This article presents Tarski's Address at the Princeton Bicentennial Conference on Problems of Mathematics, together with a separate summary. Two accounts of the discussion which followed are also included. The central topic of the Address and of the discussion is decision problems. The introductory note gives information about the Conference, about the background of the subjects discussed in the Address, and about subsequent developments to these subjects.

Julius König is famous for his mistaken attempt to demonstrate that the continuum hypothesis was false. It is also known that the only positive result that could have survived from his proof is the paradox which bears his name. Less famous is his 1914 book Neue Grundlagen der Logik, Arithmetik und Mengenlehre. Still, it contains original contributions to logic, like the concept of metatheory and the solution of paradoxes based on the refusal of the law of bivalence. We are going to discover them by analysing the content of the book.

We propose an original use of techniques from random graph theory to find a Monadic (Minimal Scott without equality) sentence without an asymptotic probability. Our result implies that the 0-1 law fails for the logics (FO2) and] (Minimal Gödel without equality). Therefore we complete the classification of first-order prefix classes with or without equality, according to the existence of the 0-1 law for the corresponding fragment. In addition, our counterexample can be viewed as a single explanation of the failure of the 0-1 law of all the fragments of existential second-order logic for which the failure is already known.