 At this point in the 1930s, however, several other strands of thinking about logic now coalesced. The intellectual situation was highly complex. The famous papers by Carnap, von Neumann, and Heyting at the 1931 Königsberg congress had identified the logicist, formalist, and intuitionist schools: their debates were to shape thinking about the foundations of mathematics for the next several decades. A search for secure foundations, and in particular for an avoidance of the set-theoretical paradoxes, was something they shared, and that helped to tip the balance in favor of first-order logic. In the first place (as Weyl and Skolem had already pointed out, and as was at least implicit in the Hilbert program) there were good constructivist and philosophical reasons for avoiding higher-order quantification wherever possible, and for restricting one’s logic to the first order. Secondly, several unambiguously first-order formulations were now given of Zermelo-Fraenkel set theory, and also of von-Neumann-Bernays-Gödel set theory (which permits a finite axiomatization). The first-order nature of these theories was stressed in a number of publications from the 1930s: by Tarski (1935), Quine (1936), Bernays (1937), and Gödel (1940). As a practical matter, these first-order set theories sufficed to formulate all existing mathematical practice; so for the codification of mathematical proofs, there was no need to resort to higher-order logic. (This confirmed an observation that Hilbert had already made as early as 1917, though without himself fully developing the point.) Thirdly, there was an increased tendency to distinguish between logic and set theory, and to view set theory as a branch of mathematics. The fact that higher-order logic could be construed as (in Quine’s later phrase) “set theory in sheep’s clothing” reinforced the other tendencies: “true” logic was first-order; higher-order logic was “really” set theory. By the end of the decade, a consensus had been reached that, for purposes of research in the foundations of mathematics, mathematical theories ought to be formulated in first-order terms. Classical first-order logic had become “standard”.