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An Introduction To Non-aristotelian Systems And General Semantics.

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INTRODUCTION
51
let me say at once that in this 'similarity of structure' we find the only positive 'knowledge* of 1933, and, perhaps, of any date.
So far, I am in full agreement with the great work of Spengler. More than that, The Decline of the West may be considered as a preliminary and preparatory survey of the great cultural spasms which have rocked mankind. It may be instructive, in the meantime, to point out some differences, and the eventual difference of conclusions, between the present work and the work of Spengler.
The difference, to start with, is in language. Spengler announces his work as 'intuitive and depictive through and through, which seeks to present objects and relations illustratively instead of offering an army of ranked concepts'.
My own aim is not merely descriptive, but structural and analytical, and so I must use a different language, helping to discover semantic psychophysiological mechanisms of the events of which Spengler is giving us a very exceptional picture.
Spengler missed two points: that mathematics must be considered a language; and that the connection which he asserts between the mathematics of each period and other achievements is more general than he suspects and applies to the inherent structure of languages, in general, and the s.r of each period, in particular.
Although his analysis is in effect A, yet the A issues are not formulated clearly or consciously; nor does he mention that the present-day accepted definition of number in terms of classes is still A. It is true that he considers 'forms' and the use of number as relations, but he does not emphasize that number has not been formally defined as a relation, which is essential in a-system. His 'form' is still static and not dynamic structure; nor did he discover that the only possible content of knowledge is structural, a fact which is the semantic factor responsible for 'cultures', and 'periods', and everything else in human development.
This present work is in great sympathy with the momentous work of Spengler; but, as it culminates in a-system, it goes further than his, and is more workable and more practical, confirming the general contention of Spengler, that cultures have their periods of growth and development and that, so far, without conscious human intention, they are superseded by others.
We should notice once more in this respect that the issues we deal with, whenever human psycho-logical reactions are involved, are circular, as distinguished from animal reactions. Human structures, in language or in stone, reflect the psycho-logical status, feelings, intuitions, structural metaphysics, and other s.r, of their makers and periods; and,