Giorgio Lando

reflexive and antisymmetric. While these latter claims do not figure as axioms in the presentation of CEM from above, they are nonetheless CEM theorems. Thus, mereological monism is committed to them.

Transitivity, that is, the principle that if a thing x is part of a thing y that is part of a thing z, then x is part of z as well.

Transitivity tends to hold when these terms are understood in a nonselective way, while Transitivity tends to fail for selective parthood, which is not the subject matter of mereologydis.

A biologist will consider a mitochondrion to be a part of a cell, and the cell a part of a tissue, but would deny that the mitochondrion is a part of the tissue.

The spatial sense of parthood (assumed as prototypical) makes Transitivity quite a solid principle. If something is in something that is in turn in something else (where this being in is spatial), then it seems quite uncontroversial that the first thing is in the third.

the selective varieties of parthood can be seen as specializations of general, nonselective parthood.

The extension of parthood (which is a binary relation) is a set of ordered couples, such that their first member is part of the second member.

But only some of these ordered couples are such that their first member is a functional part of the second, or such that their first member is a direct part of the second.

In cases where Transitivity seems to fail, we can deny that at least one of the relations involved is parthood.

Set-theoretic membership is not transitive