Consider the following axiom set, in which x's, y's, and "on" are the undefined terms:
Axiom 1. There exist exactly five x's.
Axiom 2. Any two distinct x's have exactly one y on both of them.
Axiom 3. Each y is on exactly two x's.
How many y's are there in the system? Prove your result.
Solution (so far):
I think, there the number of y's is undefined because Axiom 2 and Axiom 3 contradict each other.