Everything is Knowable – How to Get to KnowWhethera Proposition is True

Abstract

AbstractFitch showed that not every true proposition can be known in due time; in other words, that not every proposition isknowable. Moore showed that certain propositions cannot be consistently believed. A more recent dynamic phrasing of Moore‐sentences is that not all propositions are known after their announcement, i.e., not every proposition issuccessful. Fitch's and Moore's results are related, as they equally apply to standard notions of knowledge and belief (S5 andKD45, respectively). If we interpret ‘successful’ as ‘known after its announcement’ and ‘knowable’ as ‘known after some announcement’, successful implies knowable. Knowable does not imply successful: there is a propositionϕthat is not known after its announcement but there is another announcement after whichϕis known. We show that all propositions are knowable in the more general sense that for each proposition, it can become known or its negation can become known. We can get to knowwhetherit is true: ◊(Kϕ ∨ K¬ϕ). This result comes at a price. We cannot get to know whether the propositionwastrue. This restricts the philosophical relevance of interpreting ‘knowable’ as ‘known after an announcement’.