310 V. MATHEMATICS ALANGUAGE
The difficulties which we have are mostly man-made, and so only mankind can remedy them, and any attempts to escape from
m.o reality only aggravate the situation.Lack of space does not allow me to dwell here on many other aspects of mathematics which are of neurological structural importance, except to mention the theory of statistics and probability. All human knowledge is neurologically due to a process of abstracting in different orders, giving us the only structural knowledge of processes, which, in 1933, must always be considered on three levels, the macroscopic, the microscopic, and the sub-microscopic.
Because the nervous system is an abstracting, integrating mechanism, all human psycho-neurological reactions and, particularly, psychological, to be similar in structure,
must be based on the mathematical theories of statistics and probability. On the objective level, we deal with absolute individuals, and so all statements, or higher order abstractions, can only be probable. Historically, mathematicians have elaborated not only both theories, but Boole, in his Laws of Thought, extended the mathematical approach to 'logic' in connection with the theory of probability. Finally, the difficulties of the law of excluded third have been solved by Lukasiewicz and Tarski^{10} in their 'many-valued logic', which, when N increases indefinitely, merges with the mathematical theory of probability, a result reached independently by a different type of analysis in the present system. Any possible future scientific A, non-el 'logic', which I call general semantics, must be built on this structurally more correct foundation. It should be noticed that the notions of probability are very flexible, and entirely cover our structural needs, the field of degrees of probability ranging from impossibility to certainty. This new semantics involves entirely new affective attitudes, and underlies new and better balanced s.r.Under such conditions, the restricted 'uncertainty principle' of Heis-enberg becomes a structural, most revolutionary, and creative general principle, transferring the laws of two-valued 'cause and effect' from the realm of gambling on words by 'philosophers' to the scrutiny of scientists, and establishing oo-valued 'determinism' on a neuro-mathe-matical base of 'the greatest probability'. Methodologically and psychologically, this requires full consciousness of abstracting, achieved, as yet, by extremely few of us, even among physicists and mathematicians. Then the 'law' of two-valued 'cause and effect', instead of depending on the el and objectified older interpretations, will be based on the mathematical, and much more reliable, oo-valued principle of greatest proba- |
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