Making Inferential Commitments Explicit

Abstract: Reflection principles are principles intended to express the soundness of a given theory. By Gödel’s theorems, these are logically independent of the corresponding theories. Still, they appear to enjoy a special epistemological status. The idea relates to the fact that there seems to be something wrong with accepting a theory without somehow acknowledging its soundness. It has been suggested, in turn, that such principles should be in some way available to those accepting a theory. Interestingly, the extension of theories by such principles enables one not only to live up to one’s epistemic responsibilities but, furthermore, to establish fascinating proof-theoretic results. These developments resulted in the establishment of a fruitful research program. However, the cogency of such a program has been questioned. In particular, Walter Dean argued that the project clashes with the idea of epistemic stability. He contends that the principles are not immediately available, and so the idea requires further defense. In the present talk, I aim to show that the addition of reflection principles is legitimate and that the project concerned with them is in good shape. I will argue that the available responses to Dean’s arguments are inadequate for those who want to defend interesting versions of these ideas. Moreover, I will present three different ways in which some form of reflection can be made satisfactorily available for those endorsing a given theory.