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An Introduction To Non-aristotelian Systems And General Semantics.

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tendency is apparent, leading to revision of the mathematical notions of
infinity. For instance, the Zi-system involves several structural 'infinity' assumptions. In it, a line has infinite length; the space constant is infinite; and the natural unit of length is also infinite. In the JV-system, the velocity of light is assumed unconsciously to be infinite, a structural assumption false to facts. The A -system involves also false to facts infinity assumptions, explained later. It is extremely interesting to note that in any system a similar result follows from the introduction of these different 'infinities'; namely, when such an 'infinity' is introduced in the denominator, it makes the whole expression vanish. When, in the observation of actual facts, we miss some characteristic entirely; for instance, order, it leads to the introduction of some 'infinity' somewhere. In other words, faulty, insufficient observation leads to the introduction somewhere in our systems of some fanciful 'infinities'.
I must emphasize again the semantic difficulties which beset us, in the formation of a new and-system, mainly because of the lack of scientific non-el psycho-logics and general semantics. Having no general theories to guide us in our researches, we must select some other devices. We can survey those achievements of mankind which have proved to be the most beneficial and of most lasting value, study their structure and try to train ourselves, and our s.r, in repeating the psycho-logical processes and methods which have made them. In this way, we are led to the study of the structure of mathematics and science, and acquire the habit of rigorous and critical 'thought' and acquire new s.r. Naturally, such a method is wasteful; it would be simpler to have general nan-el theories, which I have proposed to call general semantics and psycho-logics, replacing the older el 'logic' and 'psychology', and study these short, structurally correct, ready-made formulations to train our s.r rather than to study the actual performance of scientists and mathematicians, and formulate these generalizations for ourselves. But, until the present work, this could not be done.
For these reasons, we shall have to make, in the following chapters, a short survey of different scientific achievements without going into technical details, but giving enough of these details to indicate structure and its bearing on s.r. Every thing given will be strictly of an elementary character, and the intelligent reader will find no special difficulties in following the survey.
The selection of suitable material presented a very serious problem. I consulted with many friends and used my best judgement, backed by some experience. An important factor was the class of readers for whom this book is written. Sooner or later a new branch of science must be