A very wise person of our acquaintance once said, 'Read old books to get new ideas'. Here, we pursue the ideas presented in old books by Lev Vygotsky and George Herbert Mead as a means to account for the differences in social life between human and non-human primates and, by extension, their cognition. We consider the contrasting perspectives of Vygotsky and Mead on the links between thought and language, and relate these to subsequent developments in the study of animal cognition, and the emergence of the fields of embodied and distributed cognition. We then use this synthesis to argue that, as Wundt originally suggested, the study of social life must be fundamentally social and situated, and cannot be a laboratory endeavour focused solely on processes within individuals. We use developments in social network analysis (specifically a new formalisation of social networks, which can be presented as multi-dimensional mathematical objects, 'tensors') to explore the possibilities of a new approach to comparative social cognition. This approach recognizes that sociality and behaviour are constitutive of cognition and not simply its visible manifestation, and emphasizes that there is no such thing as a social brain in isolation, but a complex nexus of brain, body and world. Presented by Louise Barrett, Peter Henzi and David Lusseau (Psychology, University of Lethbridge, Canada). Creative Commons Attribution-Non-Commercial-Share Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/