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SUPPLEMENT III |
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reversed order of ascribing to the world the structure of an inherited primitive language. (14)G) The investigation of the potentially known structure of languages in which we predict and then verify the predictions empirically, appears as an important method for the discovery of the structure of the world. (15)
H) Investigations disclose that all
At el languages and disciplines built on them (older 'psychologies', 'logics'. , and, based on them, economics, sociology, politics, 'ethics'. , reflected in turn in our institutions, systems.,) are not structurally similar to the world and our nervous system, as they verbally divide what empirically cannot be divided. Under such conditions neither a higher grade civilization, nor general sanity, nor paradox-free science and mathematics are possible. In el languages, our verbal predictions are not verified empirically, and not being able to foresee we must proceed by animalistic 'trial and error'. (16)I) Mathematics appears as a very limited but the only language in existence, in the main similar in structure to the world around us
and the nervous system. (17)J) From the study of mathematics, mathematical physics, and physics, we learn, and will continue to learn, the fundamentals of
m.o structure. It is no mystery that all chemistry has become a branch of physics, all physics can be made a branch of geometry, all geometry a part of analysis, and all analysis a part of general semantics. The present work shows that the analysis of all human, problems of daily life or science becomes dependent on general semantics which on the verbal levels becomes generalized mathematics. Thus mathematics, mathematical physics, and physics become the most important disciplines from which we learn most about structure, - the only 'content of knowledge'. (18)K) The older
el 'psychologies' and 'logics' for their maximum usefulness must be transformed into unified non-el psycho-logics and general semantics, possible only after studying all forms of human behaviour, mathematics included. (19)L) The study of mathematics as a form of human behaviour, appears necessary prior to the possibility of formulating any laws of semantics. (20)
M) The problem of mathematical foundations do not belong to mathematics but to psycho-logics which would not disregard anthropology, and would not be vitiated by our persistence in the use of structurally inappropriate
el 'psychologies', 'logics', and an innocence of mathematics. (21)N) The 'intuitional' and the 'intuitional' formalist schools of mathematics must be considered as a legitimate, yet not properly formulated, protest against the older elementalism. (22)
O) The general semantic school will represent the
non-el and A. school of mathematics. (23)P) The present crisis of mathematics ultimately depends on the meanings and use of a few terms such as 'all', 'there is', 'infinite'. , which solution depends on a non-el theory of meanings, which ultimately can be solved by transforming |
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