Neo-Logicism An Ontological Reduction of Mathematics to Metaphysics 2000 2 citations ? 1 self

Abstract:  It is now well accepted that logicism is false. The primitive notions and proper axioms of mathematical theories are not reducible to primitive logical notions and logical axioms. Even the idea underlying logicism appears to be somewhat problematic, for if the existence claims of mathematics are to be reducible to logical truths, then it would seem that the logicist has to assert the existence of objects of some kind. Though a case can, and has, been made for thinking that logic can contain or imply existence claims, the matter is at least controversial and so there is at least a question as to whether a reduction of mathematics to a logic with existence claims would constitute a reduction of mathematics to logic.