Mutual perceptual knowledge is a prevalent feature of our everyday lives, yet appears to be exceptionally difficult to characterise in an acceptable way. This paper argues for a renewed understanding of Stephen Schiffer’s iterative approach to mutual knowledge, according to which mutual knowledge requires an infinite number of overlapping, embedded mental states. It is argued that the charge of ‘psychological implausibility’ that normally accompanies discussion of this approach can be offset by identifying mutual knowledge, not with the infinite iterations themselves, (...) but with the finite base which Schiffer proves is capable of generating those iterations. An understanding of this finite base as a primitive, relational property holding between two or more people, allows us to understand the iterations as an implicit and ‘harmless’ intrapersonal feature of what is an interpersonal phenomenon. The paper concludes by relating the account to joint attention in infant interaction. (shrink)