The logic of lost lingens

Abstract

In this paper I aim for two targets. The first is to extend standard doxastic logic via the inclusion of multiple belief operators: there ought to be one such operator for each believer. The usefulness, indeed, the necessity of this extension is quite apparent for there is a clear need to express propositions concerning one person’s beliefs about another’s beliefs. In standard doxastic logics, the subscript on the belief operator is largely an unnecessary flourish faciliating an easy English reading of the symbolism. But it is not difficult to extend the standard doxastic logic to include multiple operators, where the subscript plays a genuine role. The second target is more nebulous and presents greater difficulties. It can be approached by considering an old puzzle about doxastic logic, raised first, I think, by Hector Neri Castafieda.’ The problem is particularly obvious once one begins to think of a doxastic logic with multiple operators over which identity substitutions are allowed. The problem is one about the iteration of belief operators; it shows that the general iteration principle: