The Frege-Russell line was represented by Carnap, who came to Vienna
in 1926, and Wittgenstein, who began discussions with the Circle soon after
(see Figure 13.6). Both had had formative contact with Frege early in their
careers: Carnap had been a pupil at Jena during 1910–1914, and Wittgenstein
visited Frege for early advice on his intellectual path in 1911 and again in
1912; thereafter Frege steadily encouraged Wittgenstein by correspondence
while he was writing the Tractatus during the First World War (Monk, 1990:
36, 70, 115–157). Frege, who had gone without significant professional off-
spring all his life, suddenly acquired two. Both were strongly affected by
Russell. Wittgenstein was Russell’s personal disciple, anointed to carry out the
logicist program. Carnap was galvanized into action in 1921 upon reading
Russell’s programmatic appeal for a movement of philosophers trained in
science and resistant to misleading literary methods, which Carnap took—
naturally enough as a Frege protégé—as directed at him personally (Coffa,
1991: 208). He entered into correspondence with Russell, and began to build
the foundations of knowledge on a Russell-like perfect language hierarchized
through the theory of types. Although Wittgenstein had already gone beyond
the theory of types with devices of his own, there remained enough sense of
commonality that in the late 1920s, Wittgenstein suspected Carnap of stealing
his ideas and excluded him from his own personal meetings with the Vienna
Circle (Coffa, 1991: 405). They are network stepbrothers, working out of the
same patrimony, and thus rivals in the attention space.
The Hilbert lineage is represented in the Vienna Circle network by several
former pupils, including the mathematics professor Hans Hahn, who had
originally brought Schlick to Vienna and was a main organizer of the Circle
(DSB, 1981: 14:88–92, 281–285; Wang, 1987: 52–57, 76–88). Gödel was
Hahn’s protégé; Hahn also taught Popper, who entered the periphery of the
Circle in the same year that Gödel announced his famous proof. In the 1920s
the Hilbert school made strenuous efforts to prove the consistency of arithme-
tic; among the most active was Reichenbach’s colleague at Berlin during
1927–1929, von Neumann, who worked on a new axiomatization soon picked
up by Gödel. The opposite camp, the Brouwer intuitionists headquartered at
Amsterdam, also became entwined with the Vienna network and its issues.
Hermann Weyl, who, like Reichenbach, had studied with Hilbert at Göttingen,
had in the 1920s shifted to the Brouwer camp, mixing intuitionist and formalist
methods in the attempt to reconstruct mathematics from the intuitionist side.
These same mathematicians were intensely active at this time in the foundations
of the new physics of relativity and quantum mechanics, overlapping with the
central preoccupations of the physicists in the Vienna Circle. Further overlap
occurred when Karl Menger, one of Hahn’s favorite pupils, went to study with
Brouwer in 1925–1927 before returning to Vienna, where he joined the circle
The Post-revolutionary Condition^ •^725