THE PHILOSOPHICAL FOUNDATIONS OF ALTERNATIVE SET THEORY*
| Autor: | Petr Vopěnka |
|---|---|
| Rok vydání: | 1991 |
| Předmět: |
Classical mathematics
Class (set theory) Unsharpness media_common.quotation_subject Alternative set theory Infinity Computer Science Applications Theoretical Computer Science Control and Systems Engineering Modeling and Simulation Calculus Set theory Semiset Mathematical economics Information Systems Mathematics media_common Universe (mathematics) |
| Zdroj: | International Journal of General Systems. 20:115-126 |
| ISSN: | 1563-5104 0308-1079 |
| DOI: | 10.1080/03081079108945019 |
| Popis: | This paper deals with philosophical fundamentals of Alternative Set Theory and its relation to classical mathematics. The key problem is a possibility to mathematize the phenomenon of horizon and the corresponding infinity. Serious criticism of classical set theory is given, especially in connection with its understanding of this phenomenon. The relation between classical and natural infinity (studied by AST) is presented and the difference between AST and Non-standard analysis is discussed. At the end, the fundamental notions of AST are briefly characterised, specifically that of sets, classes, semisets, and the extended universe. The encompassing of the vagueness (unsharpness) phenomenon by AST, and the concepts of static and dynamic AST are also discussed. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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