Philosophy of Mathematics Seminar


Philosophy of Mathematics seminar


Eileen Nutting, Kansas

Approaches to Ordinal Abstraction 

There are two general approaches to ordinal abstraction. On the first, ordinals are abstracted from well-orderings. On the second, they are abstracted from elements positioned within such orderings. On either approach, avoiding the Burali-Forti Paradox requires setting restrictions on the application of ordinal abstraction. Several such restrictions have been proposed. I will offer an alternative that can be applied to ordinal abstraction on either approach, and I will argue that it is preferable to the restrictions in the literature. This alternative relies on Øystein Linnebo’s account of dynamic abstraction.