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A structuralist view of Lagrange’s algebraic analysis and the German combinatorial school. (English) Zbl 0862.01013

Echeverria, Javier (ed.) et al., The space of mathematics. Philosophical, epistemological, and historical explorations. Revised papers from a symposium on structures in mathematical theories, Donostia/San Sebastian, Basque Country, Spain, September 1990. Berlin: Walter de Gruyter. Grundlagen der Kommunikation und Kognition. 280-295 (1992).
The author argues that it is incorrect to assume that the great majority of Germany’s early 19th century mathematicians had a Kantian position with respect to the nature of mathematics. He illustrates the views of the combinatorial school, to which also Ohm belonged, with a discussion of Spehr’s 1826 textbook of infinitesimal analysis. In the combinatorial school, analysis was seen as a theory of symbolic expressions. The notion of continuity and the infinitesimal calculus were viewed as belonging merely to the realm of the applications of analysis. The author also briefly compares the formalist combinatorial analysis with Cauchy’s conceptual approach to the foundations of analysis. He argues that the combinatorial approach was in some respects equally successful.
For the entire collection see [Zbl 0839.00019].

MSC:

01A55 History of mathematics in the 19th century
26-03 History of real functions

Biographic References:

Lagrange, J. L.
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