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)