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A theory of cognitive architecture should explain why systematicity is a necessary, not just possible consequence of the theory's core principles and base assumptions, without relying on arbitrary (ad hoc) modifications to close explanatory gaps. Cognitive capacities are systematically distributed around common structures. Category theory, a mathematical theory of structure, provides a framework for a theory of systematicity that explains the nature of these structures. Underlying each collection of systematically related capacities is a categorical universal construction: each capacity is uniquely composed of a common (universal) component and capacity-specific component; constructions not admitting this form of compositionality are not categorical universal constructions. Hence, our category theoretical explanation transcends problems with other (classical/symbolic, connectionist) approaches, which admit both systematic and non-systematic architectures.

In its classical form, the systematicity of cognition is constitutively tied to the compositionality of the vehicles of cognition. A burgeoning research program in the cognitive sciences suggests that, in many cases, cognitive systems are interaction dominant. I will describe several examples of research showing that cognitive systems are interaction dominant, and argue that interaction dominance is inconsistent with the compositionally of the vehicles of cognition. As goes compositionality, so goes classical systematicity. So, to whatever extent cognitive systems are genuinely interaction dominant, cognition is not classically systematic.

If there is a line between semantics and pragmatics, where is it drawn? In this essay I propose that appreciating a sentence is subject to two sets of processes: linguistic (viz., syntactic, semantic) driving the composition of shallow propositions, and unbounded pragmatic (viz., thinking). In section 1, I discuss some guiding assumptions on cognitive architecture, which constrain the nature of linguistic and cognitive representations and processes—and by implication, the conception of the semantics/pragmatics divide I have to offer. The phenomena I examine in section 2, relying on linguistic arguments and experimental evidence, suggest that for certain constructions there is an early “literal” process of interpretation followed by a period of uncertainty, indicating that the early linguistic computations produce a “shallow” semantic representation, not a fully enriched one. The cases I discuss, culminating in metaphors and so-called indeterminate sentences, challenge the prowess of linguistic computations for resolving—even suggesting—interpretations.