A Scale of Quantity. Kant and Peirce on Mathematical Reasoning

The paper examines Peirce’s interpretation of Kant’s philosophy of mathematics, with special reference to Kant’s notion of “construction”, and its transformation into a theory of diagrammatic reasoning. For Peirce, all deductive or mathematical reasoning proceeds by the construction and manipulation of diagrams. Peirce does not accept Kant’s idea that only concepts of quanta and quantitas can be constructed. Logical concepts and relations, although they are not quantitative, can be diagrammatized, namely “constructed” in Kant’s sense. What is quantitative in logical construction is not the object that is constructed, but the means of constructing it. This shift from the Kantian idea that the object is quantitative to the idea that the means to construct it is quantitative is operated by Peirce’s notion of a “scale of quantity”, that is, the idea that in mathematical reasoning an intermediate, quantitative construction is introduced and removed afterwards. The paper consid ers two examples of “construction” of syllogistic logic, Euler diagrams and Boolean algebra. Both are “scales of quantity”, that is, quantitative objects having quantitative relations that serve to the representation of non-quantitative objects having non-quantitative relations.