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An Introduction To Non-aristotelian Systems And General Semantics.

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758
SUPPLEMENT III
In a-system, for structural reasons, we must retain the general implications of the term 'apple', so we retain the word. We must make our language extensional in principle, and the name 'apple' an individual name, by calling it 'applet', 'apple2\ . The combination of letters 'a-p-p-1-e' implying similarities, the subscripts 1, 2 . , implying individual differences, which automatically prevent identification. But this is not enough. Our 'applei' represents a name applied to an object and a process; its meaning becomes only one-valued when we assign to it at least a definite date. Thus the objective 'applei'
may be a very appetizing affair, and 'applei (Jan. i, 1932.)' an un-edible wet splash. It should be noticed that the fundamental difference between the A and systems turns out to be a difference of semantic attitudes. The scientific facts are not changed. The 'apple' of 'Adam' or our own did not differ in essential characteristics under discussion. In both the A. and systems we actually deal, in principle, with many-valued processes. The important problem is to adjust the structure of our verbal processes to the structure of the world; hence a -system must be made extensional, non-el, four-dimensional,. Here once more, as in general semantics, the ascribing of one value (or at least limited to a small range of values in practice), in a given situation (context), eliminates paradoxes and contradictions on the older 'logical' grounds. We should notice that the multiordinal terms must be considered as names for many-valued s.r, depending upon the order of abstractions; hence the name multiordinal. Names for happenings on the objective levels apply to many-valued processes but should not be considered multiordinal. All the psycho-logics of the differential calculus, 'space-time', enter here, yet the whole field is covered semantically if we entirely abandon the 'is' of identity. Instead of training in 'allness' and 'isness''this is this', we shall train in non-allness, and non-isness'this is not this', in connection with a special diagram called the Structural Differential.
Experience and experiments show that the above seems essential for sanity. It is interesting to notice that mathematics has produced a language similar in structure to the human nervous system. Roughly the central part of the brain which we call the thalamus is directly connected with the dynamic world through our 'senses' and with those semantic manifestations which we usually call 'affective', 'emotions'. , all of which manifest themselves as dynamic. The cortex which gives us the static verbal reactions and definitions, is not connected with the outside world directly but receives all impulses through the thalamus. On semantic levels the thalamus can only deal with dynamic material, the cortex with static. Obviously for the optimum working of the human nervous system, which represents a cyclic chain, where the lower centres supply the material for the higher centres and the higher centres should influence the lower, we must have means to translate the static into dynamic and the dynamic into static; a method supplied exclusively by mathematics.
With the above considerations we must discriminate between our semantic capacities for infinite divisibility of finites, and for the generation of infinite postulated processes which by definition cannot be exhausted. If we use a three-