726 X. ON THE STRUCTURE OF 'MATTER'
most important research method. The more languages (theories) we have for analysis and structural comparison, the more glimpses do we get at the structure of the world. The newer quantum mechanics give us enormous material of a linguistic, structural, and semantic character.
It is natural that this wisdom can come only from the study of the structure of the highest developed languages in existence, which are mathematical languages. If we want progress in any line of human endeavour, this progress is always dependent on the languages we use, since what we call 'progress' is a co-operative affair and therefore dependent on means of communications and languages.
From the point of view of structure, we deal with a world of absolute individuals and therefore our languages must be such as to reflect such individuality. We already know that this involves an extensional attitude and methods, which historically have produced mathematics as the only language which as yet reflects in structure the world around us.
With the newer quantum mechanics, the old 'discontinuity' resolves itself into an essential individuality, as noticed by Bohr, perfectly foreign to the older theories.
History proves that we were slow in arriving at that point. Our tragedies began when the 'intensional' biologist Aristotle took the lead over the 'ex-tensionaP mathematical philosopher Plato, and formulated all the primitive identifications, subject-predicativism . , into an imposing system, which for more than two thousand years we were not allowed to revise under penalty of persecution. Mathematics was not particularly encouraged, but at least, not persecuted, so that it was developed into the present day great linguistic system. The theory of function involves semantic factors of non-identification.
The invention of the differential and the integral calculi, represents the two great structural and psycho-logical aspects of analysis and differentiation, versus synthesis and integration.
The application of these methods led us to differential geometries, to methods-of treating 'fulness', and to 'contact' methods. 'Fulness' necessitated geometries of higher dimensions, impossible in 'absolute emptiness', and so the fusion of geometry with physics became possible. The four-dimensional world of Minkowski and the theory of Einstein finally achieved this fusion. The next step was the invention of the new quantum mechanics, where all these important, nay, all-important, structural, semantic, and linguistic achievements find their culmination. The old primitive metaphysics become too 'materialistic' for an enlightened age.
Without legislating about the 'truth' or 'falsehood' of the newer mechanics, as a matter of human behaviour these theories are the best indications and examples of the structure of human 'knowledge', which I have attempted to formulate in this work as a general theory.
The A -system was strictly interconnected with primitive-made structural assumptions or metaphysics, reflected in the structure of the older languages and in the el notions about language, 'psychology', 'logic', and the pre-scientific