 Ultimately, Kant claims that it is “only the concept of magnitudes” (quantities) that can be constructed in pure intuition, since “qualities cannot be exhibited in anything but empirical intuition” (A714/B742) (Sutherland 2004a, 2004b, 2005a, 2021). This leads to a principled distinction between mathematical and philosophical cognition: while philosophical cognition is confined to the results of an abstract conceptual analysis, mathematical cognition is the result of a “chain of inferences that is always guided by intuition”, that is, by a concrete representation of its objects (Hintikka 1967; Parsons 1969; Friedman 1992; Hogan 2020). Kant strains somewhat to explain how the mathematician constructs arithmetic and algebraic magnitudes, which are distinct from the spatial figures that are the object of geometric reasoning. Drawing a distinction between “ostensive” and “symbolic” construction, he identifies ostensive construction with the geometer’s practice of showing or displaying spatial figures, whereas symbolic construction correlates to the act of concatenating arithmetic or algebraic symbols (as when, for example, “one magnitude is to be divided by another, [mathematics] places their symbols together in accordance with the form of notation for division…”) (A717/B745) (Brittan 1992; Shabel 1998).