Frege on Numbers: Beyond the Platonist Picture*

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, in particular about the natural numbers. I will also focus mostly on Frege's corresponding remarks in 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 in 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, naive 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 in the sense of considering them in connection with his general approach in Foundations and Basic Laws. Connected with that I will distinguish two very different ways in which platonism in itself can be understood. The "context" I have in mind thus consists in Frege's general approach, supplemented by a differentiated understanding of platonism.