The problem of material constitution is that the following assumptions are all plausible, but together lead to a contradiction The Existence Assumption (i) there is an F and there are ps that compose it The Essentialist Assumption (ii) if the ps compose an F, then they compose an object that is essentially such that it bears a certain relation R to its parts The Principle of Alternative Compositional Possibilities (PACP) (iii) if the ps compose an F, then they compose an object that can exist and not bear R to its parts The Identity Assumption (iv) if the ps compose both a and b, then a is identical with b The Necessity Assumption (v) if a is identical with b then a is necessarily identical with b The problem of material constitution has been illustrated with several puzzles over millennia Heres one of them, the Growing Argument, first presented in an ancient play: The scene in which it appears depicts a person who, hoping to collect a debt from a friend, receives instead a philosophical argument. The upshot of the debtor’s argument is that since a person is identical with the aggregate of particles that constitutes [them], any addition of particles will result in a new person (since it will result in a new aggregate); but, of course, they (the debtor) has undergone many such additions since the debt was contracted, so they cannot now be considered the same person as the one who contracted the debt. Consequently, they do not owe any money. (Rea, 529) The argument involves an Existence Assumption, there is a human person composed of particles It involves an Essentialist Assumption, namely, where this is a human person composed of particles, there is an aggregate of particles where an aggregate is such that it must be made up of just the things that compose it, so any addition (or subtraction) to it destroys that aggregate in other words, there is an object such that, necessarily, for all qs and t, the qs compose z at t only if z bears R1 to the qs, where R1 is defined as follows: z bears R1 to the qs =DF there is no time t such that z exists and the qs do not compose z at t. The Identity Assumption is made; thus, one assumes that the human person is identical to the object that cannot gain or lose material parts

The Necessity Assumption is made, otherwise one could assume that the person is identical to different aggregates at different times Once one adds the (PACP) to the mix, one gets a contradiction and this assumption is plausible, for it is natural to assume that a person can take on (or lose) some of the particles that make them up But, then, one is led to claim that the person who borrowed the money is the same person now (because, although, they gained or lost some bits, this does not destroy them) and the person who borrowed the money is not the same person now (because that aggregate, which is supposed to be identical to the person, has been destroyed) The Ship of Theseus puzzle is a near relative of the one presented by the Growing Argument Here it is: Consider the Ship of Theseus: a wooden ship that, over the course of time, gradually undergoes the replacement of each of its constituent planks. Clearly, it seems, the ship survives each individual replacement; hence, there is good reason to think that the ship that exists once the series of replacements is complete is the ship we originally started out with. But now suppose someone takes the discarded planks and puts them back together in their original form as a ship: it seems that there is also good reason to think that this ship is the ship we started out with. But, of course, both ships cannot be the Ship of Theseus; so the question is, Which of the final two ships is identical with the original? (Rea, 532) The puzzle here is often thought to turn on the appropriate (diachronic) criterion of identity for material objects, in particular, whether the criterion is continuity of form or continuity of matter the puzzle arises because we are supposed to have intuitions that pull in different directions Rea, however, does not think this puzzle is about criteria of identity, he thinks the crucial question here is How is the Ship of Theseus related to its (material) parts? hence, not surprisingly, Rea thinks this is a puzzle about material constitution Rea points out that the crucial question of the Growing Argument is How is a human being related to its (material) parts? So the Ship of Theseus presents a version of the problem of the material constitution it involves the five assumptions and leads to a contradiction, by rejecting one of the assumptions, one can resolve the puzzleand thereby answer the question of which of the final two ships is the Ship of Theseus The argument involves an Existence Assumption, there is a ship composed of planks (or particles or whatever) It involves an Essentialist Assumption, namely, that a ship (or a material object) cannot undergo the complete replacement of its parts

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in other words, if the ps compose a ship at time t, then there is a z such that the ps compose z at t and, necessarily, for all qs and t, the qs compose z at t only if z bears R2 to the qs, where R2 is defined as follows: z bears R2 to the qs =DF for some n 1, at every time t, at least 1/n of the qs compose z the (PACP) is made, because one assumes that a ship can undergo complete part replacementso a ship need not stand in the relation R2 to its parts The Identity Assumption is made; thus, one assumes that, at the beginning, there is just a single ship composed of the planks The Necessity Assumption is made, otherwise one could assume that the two ships at end of the puzzle were identical to the original ship, but now are not (because the two ships at the end are obviously distinct) So in the end, one seems committed to claiming that the reassembled ship is identical to the original one and the continuously repaired ship is identical to the original, in which case the reassembled ship is identical to the continuously repaired ship and that the reassembled ship is distinctnot identical withthe continuously repaired ship This is a contradiction!

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