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An Introduction To Non-aristotelian Systems And General Semantics.

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methods. As soon as we have functions, we can represent a functional calculus as an operational calculus. This involves a more behaviouristic semantic attitude and so leads to the possibility of translation of either method into the other. Ultimately these are psycho-logical transformations and translations.
We should not be surprised to find that in the development of the newer quantum mechanics the operational calculus plays just such a role.
Now our older macroscopic experience, which affected our lower nerve centres, gave rise to the elementary geometrical structural notions of 'lines', 'surfaces', 'volumes', . For the building of physics we had to introduce 'time', 'motion', . In older days we did not realize that these give us forms of representation and that it is optional with us which forms we will accept as fundamental or use as a starting point.
The old descriptive apparatus posited structurally an absolute and immutable 'space' (emptiness), 'time', 'matter' out of which we built up a verbal definition for 'motion'. The semantic attitude of all of us, scientists included, depended upon identification. We ascribed lower-centre significance to higher-centre abstractions. We did not discriminate enough between the macroscopic and small scale events. So we had 'geometrical optics' in which we 'perceived' a ray of light (in a dusty room, let us say) as a 'straight line'. Further investigation disclosed that the 'rays' on one level of abstraction were waves on another, but they were not perceived as waves by the lower centres.
But through our lower centres we had acquaintance with some waves, such as in water; so representation for waves was developed. A wave-theory still remained intuitively workable, even when we dealt with waves which we could not see. Now the equations of waves are well known. It is then possible to translate a non-intuitive matrix mechanics, when we treat matrices as operators, into a functional calculus which has an intuitive geometrical wave representation.
This is precisely what has happened and now, perhaps for the first time in human history, we have all the aspects of a theory being worked out simultaneously, with mutual co-operation of all workers and the use of methods which are mutually complementary from the neurological side. There seems little risk in predicting that because of these neurological factors the newer quantum mechanics will give extremely rapid and far-reaching results. When scientists become aware of the structural semantic and neurological issues involved, perhaps such achievements will be multiplied consciously, instead of being a kind of coincidence.
Personally, I am convinced that these new achievements are not simply coincident. It seems that the abolishment of the old, el, static 'absolute space' and 'absolute time' has relieved the younger scientists from a semantic blockage. This release was due to the bold stroke of genius of Einstein in refusing to use the vicious aristotelian 'is' of identity. As soon as we realize that words are not the objective levels, we gain an unconscious semantic freedom in handling words, as words. At once this freedom is bound to produce many different forms of