This paper explores a non-normal logic of beliefs for boundedly rational agents. The logic we study is the result of dropping positive introspection for knowledge in the system developed by Stalnaker [1]. In that system beliefs are not closed under conjunction, but they are required to be pairwise consistent, a requirement that has been called agglomerativity elsewhere. While bounded agglomerativity requirements, i.e., joint consistency for every n-tuple of beliefs up to a fixed n, are expressible in that logic, unbounded agglomerativity is not. We study an extension of this logic of beliefs with such an unbounded agglomerativity operator, provide a sound and complete axiomatization for it, show that it has a sequent calculus that enjoys the admissibility of cut, that it has the finite model property, and that it is decidable.