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Philosophy of Sciences

2015 year, number 1

Gödel's subjective mathematics and self-evident truths

V.V. Tselishchev
Institute of philosophy and law SB RAS, Novosibirsk
Keywords: Godel, obvious truth, subjective mathematics, objective mathematics, incompleteness theorem, axiom


The article discusses the relationship between subjective or human mathematics and objective mathematics, introduced by K. Gödel for the interpretation of his incompleteness theorems. It is shown the connection of this distinction with the concept of a mathematical certainty as epistemological characteristic of mathematical thinking. The connection between the concepts of mathematical determinacy and the notion of obvious truths of mathematics in the form of axioms is established. The difference between obvious truths of elementary arithmetic and of higher syntactic structures associated with the effect of coding is considered.