Erik C. Banks
Kant, Herbart and Riemann
Introduction
Johann Friedrich Herbart (1776–1841) succeeded to
Kant’s chair at Königsberg in 1809. He is known today as a philosopher of
education and as a seminal psychologist; but in the 19th century,
Herbart’s metaphysics and psychology had an extraordinary, still largely
undocumented, influence on science and mathematics. Bernhard Riemann, in his
famous 1854 Probevorlesung on geometry, named as his influences only C.
F. Gauss and “some philosophical investigations of Herbart”. Hermann Grassmann’s
groundbreaking Ausdehnungslehre (1844) was influenced by Herbart. And
Ernst Mach, the Austrian physicist-philosopher, was a devoted Herbartian in his
youth, whose theory of space drew on Herbart’s Metaphysik. In his
Knowledge and Error, Mach referred to Herbart’s metaphysics as a model
for a “chemical manifold” of energies (electromagnetic, gravitational and
thermal) for a future physics, mature enough to dispense with space:
Our intuitions of space and time form the most
important foundations of our sensory view of the world and as such cannot be
eliminated. However this does not prevent us from trying to reduce the manifold
of qualities of place-sensations to a physiological-chemical manifold. We might
think of a system of mixtures in all proportions of a number of chemical
qualities (processes). If such an attempt were one day to succeed, it would lead
also to the question whether we might not give a physical sense to the
speculations that Herbart, following Leibniz, conducted as regards the
construction of intelligible space, so that we might reduce physical space to
concepts of quality and magnitude. There is of course much to be objected to in
Herbart’s metaphysics. His tracking down of contradictions that are in part
artificially contrived and his eleatic tendencies are none too attractive, but
he will hardly have produced nothing but errors.
What in the metaphysics and psychology of this “minor”
philosopher made such an impression on three first-class minds of the nineteenth
century?
Kant-Studien, Walter de Gruyter
Print ISSN: 0022-8877
Volume: 96, 08/2005
Pages: 208 - 234
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