What is central to the progression of a sequence is the idea of succession, which is fundamentally a temporal notion. In Kant's ontology numbers are not objects but rules (schemata) for representing the magnitude of a quantum. The magnitude of a discrete quantum 11...11 is determined by a counting procedure, an operation which can be understood as a mapping from the ordinals to the cardinals. All empirical models for numbers isomorphic to 11...11 must conform to the transcendental determination of time-order. (...) Kant's transcendental model for number entails a procedural semantics in which the semantic value of the number-concept is defined in terms of temporal procedures. A number is constructible if and only if it can be schematized in a procedural form. This representability condition explains how an arbitrarily large number is representable and why Kant thinks that arithmetical statements are synthetic and not analytic. (shrink)

According to Kant, we refer to what is out there in the world by performing a demonstrative act, like pointing at an object with a finger. A Kantian mode of demonstrative reference is characterized by the existence of a real, 2-placed affective relation between an intuiting subject and the referent. Parsons suggests that Kantian intuition is both singular and immediate, and immediacy demands an object of intuition to be present, a condition clearly satisfied by objects within our immediate perceptual field. (...) But since we do not have an immediate relation with remote objects, the scope of our demonstrative reference is severely restricted by intuitional immediacy. I wish to develop a global Kantian intuition in order to extend the scope of demonstrative reference. Kant's ontology of space entails that the global representability of space be given to an intuiting subject as a form of intuition. According to Melnick, Kantian intuition is a kinematic operation which involves directing attention and moving about. To make contact with the world, the subject must move away from its locale: although a spatially remote object is not immediately present, we can shift our location by taking a path such that W will become so. Once we are close enough to be affected by W, we will be able to point at W and say "This." Thus, the intuitive scope of demonstrative reference is globalized as we shift our location. (shrink)