Home // International Journal On Advances in Intelligent Systems, volume 5, numbers 3 and 4, 2012 // View article

Beyond the Zermelo-Fraenkel Axiomatic System: BSDT Primary Language and its Perspective Applications

Authors:
Petro Gopych

Keywords: Infinity; meaning; subjectivity; phenomenology; context; categorization; attention; randomness; complexity; continuity-discreteness unity and uncertainty; arithmetization; continuum hypothesis; super-Turing computations

Abstract:
A formalization of the recently proposed infinity hypothesis implying the common coevolution of the universe, life, mid, language, and society gives a possibility to introduce strict definitions of meaning and subjectivity, which spread beyond the traditional mathematics. This hypothesis leads to a semantic mathematics that is an implementation of the von Neumann’s idea of a low-level “primary language” (PL). In this paper the formalization of this infinity hypothesis is further developed and some of its consequences are considered. In particular, a phenomenology formalization, definite and conditional meanings of the PL’s words, their meaning complexity, categories and subcategories (hierarchies) of meaningful words, a way of the presentation of real numbers, the Cantor’s continuum hypothesis, the PL’s continuity-discreteness unity and uncertainty, non-Gödelian arithmetization by natural numbers and its relation to Chaitin’s Omega-numbers, convention on truth, meaning ambiguity of words of different meaning complexity and its relation to Burali-Forti paradox are discussed. A validation of the PL is given. Some examples of meaningful computations using the technique of recently developed binary signal detection theory (BSDT) and the BSDT PL’s perspective applications to solving the problems concerning the brain, mind and their faculties are briefly considered. It is emphasized super-Turing computations are typical for the BSDT PL as well as animal and human regular everyday meaningful communication.

Pages: 493 to 517

Copyright: Copyright (c) to authors, 2012. Used with permission.

Publication date: December 31, 2012

Published in: journal

ISSN: 1942-2679