THE PHILOSOPHICAL FOUNDATIONS OF ALTERNATIVE SET-THEORY

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. © 1991, Taylor & Francis Group, LLC. All rights reserved.