Kant, Herbart and Riemann

Abstract

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 19^th 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?