 Like Lewis, Gilbert recognizes that human agents do not in fact have unlimited inferential capacity. To generate the infinite hierarchy of mutual knowledge, Gilbert introduces the device of an agent’s smooth-reasoner counterpart. The smooth-reasoner counterpart \(i'\) of an agent \(i\) is an agent that draws every logical conclusion from every fact that \(i\) knows. Gilbert stipulates that \(i'\) does not have any of the constraints on time, memory, or reasoning ability that \(i\) might have, so \(i'\) can literally think through the infinitely many levels of a common knowledge hierarchy.