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An Introduction To Non-aristotelian Systems And General Semantics.

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cut structure. Under aristotelianism, these differentiations were impossible, and so the problems of linguistic structure, propositional and doctrinal functions., were neglected, except in the recent work of mathematicians. The entirely general semantic influence of these structural conditions becomes obvious when we realize that, no matter whether or not our doctrines are traced down to their doctrinal functions, our semantic processes and all 'thinking' follow automatically and, by necessity, the conscious or unconscious postulates, assumptions., which are given (or made conscious) exclusively by the doctrinal function.
The terms 'proposition', 'function', 'prepositional function', 'doctrinal function'., are multiordinal, allowing many orders, and, in a given analysis, the different orders should be denoted by subscripts to allow a differentiation between them. When we deal with more complex doctrines, we find that in structures they represent higher order doctrines, or a higher whole, the constituents of which represent lower order doctrines. Similarly, with doctrinal functions, if we take any system, an analysis will discover that it is a whole of related doctrinal functions. As this situation is the most frequent, and as 'thinking', in general, represents a process of relating into higher order relational entities which are later treated as complex wholes, it is useful to have a term which would symbolize doctrinal functions of higher order, which are made up of doctrinal functions of lower orders. We could preserve the terminology of 'higher' and 'lower' order; but as these conditions are always found in all systems, it seems more expedient to call the higher body of interrelated doctrinal functions, which ultimately produce a systema system-function. At present, the term 'system function' has been already coined by Doctor H. M. Sheffer3; but, to my knowledge, Sheffer uses his 'system function' as an equivalent for the 'doctrinal function' of Keyser. For the reasons given above, it seems advisable to limit the term 'doctrinal function' to the use as introduced by Keyser, and to enlarge the meaning of Sheffer's term 'system function' to the use suggested in the present work, this natural and wider meaning to be indicated by the insertion of a hyphen.
In a -system, when we realize that we live, act., in accordance with non-el s.r, always involving integrated 'emotions' and 'intellect' and, therefore, some explicit or implicit postulates which, by structural necessity, utilize variable, multiordinal and oo-valued terms, we must recognize that we live and act by some system-functions which consist of doctrinal functions. The above issues are not only of an academic interest, as, without mastering all the issues emphasized in the present work, it is