Abstract

Bernard Bolzano notoriously rejected Immanuel Kant’s claim that arithmetic and geometry were grounded on synthetic a priori judgements based on pure intuition. According to Bolzano, only analysis of concepts could ground the generality of mathematical statements and proofs; such a stand would later lead to logicism. Far from going in this way, however, Charles Sanders Peirce, who was one of the fathers of formal logic but also a great admirer of Kant, provided semiotic reasons to believe that diagrams do have a general meaning and that they can provide a knowledge which is both general and “ampliative”. Unlike mere logical analysis, diagrams help to explore concepts by going somehow “outside of them” in such a way that new knowledge is gained. This provides new support to Kant’s notion of intuitive construction, which is supposed to be both deductive and inventive.