In fact, there are quite a lot of concepts that are imaginable but not logically possible. Any time a mathematician uses a proof by contradiction, they're using such a concept.

We can state very clearly what it would mean to have an algorithm that solves the halting problem. It is only because we can conceive of such an algorithm, and reason from its properties to a contradiction, that we can prove it is impossible.

Or, put another way, yes, we can conceive of halting solvers (or zombies), but it does not follow that our concepts are self-consistent.