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- W74928388 abstract "The idea of infinity without which the mathematics is impossible, is entered into system of Principia Mathematic by means of an infinity axiom. The infinity axiom is needed in PM because some features of definition of natural number concept and axiomatization of arithmetic by J. Peano. However there is a question. Is it possible to introduce the idea of infinity on other bases? There are such attempts. Purely analytically the idea of infinity can be introduced on the basis of the definition of the natural number concept offered by G. Frege, or on the basis of G. Cantors theorem. However such attempts are logically unreasonable, as they lead to contradictions. The idea of infinity cannot be introduced a posteriori because nothing reality says about its necessity. Hence, the axiom is just necessary. Russell treats the infinity axiom as a substantial statement about the world." @default.
- W74928388 created "2016-06-24" @default.
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- W74928388 date "2010-01-01" @default.
- W74928388 modified "2023-09-24" @default.
- W74928388 title "Б. Рассел о бесконечности" @default.
- W74928388 hasPublicationYear "2010" @default.
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