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An Introduction To Non-aristotelian Systems And General Semantics.

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disciplines in relation to the living organism. Quite probably, when the above issues are fully realized, these specialists, future psycho-logicians and semanticians, will begin to study mathematical methods and pay attention to structure, and a number of mathematicians, in their turn, will become psycho-logicians, psychiatrists, semanticians,. When this happens, we may expect marked advance in these lines of endeavour.*
In the course of this book, it will be shown that the structure of human knowledge precludes any serious study of 'mental' problems without a thorough mathematical training. We shall take for granted all the partial light thrown on man by existing disciplines and shall make some observations from the study of the neglected forms of human behaviour, such as mathematics, exact sciences, and 'insanity', and with these new data re-formulate, in the rough, all available data at hand in 1933.
At the present early stage of our enquiry, we must, of necessity, be often vague. Before we give the new data, it is impossible to speak in a more definite way. Besides, in such a general survey, we shall have to use what I call multiordinal terms. At present, all the most humanly important and interesting terms are multiordinal, and no one can evade the use of such terms. Multiordinality is inherent in the structure of 'human knowledge'. This multiordinal mechanism gives the key to many seemingly insoluble contradictions, and explains why we have scarcely progressed at all in the solution of many human affairs.
The main characteristic of these multiordinal terms is found in that they have different meanings in general, depending on the order of abstractions. Without the level of abstraction being specified, a m.o term is only ambiguous; its use involves shifting meanings, variables, and therefore generates, not propositions, but propositional functions. It may not be an exaggeration to say that the larger number of human tragedies, private, social, racial., are intimately connected with the non-realization of this multiordinality of the most important terms we use.
A similar confusion between orders of abstractions is to be found in all forms of 'insanity', from the mildest, which afflicts practically
♦There are already signs that the more serious workers, as, for instance, the Gestalt 'psychologists', begin to feel their handicaps. Others, as yet, do not seem to realize the hopelessness of their endeavours - as best exemplified by the American school of Behaviourists, who seem to think that the splendid name they have selected will solve their problems. It would be very interesting to see the Behaviourists deny that the writing of a mathematical treatise, or of some new theory of quantum mechanics represents a form of human behaviour which they should study. Some day they must face the fact that they have neglected to consider a great many forms of human behaviour - the most characteristic forms at that - and that, therefore, they could not produce an adequate theory of the nature of the 'human mind'.