Willard Van Orman Quine

224 daniel isaacson
Fundamental Laws of Arithmetic, which was to have provided a
fully explicit formal derivation of arithmetic from logic, Bertrand
Russell (1872–1970) wrote to Frege, informing him that his axiom
system was inconsistent. Frege was devastated, and Russell devoted
the next decade to finding a consistent system of logic that would
allow the derivation of arithmetic and of mathematics more generally.
The result was the three-volume Principia Mathematica (1910 –
13), written jointly with Alfred North Whitehead.
The system of Principia Mathematica is apparently consistent but
makes use of two axioms that are difficult to defend as logically or
analytically true, or even true at all, namely, the axiom of infinity
and the axiom of reducibility. Even so, despite these vicissitudes, by
the end of the first decade of the twentieth century, the possibility
of establishing mathematics as analytic on the basis of the significant
development of mathematical logic that had already occurred
seemed highly promising. It also heightened the prospects for a type
of empiricism that viewed all substantive knowledge, what Hume
had called “matters of fact,” as based ultimately on sensory experience
and all knowledge of relations of ideas, most crucially mathematics,
as based on logical definition and deduction. The philosophers
who did most to achieve and espouse this position were a group
based in Vienna who came to call themselves the Wiener Kreis, the
Vienna Circle, with organized allies in Berlin and kindred souls in
Poland and Scandinavia.
The beginnings of the Vienna Circle date from 1907, when three
members of the faculty of the University of Vienna, the mathematician
Hans Hahn, the economist Otto Neurath, and the physicist
Philipp Frank, came together to discuss philosophy of science. In
1922, at the instigation of these three, Moritz Schlick was appointed
Professor of the Philosophy of the Inductive Sciences at the University
of Vienna, a post held earlier by Ernst Mach. A lively discussion
group gathered around Schlick. In 1926, Rudolf Carnap came to
Vienna as Privatdozent (the lowest rank in the German and Austrian
academic system) from Jena, where he had written a doctoral thesis
on space and also been influenced by Frege, whose lectures on logic
he had attended. Carnap quickly established himself as the leading
figure within the group. 13
In 1928, members of the group established an organization, which
they called the Verein Ernst Mach (Ernst Mach Society), for the
purpose of “propagating and furthering a scientific outlook” and
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