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An Introduction To Non-aristotelian Systems And General Semantics.

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abstractions and so become impervious to contradictions with 'reality' and impervious also to higher order experience.
The infant, and the rest of us, identify a great deal because of the reasons given above. Investigations show that most of human difficulties, public, private, or scientific are due to this A s.r, which accounts for the infantile state of our commercial so-called civilization. Identification abolishes the natural order of evaluation, but so does also an unconscious assumption of an 'infinite velocity' of a process. The A trilogy involved some fanciful 'infinity' assumptions. Thus in the A -system the velocity of nerve currents, which is known to be 126 metres per second in the human nervous system, is at present assumed unconsciously as 'infinite', made evident by the elementalism of 'intellect' or 'emotions'. , as something 'by themselves' and detached. In the jE-system the length of a line, the space constant, and the natural unit of length were assumed 'infinite'. In the JV-system the velocity of light, known to be finite, was unconsciously assumed to be 'infinite'. In the trilogy these unjustified or meaningless 'infinities' have been eliminated. 'Infinite velocity' of a process has no meaning. It represents only a play upon symbols. Velocity is defined as v = s/t. If we assumeand write, this 'velocity' lacks one of
the fundamental factors of its definition; namely, t, and so such an expression ceases to define anything at all and has no meaning, although it may be a symbol for a semantic disturbance. But the results of such delusional s.r are far reaching, no matter how mild they might be in degree. In a process propagated with 'infinite' velocity there would be no transition or delay in action, and therefore such a process would not be ordered. Vice versa, the disregard of order in our observations must introduce some mythological 'infinities' somewhere. So we see that the semantic process of identification is intimately connected with 'infinity' assumptions, both abolishing order. Training in natural order trains s.r away from delusional evaluation, abolishes pathological identification of different degrees and fanciful 'infinities'.
Thus we see that the problems of mathematical 'infinity' are extremely complex and involve many fundamental considerations never analysed before in connection with the semantic process of identification. Once these problems are analysed and formulated from a , non-el, structural point of view the problems of 'excluded third' become secondary in importance, easily managed under the creative freedom of the coveted 'consciousness of abstracting'.
Let me recall for continuity, that the mathematicians recognize at present, two kinds of 'infinities'. One with which we are familiar from our school days, symbolized by oo, Cantor calls 'potential' infinity and defines as a variable finite, the misunderstanding of which introduces paradoxes even in high schools; the other, the 'actual' infinity, which introduces paradoxes in universities. All these paradoxes are due, as the present enquiry shows, to fundamental fallacies in connection with semantic processes of identification which we learn at home and in elementary schools.
The process of identification of different orders of abstractions may be due to pathological conditions, to ignorance, to 'thoughtlessness', to lack of