For Leibniz, two or more CIC (Complete Individual Concepts) are composssible
if it is possible for them to be instantiated in the same possible world. The issue of
how to determine if two CIC are compossible or incompossible is a debated topic.
If the only predicates contained in a CIC are monadic ones and this means that they
have the form Fx, then it becomes unclear how any two CIC could ever be
inconsistent or incompossible.1 Mates thinks that the solution to the compossibility
problem is somehow connected with the doctrine of universal expression, what he
calls the mirroring principle. He says,
the “mirroring” principle clearly implies that concepts belonging to
different possible worlds must be incompossible. It may be illustrated with
Adam and Eve. Adam would not have been the same person if he had not
been the husband of Eve, nor would Eve have been the same person if she
had not been the wife of Adam; thus neither Adam nor Eve could have
existed without the other. (76-7)
I agree with Mates that universal expression is essential to this problem, but Mates
does not make clear exactly how CIC are incompossible. We know that concepts
belonging to different worlds are incompossible. What we want to know is how
we know whether or not they are incompossible without appeal to their being in different possible worlds!
