Combining Universal Epistemology with Formal Axiology in a Multimodal Formal Axiomatic Theory “Sigma + 2C”, and Philosophical Foundations of Mathematics

Authors

  • Vladimir Lobovikov Institute of Philosophy and Law UB RAS (Yekaterinburg)

DOI:

https://doi.org/10.47850/RL.2023.4.4.88-113

Keywords:

formal axiomatic theory of knowledge; a-priori knowledge; empirical knowledge; Kant’s apriorism; Hilbert’s formalism; Gödel’s incompleteness theorem; two-valued algebraic system of formal axiology

Abstract

The paper is devoted to investigating Kant’s apriorism underlying Hilbert’s formalism in philosophical foundations of mathematics. The target is constructing a formal axiomatic theory of knowledge in which it is possible to invent formal inferences of formulae-modeling-Hilbert-formalism from the assumption of Kant apriorism concerning mathematics. The scientific novelty: a logically-formalized axiomatic system of universal philosophical epistemology called “Sigma +2C” is invented for the first time as a generalization of the already published formal epistemology system “Sigma +C”. In comparison with “Sigma +C”, a new symbol is included into the object-language-alphabet of S+2C, namely, the symbol standing for the perfection-modality “it is complete that…”. Also, one of axiom-schemes of “Sigma +C” is generalized in “Sigma + 2C”. In “Sigma +2C”, it is proved deductively that under the assumption of a-piori-ness of mathematical knowledge, its completeness and consistency are equivalent.

Author Biography

Vladimir Lobovikov, Institute of Philosophy and Law UB RAS (Yekaterinburg)

Doctor of Philosophical Sciences, Principal Scientific Researcher

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Published

2023-12-13

How to Cite

Lobovikov В. О. (2023). Combining Universal Epistemology with Formal Axiology in a Multimodal Formal Axiomatic Theory “Sigma + 2C”, and Philosophical Foundations of Mathematics. Respublica Literaria, 4(4), 88–113. https://doi.org/10.47850/RL.2023.4.4.88-113

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