synthetic and analytic a priori. Here too was a background, including Leibniz’s
alignment of physical relationships among monads with logical relations of
subject and predicate, and more recently the questions of the nature of mathe-
matical knowledge stirred up by the 1764 Berlin prize question. Lambert’s
entry had discussed what analysis meant in mathematics and attempted a
reform of Wolffian logic. Kant now took a new tack. Since Euclid, mathematics
had been regarded as an a priori science, independent of experience, and the
prototype of certainty. In the view of Lambert and others, a priori necessity is
manifested only in the analytical method, which investigates the implications
contained in its definitions and axioms (Coffa, 1991: 9–16). Such knowledge
is tautological. This was unacceptable to Kant, a practicing scientist rather
than a pure mathematician, who wanted mathematical laws to express real
relations discovered by empirical research. Kant decided that mathematics
must be synthetic rather than analytical, that is, providing knowledge which
is non-tautological, ampliative judgements (Erweiterungsurteile, in contrast
to analytical judgments, which are merely clarificatory, Erläuterungsurteile).
Judgments which are synthetic a priori are both certain and informative, going
beyond mere knowledge of concepts. Since mathematical knowledge exists,
there are no doubt such things as synthetic a priori judgments; by extension,
this should prove the secure foundation for scientific laws.
Kant regarded his discovery of the synthetic a priori as “the first step” in
his critical philosophy (Coffa, 1991: 15). In 1772 Kant announced to friends
that he was on the path to a new philosophy, although it took another nine
years to work out a final draft. The ultimate step was to move causality and
substance into the sphere of the a priori, along with space and time. This could
be done if all were now regarded as categories of the understanding, imposed
on experience, and through which all experience is filtered. But if the categories
of causality and of time-space relationships, measurable by mathematics and
describable in geometry, are a priori necessary in all experience, their a prior-
iness does not prevent them from revealing knowledge which goes beyond mere
subjectivity, and beyond the tautological implications of concepts.
Kant now had a critical tool capable of cutting off theological and spiritu-
alist speculation. At the same time, he believed that it validated not only science
but also the rightful activity of philosophy as the perfection of scientific
research from the theoretical side. Early in his career Kant had proposed the
nebular hypothesis of the origins of the planetary orbits by deduction from
Newtonian laws. Later, in the midst of his great Critiques, Kant went back to
attempting to ground all scientific principles in the categories of time and space
by way of intermediary concepts such as impenetrability and weight.^32 Philoso-
phy meets empirical science halfway; the principles discovered by science,
although not dictated by philosophy, were to be progressively generalized and
Intellectuals Take Control: The University Revolution^ •^653