Diagrammatic Reasoning: Some Notes on Charles S. Peirce and Friedrich A. Lange

According to the received view, Charles S. Peirce's theory of diagrammatic reasoning is derived from Kant's philosophy of mathematics. For Kant, only mathematics is constructive/synthetic, logic being instead discursive/analytic, while for Peirce, the entire domain of necessary reasoning, comprising mathematics and deductive logic, is diagrammatic, i.e. constructive in the Kantian sense. This shift was stimulated, as Peirce himself acknowledged, by the doctrines contained in Friedrich Albert Lange's Logische Studien (1877 Lange, F.A. 1877. Logische Studien: Ein Beitrag zur Neubegründung der formalen Logik und der Erkenntnisstheorie, H. Cohen, ed., Iserlohn: Verlag von J. Baedeker (LS). [Google Scholar]). The present paper reconstructs Peirce's reading of Lange's book, and illustrates what, according to Peirce, was right and what was problematic in Lange's account of reasoning. It further seeks to explain how Peirce's theory of deductive reasoning was a combination of Kant's philosophy of mathematics and Lange's philosophy of logic.