 It is evident from the work done in the twenties surveyed above that the problem of finding a formal solution to the semantical paradoxes, such as the Liar and the Richard paradox, remained essentially open. Type-theoretic solutions had not been pursued to the extent of providing a systematic formal analysis of semantical notions (like truth or definability). But why would this problem be worth studying from a logical and mathematical point of view? As a matter of fact, semantical notions—in particular the notion of definability—were more or less explicitly used in certain parts of set theory (descriptive set theory) and in more “set theoretically inclined” parts of function theory, which were cultivated by Polish mathematics in the twenties. At the same time, the project of a formal methodology and of a scientific semantics was developed by prominent Polish philosophers and logicians working in Lvov (now Lviv) and Warsaw (Lesniewski, Łukasiewicz, Chwistek; see Wolenski 1995 and the entries on  Lesniewski,  on  Łukasiewicz  and on the  Lvov-Warsaw school).  For instance, Chwistek attempted an elementary semantics on the ground of a nominalistic foundational program, where sets are identified with propositional functions, extensionality is rejected and the fundamental notion of semantics is the substitution relation “\(H\) is the result of the substitution of \(G\) for \(F\) in \(E\)” (Chwistek 1933, p. 374). In this stimulating environment, Tarski developed his fundamental analysis of semantical paradoxes, first dating back to 1929 and 1930, reported by Łukasiewicz to the Polish Society of Sciences in Warsaw in 1931 and then detailed in the long memoir of 1935 (see the entries on  Tarski  and on  Tarski’s truth definition).