sense but also reference. Frege’s Platonism, when broadened into an epistemol-
ogy, gave rise to the imperious claims of logical positivism.
At the same time Frege opened the path for Wittgenstein and the recogni-
tion that a language or symbol system contains multiple levels. He forces us
to see that all our intellectual activity takes place in a language, and exposes
confusions between various levels within the language and what the language
is talking about. One offshoot was the belief that philosophical problems are
merely mistakes of this sort, which could be cleared away by careful analysis.
Both the positivist and the analytical movements eventually discovered that
matters could not be disposed of so easily. That too was foreshadowed in Frege.
The world is more complex than is apparent in subjects and predicates, or in
the distinction between the factual-empirical realm and the logical-conceptual.
Frege points out that making definitions is not an arbitrary act of subjective
creation; definitions show their worth by their fruitfulness in the chain of
argument. Definitions have consequences that cannot be known in advance.
“The mathematician cannot create things at will, any more than the geographer
can; he too can only discover what is there and give it a name.” Yet “obser-
vation itself already includes within it a logical activity” (Frege [1883] 1980:
99, 108). Recasting the refinements of abstract mathematical argument into
tools for philosophy, Frege opened a puzzle space containing room for many
positions.
In the eyes of the twentieth-century formalist school, the greatest figure of
the previous century was Frege. He is depicted as the turning point in all
modern histories of logic (Wedberg, 1984; Kneale and Kneale, 1984; Dummett,
1981; Coffa, 1991). In his time Frege was a minor figure, a mathematician in
a not particularly eminent department (Jena, much declined from its glory
days), unrecognized by his profession and never promoted to Ordinarius. He
became known primarily because Russell drew on him as both ally and foil in
a more prominent network of controversies.^12 Frege was not entirely isolated
in the networks, but he was treated as supernumerary among the more central
debates of the German attention space. Eventually the creative splits of the
mathematical network came into contact around him. In the late 1890s Frege
corresponded with the formalist radicals Peano, and Hilbert, the future leader
of one wing of the mathematical foundations controversy. A few years before
his encounter with Russell in 1902, Frege entered into correspondence with
Husserl, another ex-mathematician working on the broader implications of the
foundations of mathematics. Creativity occurs by structural opposition and
recombination of networks. In Husserl, two antagonistic networks come to-
gether. When Frege critiqued Husserl’s book in 1894, he made contact with a
pupil of Brentano, the most famous representative of the empiricist logic which
Frege was combatting. Frege is a central node in the formative period of both704 •^ Intellectual Communities: Western Paths