Journal or Publication Title:

Իմաստություն=Wisdom=Мудрость

Date of publication:

2017

Volume:

9

Number:

2

ISSN:

1829-3824 ; e-2738-2753

Corporate Creators:

Խ․ Աբովյանի անվան հայկական պետական մանկավարժական համալսարան

Coverage:

18-28

Abstract:

The author of this article critically analyses the proof of Gödel’s famous theorem on the incompleteness of formalized arithmetic. It is shown that Gödel’s formalization of meta-mathematics provides a proof of the incompleteness not of mathematical science but of the system of formalized meta- mathematics developed by Gödel himself. The arguments against the idea of the formalization of meta-mathematics are presented. The article suggests also an interpretation of the essence of mathematical truth. It is noted that the refutation of Gödel’s proof does not suggest returning to Hilbert’s program of formalism since the formalization of an axiomatic theory can’t exclude the appearance of paradoxes within its framework. It is shown that the use of self-referential Gödel’s numbering in a formalized system leads to the emergence of a Liar type paradox – a self-contradictory formula that demonstrates the inconsistency of that same system.

Place of publishing:

Երևան

Publisher:

Տիգրան Մեծ

Format:

pdf

Identifier:

oai:arar.sci.am:370375

Language:

en