the dynamism not only of human beings but of the universe as well. Every
object in the world is negative, in a state of privation which drives it into
activity.
The dialectic is a frame within which Hegel can theorize every field of
research, and thereby implicitly legitimize all of them as food for the philo-
sophical faculty. The longest section of Hegel’s Phenomenology, taking up
about 75 percent of the text, is an application of the method to “Free Concrete
Mind,” which comprises all the fields of natural science, as well as psychology,
human social institutions, politics, law, religion, and art. Hegel’s system en-
compasses empirical research; observation is a function of Reason, and more-
over Laws which are uncovered in scientific investigation are really existing
forces within nature. This is Kant’s theoretical completion of empirical research
in a much more assertive form. Hegel finds particularly apt the study of organic
existence. The unfolding of the plant from seed to bud to blossom can be
described as a progression of negations and sublations, flowing from a preg-
nant potentiality. He is harsh against downward reductions; Lavater’s physi-
ognomy is critiqued along with the current scientific fad of phrenology as tying
the inner spirit down to its sensory appearances.
One field Hegel eschews: mathematics. Quantity is only an external char-
acteristic of being, whose real essence defies formalization.^37 In part this shows
a dislike of the mathematical method of proceeding by formally circumscribed
axioms and operations, which ignore the larger interrelation of all concepts
and the process of dialectical reconceptualization by which insight grows.
Quantity, Hegel argues, is ultimately qualitative; the law is that quantity
eventually reaches points where it passes into qualitative change, as water at
a certain temperature turns into ice. Hegel is breaking here not only with Kant,
for whom mathematical laws are the essential form of science, but also with
virtually the entire philosophical tradition up to this time, and especially the
modernists: Descartes, Spinoza, and Leibniz.
This was not just an idiosyncrasy of Hegel. Since his day philosophers have
divided into those who assimilate philosophy to mathematical logic (the lineage
from Bolzano and Frege through Russell), and those (in what twentieth-century
anglophone philosophers somewhat inaccurately call the Continental tradition)
who reject mathematics. No doubt Hegel had immediate motivations, espe-
cially his rivalry with Fries, a neo-Kantian who criticized the qualitative Natur-
philosophie while proposing a rival speculative natural history with fanciful
mathematical laws.^38 To depersonalize the rivalry, Hegel had a good sense for
the moods of academic disciplines, and he might have felt the embarrassment
that pseudo-mathematics like that of Fries was creating in the eyes of profes-
sional mathematicians. The technical frontiers of mathematics were moving
far beyond the competence of non-specialists. And indeed, although Hegel
Intellectuals Take Control: The University Revolution^ •^659