  In this way the theories of the form ZFC+LC, where LC is a large cardinal axiom, provide a yardstick for measuring the strength of theories.  They also act as intermediaries for comparing theories from conceptually distinct domains: Given ZFC+φ and ZFC+ψ one finds large cardinal axioms Φ and Ψ such that (using the methods of inner and outer models) ZFC+φ and ZFC+Φ are mutually interpretable and ZFC+ψ and ZFC+Ψ are mutually interpretable.  One then compares ZFC+φ and ZFC+ψ (in terms of interpretability) by mediating through the natural interpretability relationship between ZFC+Φ and ZFC+Ψ.  So large cardinal axioms (in conjunction with the dual method of inner and outer models) lie at the heart of the remarkable empirical fact that natural theories from completely distinct domains can be compared in terms of interpretability.