comes a fourth kind of philosophical creativity: counter-movements to keep
challengers out.
Modern philosophies are heavily influenced by the expansion of science
within the universities, but not, as contemporary ideologies often had it, by
becoming a mere branch or ancillary of science. The dynamics of intellectual
networks, including the way they adjust to changes in the organizational
base, remain fundamentally the same throughout world history. If modern
European intellectuals differ from their predecessors, it is by adding onto the
basic mechanisms they share with Asian and with ancient and medieval West-
ern philosophers two further developments: rapid-discovery science and the
autonomous research university with its proliferation of specialized disciplines.
Modern academic philosophy, as the most abstract and reflexive of disciplines,
takes as its problem space the results of these two revolutions. That is why
mathematics became the instigator of so much of modern philosophy, even on
the rebound and in fields far removed from logic and philosophy of science.
Methodological disputes built up within mathematics when the discipline
became academicized. From the foundational crisis of mathematics at the
turn of the century flowed the logical positivism of the 1920s, coming into
full bloom in the Vienna Circle by meshing with methodological disputes in
physics and with Neo-Kantianism. Another branch of the same networks
produced phenomenology, which gradually sharpened its rivalry with and
rejection of the mathematicians by giving birth to existentialism. The intrusion
of logical formalism into philosophy energized in reaction a third large move-
ment of twentieth-century philosophy, ordinary language. Both directly and
through the dynamics of intellectual conflict, the major schools of modern
philosophy all resulted from interdisciplinary pressures originating in mathe-
matical science.
There is a deeper sociological reason why this would be so: by the genera-
tion of 1835–1865, mathematics had become the intellectual network which
had achieved the highest degree of self-consciousness on its structures of
argument; indeed, to a large extent this focus on its own operations constitutes
the subject matter of higher mathematics. The next round of philosophy was
taken over by the concepts and controversies arising from this new pitch of
intellectual reflexivity.
Disciplinary border-crossings flow both ways at various times. First, mod-
ern rapid-discovery science proclaimed its independence, even its supersession
of philosophy; not long after, scientists were creating issues at a high level of
abstraction that eventually bid to capture the center of the philosophical
attention space. The movement of formal logic was created largely by mathe-
maticians migrating onto philosophical turf. Frege, Boole, and Peano were
The Post-revolutionary Condition^ •^695