The following is quoted from Set Theory and the Continuum Problem by Raymond M. Smullyan and Melvin Fitting.
So far, no attempts have been the slightest bit successful in determining whether the continuum hypothesis is true or false! Another question not to be confused with the truth or falsity of the continuum hypothesis is whether it can be formally proved or disproved from the present day axioms of set theory. This question is completely settled.
I always thought that when a statement is not provable nor disprovable, then it is up to convention to decide whether it is true or false. How can we determine the truth of CH if we know it is not provable nor disprovable?
Please explain in layman's language.