1. Some maintain that a hand, and that same hand made into a fist, are identical. And there are those who would say the same about a piece of bronze and the statue made out of it, namely, that they are identical at every time at which both exist. This is not an unreasonable thing to say. After all, fist and hand, statue and bronze, are spatially coincident and neither has a physical part the other doesn't have. A fist is just a certain familiar arrangement of hand-parts. There is no part of the fist that is not part of the hand, and vice versa. So at looks as if first and hand are identical. But we need to be clear as to what identity is.
2. Identity is standardly taken to be an equivalence relation (reflexive, symmetrical, transitive) governed by the Indiscernibility of Identicals (InId) and the Necessity of Identity (NecId). The first principle says that, if two items are numerically identical, then they share all properties. The second says that if two items are numerically identical, then this is necessarily the case. Both principles strike me as beyond epistemic reproach. 'Identity' is short for 'numerical identity.'
3. Despite the considerations of #1, it looks as if fist and hand, statue and hunk of bronze, cannot be identical since they differ in their persistence conditions. The hunk of bronze can, while the statue cannot, survive being melted down and recast in some other form. The hand can, while the fist cannot, survive adoption of a different 'posture.' In both cases, something is true of the one that is not true of the other. So even at the times at which the fist is the hand, and the bronze is the statue, the two are not identical: the 'is' is not the 'is' of identity. It is the 'is' of composition and what you have are two things, not one.
What I have just given is a modal discernibility argument. Let me spell it out. Consider a time t at which the hand is in the shape of a fist. At t, the hand, but not the fist, has the modal property of being possibly such as to to be unfisted. So the hand cannot be identical to the fist given that, for any x, y, if x = y, then x, y share all properties.
But there is also this nonmodal discernibility argument. The hunk of bronze existed long before the statue came into existence, and the hunk of bronze exists while the form of a statue. So the hunk of bronze exists at more times that the statues does, which implies the the hunk of bronze is not identical to the statue.
There is also this consideration. Identity is symmetrical. So we can say either fist = hand or hand = fist. But is it the fist or the hand that both are? Intuitively, it is the hand. The hand is the fundamental reality here, not the fist. So how can fist and hand be identical? It seems that fist and hand are numerically distinct, albeit spatially coincident, concrete individuals.
4. The Law of Excluded Middle seems very secure indeed, especially in application to presently existing things. So either the fist is identical to the hand, and there is just one thing, a fisted hand, or the fist is not identical to the hand and there are two spatially coincident things, a fist and a hand. So which is it?
5. If you say that the fist = the hand, then when you make a fist nothing new comes into existence, and when the potter makes a pot out of clay, nothing new comes into existence. And when a mason makes a wall out of stones, nothing new comes into existence. He started with some stones and he ended with some stones. Given that the stones exist, and that the mason's work did not cause anything new to come into existence, must we not say that the single composite entity, the wall, does not exist? (For if it did exist, then there would be an existent in addition to the stones.) But it sounds crazy to say that the wall the mason has just finished constructing does not exist.
6. If, on the other hand, you say that the fist is not identical to the hand, then you can say that the making of a fist causes a new thing to come into existence, the fist. And similarly with the statue and the wall. After the mason stacks n stones into a wall, he has as a result of his efforts n +1 objects, the original n stones and the wall.
But this is also counterintuitive. Consider the potter at his wheel. As the lump of clay spins, the potter shapes the lump into a series of many (continuum-many?) intermediate shapes before he stops with one that satisfies him. Thus we have a series of objects (proto-pots) each of which is a concrete individual numericallt distinct from the clay yet (i) spatially conicident with it, and (ii) sharing with it every momentary property. And that is hard to swallow, is it not?
7. We appear to be at an impasse. We cannot comfortably say that the fist = the hand, nor can we comfortably say that the fist is not identical to the hand. Nor can we comfortably give up LEM. If there are no fists, statues, walls, artifacts generally, then there cannot be any puzzles about their composition. But we cannot comfortably say that there are no such things either.
Do we have here an example of a problem that is both genuine but insoluble?