The ontological implications of neo-Fregeanism

Abstract

Neo-Fregeanism is a combination of two ideas: logicism, according to which arithmetic can be derived from logic plus definitions, and Platonism, according to which there are mathematical objects (which are abstract). Neo-Fregeans propose a new interpretation of Frege's principles of abstraction (mainly the so-called Hume's Principle) and of the role of reconceptualization and implicit definition for the introduction of numbers into our ontology. I analyze the ontological implications of neo-Fregeanism, not only for mathematics, but for abstract entities in general. After briefly introducing some of the main elements of neo-Fregeanism, I present two possible readings of its ontological implications and I argue that none of them gives the desired results.