 The conclusion of Hintikka’s argument is that our ordinary notion of truth is misrepresented by \(\mathbf{ZFC}\). Furthermore, by Tarski’s undefinability result the situation cannot be improved by adding further axioms to \(\mathbf{ZFC}\). In Hintikka’s judgment, axiomatic set theory is a systematic but futile attempt to capture on the first-order level truths of standardly interpreted second-order logic. Like Gödel (1947), also Hintikka holds that the concepts needed to state, say, the continuum hypothesis are sufficiently well-defined to determine the truth-value of this conjecture. The continuum hypothesis does not receive its meaning from phrasing it in \(\mathbf{ZFC}\). Gödel and Hintikka agree that the independence results due to Gödel himself and Paul Cohen do not by themselves show anything about the truth or falsity of the continuum hypothesis. But unlike Gödel, Hintikka finds the derivability of any conjecture whatever in \(\mathbf{ZFC}\) (or in any of its extensions) simply irrelevant for the truth of the conjecture. For Hintikka, it is a ‘combinatorial’ question whether every infinite subset of the reals is either countable or else has the cardinality of the set of all reals – a question properly conceptualized within second-order logic. This is what Hintikka takes to be the pretheoretical sense of the truth of the continuum hypothesis, and that is not captured by  \(\mathbf{ZFC}\).[80] 