Thursday, October 13, 2005

on identity

I proposed the following argument over at Maverick Philosopher:
How's this for an example of two things that are one? Abe walks into the lunch room and asks Bart, "Where is the cookie that was sitting here?"

Bart answers, "It no longer exists."

Craig says, "It is in Bart's stomach."

Isn't it the case that both Bart and Craig made true statements about the same object and that the statements contradict each other? One way of resolving this is to say that the original cookie was two individuals in one.
Bill Vallicella answers
... What is in Bart's stomach is not K, but K's matter. K is not identical to its matter but is a composite of form and matter. There is no contradiction since the predicates 'nonexistent' and 'existent' are true of different things, K and K's matter....
I think that he can only get away with this answer because my example was so simple, so I decided to brush up and post a note that I wrote several years ago, one that contains some more sophisticated examples.

There is a house on the beach with a large pile of sand in the yard. One day a guest visits the house to find the pile gone and asks the owner what happened to it. Consider the two following scenarios:

1. The owner says, "a bulldozer pushed the pile against that wall." implying that the pile against the wall is the same as the pile that was in the middle of the yard.

2. The owner says, "the wind last night blew it away and built up the pile against that wall." implying that the pile against the wall is not the same as the pile that was in the middle of the yard.

Now in both cases the pile against the wall contains the same grains of sand, and the same form, the only difference is in how it came to be there. There are several possible responses to this story. First, we could say that the owner was simply mistaken in one or another of the scenarios ‑‑the pile against the wall was the same in both scenarios, either it was or it wasn't the same as the one in the yard. Another possibility is to simply accept that the identity of a pile of sand actually depends on how it was constructed. A third possibility is to suggest that the identity of the pile of sand is a relative matter, that there is no objective truth of the matter, it just depends on how the observer chooses to construe the situation.

I build a toy robot out of legos, with claws for hands. Call the toy A. Now I remove the left claw and call the resulting toy B. Is A=B? There are two possible answers:

1. Yes. The toy is an enduring perceptual whole according to our physical intuitions, and removing the claw does not undo the physical identity of the remainder.

2. No. The toy consists of its parts, and when the parts change the identity of the toy changes.

Answer 1 is the most natural because if you take 2 seriously it has odd consequences such as the fact that when you change a tire on your car, you have a different car. However, 1 has the problem that because it relies on an intuition of physical wholeness, its application is limited by our intuitions. What happens when you take off the whole left arm? What about when you take off both arms and both legs? What happens if you take away everything except one block? At some point you no longer have the same toy, but it is not clear when this happens.

Each answer is true in some sense, but there is no single sense in which both are true. I'm not suggesting that we can simply believe what we want. If you construe the toy as in 1, then it is an objective fact that A=B. If you construe the toy as in 2, then it is an objective falsehood that A=B. The only subjective element is in how you construe the identity of the toy.

Since it is impossible for A=B and A=/=B both to be true at the same time and in the same way, it must be the case that there are actually multiple identities for A. Just by saying that A is "the toy" you do not unambiguously describe A. I claim that there are at least two individuals involved here: construing A as in 1, we get A1 which is numerically the same as B. Construing A as in 2, we get A2 which is numerically distinct from A1 (and B).

The consequence of this is we have two different objects occupying the same space, and both objects are physical. Now what do we say about A? Is A=A1 or A=A2? Apparently not, because if one of those numerical identities held, then the original question (A=B?) would be objectively settled.

Now we might be inclined to say that A does not exist at all as an object, but rather that "A" is just an ambiguous name for A1 or A2.
But then we have similar arguments for showing that "A1" and "A2" are ambiguous. Suppose that I take the pieces of the toy apart and put them in a bag, and call the contents of the bag C. Is A1=C or A2=C? There are two choices for the question if A1=C:

3. Yes. The material of A1 is the dominating criterion, so A1=C.

4. No. The structure of A1 is the dominating criterion, so A1=/=C.

There are also two choices for the question of A2=C:

5. Yes. The collection of objects is a set, so A2=C.

6. No. The collection of objects is a structured set, so A2=/=C.

If any of these answers is rejected, I claim that I can come up with an analogous situation where many, if not most speakers would choose that answer. If I'm right, then all answers are equally valid, and we have four more objects to consider: A3, A4, A5, and A6. Furthermore, I believe this process can be continued indefinitely, if not with this particular example, then with other examples. So I claim that A, A1, A2, A3, A4, A5, and A6 are all legitimate physical objects.

It is not that the name "A" is ambiguous, it is that A is an indeterminate concept. This should not surprise us since we deal with indeterminate concepts all the time in normal thought. When I get hungry, I sometimes get in my car and just start driving (I often eat out). I'm thinking that I want to get something to eat, but I don't have anything particular in mind. The concept of something to eat is indeterminate. And since I am neither producing nor thinking the words "something to eat", there is no possibility of linguistic ambiguity.

Does this mean that physical objects are just concepts? Am I an idealist?

As I pointed out a previous post, logicism as reductionism, the only things that can be present to our minds are concepts. I cannot import the Golden Gate Bridge into my head to think about it. The only thing that is immediately present to my mind is a concept of the bridge. Since I can't immediately access anything besides concepts, does it make any sense to postulate the existence of anything besides concepts?

I'm just askin' is all.

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