 Herbart’s ideas influenced Riemann (see Scholz 1982). Riemann regarded natural science as the attempt to understand nature by the use of precise concepts, which are to be modified in the light of new experiences. He expected the most successful concepts to be quite abstract, and agreed with Herbart that they are not a priori in the Kantian fashion. It was their origin in observation or experiment that gave these concepts their significance for science, but Riemann allowed for a constant process of corroboration and revision. In notes he wrote for himself (see Riemann Werke 1990: 539) Riemann said that he agreed with Herbart in matters of psychology and epistemology, but not ontology or with his ideas about the construction of the concepts of space, time, and motion. The disagreement masks a deeper sympathy. Herbart had advocated a three-dimensional real world of causally connected but discrete 'monads' (with windows, to use Leibniz's phrase), which the mind treats via the concept of a continuum, which it supplies, thereby turning its discrete experiences into spectra of possibilities. Riemann saw no reason to restrict attention to three dimensions, and moved the continuous spectra of possibilities into the very general geometrical concepts he was creating.