Historical aspects of the foundations of error theory. (English) Zbl 0855.01009

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. 253-279 (1992).
This is an extended English version of the author’s German paper of 1991 [Zum hypothetischen Charakter mathematischer Beweise. Jahrbuch 1990, Humanismus Tech., Jahrb. 34, 55-80 (1991; Zbl 0727.01011); see also Hist. Math. 12, 258-260 (1985; Zbl 0569.01008)]. Four problems are being discussed: 1. Systematic and methodological aspects. 2. The most important proofs and the contemporary criticisms of them. 3. The hypothesis of elementary errors. 4. The principle of the arithmetical mean. All these questions depend more or less on the mathematical description of reality, because the method of least squares is a veritable pivot between pure and applied sciences. The different authors came to very different conclusions because they did not agree with another on the underlying philosophy.
For the entire collection see [Zbl 0839.00019].
Reviewer: H.Grimm (Jena)


01A55 History of mathematics in the 19th century
62-03 History of statistics
00A30 Philosophy of mathematics