Everything is learnable, once it is settled

Abstract

Since Fitch’s proof that not all propositions are knowable, philosophers have analysed the concept of knowability and sought a schema for the knowable propositions. A recent development in dynamic epistemic logic (DEL) has been to read ‘knowable’ as ‘known after an announcement’. Arbitrary Public Announcement Logic (APAL) and Sequential Public Announcement Logic (SPAL) are two DELs that have depicted this reading of knowability. We argue that neither APAL nor SPAL provide a satisfactory and principled schema of the knowable propositions. Instead, we claim that knowability is linked with settledness; stability of truth. We augment SPAL with a settled operator to create a new logic, Dual Sequential Public Announcement Logic (DSPAL). We prove in DSPAL a principled schema of knowability, that all settled propositions are knowable.