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Prediction of the next value of a function
(1981)
The following model of inductive inference is considered. Arbitrary set tau = {tau_1, tau_2, ..., tau_n} of n total functions N->N is fixed. A "black box" outputs the values f(0), f(1), ..., f(m), ... of some function f ...
Вокруг теоремы Геделя
(Latvia State University, 1981)
Проведен методологический анализ природы математики. Показано, что сущность математического метода состоит в исследовании застывших моделей. Обоснована несостоятельность утверждений об ограниченности аксиоматического метода. ...
Platonism, intuition and the nature of mathematics
(Bulgarian Academy of Sciences, Sofia, 1988)
Platonism is an essential aspect of mathematical method. Mathematicians are learned ability " t o l i v e " in the "world" of mathematical concepts. Here we have the main source of the creative power of mathematics, and ...