Online research in philosophy

This article is an extended critical study of Kit Fine’s The limits of abstraction, which is a sustained attempt to take the measure of the neo-logicist program in the philosophy and foundations of mathematics, founded on abstraction principles like Hume’s principle. The present article covers the philosophical and technical aspects of Fine’s deep and penetrating study.

Kit Fine develops a Fregean theory of abstraction, and suggests that it may yield a new philosophical foundation for mathematics, one that can account for both our reference to various mathematical objects and our knowledge of various mathematical truths. The Limits of Abstraction breaks new ground both technically and philosophically.