DOI: 10.2298/theo2603053a ISSN: 0351-2274
How do we know what we know when we know the axioms?
Milos AdzicTyler Burge reconstructs Frege’s epistemology as Euclidean rationalism, treating primitive logical laws as self-evident and proofs as displaying an objective order of justificatory dependence. This paper argues that this proposition-first reconstruction misses a central feature of Frege’s logic. Frege’s demand for gapless proof and the structural machinery reconstructed by Schroeder-Heister in Grundgesetze §48 require deductions to be distinguishable, licensed and composable. General proof theory and categorical proof theory make explicit the mathematical structure: deductions are arrows, their composition corresponds to cut, and their equality calls for independent criteria. Philosophy of logic must answer to the mathematics of deduction.