Language—often said to set human beings apart from other animals—has resisted explanation in terms of evolution. Language has—among others—two fundamental and distinctive features: syntax and the ability to express non-present actions and events. We suggest that the relation between this representation (of non-present action) and syntax can be analyzed as a relation between a function and a structure to fulfill this function. The strategy of the paper is to ask if there is any evidence of pre-linguistic communication that fulfills the function of communicating an absent action. We identify a structural similarity between understanding indexes of past actions of conspecifics (who did what to whom) and one of the simplest and most paradigmatic linguistic syntactic patterns – that of the simple transitive sentence. When a human being infers past events from an index (i.e., a trace, the conditions of a conspecifics or an animal, a constellation or an object) the interpreters’ comprehension must rely on concepts similar in structure and function to the ‘thematic roles’ believed to underpin the comprehension of linguistic syntax: in his or her mind the idea of a past action or event emerges along with thematic role-like concepts; in the case of the presentation of, e.g., a hunting trophy, the presenter could be understood to be an agent (subject) and the trophy a patient (direct object), while the past action killed is implied by the condition of the object and its possession by the presenter. We discuss whether both the presentation of a trophy and linguistic syntax might have emerged independently while having the same function (to represent a past action) or whether the presentation of an index of a deed could constitute a precursor of language. Both possibilities shed new light on early, and maybe first, language use.