Kripkes skepticism and its overcoming in the context of ontoepistemologicalopposition realism/relativism

E.V. Borisovs critical argumentsconcerning V.A Surovtsevs and V.A. Ladovs researches on rule-following problem areconsidered in this article. In the first section of the article the theme of foundations of S. Kripkesskepticism concerning rule-following are discussed. The author agrees with Borisovs critical argumentsthat V.A. Ladov and V.A Surovtsev are not correct in their consideration of foundations of skepticalchallenge. However it is emphasized that the authors of Wittgenstein and Kripke do not sufficientlyexpressed their thought. Actually the arguments of Ladov and Surovtsev do not contradict ofBorisovs interpretation. In the second section of the article it is asserted that Kripke indeed treated arule as unambiguously fixed for infinite cases of its application. In this point author of the article doesnot agree with Borisovs point of view. In the third part of the article it is discussed so-called defectrules. Author asserts that it is not reasonable to say about invisibility of methodological procedures offixation of standard rule and defect rule. With respect to Borisovs interpretation this section is criticaltoo. Furthermore, E.V. Brisov considers the variant of straight solution of rule-following problempresented in Wittgenstein and Kripke. The author of this article agrees with critical arguments. Howeverit is emphasized that the research on mathematical induction should be transmit to higher level.Finally, the author of the article estimates Borisovs mode of the straight solution of the rule-followingproblem presented in his writings. This mode of the solution is acknowledged as sophisticated andvery important. It is not doubt that this mode of the solution of the rule-follow problem needs in morecareful critical analysis but at the present moment the author of the article does not fix any defects inBoriovs reasoning. This mode of the solution is very important because of different variants of skepticalsolution of the rule-following problem prevails in contemporary analytic philosophy. Borisovssolution shows that, at least, we can say about meanings of mathematical symbols as universal andexactly fixed essences.

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