Philosophy of Mathematics seminar

Kit Fine, NYU

Postulation and Possibility  

Procedural Postulationism shares with the traditional form of postulationism, advocated by Hilbert and Poincare, the belief that the existence of mathematical objects and the truth of mathematical propositions are to be seen as the product of postulation. But it takes a very different view of what postulation is. For it takes the postulates from which mathematics is derived to be imperatival, rather than indicative, in character; what is postulated are not propositions true in a given mathematical domain, but procedures for the construction of that domain. This talk will consider the question of the sense in which procedural postulationism can be considered to be a form of potentialism.

See https://as.nyu.edu/content/dam/nyu-as/philosophy/documents/faculty-documents/fine/accessible_fine/Fine_Unrestricted-Quantification.pdf and https://www.nyu.edu/gsas/dept/philo/courses/rules/papers/Fine.pdf. See also James Studd, Everything, More or Less: A Defence of Generality Relativism, Chapter 6 “Modal operators” and Chapter 7 “Russell Reductio Redux”, Oxford University Press, 2019.