A Logically Formalized Axiomatic Epistemology System ? + C and Philosophical Grounding Mathematics as a Self-Sufficing System

Vladimir Olegovich Lobovikov
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Vladimir Olegovich Lobovikov: Laboratory for Applied System Investigations, Ural Federal University, 620075 Yekaterinburg, Russia

Mathematics, 2021, vol. 9, issue 16, 1-13

Abstract: The subject matter of this research is Kant’s apriorism underlying Hilbert’s formalism in the philosophical grounding of mathematics as a self-sufficing system. The research aim is the invention of such a logically formalized axiomatic epistemology system, in which it is possible to construct formal deductive inferences of formulae—modeling the formalism ideal of Hilbert—from the assumption of Kant’s apriorism in relation to mathematical knowledge. The research method is hypothetical–deductive (axiomatic). The research results and their scientific novelty are based on a logically formalized axiomatic system of epistemology called ? + C, constructed here for the first time. In comparison with the already published formal epistemology systems ? and ?, some of the axiom schemes here are generalized in ? + C, and a new symbol is included in the object-language alphabet of ? + C, namely, the symbol representing the perfection modality, C: “it is consistent that…”. The meaning of this modality is defined by the system of axiom schemes of ? + C. A deductive proof of the consistency of ? + C is submitted. For the first time, by means of ? + C, it is deductively demonstrated that, from the conjunction of ? + C and either the first or second version of Gödel’s theorem of incompleteness of a formal arithmetic system, the formal arithmetic investigated by Gödel is a representation of an empirical knowledge system. Thus, Kant’s view of mathematics as a self-sufficient, pure, a priori knowledge system is falsified.

Keywords: logically formalized axiomatic system of epistemology; a priori knowledge; empirical knowledge; Kant’s apriorism; Hilbert’s formalism; Gödel’s incompleteness theorem; two-valued algebraic system of formal axiology (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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