The extent to which languages share properties reflecting the non-linguistic constraints of the speakers who speak them is key to the debate regarding the relationship between language and cognition. A critical case is spatial communication, where it has been argued that semantic universals should exist, if anywhere. Here, using an experimental paradigm able to separate variation within a language from variation between languages, we tested the use of spatial demonstratives-the most fundamental and frequent spatial terms across languages. In n = 874 speakers across 29 languages, we show that speakers of all tested languages use spatial demonstratives as a function of being able to reach or act on an object being referred to. In some languages, the position of the addressee is also relevant in selecting between demonstrative forms. Commonalities and differences across languages in spatial communication can be understood in terms of universal constraints on action shaping spatial language and cognition. Main Speakers of different (spoken) languages share the same perceptual apparatus, so one might expect that the world’s 7,000 or so living languages 1 may have evolved communication systems that also share common properties 2 , 3 . Yet the idea that there are universals in communication systems has been challenged with studies documenting extensive cross-linguistic variation in domains closely yoked to perception, including colour naming 4 – 8 and spatial communication 9 – 11 . Typological studies across large samples of languages have shown that around half of the world’s languages have binary demonstrative systems (as in English), while 40% or so possess a three-way demonstrative system (for example, Spanish), with the remaining languages employing four or more demonstrative contrasts (for example, Navajo) 16 , 30 . Accounts of demonstratives vary both within and between languages. A prominent debate in the literature is whether (spatial) demonstrative use is primarily associated with an egocentric, body-oriented strategy to direct attention to objects or places in space 31 – 37 , or whether demonstratives are social and interactive terms rather than terms for spatial reference 38 – 43 . While these approaches are not mutually exclusive 19 , they have framed recent discussions of demonstrative systems between and within languages. Binary systems in linguistic treatments of demonstratives are often assumed to contrast distance, with a proximal term used for an object (referent) near a speaker and a distal term for an object far from a speaker 31 – 37 (Fig. So rather than the position of objects in Euclidean space per se determining demonstrative choice in English, it is the ability to act on an object that is important, associated with the perceptual distinction between peripersonal/reachable versus extrapersonal/non-reachable space (served by different brain systems and involving action selection) 44 . Contact or control of an object by the speaker has been proposed as a universal feature of all demonstrative systems (distinct from relative distance) 37 . Fig. 1 Conceptual models of demonstrative choice as a function of object distance and addressee position (manipulated in the experiments). Demonstrative Systems 1–3 represent hypothetical models of demonstrative use in a three-term language structured in terms of egocentric distance alone (Demonstrative System 1), territories of the speaker and addressee (Demonstrative System 2) or egocentric distance and shared space (Demonstrative System 3). D1, D2 and D3 represent distinct demonstrative forms. 1 , Demonstrative System 3), Jungbluth argues that Spanish demonstratives operate as (relative) distance-based terms, but when the speaker and addressee are face to face, demonstratives encode locations within or outside of the For example, they include languages that are typically considered to be person centred (such as Spanish and Japanese), languages that describe spatial relations using cardinal directions more than other languages (such as Tseltal) and languages with two, three or more spatial demonstrative terms. Results The participants provided six responses for each of the region (three) × addressee position (two) combinations (collapsing across the locations within each region). While the results are consistent with a mere distance effect, the steep drop-off in proximal term use when the referent is outside of reach suggests that the use of proximal and distal terms across all languages specifically maps onto a reachable/non-reachable (peripersonal/extrapersonal space) distinction, consistent with previous results from English and Spanish 34 – 36 (which manipulated reachability directly). The data are thus consistent with the discovery of a semantic universal for this essential linguistic category, with all languages expressing the distinction between reachable and non-reachable space 34 – 37 . The importance of the reachability versus non-reachability of an object as a universal constraint on spatial communication systems is in line with approaches to the origins of language and theory of mind through action. It has been proposed that a child moves from reaching/not reaching to pointing behaviour and ultimately to symbolic communication from gestures (ontogenetic ritualization 61 , 62 ). There is some evidence to support this in a study on shrinking in the demonstrative system of Spanish–Norwegian bilinguals who maintain the peripersonal/extrapersonal space contrast over time but lose the use of the third distal term in their native (Spanish) language 63 . This suggests that languages with many demonstrative contrasts may reduce over time while nevertheless preserving the basic action system contrasts underlying space. The presence of a common egocentric proximal/reachable–distal/non-reachable distinction across languages reinstates the centrality of egocentric spatial relations in spatial language and spatial cognition.