Abstract
The symbolic representations of groups form the foundation for the symbolic representations of numbers. Had we only the authentic representations of groups, then the number series would at best end with twelve, and we would not even have the concept of a continuation beyond that. Along with the obvious lack of restriction on the symbolic expansion of groups, the same is also given for numbers, as we will soon see.
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Notes
Cp., e.g., H. Hankel, Zur Geschichte der Mathematik in Alterthum und Mittelalter, Leipzig 1874, pp. 10 and 12.
I speak above of an “imitation” of groups with respect to their number by means of clusters of fingers. This mode of expression, although incorrect, is nevertheless appropriate here, because it is suited to the mental level concerned. The psychical activities brought to bear upon the sensible groups supply concepts which the more naïve consciousness regards as abstract positive Moments of the respective intuitions themselves. Quite as beauty and ugliness, or goodness and wickedness, are judged to be inherent characteristics of external things, so also twoness, threeness, etc., are judged to be inherent characteristics of external groups.
E. B. Tylor, Einleitung in das Studium der Anthropologie und Civilisation (translated by G. Siebert), Braunschweig 1883, p. 376.
Op. cit., p. 11.
Profuse illustrations supporting the presentations of this section are found in the celebrated anthropological and linguistic works of Tylor, Lubbock, and Pott among others.
W, Th. Preyer’s treatise, “Über unbewusstes Zählen,” first appeared in the Gartenlaube, 1886 (See pp.15 & 36), and is reprinted again in the collection of his scientific essays that has recently appeared. How seriously Preyer takes the hypothesis of the unconscious is shown by the accompanying physiological explanations. According to these, the movements corresponding to the intellectual activity of enumerating “… ultimately run unconsciously along the nerve fibers and cells in the brain that are used very often” and “approximate to reflex movements.”
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Husserl, E. (2003). The Symbolic Representations of Numbers. In: Philosophy of Arithmetic. Edmund Husserl, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0060-4_13
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