lytical but synthetic, while remaining a priori. It follows that there does exist
a form of knowledge which is both certain and informative, going beyond mere
knowledge of concepts. Kant went on to investigate what are the categories of
synthetic a priori understanding, concluding that time, space, and causality are
categories through which all experience is necessarily filtered, and in whose
necessary regularities all valid scientific knowledge can be formulated. Kant’s
transcendental method opened up a whole new playing field—in fact two such
fields—for philosophers, quite apart from whatever science can be grounded
in this way. One is the path into Idealism, constructing all of reality from the
working out of consciousness. The other path, which has proven to be more
enduring, is the critical aspect of Kant’s transcendental method. It is a method
of working backwards, investigating in any field of experience what is neces-
sarily presupposed for that experience to be formulated.
This method makes critical epistemology into the central philosophical
question. At the same time—a point that was to provide grounds for a huge
neo-Kantian movement in the burgeoning university system—it makes the
philosopher the arbiter of the knowledge conditions of every other intellectual
discipline. In Kant’s own generation this method spread like wildfire because
it proclaimed the autonomy of philosophical intellectuals over theology, indeed
giving philosophy the position of pronouncing on the conditions for knowl-
edge claims in theology as in every other field. This Kantian critical epistemol-
ogy was the ideology of the university revolution. And since the research
university has been the key organizational base for intellectuals ever since, we
are all post-Kantians, ever since anchored around the centrality of critical
epistemology.^27
These movements from Descartes to Kant were parts of one wave, spilling
over from the first round of the mathematical revolution. The second wave of
higher or reflexive, self-consciously abstract mathematics was the catalyst for
the philosophies of the turn of the 1900s. It started off with persons who
pursued (at least initially) mathematical careers—Frege, Husserl, Russell—and
ramified into the movements not only of logical positivism, the Vienna Circle,
and analytical philosophy generally, but also into phenomenology and existen-
tialism. The mathematical movement toward rigor, reflexivity, and the delib-
erate creation of higher-order formal systems stimulated philosophy in several
ways. Reflexivity and higher-order abstraction became topics for discussion in
their own right, leading to devices such as Russell’s theory of types and
Husserl’s layers of phenomenological reduction or epochê. Higher mathematics
encourages the formulation of new languages, which Frege pioneered in logic,
and his followers attempted for all the verbal realms. And it turned up its own
deep troubles, in the debate over the foundations of mathematics which gen-
eralized to philosophical turf and energized the action at Cambridge, Göttin-
gen, and Vienna.
852 •^ Meta-reflections