What is Super Semantics? *

Formal semantics was born from an attempt to state explicit rules to predict the truth conditions of natural language sentences. But this goal can be extended beyond language stricto sensu, to a variety of representational systems in nature. This was part of the program of semiotics (e.g. Morris 1938), construed as a general theory of signs; but it never got integrated to the research program of formal semantics. We argue for such an integration, on two general grounds. First, the class of objects that interact with or display uncontroversially linguistic properties is larger than was initially thought. Spoken and especially sign language make use of rich iconic resources which interact with logical structure but cannot be captured without a 'formal semantics with iconicity'. In addition, recent comparisons between sign, speech and gestures strongly suggest that language is multi-modal and that gestures are full citizens of the linguistic world: they trigger familiar inferential types (presuppositions or supplements) when they co-occur with or follow words; and when they fully replace words, their informational content gets divided among familiar slots of the inferential typology, and they even follow a 'gestural grammar' that is in part reminiscent of sign language grammar. Second, independently from these language-internal motivations, the proposed extension leads to a far broader typology of meaning operations in nature, one that includes animal meanings, pictorial meanings, musical meanings, and more. This makes it possible to explore new connections among these domains, for instance between vocal and gestural iconicity, between musical inferences and animal signals, or between visual narratives and music.