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An Introduction To Non-aristotelian Systems And General Semantics.

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knowledge'. We should notice that with the confusion of orders of abstractions, and by the use of m.o terms, without realizing their as-valued character, we may always construct an endless array of such verbal arguments to befog the issues, but that as soon as we assign a definite order to the m.o terms, and so settle a specific single meaning in a given context for the many meanings any m.o term may have, the difficulties vanish.
As the above analysis applies to all m.o terms, and these terms happen to be most important in our lives, there is no use in trying to avoid these terms and the consequences of using them. Quite the contrary; often it is structurally necessary to build a m.o term - for instance, 'abstracting' - we must take for granted that it has many meanings, and indicate these meanings by assigning to the term the definite order of abstraction. Thus, such a term as 'abstracting' or 'characteristic'., might be confusing and troublesome; but 'abstracting in different orders'., is not, as in a given context we may always assign the definite order and single meaning to the term.
It has been repeatedly said that a m.o term has, by structural necessity, many meanings. No matter how we define it, its definition is again based on other m.o terms. If we try to give a general 'meaning' to a m.o term, which it cannot have, further and deeper analysis would disclose the multiordinality of the terms by which it is defined, restoring once more its multiordinality. As there is no possibility of avoiding the above structural issue, it is more correct and also more expedient to recognize at once the fundamental multiordinality of a term. If we do so, we shall not get confused as to the meaning of such a term in a given context, because, in principle, in a context its meaning is single and fixed by that context.
The semantic benefits of such a recognition of multiordinality are, in the main, sevenfold: (1) we gain an enormous economy of 'time' and effort, as we stop 'the hunting of the snark', usually called 'philosophy', or for a one-valued general definition of a m.o term, which would not be formulated in other m.o terms; (2) we acquire great versatility in expression, as our most important vocabulary consists of m.o terms, which can be extended indefinitely by assigning many different orders and, therefore, meanings; (3) we recognize that a definition of a m.o term must, by necessity, represent not a proposition but a propositional function involving variables; (4) we do not need to bother much about formal definitions of a m.o term outside of mathematics, but may use the term freely, realizing that its unique, in principle, meaning in a given context is structurally indicated by the context; (5) under such struc-