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.