deeper troubles about plurality and substance, causality and relation. Mono-
theism is not the only way some of these questions can be reached, but it makes
them especially acute, and produces abstract philosophy even quite early in a
network’s history, as in the case of early Islamic thinkers. A monotheistic
argumentative community generates proofs of God, rising to acute levels about
just what is proved and not proved; the proof game becomes freed up as an
intellectual terrain in its own right.
The network dynamics just outlined have occurred throughout the literate
civilizations of the world, with some variations in emphasis: China did not go
far in the epistemology-metaphysics sequence and, after the Han dynasty,
focused on a cosmology-ethics fusion on a moderate level of abstraction;
Islam, Judaism, Christendom, and Europe reaped the strongest consequences
of the monotheist impetus, which is found also to some extent in later medieval
Indian philosophy. Besides the cosmological and epistemology-metaphysics
sequences, there is a third major pathway in world philosophy: mathematics.
This has been most important in modern Europe, where the takeoff in modern
mathematics coincided with that of modern philosophy. Its effects are most
visible in the networks around Descartes, Leibniz, and Newton, and again
with Frege, Husserl, Carnap, and Gödel on the Continent, and the British
lineage from Boole to Russell and Wittgenstein. If we add the anti-mathemati-
cal side of these same networks (e.g., Berkeley, Heidegger, Moore, and the later
Wittgenstein), creating their positions by opposition, we can say modern
European philosophy is driven by mathematics.
Let us be careful to understand what this means. European philosophy is
not driven only by mathematics; it combines all of the major processes just
outlined. It has continued a series of high-density debates and is heir to
monotheism, going through the period of religious secularization at just this
time and thereby traversing again the territory of deep troubles in the God
concept. In fact it went through this terrain twice: in the 1600s, at the end of
the religious wars, and again in the 1800s with the spread of the German
university revolution which seized secular control of the bastion of religious
education, setting off the Idealist metaphysics which served as a halfway house
for philosophers on religious turf. The revolutions of modern mathematics
were superimposed upon all this. The social conditions for the other routes are
present elsewhere; in medieval India and Islam there are many parallels to
European thought from Descartes to Bradley, because there were high-density
communities of debate which also traversed, if in different directions, the
terrain between sheer religion of reason and anthropomorphic monotheism.
Mathematics is the ingredient which makes European philosophy unique,
driving it to especially high levels of abstraction and reflexivity.
Is mathematics just a contingent external intrusion upon philosophy? Not846 •^ Meta-reflections