288 V. MATHEMATICS A A LANGUAGE |
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The main object of the present chapter is to explain that the structure of the human nervous system is such that, on some levels, we produce dynamic abstractions; on others, static. As the organism works as-a-whole, for its optimum working, and, therefore, for sanity, we need a language, a method, which may be translated into a
s.r by which to translate the dynamic into the static, and vice versa; and such a language, such a method, is produced and supplied by mathematicians. To some readers, these remarks may appear so obvious as to make it unnecessary to write them, but I have found, through personal observation of reactions of different individuals, and by a careful survey of the literature of the subject, that even many mathematicians and physicists do not have this s.r in all problemsor, at least, they do not know how to apply it.In Part VII, elementarymethods are worked out, which supply the neurological semantic benefits of the calculus, very easily imparted to even small children
without any mathematical technique, and establishing in them a mathematical attitude toward all language in general, training them in the only structural psycho-logics of sanity; namely, that of the calculus, which thus becomes the foundation of healthy and normal human s.r. And this, let us repeat again, without any mathematical technique. We find, also, that there are simple and physiological means, based on structure, of training our s.r and imparting the feel for the structural stratification inherent in the consciousness of abstracting.To start with, let me mention briefly a quite unexpected, unconscious, structural
biological characteristic of mathematics; namely, its (in the main) non-el, organism-as-a-whole character.From the time of Aristotle, biologists, physiologists, neurologists, 'psychologists', psychiatrists and others have spoken a great deal about the organism-as-a-whole; yet, they have not seemed to realize that if they produce
el terms, they cannot apply the non-el principle.It will probably not be an exaggeration to say that the majority of mathematicians have never heard of this principle, and that, if they have, they paid no attention to it; yet, in practice, they have applied it very thoroughly. The main mathematical terms are non-el, organism-as-a-whole terms which apply to 'senses' as well as to 'mind'. For instance, relation, order, difference, variable, function, transformation, invariance., can mostly be seen as well as 'thought' of. The use of such terms prevents our speculation from degenerating into purely el speculations on words, a process always closely related to the morbid semantic manifestations of the 'mentally' ill. and obviously based on the pathological confusion of orders of abstractions, involving inappropriate evaluation. |
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