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Hermann Grassmann’s contribution to the construction of a German “Kulturnation”. Scientific school grammar between Latin tradition and French conceptions. (English) Zbl 0907.01027

Schubring, Gert (ed.), Hermann Günther Graßmann (1809-1877): visionary mathematician, scientist and neohumanist scholar. Papers from the sesquicentennial conference on 150 years of “Lineale Ausdehnungslehre” - Hermann G. Graßmann’s work and impact, Lieschow / Rügen, Germany, May 23–28, 1994. Dordrecht: Kluwer Academic Publishers. Boston Stud. Philos. Sci. 187, 87-113 (1996).
Why would a school teacher, Graßmann, be expert in language? It was part of the Prussian school system to require that teachers qualify to teach at lower or higher level in the various subjects, such certification being done by rigorous examination: a 3 or 4 hour oral examination by University professors in subjects such as mathematics, philosophy, philology, German, physics, Latin, Greek, even Sanskrit and other ancient languages. Such linguistic training was extremely highly valued in Prussia for appointment and promotion in the civil service: many long-fought discussions in social and professional circles in the Berlin of Graßmann and Dirichlet (1827-1855) attest to this, the supremacy of philology vis-à-vis mathematics and science for training. So it was natural that Graßmann would have some interest. It is natural for mathematicians to seek order, not only in their own field but elsewhere: see Turner’s article on Graßmann and colour for a further example. Graßmann wrote about German and Latin; he produced his aspiration law; he promoted system, understanding, sequence, consistency: “scientific” study, broken into phonetics, syntax, ideas, historical-comparison. Graßmann and his brother Robert wrote of syntax: forms and their meaning, and of ideas: their representation in language, i.e., the interplay of the form of expression and of an idea and the idea itself. This interplay also occurs in the aspirate law: the regular aspirations of the labials \(p\), \(b\); the dentals \(t\), \(d\); the guttarals \(k\), \(g\), as seen in writing; and then there were the exceptions. Graßmann saw that the original speech forms were expressed in writing: therefore written (exception) forms should have had a now unavailable speech expression, and his reconstructions gave a pattern to place the exceptions in a system. His work here is part of him, as a systematic, consistent, scientific person; part of the Prussian education milieu of his time; part of a formed and educated man. Hültenschmidt’s essay fleshes out these bones I have abstracted from her pages.
For the entire collection see [Zbl 0853.00027].

MSC:

01A55 History of mathematics in the 19th century
01A70 Biographies, obituaries, personalia, bibliographies

Biographic References:

Grassmann, H. G.
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