Ordinals by Abstraction1
Bob Hale · 2021
NB: Abstract added by Editors . In his contribution, Bob Hale aims at providing a theory of ordinals on neo-logicist bases. In this respect, two main goals have to be accomplished. First and foremost, consistency is to be retained, since Burali-Forti’s paradox easily arises from a naïve ordinal abstraction principle accompanied by unrestricted second-order logic. Second, such a reconstruction should not be provided on the basis of set theory but rather in a purely neo-logicist setting. Hale achieves both goals by modifying Shapiro and Wright’s definition of indefinite extensibility in Shapiro and Wright (2006) , on the one hand, and relying on Hume’s Principle, on the other.