A fundamental property of language is that it can be used to refer to entities in the extra-linguistic physical context of a conversation in order to establish a joint focus of attention on a referent. Typological and psycholinguistic work across a wide range of languages has put forward at least two different theoretical views on demonstrative reference. Here we contrasted and tested these two accounts by investigating the electrophysiological brain activity underlying the construction of indexical meaning in comprehension. In two EEG experiments, participants watched pictures of a speaker who referred to one of two objects using speech and an index-finger pointing gesture. In contrast with separately collected native speakers’ linguistic intuitions, N400 effects showed a preference for a proximal demonstrative when speaker and addressee were in a face-to-face orientation and all possible referents were located in the shared space between them, irrespective of the physical proximity of the referent to the speaker. These findings reject egocentric proximity-based accounts of demonstrative reference, support a sociocentric approach to deixis, suggest that interlocutors construe a shared space during conversation, and imply that the psychological proximity of a referent may be more important than its physical proximity.