11 ottobre 2018: F. Bellucci: Peirce On Diagrammatic Reasoning
Seminars on Pragmatism and the Sciences
Francesco Bellucci (University of Bologna)
Peirce On Diagrammatic Reasoning
11 ottobre 2018, ore 14:30
Sala Paci, Direzione del Dipartimento di Filosofia, Università degli Studi di Milano, Via Festa del Perdono 7 – 20122, Milano
It is known that Peirce’s doctrine of diagrammatic reasoning derives from Kant, but the details of the derivation have not been fully clarified. In the Discipline of Pure Reason, Kant says that mathematical cognition is cognition from the construction of concepts, where to construct a concept means to exhibit that concept a priori in intuition. Construction can be ostensive (as in geometry) or symbolic (as in algebra). Peirce agrees with Kant that mathematical reasoning is constructive, but extends this idea to the whole of deductive reasoning: all deductive reasoning is mathematical reasoning, and all mathematical reasoning is diagrammatic reasoning, i.e. reasoning based on construction, observation, and manipulation of diagrams. As for Kant, for Peirce diagrams can be of two main kinds: geometrical and algebraical. The generalization of Kant’s philosophy of mathematics into a doctrine of diagrammatic reasoning was influenced, as Peirce himself acknowledges, by F. A. Lange’s Logische Studien, in which it was argued that the intuition of space is the source of the necessary and yet synthetic character of both logical and mathematical reasoning.
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