MINIMIZING THE EFFECTS OF INTENSIONALITY IN THE “BEST AND MOST GENERAL VERSION” OF GÖDEL’S SECOND THEOREm
Vitaliy Valentinovich Tselishchev1,2, Aleksandr Valerievich Khlebalin1
1Institute of Philosophy and Law, Siberian Branch of the Russian Academy of Science, 8, Nikolaev st., 630090, Novosibirsk, Russia
2Novosibirsk National Research State University, 2, Pirogov st., 630090, Novosibirsk, Russia
Keywords: интенсиональность, Вторая теорема Геделя, непротиворечивость, обоснованность, принцип рефлексии, формальная система, доказательство, intensionality, Gödel Second Theorem, consistency, soundness, principle of reflection, formal system, proof
Abstract
The article is devoted to the method of eliminating the consequences of the intensionality of Gödel's Second Incompleteness Theorem. The method proposed by Gödel himself is called the “best and most common version” of the Second theorem. Consideration of (non-standard) systems with built-in consistency, in which consistency is provable within the system, reveals two points of view: the first is the semantic uncertainty of such systems, and the second is in attempts to strengthen the Second Theorem. Gödel introduced the concepts of internal and external consistency, and the transition to the principle of reflection as a more adequate formulation in its terms of the Second Theorem, has the goal of minimizing intensional aspects in metamathematical discourse.
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