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An Introduction To Non-aristotelian Systems And General Semantics.

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92
II. GENERAL ON STRUCTURE
Einstein but for Einstein. Similar remarks could be made about this present work; and again this would not be an argument against this work, but for it. All these new systems represent methodological and structural advances, and will have played their semantic roles even if some day they should be dismissed and systems of different structure take their place.
Historically, attempts in the direction of a discipline have been very numerous. Indeed, the invention of any new important term of a non-subject-predicate character, or of a functional character, was, in itself, an attempt in the direction. All sciences have had to abandon the common vocabularies and build their own terminologies, many of which are also A. Although all these attempts have been made, and have quite often been successful in their fields, to the best of my knowledge, they were not made consciously. The term accepted here; namely, 'non-aristotelian' is very useful, not only because it is appropriate and illustrates very well what we have to contend with, but also because it places the emphasis properly and makes us conscious of the structural issues. The fact that the three new non-systems have as much in common as the older three had, recommends and justifies the use of the term. The new problem which looms up; namely, the validity or non-validity of the A law of the excluded third, leads automatically to the non-chrysip-pian and oo-valued 'logics', which merge with the theory of probability.1 According to the accepted use, it is enough to build a system differing from an older system by one single postulate, to justify (for instance) the name 'non-euclidean'.
The scope of this particular chapter does not permit me to enlarge upon this difficult and important problem as to the differences between the A andsystems, but for orientation, a short list of structural differences is given here; all of which involves new semantic factors.
The primitive form of representation which Aristotle inherited, together with its structural implications and his 'philosophical grammar', which was called 'logic', are strictly interconnected, so much so that one leads to the other.
In the present .-system, I reject Aristotle's assumed structure, usually called 'metaphysics' (circa 350 B.C.), and accept modern science (1933) as my 'metaphysics'.
I reject the following structurally and semantically important aspects of the A -system, which I shall call postulates, and which underlie the -system-function:
1) The postulate of uniqueness of subject-predicate representation