The doctrine of the resurrection of the flesh generally implies that for each human person who is separated from their ‘body’ at death, they will someday be restored to their proper body after death. Now, the significance of this statement can hardly be missed: it does not imply that they will simply have a body once again, but that they will re-animate their own bodies. This has always presented an interesting puzzle for me, precisely because we know that bodies decay, decompose, and those same molecular, or even atomic “parts” are recyclable in such a way that I may now have some bit of my physical body which was once some minute part of somebody else’s body. However, if two people share one and the same ‘part’ or set of parts, then how is it that their bodies will be ‘restored’ to them?
There are a few ‘solutions’ I can make out. The first is simply to say that although counter-factually people may possibly share some part or set of parts which once belonged to another’s body, God has simply ensured that this doesn’t happen to human beings. This answer is obviously wrong. To see this take the example of cannibalism in which it is clear that the parts of one human being are absorbed into the other (become parts in the other). Moreover, cannibalism isn’t just a theoretical atrocity, but one which has been committed by some human people at some times.
The second answer is that some individual things may be bi-located, so that the same part which belonged once to Tim and then afterwards to Tom, belongs to both Tim and Tom at the same time. Although I do think bilocation is logically coherent (and thus possible), there may yet be problems with this view. For instance, if bilocation is true, then one would presumably think that whatever happened to the “part” (or particle) at one of its ‘extensions’, would presumably have the same effect as all other extensions. In other words, those familiar with what is called in physics “spooky action at a distance” will be at least familiar with the concept of two particles which are the same, which when separated such as to have no physical contact in any sense, or any sort, one can operate on the one and see the exact same effects in the other at a distance. The only solutions to that problem are that there is some physical connection which we do not know about, or else that substances in the metaphysical sense exist, and that both particles belong to the same substance/thing/subject. If at the resurrection multi-locative theories of bodily restoration are true, however, then what one subject does with/to her body may/will also bring about effects in what other people experience in their bodies, and that seems to be a rather odd way of thinking about our resurrected state.
Another answer might be that the body is not determined by its parts but by its proportions. In other words, God will restore to you an aggregate of parts put together in such a way that accurately reflects what your body had been. The problems with this are obvious as well, however, since it ignores the fact that resurrected bodies are in a glorified state which makes them difficult even to recognize (consider how Christ’s appearance was a strange thing for his disciples to witness, some failing even to recognize him like on the road to Emmaus). Moreover, it also fails to take into account the teachings of the Magisterium of such points, which seems very shy about such ‘resolutions’, and instead has affirmed time and again that the body being restored at the resurrection is identical with the body we have now – our body.
The final answer, which is perhaps the one to which I have been the most attracted of late, is a solution proposed by something like Leibniz’ monadology. In other words, the idea that Matter supervenes on substance, so that some subject’s body is just a result of a phenomenally-real composite of proportions created by an infinite aggregate of monads (or immaterial substances) all standing in some relationship. I had thought, however, that this view fell short of what is permissible from a Catholic perspective given what the Magisterium taught about eschatology (last things, including resurrection). However, recently on Jimmy Akins podcast, where he actually read from the documents of the congregation for the doctrine of the faith, it became clear that the Church was keen on affirming that the resurrected body was identical with ‘our body’ in this life, and yet that it was not necessary that it be composed of the same matter per se.
Thus, this final solution is the one I remain most attracted to.