This paper deals with an attempt of the mathematician Riemann to develop an outstandingly broad view of the philosophy of nature encompassing basic phenomena of both the material and the mental world. Riemann's draft is traced in its main aspects, and is accompanied by a comparison with certain chapters in the philosophical writings of Herbart that were particularly relevant to Riemann's conception of mathematics and science on the whole. This applies, in particluar, to the epistemological background and to Herbart's theory (...) of the Self. (shrink)