Lano, K., The intuitionistic alternative set theory, Annals of Pure and Applied Logic 59 141–156 The Alternative Set Theory, as defined in Vopenka and Sochor, demonstrates how a set theory which avoids actually infinite sets can serve as a framework for much of classical mathematics. This paper defines a theory which can serve as an intuitionistic analogue of AST, and examines motivations for alternative formulations of classical AST from an intuitionistic and finitistic viewpoint. The intuitionistic AST uses appropriate modifications of (...) the concepts of AST, with the notion of feasibility replacing finiteness, and with new distinctions between alternative definitions of Countable Class and Revealment. Results of classical AST which are still valid in this new system are given, and an interpretation of the corresponding classical system in the intuitionistic system is defined. This shows that the adoption of an intuitionistic logic does not essentially deprive us of classical methods or results for AST. (shrink)

Provides an overview of Mark Sharlow's philosophical work with summaries of his positions. Includes references and links to his writings.

This is not a normal book. It is a collection of transcripts of talks that I gave between the year 2003 and now. I gave most of these talks on the spur of the moment, without making notes ahead of time. (“Impromptu” is the usual term for that dangerous way of speaking.) One of the “talks” is not a transcript, but a set of notes for a talk I never gave. Any organization or order in the talks is purely coincidental—or (...) at least it’s not all my fault. (shrink)