The paradox of increase

[FIRST PARAGRAPHS] It seems evident that things sometimes get bigger by acquiring new parts. But there is an ancient argument purporting to show that this is impossible: the paradox of increase or growing argument.

Here is a sketch of the paradox. Suppose we have an object, A, and we want to make it bigger by adding a part, B. That is, we want to bring it about that A first lacks and then has B as a part. Imagine, then, that we conjoin B to A in some appropriate way. Never mind what A and B are, or what this conjoining amounts to: let A be anything that can gain a part if anything can gain a part, and let B be the sort of thing that can become a part of A, and suppose we do whatever it would take to make B come to be a part of A if this is possible at all. Have we thereby made B a part of A?