tag:blogger.com,1999:blog-4667288583830493271.post817968677453027574..comments2023-10-31T06:14:24.897-07:00Comments on Philosophy in Progress: Epistemology verses Foundations in Philosophy of MathSharon Berryhttp://www.blogger.com/profile/17434076853502881274noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-4667288583830493271.post-30513200628511343292012-09-12T12:39:07.091-07:002012-09-12T12:39:07.091-07:00The foundations of mathematics and epistemology ar...The foundations of mathematics and epistemology are different (though not inherently disjoint things). Research suggests that the human mind favors a fundamentally connectionist framework in terms of knowledge and knowledge aggregation (e.g. Churchland 1987). While mathematics is the fundamental language of truth, certain disciplines, such as the study of "fuzzy sets" may provide a framework for modeling epistemology.<br /><br />The axiom of choice is one of the fundamental axioms of the language of math, and has very special properties in that it allows us to extend, under certain circumstances, properties from finite sets to infinite sets. This comes at a (somewhat abstract) price, e.g. the Vitali set and Banach-Tarski paradox, among others. But nevertheless, it provides an indispensable tool for the structure of mathematics.Anonymoushttps://www.blogger.com/profile/11483836424011472880noreply@blogger.com