IS GOODSTEIN THEOREM A GODELIAN SENTENCE?
Vitaliy Valentinovich Tselishchev1,2, Aleksandr Vlaimirovich Bessonov2
1Novosibirsk National Research State University, 2, Pirogov st., Novosibirsk, 630090, Russia
2Institute of Philosophy and Law, Siberian Branch of the Russian Academy of Science, 8, Nikolaev st., Novosibirsk, 630090, Russia, e-mail: leitval@gmail.com
Keywords: теорема Гудстейна, геделево предложение, тезис Исааксона, формальная арифметика, Goodstein's theorem, GГ¶delian sentence, Isaacson's thesis, formal arithmetic
Abstract
The paper considers the question of the degree to which Goodstein's theorem may be considered to be an analogue of a true, but not provable Gödelian sentence. It is shown that such an interpretation leads to Isaacson's thesis, according to which the demonstration of the truth of real mathematical analogues of the Gödelian sentence in the formal language of arithmetic uses conceptual resources that go beyond the resources required to understand the basic arithmetic of finite natural numbers. The plausibility of the thesis is disputed from the point of view of the incomprehensibility of the arithmetic content of the Gödelian sentence.
|
