I have recently run into this wikipedia article on mereology. I was surprised I had never heard of it before and indeed it seems to be seldom mentioned in the mathematical literature. Unlike set theory, which is founded on the idea of set membership, mereology is built upon what I consider conceptually more elementary, namely the relation between parts and the whole.

Personally, I have always found a little bit unsatisfactory (philosophically speaking) the fact that set theory postulates the existence of an empty set. But of course there is the technical aspect and current axiomatizations of set theory seem to be quite good regarding what it allows us to prove.

Now it seems there have been some attempts to relate mereology and set theory, and according to the article, some authors have recently tried to deduce ZFC axioms as theorems in certain axiomatizations of it. Yet, apparently only a couple of well trained mathematicians (one of them Tarski) have discussed mereology, since most people have shown indifference towards the whole subject.

So my questions are: how is it that mereology had no success as a possible foundation for mathematics? Are axiomatizations based on mereology not suitable for most developments or simply not worth the while? If so, which would be the technical reason behind?

I have recently run into this Wikipedia article on mereology. I was surprised I had never heard of it before and indeed it seems to be seldom mentioned in the mathematical literature. Unlike set theory, which is founded on the idea of set membership, mereology is built upon what I consider conceptually more elementary, namely the relation between parts and the whole.

Personally, I have always found a little bit unsatisfactory (philosophically speaking) the fact that set theory postulates the existence of an empty set. But of course there is the technical aspect and current axiomatizations of set theory seem to be quite good regarding what it allows us to prove.

Now it seems there have been some attempts to relate mereology and set theory, and according to the article, some authors have recently tried to deduce ZFC axioms as theorems in certain axiomatizations of it. Yet, apparently only a couple of well trained mathematicians (one of them Tarski) have discussed mereology, since most people have shown indifference towards the whole subject.

So my questions are: how is it that mereology had no success as a possible foundation for mathematics? Are axiomatizations based on mereology not suitable for most developments or simply not worth the while? If so, which would be the technical reason behind?