Download PDFOpen PDF in browserAll Science as Rigorous Science: the Principle of Constructive Mathematizability of Any TheoryEasyChair Preprint no. 319915 pages•Date: April 20, 2020AbstractA principle, according to which any scientific theory can be mathematized, is investigated. Social science, liberal arts, history, and philosophy are meant first of all. That kind of 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. The main statement is formulated as follows: Any scientific theory admits isomorphism to some mathematical structure in a way constructive (that is not as a proof of “pure existence” in a mathematical sense). 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. The sketch of the proof is organized in five steps: (1) a generalization of epoché; (2) involving transfinite induction in the transition between Peano arithmetic and set theory; (3) discussing the finiteness of Peano arithmetic; (4) applying transfinite induction to Peano arithmetic; (5) discussing an arithmetical model of reality. Keyphrases: axiom of choice, axiom of induction, axiom of transfinite induction, eidetic reduction, Epoché, Gödel mathematics, Hilbert mathematics, information, phenomenological and transcendental reduction, Phenomenology, principle of universal mathematizability, quantum information, quantum mechanics
