Frege on Numbers

Abstract

Gottlob Frege is often called a platonist. In connection with his philosophy we can talk about platonism concerning three kinds of entities: numbers, or logical objects more generally; concepts, or functions more generally; thoughts, or senses more generally. I will only be concerned about the first of these three kinds here, particular about the natural numbers. I will also focus mostly on Frege's corresponding remarks The Foundations of Arithmetic (1884), supplemented by a few asides on Basic Laws of Arithmetic (1893/1903) and Thoughts (1918). My goal is to clarify which sense the Frege of Foundations and Basic Laws is a platonist concerning the natural numbers.1 My strategy will be to look at Frege's platonism in context. To do so seems to me important because a direct, approach to platonism often leads nowhere, or at least not very far. Furthermore, Frege's corresponding views are not naive, as I will try to show. (What is meant by naive here will become clear shortly.) For that purpose I will contextualize Frege's platonist statements the sense of considering them connection with his general approach Foundations and Basic Laws. Connected with that I will distinguish two very different ways which platonism itself can be understood. The context I have mind thus consists Frege's general approach, supplemented by a differentiated understanding of platonism.