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Albert Lewis's article analysing the influence of Friedrich Schleiermacher on Hermann Grassmann, stimulated many different studies on the founder of ndimensional outer algebra.Following a brief outline of the various, sometimes diverging, analyses of Grassmann's creative thinking, new research is presented which confirms Lewis's original contribution and widens it considerably. It will be shown that:i. Grassmann, although a selftaught mathematician, was at the centre of a hitherto understated intellectual trend, which was defining for Germany. Initiated by Pestalozzi's concept of elementary mathematical (...) 

Helmholtz's theory of space had significant impact on Schlick's early ?critical realist? point of view. However, it will be argued in this paper that Schlick's appropriation of Helmholtz's ideas eventually lead to a rather radical transformation of the original Helmholtzian position. 



Extension is probably the most general natural property. Is it a fundamental property? Leibniz claimed the answer was no, and that the structureless intuition of extension concealed more fundamental properties and relations. This paper follows Leibniz's program through Herbart and Riemann to Grassmann and uses Grassmann's algebra of points to build up levels of extensions algebraically. Finally, the connection between extension and measurement is considered. 

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 (...) 