In the case of a person whose molecules are constantly changing, I would say that the person's original molecules aren't the only ones that can make up the same person. At any given time, the set of molecules that constitute that person change.

What if we have a person A made up of set of molecules M such that A is defined as A = the object made up of the set of molecules M. Person A scratches his skin and loses molecule x so that M = (M - x). He then grows new skin and adds molecule y, making the assignment M = (M + y)

Neither of these changes to M disrupts the definition A = M

I think in this way changing the memberships of set M doesn't really need to disrupt the definition of A as long as the majority of the members of set M stay the same over a short period of time.

Basically, when we add y to M, y becomes a member of M. So if we later removed other molecules from M but leave y, we could say y has earned membership in M and therefore can represent the same M even though it wasn't an original member of M

What if we have a person A made up of set of molecules M such that A is defined as A = the object made up of the set of molecules M. Person A scratches his skin and loses molecule x so that M = (M - x). He then grows new skin and adds molecule y, making the assignment M = (M + y)

Neither of these changes to M disrupts the definition A = M

I think in this way changing the memberships of set M doesn't really need to disrupt the definition of A as long as the majority of the members of set M stay the same over a short period of time.

Basically, when we add y to M, y becomes a member of M. So if we later removed other molecules from M but leave y, we could say y has earned membership in M and therefore can represent the same M even though it wasn't an original member of M

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Well, I'd like to say a few things about what you said...

Any given set has a property known as its cardinality; i.e. the number of members of that set. This is one property which uniqely determines a set - if set A has some cardinality different from that of set B, then it is not the case that set A = set B.

To "add" a set to a given set, is an operation called the union of two sets. Basically, it puts two sets together into one larger set. This is a technical complaint - your terminology and notation appear to be incorrect.

In any case, you talk about taking some subset x (the molecules person A loses) out of M, and then uniting some other set y (the molecules person A gains) with M. However, since the cardinality of what you refered to as M is changed, it is not the case that A is still equal to M. Also, in taking members out of M, you are actually making an entirely new set. In short, what you are talking about is not a sound way of treating sets.

In fact, if what you are saying is true, then it is not the case that when you remove any part of A that you are removing members of the set M. Why? Because there is no property that you defined of a set that pertains to the relationship between the members of M. Basically, even after scattering the parts of A all over the universe, which would probably be pretty messy since A is a person, the set M still exists. It is just some arbitrary set of atoms, and since those atoms are still out there, the set still exists.

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