The problem with thinking that "objects endure through change" or "objects can survive some loss of parthood" is that the claim falls victim to a sorites series. Sorites paradox is the paradox of the heap. Many philosophers see this problem as a problem of language, but the form of the argument can be applied just as simply in the context of ordinary objects.
A sorites series takes a certain form. It first points out a clear case of some state of affairs – “there is a heap.” Next, it endorses a principle of tolerance, that small changes can be made to that state of affairs without jeopardising the right application of the corresponding predicate – “it is still a heap when one grain of sand is taken away.” Finally, it repeatedly applies the reasoning of the principle of tolerance to get to an absurd conclusion – “one grain of sand is a heap.” (You can see longer explanations of this in my previous posts here and here.)
Now imagine an ordinary object such as a rock. For the sake of simplicity, imagine that the rock and the rest of physical reality is made up of discrete part-less simples, atoms. (It is not relevant what the character of these constituents are, you can imagine they are the end result of infinite scientific inquiry if you like. The argument goes through insofar as you believe that there are objects such as rocks and that these objects and the world can properly be broken up into parts.) These atoms are the parts of the rock. Now imagine that the rock loses one of these atoms. The rock, it can reasonably be said, on any common-sense formulation of the premise that objects endure through change, retains its identity. But in accepting this principle we accept what is an analogue to the principle of tolerance, allowing us to construct a sorites series.
Thus, in argumentative form, we have so far that:
(1) There are rocks.
(2) They are made up of a number of atoms n.
(3) If some rock lost one of its atoms it would still be the rock.
Premise (3) is the premise that objects endure through some change, and accepting it is the fatal step. By repeatedly applying the reasoning, the premise allows us to take off one atom at a time until we reach only one left while being logically committed to affirming the continued existence of the same rock. We get the conclusion:
(4) Therefore, something is still a rock if it loses all but one of its atoms.
However, it seems one atom cannot be a rock, firstly, because common sense denies this. But secondly, because we can construct this beautiful argument:
(5) If one atom composes a rock, then all atoms are rocks.
(We can say this because if all it takes to be a rock is just to be an atom, then why can't any old atom be a rock?)
(6) If all atoms are rocks, and the universe is made up of atoms, then the universe is made up of rocks.
(7) The universe is made up of rocks.
This is an unacceptable conclusion. We have to say more than just that common sense denies that one atom composes a rock, we must say that it is impossible for one atom to be a rock. Otherwise, the term and objects themselves are reduced to triviality and the universe is made up of rocks! However, this only pushes out the problem as we can construct a sorites series in the opposite direction. Here too common sense would endorse a principle of tolerance. Namely, that the addition of one atom to one other atom, would not compose a rock. Thus, beginning from where the last argument took us:
(8) It is impossible for one single atom to be a rock.
(9) Something that is not a rock is still not a rock if it gains a single extra atom.
(10) Therefore, there are no collections of atoms, n, that compose rocks.
(11) There are no rocks.
Premise (10) follows from the previous premises for the same reason (4) followed from (3). And finally, we are faced with a contradiction between (1) and (11). The only principle we had to rely on was the common-sense postulate that objects can endure some loss of parthood. In responding to a contradiction, one contradictory premise must be discarded. But if we discard (11), that there are no rocks, as common sense would like to, you are forced into accepting (7), that the universe is made of rocks. Thus, this argument suggests we must discard (1), that there are even rocks at all.
You could try and be sneaky and deny the principle of tolerance and say that two atoms could in fact be a rock. But two atoms are emphatically not a rock in any meaningful way. Plus, you would be exposed to an argument that said that every collection of two atoms would then be rocks that would thus make up the universe. You will have cut down your ontology of objects by half but I'm pretty sure reality still doesn't rock that much!
One may be sceptical of the use of atoms in the argument. However, this argument will work even if we conceive of objects as regions of space. Rocks could be affirmed as continuous regions, rather than a collection of discrete parts. However, as long as one admits that some change could occur (the rock could be chipped slightly) while remaining that object, the same conclusions will always follow. Any allowance of any kind of degree of any kind of change in the parts of any object whatsoever will lead to the reductio ad absurdum constructed above.
This kind of thing can be constructed for any proposed object whatsoever and it is the consequence of any definition of objects that includes identity through change. If this argument succeeds, then we have reason to think there are no objects at all. Unless, of course, you think any distribution of matter can arbitrarily be described as any object. But at that point objects become explanatorily meaningless, and we are better off dispensing with them as mind-independent features of reality.
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