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COMPLETENESS OF LOGICAL AND MATHEMATICAL FORMAL SYSTEMS: TYPES AND SPECIFICS

https://doi.org/10.25205/2541-7517-2018-16-1-5-19

Abstract

The article deals with the expansion of the concept of the completeness of a logical system. It is assumed that the generally accepted practice of correlating the concept of completeness primarily with the logic of the first order is due to purely historical circumstances. It is shown that when using first-order logic as a means of mathematical theorizing, the completeness of the logical system does not reflect the important features of the application of logic to mathematics. It is demonstrated that the distinction between deductive, semantic and descriptive completeness leads to a new understanding of the role and nature of logic.

About the Authors

V. V. Tselishchev
Institute of Philosophy and Law SB RAS; Novosibirsk State University
Russian Federation


A. O. Kostjakov
Novosibirsk State University
Russian Federation


References

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Review

For citations:


Tselishchev V.V., Kostjakov A.O. COMPLETENESS OF LOGICAL AND MATHEMATICAL FORMAL SYSTEMS: TYPES AND SPECIFICS. Siberian Journal of Philosophy. 2018;16(1):5-19. (In Russ.) https://doi.org/10.25205/2541-7517-2018-16-1-5-19

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ISSN 2541-7517 (Print)