Frege's Curiously Two-Dimensional Concept-Script

In this paper I argue that the two-dimensional character of Frege’s Begriffsschrift plays an epistemological role in his argument for the analyticity of arithmetic. First, I motivate the claim that its two-dimensional character needs a historical explanation. Then, to set the stage, I discuss Frege’s notion of a Begriffsschrift and Kant’s epistemology of mathematics as synthetic a priori and partly grounded in intuition, canvassing Frege’s sharp disagreement on these points. Finally, I argue that the two-dimensional character of Frege’s notations play the epistemological role of facilitating our grasp of logical truths (foundational and derived) independently of intuition. The rest of this paper critically evaluates Frege’s view and discusses Macbeth’s (2005) account