 As noticed many years ago by Kreisel and quite aptly recalled by Dean 2020, p. 541, the right question to deal with is not how to get rid of paradoxes or to solve them: instead, the fruitful problem is to get something out of them. Indeed, paradoxes can be converted into plain undecidability/undefinability theorems, and this is the consequence of a systematic methodology: with the work of Gödel and Tarski, paradoxical arguments are reshaped into fixed point results, while the semantic conception of truth gives rise to a formalization of semantics itself, yielding firm grounds for systematic metamathematical investigations, as can be seen from several early contributions by a number of logicians, e.g. Kreisel 1950, Wang 1955. For instance, arithmetizing semantics yields a refinement of the completeness theorem, the so-called arithmetized completeness theorem ART: every recursive consistent theory has a model in which the function symbols are replaced by primitive recursive functions and the predicate symbols are replaced by predicates which are definable with just 2 quantifiers in a version of formal number theory (cf. Hilbert and Bernays 1939, p. 293 and Feferman 1960). By adding an arithmetic sentence Con(S) expressing the consistency of a set theory S as a new axiom to elementary number theory, one can prove in the resulting system arithmetic translations of all theorems of S. A by-product of this metamathematical formalization is a de facto unification of set theoretic and semantic theoretic paradoxes, in the sense that paradoxes of either sort become tools for proving incompleteness and undecidability. Typically, a given paradoxical notion is formalized as a predicate in a language of a theory interpreting (at least a fragment of) number theory Z; one then applies diagonalization, self-reference, etc., in order to get statements which correspond to number theoretic sentences that becomes undecidable or unprovable given a consistency assumption.