Towards the History of Monadology as a Doctrine of Discontinuous Unity

Abstract

The Russian mathematician of the second half of the XIX c. N.V. Bugaev followed Leibniz in his general view of monads. Bugaev’s general world view was based on the principles of monadology while in his philosophy of science he opposed arhythmology including different branches of discrete mathematics and the analytic methods. Among Bugaev’s students the Priest Pavel Florensky was developing (especially in his dissertation) the idea of the particular importance of the research of noncontinuous elements for the different fi elds of knowledge of the early XX century. Later the same conclusion was expressed in a special lecture of A.N. Kolmogorov whose previous teacher had been N.N. Luzin (another student of Bugaev). The idea of the role of discrete elements for the scientifi c innovations of the last period is illustrated by the results of the modern phonology. The average number N of the phonemes in a language is defi ned by the inequality 10 < N > 23 ・ 10. From the evolutionary point of view it corresponds to the quantity of signals in the communication systems of monkeys and apes (and other high mammals). The change in the development of human language was made not by the growth of the number of symbols, by their new function. The earlier signs became elements that helped to differentiate the words with different meanings. The author believes that the whole problem of the atoms of languages and other sign systems might be reappraised from this point of view. The talk of V.V. Ivanov is followed by discussion.