Peano numerals as buck-stoppers

I will examine three claims made by Ackerman (1978) and Kripke (1992). First, they claim that not any arithmetical terms is eligible for universal instantiation and existential generalisation in doxastic or epistemic contexts. Second, Ackerman claims that Peano numerals are eligible for universal instantiation and existential generalisation in doxastic or epistemic contexts. Kripke's position is a bit more subtle. Third, they claim that the successor relation and the smaller-than relation must be effectively calculable. These three claims will be examined from the framework of modal-epistemic arithmetic, i.e. arithmetic extended with certain modal, epistemic and modal-epistemic principles. I will present theorems that give support to the claims made by Ackerman and Kripke.status: publishe