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An Introduction To Non-aristotelian Systems And General Semantics.

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656 IX. ON EMPIRICAL AND VERBAL STRUCTURES
once this is realized, we cannot ascribe 'finiteness' or 'infiniteness', 'definiteness', 'rigidity'. , to terms, verbal forms, forms of representation. From this point of view we may consider the Einstein theory as an irreversible gain. If it had achieved only the elimination of various structural prejudices and dogmas, it has done well; and at least this much Einstein has already achieved.
The structural, verbal, cortical quest for invariance in our formulations also becomes apparent. The older mechanics were invariant under the galilean transformation, equations preserved their form in different systems of coordinates. In the special theory of relativity the new laws are invariant under the Lorentz-Einstein transformation. In this special, or restricted, theory of relativity only uniform relative motion was taken into account. If we generalize the principle of relativity to any kind of relative motion we pass from the restricted to the general theory, which demands that the laws of physics should be formulated in a generally invariant form for any arbitrary transformations.
For this structural, cortical reason it is necessary to express all the laws of physics in tensor equations, which satisfy such conditions of general invariance. If this cannot be done, there must be something wrong with our language, as such, and with our verbal laws. We require structural revision of those laws so as to be able to express them in tensor equations. The newtonian law of gravitation and the older form of the law of conservation of energy are perhaps the most remarkable examples. They do not survive such minimal, and yet entirely justified, structural requirements as those of the general theory of Einstein, and therefore they cannot be structurally satisfactory.
represents the equation of the spherical propagation of light with the finite velocity c. The discovery that the velocity of light is a universal constant for all observers, and the above equatipn, led historically to the re-discovery by Einstein of the Lorentz transformation which, as we have seen, has assumed such overwhelming structural importance. The meaning of these facts is worth considering. In Chapter XVII we analysed briefly the elementalistic language of 'matter', 'space', and 'time', and came to the conclusion that to eliminate objectification we must abandon the semantic disturbance and the use of the term 'is' of identity. Instead, we must use an actional functional language to describe ordered functioning, behaviour, or operations. By necessity we were led to a 'contact' method. We also discovered that in accepting the above structural methods we were compelled to discriminate between different orders of abstraction, since what we see, feel, and experience is not what we say about it. We found that on the 'objective' level of our actual activities, (manipulating instruments. ,) which represent the silent unspeakable level, we could never find a situation in which the old language of 'matter', 'space', and 'time' could be used without coming violently into conflict with the properly analysed facts. We came to the conclusion that this language was not structurally satisfactory, for verbally, 'space', 'time', and 'matter' were supposed to be quite clear-cut and separate entities, while in actual experience we never could find such separated objective entities. It became obvious that the structure of the