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Conditions of objectivity of mathematical knowledge

Annotation

L. Wittgenstein’s approach to a problem of objectivity of mathematical knowledge is analyzed. L. Wittgenstein opposed not objectivity of mathematics as that, and need of its “philosophical” justification. The option of an alternative explanation of reliability of mathematical knowledge offered to them is reduced to the statement that arithmetic identities, mathematical offers are formed as a special form of codification casual, at the same time to the steady, giving-in objective check of empirical repeatability which is shown in behavior of people. Mathematical offers at their use serve as samples (criterion) for the description and an assessment that allows them to operate acts of man. The indisputable, objective status of mathematical knowledge in such a way is provided. Mathematical offers are not any agreements as are based on not subject to doubt, standard behavioural (is wider - empirical) regularities. Thus, it is necessary to remember that in spite of the fact that arithmetic offers are obliged by the origin and relevance to existence of behavioural regularity, they belong to other level, than empirical offers. In a case with mathematics the empirical proposition “hardens” in the grammatical rule over time and carries out function of a paradigm or object of comparison.

Keywords

L. Wittgenstein; mathematics philosophy; mathematical propositions; objectivity; certainty; empirical regularity

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UDC

1(091)

Pages

36-42

References

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Received

2015-05-25

Section of issue

Questions of theory and methodology

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