Rather than juxtaposing embodiment and intersubjectivity, we argue that the two are intimately linked and form the foundations of human sociality, as well as the bases for language, with its normativity and grammar. We support the general claim with analyses from phenomenology and developmental psychology, and explicate the notion of sedimentation, according to which more objective and abstract semiotic structures, such as those of language, overlay experientially richer ones, such as the outlined intercorporeal structures. To make the argument more specific, we focus on the linguistic construal of situations lacking actual motion in dynamic terms through expressions of non-actual motion such as The road goes through the forest and He was uplifted by her words, summarizing the findings of previous studies of Swedish, English, French, Bulgarian and Thai. The analysis generalizes over notions such as fictive motion and conceptual metaphor, distinguishing between the levels of pre-linguistic motivations and linguistic conventions, unlike most approaches in cognitive linguistics. The overall proposal helps to provide an account of how linguistic meanings are not only shared, but come to embody shared intersubjective perspectives (construals) of events, by means of a diachronic process in which individual acts of reference become entrenched not just as individual cognitive routines, but as socially-sanctioned practices, i.e. linguistic norms.