out. Philosophy drives up the level of abstraction and reflexivity, promotes
periodic movements of synthesis, consciously argues over methods, and thereby
lays down epistemological principles. Transferred to the topics of naturalistic
observation and mathematics, the philosophical networks turn empirical com-
pilations into theories, lay methods of commercial arithmetic or practical
geometry into puzzle-solving contests carried out under increasingly stringent
rules. The philosophical networks import not only consciousness of abstraction
but also a social impetus to innovation. This appears to have happened in early
period of ancient Greece, for a time in the Islamic networks, and again in
Europe after 1500. But the inherent tendency of abstract philosophers to
concern themselves with cosmopolitan topics on the terrain of science does not
in itself lead to sustained scientific innovation, or indeed to consensus. There
were periods of relatively accelerated discovery in Greece and Islam, but the
research front as a whole did not become “technologized” with explicit concern
for tinkering with methods for producing new results. The rather widespread
concern of the philosophical stars of medieval Christendom with topics of
science was not sufficient to create much science.
The lesson of abortive episodes such as the Mohists, the Oxford-Paris
nominalists, and al-Birtruji’s and al-Tusi’s astronomy is that philosophical
networks by themselves can provide a temporary impetus to scientific innova-
tion. But the philosophical network itself is subject to the law of small numbers,
inherently anti-consensual in its creative periods, while the imposition of a
forced consensus in an official doctrine or the deadening effect of a scholastic
curriculum results in losing innovation entirely. Scientific takeoff is promoted
by overlap between practical mathematicians or other empirical and observa-
tional professions and the philosophical networks; but sustained development
in mathematics and science depends on growing genealogies of technologies
for rapid discovery, allowing scientists to outstrip the factionalism of the
philosophers. The impetus of philosophical competition and abstraction which
promoted Greek and Hellenistic science was lost as astronomy became trans-
formed into astrological religion, number theory into numerology, and both
into Neoplatonist cosmology. The dynamics of philosophical networks can
launch episodes of scientific discovery but can also undermine them.
The development of scientific networks is a special application of the
general process governing all intellectual change. External conditions rearrange
material bases for intellectual occupations, and these in turn lead to restruc-
turing networks, generating new alliances and oppositions in the attention
space. We have seen clues in China, where the usual segregation of mathema-
ticians and astronomers into specialized and low-status segments of the impe-
rial bureaucracy was broken down precisely during the episodes of creativity
in abstract mathematics.
552 • (^) Intellectual Communities: Western Paths