figshare
Browse
1/1
2 files

The principle of constructive mathematizability of any theory. A sketch of formal proof by the model of reality formalized arithmetically

journal contribution
posted on 2016-05-04, 14:44 authored by Васил ПенчевВасил Пенчев
Principle, according to which any scientific theory can be mathematized, is investigated. That theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure  
constructively. In thus used, the term “theory” includes all hypotheses as yet  unconfirmed as already rejected. The investigation of the sketch of a possible proof of the 
principle demonstrates that it should be accepted rather a metamathematical  axiom about the relation of mathematics and reality. Its investigation needs philosophical means. Husserl’s phenomenology is what is used, and then the 
conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is 
equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction 
with that of transfinite induction. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within 
itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics 
into Gödel mathematics therefore showing that the former is not less consistent than  the latter, and the principle is an independent axiom. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology 
of information. Thus the problem which of the two mathematics is more relevant to our being  (rather than reality for reality is external only to Gödel mathematics) is  
discussed. An information interpretation of the Schrödinger equation is involved to illustrate the above problem.

History