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An Introduction To Non-aristotelian Systems And General Semantics.

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respect to the other, c, as usual, represents the velocity of light, and the factor /3 = l/V(l-vVc«).
The most striking characteristic of these formulae is that if we assume that c, the velocity of light, is 'infinite', all the expressions containing e2 would become zero, c2 entering only in the denominators of fractions. In such a limiting case (3 = 1/V (1-0) =1/1 = 1 and x' = (x-ut), / =y, z' =z,t'=t which are the older galilean transformations.
Thus there appears the astonishing fact that all the pre-einsteinian physics and mechanics which involved the structural assumption of the galilean transformation, had a tacit structural assumption of the infinite velocity of light. This assumption, known since 1676 to be false as to facts, remained unnoticed before Einstein.
As c=3xl010 cm./sec, c2=9xl020 is a very large number, whence the fractions vx/c3 and vi/ci are very small, and |3 differs very little from unity.
If we apply the Lorentz-Einstein transformation instead of the older galilean transformation to mechanical problems, the changes are so small that they can hardly be detected by experiments, the terrestrial velocities n2 or vx being so small in comparison with the square of the velocity of light.
The galilean transformations are experimentally shown to be structurally invalid for optical and electrodynamic events. The Lorentz-Einstein transformations satisfy structurally the optical and electrodynamic events, and also apply to the older mechanical problems. We see that the Lorentz-Einstein transformations are more general, as they include the galilean transformations as a particular case when we assume c=oo.
In a few instances, where we deal with large velocities, the values of the fractions containing the square of the velocity of light become appreciable and allow experimental testing. As yet all such experiments have verified the Einstein theory.
We should repeat again that the achievement of Einstein was the building of a linguistic system similar in structure to the world, which eliminated a pathological pre-human factor of objectification of terms. Such structural elimination was bound to bring some sanity to our theories; and this fact is independent of experiments in physical laboratories. However, it is gratifying to find that experiments support (1933) the Einstein theory. It was particularly gratifying in the beginning, when physicists and Einstein himself believed that his theory would stand or fall by experiment. Today we see that this theory represents such an enormous general, structural, epistemological, psycho-logical, and methodological non-elementalistic advance, that no matter what the experiments show or may show in the future we cannot return to a language of the old, el, obviously wrong, structure of the pre-einsteinian days. As usual, the negative results are the important ones. No matter what experiments may show we shall never again accept the silent structural assumption of 'infinite' velocity for light, when we know positively that the velocity is finite. We shall never again treat terms of 'matter', 'space', and 'time' as objects - lower order abstractions, when we know that they represent terms - higher order abstractions. When