Natural language meaning has properties of both (embodied) cognitive representations and formal/mathematical structures. But it is not clear how they actually relate to one another. This article argues that how properties of cognitive representations and formal/mathematical structures of natural language meaning can be united remains one of the puzzles in cognitive science. That is primarily because formal/mathematical structures of natural language meaning are abstract, logical, and truth‐conditional properties, whereas cognitive/conceptual representations are embodied and grounded in sensory‐motor systems. After reviewing the (...) current progress, this work offers, in outline, the general formulations that show how these two different kinds of representations for semantic structures can (potentially) be unified and also proposes three desiderata for testing, in brain dynamics, the mathematical equivalence between formal symbolic representations (and their transitions), and neuronal population codes (and their transitions). (shrink)

This paper aims to show that properties of cognitive/conceptual representations and formal‐logical structures of linguistic meaning can be inter‐translated, recast, transformed into one another, and so united together, even though cognitive/conceptual representations and formal‐logical structures of linguistic meaning are apparently distinct in ontology and divergent in their form or character. While cognitive/conceptual representations are ultimately rooted in sensory‐motor systems, formal‐logical structures of linguistic meaning are abstractions detached from and independent of the actualized world. This paper sketches out the foundations of (...) how representations of linguistic meaning in terms of cognitive/conceptual structures in Cognitive/Conceptual Semantics can be unified with those in terms of formal‐logical structures in Formal Semantics. This is done by recasting cognitive/conceptual representations in terms of formal‐logical structures of linguistic meaning and re‐encoding formal‐logical structures of linguistic meaning in terms of cognitive/conceptual representations. Then, these two types of semantic representations, thus shown representationally equivalent, will be related to a series of derivations across levels in neuronal networks and dynamics. The general discussion on unifying cognitive/conceptual representations of linguistic meaning with formal‐logical structures is contextualized within the broader context of theorizing in cognitive science. (shrink)