Intrinsic Justifications for Large-Cardinal Axioms

We shall defend three philosophical theses about the extent of intrinsic justification based on various technical results. We shall present a set of theorems which indicate intriguing structural similarities between a family of “weak” reflection principles roughly at the level of those considered by Tait and Koellner and a family of “strong” reflection principles roughly at the level of those of Welch and Roberts, which we claim to lend support to the view that the stronger reflection principles are intrinsically justified as well as the weaker ones. We consider connections with earlier work of Marshall.