 Skolem’s Paradox in set theory seems to present a striking illustration of Lewis’s distinction. The Löwenheim-Skolem Theorem states that every consistent, countable set of first-order formulae has a denumerable model, in fact a model in the set of integers \(\mathbb{Z}\). Now in ZF one can prove the existence of sets with a non-denumerable number of elements such as the set \(\mathbb{R}\) of real numbers. Yet the ZF axioms comprise a consistent, countable set of first-order formulae and thus by the Löwenheim-Skolem Theorem has a model in \(\mathbb{Z}\). So ZF’s theorem \(\phi\) stating that \(\mathbb{R}\) is non-denumerable will come out true in a denumerable model \(\mu\) of ZF.