggs are all parts of me, no two of ggs have a part in common, and every part of me has a part in common with at least one of ggs. So, we can reformulate our question as follows: In virtue of what is it the case that ggs are all parts of me, no two of ggs have a part in common, and every part of me has a part in common with at least one of ggs?

But then consider the following thesis:

The Brutality of Parthood (BT): Necessarily, for any x and y, if x is a part of y, then there is nothing in virtue of which x is a part of y.

BT is relatively plausible. But it seems to me that if BT is true, then the correct answer to the question "In virtue of what is it the case that ggs are all parts of me, no two of ggs have a part in common, and every part of me has a part in common with at least one of ggs?" is "Nothing".

8 Comments:

Blogger Joshua said...

I want to give two responses. First, There might be several answers to the Special Composition Question, some of which are more informative than others. If that is right, then even if we grant that those ggs compose something in virtue of the fact that they compose you, it might be that there is something else in virtue of which the ggs compose something as well. Moreover, if we had a formulation of this other fact in virtue of which the ggs compose something, we might find it more informative than the fact that they compose you.

The second response I want to give is the following. It seems that (1) there is a possible world just like this world, except that the thing that those ggs compose is different from what they actually compose. Moreover, it also seems that (2) whatever it is in virtue of which those ggs compose something in that merely possibly circumstance is the same as that in virtue of which they actually compose something. But, since the thing the ggs compose, namely you, is not composed of those ggs in the other possible world, it follows that those ggs do not compose something in virtue of the fact that they compose you. Rather, if they compose something in virtue of any fact, it must be some other fact.

I take it that if you are going to continue to hold the claim that those ggs compose something in virtue of the fact that they compose you, then you are going to reject claim (2) in the previous paragraph. But that would be a surprising result.

7:25 AM  
Blogger rock* said...

Hi Joshua,

Your first response is interesting and I'll have to consider it more. I do think that there are cases in which something is the case in virtue of more than one fact. For instance, suppose that John is a polygamist with two wives, Mary and Sue. In that case, I'm inclined to say that both of the following are true:
a. John is married to someone in virtue of being married to Mary.
b. John is married to someone in virtue of being married to Sue.

As for your second response, I think that there are a few interpretations of this response. First, perhaps you are endorsing the following general principle:

If P in virtue of the fact that Q, then: necessarily, if P, then P in virtue of the fact that Q.

Then we could formulate your second response as follows:
1. If ggs compose something in virtue of the fact that ggs compose Greg, then: necessarily, if ggs compose something, then ggs compose something in virtue of the fact that ggs compose Greg.
2. Possibly, ggs compose something and it is not the case that ggs compose something in virtue of the fact that ggs compose Greg.
3. Therefore, it is not the case that ggs compose something in virtue of the fact that ggs compose Greg.

I agree with premise (2) of this argument. But I disagree with the general principle; I am over 5' tall in virtue of the fact that I am 5'8" tall, but I could be over 5' tall in virtue of the fact that I am 5'6" tall. And I also disagree with premise (1), since I think that ggs compose something in virtue of composing me and that
ggs could compose something in virtue of composing something else.

A more promising interpretation is this. Perhaps you have a strong intuition that there is some fact F in virtue of which ggs compose something such that necessarily, if ggs compose something, then ggs compose something in virtue of F. But it doesn't follow from this that it is not the case that ggs compose something in virtue of the fact that ggs compose me. At most it shows that if ggs compose something in virtue of the fact that ggs compose me, then ggs also compose something in virtue of some other fact. On this interpretation, then, your second response collapses into your first.

9:02 AM  
Blogger Alex said...

Rock*:

(BT) needs refinement. If x is identical to y, then there is something in virtue of which x is a part of y.

More substantively, if x is a proper part of z and z is a proper part of y, then there is something in virtue of which x is a part of y. Anyone who believes that parthood has specific structural properties such as transitivity, then, ought to reject (BT) as you've formulated it.

Another question about (BT) is why we ought to believe it in the first place. I grant that parthood (or overlap, or some other mereological relation) is conceptually primitive: that it is definable in terms of no more basic concepts. But I do not see why I ought to grant that parthood is metaphysically fundamental, which is what (BT) claims.

6:30 PM  
Blogger rock* said...

Hi Alex,

Thanks for your thoughts.

I'm inclined to agree with you that if x is identical to y, then x is a part of y in virtue of the fact that x is identical to y. The reason I'm inclined to agree is that I think that the parthood relation discussed by mereologists is the disjunctive relation being identical to or a part-sub-o of, where being a part-sub-o of is the relation expressed by the ordinary English "part". So, since I'm inclined to think that if x is identical to y, then x is identical to or a part-sub-o of y in virtue of the fact that x is identical to y. Thus, I agree with you that (BT) needs refinement.

On the other hand, I'm not convinced by your more substantive criticism of (BT). I agree that necessarily, for all x, y, and z, if x is a proper part of y and y is a proper part of z, then x is a part of z. Now let A, B, and C be such that A is a proper part of B and B is a proper part of C. I agree that it is necessary that if these conditions hold, then A is a part of C. But I'm inclined to deny that A is a part of C in virtue of the fact that A is a proper part of B and B is a proper part of C.

My position here is similar to my position with respect to objects and there singletons. I think that necessarily, for all x, if {x} exists, then x exists. But I deny that any object exists in virtue of the fact that its singleton exists.

What I think I've shown so far is that the mere fact that parthood is transitive doesn't provide any good reason to think that if A is a proper part of B and B is a proper part of C, then A is a part of C in virtue of the fact that A is a proper part of B and B is a proper part of C. I've also indicated that I deny the latter thesis, but I haven't given any reasons to deny it.

I'll admit that I simply find (BT) plausible--or, rather, that I find a version of (BT) suitable modified to avoid your first objection plausible. I've given no reasons to think it is true nor have I given any reasons to think that it is false that if A is a proper part of B and B is a proper part of C, then A is a part of C in virtue of the fact that A is a proper part of B and B is a proper part of C. All I've shown is that the reasons you presented to think that the latter are true are no good.

However:
(i) I do think that (BT) is plausible,
(ii) I think that there are good reasons to think that it is false that if A is a proper part of B and B is a proper part of C, then A is a part of C in virtue of the fact that A is a proper part of B and B is a proper part of C; but I need some time to come up with a satisfactory presentation of these reasons, and
(iii) I was more concerned with whether SCQ has an interesting answer than with whether (BT) is true.

8:26 PM  
Blogger Joshua said...

Hi Rock*,

I think my second worry involved a principle that is a little bit different than the principle that you suggest. You suggested that I might be appealing to the principle that:

(P1) if P in virtue of the fact that Q, then: necessarily, P in virtue of the fact that Q.

However, I think all that I had in mind was something like the following principle:

(P2) If the x's compose something in w1 and the x's compose something in w2 and w1 is a particle for particle duplicate of w1, then if the x's compose something in virtue of the fact that Q in w2, then they also compose something in virtue of the fact that Q in w1.

I'm not sure if this principle is true, but it at least sound fairly plausible at first. What do you think?

3:53 PM  
Blogger Christian said...

Joshua,

This is an interesting post.

But it seems to me that if BT is true, then the correct answer to the question "In virtue of what is it the case that ggs are all parts of me, no two of ggs have a part in common, and every part of me has a part in common with at least one of ggs?" is "Nothing".

Consider two different claims:

(1) In virtue of what is it the case that the ggs are all parts of me?

(2) In virtue of what is it the case that I have the ggs as parts?

It seems plausible to think that having the ggs as parts is an intrinsic property of me. But it also seems plausible to think that, that some g is a part of me is an extrinsic property of g. Assuming that extrinsic properties are grounded in intrinsic properties, that all extrinsic properties are possessed in virtue of the possession of intrinsic properties, then it seems to me that, for each g, it is not a brute fact that g is a part of me. Generalizing to all the gg's, it is not a brute fact that the gg's are parts of me. And so, the first clause in your conclusion might be resisted. One might then go on to accept the following ammendment:

In virtue of what is it the case that I have all the ggs as parts, no two of the ggs have a part in common, and every part of me has a part in common with at least one of ggs?" is "Nothing".

I have another worry, though I'm not exactly sure how to state it.

The Brutality of Parthood (BT): Necessarily, for any x and y, if x is a part of y, then there is nothing in virtue of which x is a part of y.

Suppose there is some y that has x as an improper part. One might want to say that, in this case, y has x in virtue of being identical to y. This might be a counterexample to BT. Suppose we restrict ourselves to proper parts, then I have the following, admittedly crude worry. There is a y that has a proper part, x, essentially, and a y that has a proper part, x, non-essentially. It would be good to explain why, for some ys, it has it parts essentially whereas for other ys this is not the case. But, if there is nothing in virtue of which, for any x and y, x is a proper part of y, then we lose a potential source for such an explanation.

Just for the sake of illustration, suppose that x is proper part of y in virtue of God's decreeing that x is a proper part of y and y must have x as a proper part. This would explain why y has x as a proper part essentially. Now, if God decrees that y has x as a proper part non essentially, this will explain why y has x as a proper part non-essentially. But such an explanation would entail that there is something in virtue of which y has x as a proper part.

Make sense?

5:33 PM  
Blogger Joshua said...

Hi Christian,

You said:

"Assuming that extrinsic properties are grounded in intrinsic properties, that all extrinsic properties are possessed in virtue of the possession of intrinsic properties, then it seems to me that, for each g, it is not a brute fact that g is a part of me"

I am not exactly sure how your argument goes. Are you thinking that g is a part of you in virtue of the fact that you have g as a part. Might we formulate your argument like so:

1. Christian has g intrinsically.
2. g is a part of Christian extrinsically.
3. All extrinsic properties are had in virtue of some intrinsic properties.
4. If (1)-(3), then g is a part of Christian in virtue of the fact that Christian has g as a part.
6. So, g is a part of Christian in virtue of the fact that Christian has g as a part.

I think I am suspicious of claim (3). I don't think it is false, but, I'm not sure why we should believe it is true. I also worry about a couple of simple examples. I have the property of being married extrinsically. But I have a hard time thinking of what intrinsic features might ground that particular extrinsic feature. Again, I am not saying there aren't any, just that I am unsure of what they might be.

As for your second worry. I think that is pretty interesting. But, I wonder if the brute parthood theorist will worry about it too much. Shouldn't he say that O1 has O2 essentially in virtue of the fact that O1 has O2 as a part in every possible world. Moreover, the fact that O1 has O2 as a part in any particular possible world is merely a brute matter. It may seem unsatisfying, but I wonder if the brute parthood theorist is just going to have to say some unsatisfying things.

7:48 AM  
Blogger Christian said...

Hi Joshua,

I like your argument though it's stronger than the argument I have in mind. I only wanted to say that whereas it "may" be plausible that my having g as a part is brute, it is less plausible that g's being a part of me is brute. I don't think, or at least, it's unclear to me that extrinsic properties can be had brutely.

So, I'm not sure whether your (4) is true either. I would say that

4'. If (1)-(3), then g is a part of Christian in virtue of the fact that something or other.

I don't know what it is in virtue of which g is a part of me, though my having g as a part is a good candidate.

I also worry about a couple of simple examples. I have the property of being married extrinsically. But I have a hard time thinking of what intrinsic features might ground that particular extrinsic feature.

You have it partly in virtue of existing and being a person, and plausibly those are intrinsic. I suppose I like the view that extrinsic properties are reducible to intrinsic properties plus relations, but I'll think more about why I like this view.

Shouldn't he say that O1 has O2 essentially in virtue of the fact that O1 has O2 as a part in every possible world.

I think this just pushes the question back. Why does O1 have O2 as a part in every possible world rather than only some of them? If she goes brute here too, then her thesis is stronger. It won't simply be BT since it will also make some modal facts brute. For those that think that modal facts hold in virtue of categorical facts, this will be a bad consequence. I have in mind someone like Armstrong in his "Truth and Truthmakers".

5:12 PM  

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