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An Introduction To Non-aristotelian Systems And General Semantics.

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5o
I. PRELIM IN ARIES
be necessary to analyse the issues raised, and not always solved, in this present volume.
I want to make clear only that words are not the things spoken about, and that there is no such thing as an object in absolute isolation. These assertions are negative and experimental and cannot be successfully denied by any one, except by producing positive evidence, which is impossible.
We must realize that structure, and structure alone, is the only link between languages and the empirical world. Starting w'th undeniable negative premises, we can always translate them into positive terms, but such translation has a new and hitherto unprecedented security. In the era which is passing, positive premises were supposed to be important, and we did not know that a whole-system can be built on negative premises. The new era will have to revaluate these data, and build its systems on negative premises, which are of much greater security. A priori, we cannot know if such systems can be built at all, for in this field the only possible 'proof is actual performance and the exhibition of a sample.
This has been attempted in my work, and so the possibility of such systems becomes a fact on record.
In the new era, the role of mathematics considered as a form of human behaviour and as a language will come to the fore. Means can be found, as exemplified in the present volume, to impart mathematical structure to language without any technicalities. It is enough to understand the above-mentioned negative premises and the role of structure, and to produce systems from this angle.
The role of mathematics has been and, in general, is still misunderstood, perhaps because of the very unsatisfactory definition of number. Even Spengler asserts that 'If mathematics were a mere science, like astronomy or mineralogy, it would be possible to define their object. This, man is not, and never has been, able to do.' The facts are that mathematicians have been prone to impress us with some religious awe of mathematics; meanwhile, by definition, whatever has symbols and propositions must be considered a language. All mystery vanishes in this field, and the only question is as to what kind of language mathematics represents. From the structural point of view, the answer is simple and obvious. Mathematics, although in daily life it appears as a most insufficient language, seems to be the only language ever produced by man, which, in structure, is similar, or the most similar known, to the structure of the world and of our nervous system. To be more explicit,