Thought: A Journal of Philosophy

Volume 4, Issue 4, December 2015

Higher-Order Abstraction Principles

I extend theorems due to Roy Cook (2009) on third- and higher-order versions of abstraction principles and discuss the philosophical importance of results of this type. Cook demonstrated that the satisfiability of certain higher-order analogues of Hume’s Principle is independent of ZFC. I show that similar analogues of Boolos’s NEWV and Cook’s own ordinal abstraction principle SOAP are not satisfiable at all. I argue, however, that these results do not tell significantly against the second-order versions of these principles.