Total Knowledge

In this paper, we analyse a concept of total knowledge based on the idea that an agent’s total knowledge is the strongest proposition the agent knows. We propose semantics for propositional and first-order languages with a modal operator TK representing total knowledge, and establish a result showing that total knowledge is ‘epistemically categorical’, in the sense that it determines the agent’s knowledge over a broad range of contents. We show that (subject to some restrictions) total knowledge is always total knowledge of an objective content, and that, for such objective contents, our TK-operator corresponds in a straightforward way to Levesque’s operator O.