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)

In this paper, I defend a moderately cognitive account of religious beliefs. Religious beliefs are interpreted as “worldview beliefs”, which I explicate as being indispensable to our everyday and scientific practice; my reading is nonetheless distinct from non-cognitivist readings of “worldview belief” which occasionally appear in the literature. I start with a brief analysis of a recent German contribution to the debate which on the one hand insists on the priority of epistemic reasons for or against religious beliefs, but on (...) the other hand contends that religious beliefs are worldview beliefs. This leads me to explicate a special sense of worldview beliefs, as well as their cognitive role. After that, I shed some light on a special epistemological characteristic of worldview beliefs, namely the strong involvement of “free certitude” in their acceptance. I explore the implications for the possible role of arguments for worldview beliefs, especially for worldview beliefs concerning theism. (shrink)