Символотворчество и закон постоянства
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The author's materials in this section are not known and, probably, they were not written. But among the extracts from the literature made by Florensky, there are those related to this topic (Archive of Priest Pavel Florensky).
The texts were prepared by Abbot Andronik and S. M. Polovinkin. Notes from Abbot Andronik.
Chapter on the principle of permanence in the use of symbols. Symbola permanent.
“Permanentia symbolorum. Symbola permanent.”
In the forgotten work of the program of the Hamburg Johanneum: G. N. Bubendey, – Ueber die räumliche Darstellung der imaginärer Grössen der Analysis, 1837.
Long before Ginkel and Schroeder, he formulated the law of permanence.”
G. Bubendey, – Ueber die räumliche Darstellung der imaginärer Grössen der Analysis, 1834 824, program of the Hamburg “Johanneum”.
This work is pointed out by M. Simon, – Über die Mathematik. Giessen, 1908.
Even earlier, M. Ohm spoke in the same sense, - Versuch eines Volkommen Konsequenten Systems des Mathematik. 1822. – See from him – preface to the 3rd ed. 1828, pp. XIII et seq., as well as the appendix to volume I, p. 407. - Ohm met with sharply negative criticism. – Om quotes N. Hankel – Vorlesungen über die Theorie der komplexen Zahlen. Lpz, 1867. – Hankel does not ascribe to himself absolute priority in the discovery of the principle of permanence and, in addition to the above-mentioned Ohm, on page 15 he mentions the work of Pea and other English mathematicians of 1834–1842.
W. Wundt in 3rd ed. of his “Logic” calls this principle axiomatic, despite the objections raised by G. Burckhardt to this (Vierteljahrsschrift für wissenschaftlicher) Philosophie, Bd. XIX, abstract of the 2nd ed. "Logic" by Wundt.
“This is completely wrong; this principle is a requirement expressed in the form of simplicity and expediency; whether it can be satisfied is subject to special research each time (p. 82, appendix 44). A. Ross. About the essence of mathematics. Translated by I. V. Yashunsky. Physics. St. Petersburg, 1911. [7, 690, B. MDAk].
Symbolism. Permanence. Connectivity.
At the 1st Congress on the Philosophy of Mathematics (Paris, April 6–8, 1914), “Dean outlined in essential terms the theories developed in a remarkable work entitled Symbolism and Reality in Mathematics (Symbolisme et realite dans les mathematiques). The essential aspect of mathematical symbols is that they form a system: they constitute one whole, with which each symbol is inextricably linked. Taken individually, the terms of the system (les termes) have no mathematical meaning. The construction of a so-called mathematical system is neither deductive nor inductive, but is accomplished through successive generalizations 825. Mathematics does not consist of a collection of arbitrary conditions, unless one strips the signs of all meaning, as Hilbert does. It is possible not to symbolize the systematic side of sensory reality; but as soon as we take this path, mathematics inevitably arises, and for this very reason it undoubtedly has an objective existence.”
(A. Raymond. First Congress on the Philosophy of Mathematics. P. 112. “Western Experimental Physics and Elements of Mathematics” 2nd series II, September, No. 5(617), 1914). Page 110–118.
(Proceedings and reports of the congress will be published in a separate book “Revue de Metaphysique et de Morale”
(Be sure to get both a book and a magazine!)
In another entry after this word Florensky inserts: [cf. "law of permanence" D].
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