Inverse alteroception is a newly defined mode of intersubjective phenomenology that is apparent in face-to-face interaction, the organization of logical relations, and a wide range of mappings, from gesture space and the Proscenium stage to pre-modern art, historic heraldry, and contemporary graphic design. This unique human ability requires both structuralist (a.k.a. Saussurean) and pragmatist (a.k.a. Peircean) semiotic understanding to adequately account for. Structuralism is needed to account for its closed positional status as a minimalist generative template, along with the mutually defining, socially-oriented oppositional relations that it serves to expose, featuring value-based, normative markedness hierarchies of privilege and oppression. Pragmatist semiotic points of view, are required for recognizing the origins of the phenomenon in felt bodily qualia (iconic qualisigns), its status as a general type or series of nested general types (iconic legisigns) composed of analogous part-whole relationships, and the infinite number of more specific instances through which these types are realized, plus its usefulness for diagrammatic modeling. To fully appreciate the nature and relevance of these diagrams, along with the more general class of structural/diagrammatic relations to which they belong, both traditions are needed. The structuralist approach enables us to make sense of (and critique) social ideologies. The pragmatist approach enables us to make sense of (and learn from) evolutionary origins. As such, the paper builds on other contemporary work in semiotics that obsolesces and transcends the old oppositional stalemate between structuralist and pragmatist traditions, blending them in the process via lived experiential relations of bodily cognition.