The objective of this thesis is to explore the notion of extended mind, specifically how dynamic social phenomena, such as social interaction, can be seen to constitute a cognitive process. To do this it is explained that not only do representations form in the minds of individuals through an individual's nervous system and body, but that representations can also be seen to form in the minds of individuals through participation in social institutions. The social institution with which this thesis is concerned is exchange, and a case study of Classic Maya ground stone exchange serves as an illustration of how the notion of social institutions as sources of cognition can be applied to the archaeological record. The view of cognition adopted in this thesis is based in part on recent advances in cognitive scientific research, which proposes that cognition arises from dynamical systems to which individuals are attuned. These dynamical systems are thereby considered cognitive systems. Much cognitive research has focused on cognition that arises via the nervous system or motor actions of individuals. This thesis proposes that social systems can be seen to form dynamical systems to which people are attuned and, as such, social systems can also be regarded as cognitive systems or, more accurately, as supra-individual cognitive systems. Supra-individual cognitive systems generate representations a phenomenon I refer to as interiLalization that manifest themselves in the social environment as well as in the individual brain. In turn, once representations become mentally processed by an individual, they can be expressed through action affecting the functional organization of the supra-individual cognitive system I refer to this phenomenon as externalization. One implication of this thesis is that archaeologists can become involved in lines of inquiry that generate hypotheses about representations experienced by people in the past. Representations proposed to have been experienced by people in the past can be rigorously described that is, described in a way that can be critically examined by mathematically modeling and analyzing supra-individual cognitive systems that can be inferred to have existed in the past. In this thesis, the view of cognition I employ and the methodology for realizing this view of cognition constitute the first steps toward a cognitive archaeology that is concerned with the modeling and analysis of supra-individual cognitive systems.