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, the same parts, 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. But which? What reason can there be for preferring one answer over the other?
Another possibility is to simply accept that the identity of a pile of sand actually depends on how it was constructed. There is some intuitive appeal to this answer and it will be discussed later. 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.
Therefore 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).
Notice the consequence of this: 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" that is ambiguous, it is the concept of A. A1 and A2 actually represent two different concepts that have the same extension in some circumstances but not in others. 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.
The point is the invalidity of one of the typical arguments against idealism. The argument goes like this: when two people look at a tree, are they seeing the same object or not? If they are, then the tree must be a public object rather than a private one, so it cannot be mental. If the two people do not see the same thing, then how can they both refer to the same thing in communication?
The problem with this argument is that it assumes that the two answers are mutually exclusive when they are not. The idealist can say that there is a tree1 which is private to each individual and tree2 which is public, and the two are intimately related in the same way that A1 and A2 in my example are related.
Just something to think about.