 Unfortunately for the realist, this is not the only explanation. In fact, Putnam used this very example in an early formulation of the MTA. Just because there are different models that satisfy \(\phi\) in some of which \(\mathbb{R}\) is non-denumerable but in others of which (such as \(\mu\)) \(\mathbb{R}\) is denumerable, Putnam argued, it is impossible to pin down the intended interpretation of ‘set’ via first-order axioms. Moreover, well before Putnam, Skolem and his followers had taken the moral of Skolem’s Paradox to be that set-theoretic notions are indeterminate [For further discussion, see the entry on  Skolem’s paradox].