mathematicians their entire professional lives; Bolzano was primarily a mathe-
matician, and Peirce’s only academic appointment was in a mathematics de-
partment; Russell, Whitehead, and Husserl all began as mathematicians before
finding positions in philosophy; Carnap and Wittgenstein studied mathematical
science before entering the philosophical network.
The pioneers of formal logic received scant attention in their own times.
Mathematical logic was a tangential interest among mathematicians as among
philosophers, and it is a good question how this obscure area became the de-
fining identity of a large movement of twentieth-century philosophers. Within
philosophy, formal logic was regarded as a stagnant area where little of im-
portance had been developed for centuries. Midcentury tendencies toward an
inductive logic (such as those of Whewell and Mill) further denigrated the
traditional syllogistic forms, leading away from a logical calculus and toward
empiricism. Nevertheless, within the German philosophical attention space,
deductive logic was slowly rising as a topic of controversy. On one side, Cohen
and the Neo-Kantians identified philosophy with the investigation of the logics
guaranteeing the validity of each intellectual discipline; on the other side, the
movements of Wundt and Brentano proposed to derive logic from empirical
psychology. This empiricist tendency acquired increasing fame in the 1880s
and 1890s as the physicist Mach joined forces with the new laboratory psy-
chologists, grounding his phenomenalist positivism on the propensity of the
nervous system toward economy of thought.
The self-conscious takeoff of the formal logic movement came with Russell
and his network in the early 1900s. It then became an ideology within phi-
losophy, expanding beyond the specialized enterprise of building a logic system
for the foundations of mathematics into a program to reconstruct all of
philosophy and purge everything which could not be reconstructed. The logical
formalists claimed to be putting first mathematics, then science in general, on
a secure foundation. In fact these issues had arisen over and above the actual
practice of scientists and mathematicians, and doubtless their fields would have
continued much the same without the activity of the logicians. This is why the
mathematicians who discovered the new logical tools tended to migrate onto
philosophical turf, where they could get a better hearing.
Typically an intellectual movement in philosophy is fruitful when it opens
a vein of troubles. Counterintuitively, the largest philosophical attention-getter
is not a method which solves all its problems as promised; this would dry up
the life flow of the field, leaving nothing for later generations to work on. A
successful movement hits on a method which seems to promise a great deal,
while in fact encountering unanticipated difficulties. These problems give rise
to new efforts at solution, and to rival tendencies within the movement; the
result is intellectual conflicts which publicize and energize, provoking further
696 •^ Intellectual Communities: Western Paths