higher mathematics has been central to the various branches of anti-positivists;
the postmodernism of the late 1900s loudly echoes the themes of the mathe-
matical foundations crisis, for those who have ears to hear.^28
The drive of the mathematical networks into higher abstraction and re-
flexivity is what gives the distinct edge to the philosophy of the modern West.
Of course, the abstraction-reflexivity sequence in general also drives up the
level of reflexivity, but this has become hyper-accelerated in the West by the
long-term tendencies of two disciplinary networks. It is this which has pro-
duced the latest round of self-consciousness about symbol systems that seems
to be cutting away the very ground beneath one’s feet.
The intellectual situation since about 1700 in this respect is historically
unique. An anti-mathematical stance of this sort would have been inconceiv-
able to most Greek, Islamic, and medieval Christian philosophers,^29 for whom
mathematics would have been not seen as a bringdown to mundane calculation
but as the essence of the transcendental, even mystical hierarchy. Mathematics
was the ally of religion and faith. It was only after the great reversal of
alliances, at the time of the secularization of the intellectual world in the late
1600s, that an anti-science and anti-mathematical front appeared. Moreover,
this front consisted not merely of religious reactionaries, but of a secular
opposition to the main line of philosophical development.
The break began as an opposition formed to the Cartesian-Hobbesian
ontology of extended substance. Newton, a hero for the scientific movement,
was nevertheless anchored in the anti-Cartesian–anti-Hobbesian network, the
Cambridge Platonists; the quarrel between Newtonian action-at-a-distance
(“occult qualities” to its enemies) and the Cartesian physics of solidly filled
space was the opening clash on the new battle lines. It was philosophers flowing
from Newton’s network—Berkeley, Hume—who went on to do the most
damage to the claims of mathematical science as a comprehensive philosophy.
Henceforward every development in the mathematically driven sequence of
higher abstraction and reflexivity had a counterpart on the anti-mathematical
side: Kantian transcendentalism promoted aesthetic Idealism as well as Hegel’s
denigration of mathematics as an outmoded and superficial consciousness on
the level of mere calculation. Mathematical and anti-mathematical inspiration
became the deep troubles of philosophical creativity.
The struggle for and against mathematical formalism became the chief
dividing line in philosophy after 1900. Husserl put forward phenomenology
as “rigorous science” in order to solve the crisis of modern thought, by which
initially he meant the foundations crisis just then bursting into the open in the
programmatic battles of formalists and intuitionists. The phenomenological
movement then migrated en masse to the other side of the field, as the later
Husserl himself, and his existentialist offshoots, came to see formalization as
Sequence and Branch in the Social Production of Ideas^ •^855