Abstract
Cognitive science recognizes two kinds of systematicity: (1) as the property where certain cognitive capacities imply certain other related cognitive capacities (Fodor and Pylyshyn); and (2) as the principle that analogical mappings based on collections of connected relations are preferred over relations in isolation (Gentner). Whether these kinds of systematicity are two aspects of a deeper property of cognition is hitherto unknown. Here, it is shown that both derive from the formal, category-theoretic notion of universal construction. In conceptual/psychological terms, a universal construction is a form of optimization of cognitive resources: optimizing the re-utilization of common component processes for common task components. Systematic cognitive capacity and the capacity for analogy are hallmarks of human cognition, which suggests that universal constructions (in the category-theoretic sense) are a crucial component of human cognitive architecture.
Highlights
Cognitive science recognizes two kinds of systematicity
Summary and further directions The category theory concept of a universal construction was introduced to address a limitation of the classical explanation for F-systematicity: i.e. the lack of an explanation as to why the grammars constituting cognitive architecture are just the systematic ones
The category theoretical explanation says that the structures supporting systematicity are the universal/optimal ones, in a precisely specified, formal sense
Summary
One kind of systematicity is the property of cognition where the capacity for certain cognitive abilities implies the capacity for certain other cognitive abilities, i.e. capacity is distributed around equivalence classes of cognitive abilities [1]. Another kind of systematicity is the preference for analogical mappings based on collections of connected relations over relations in isolation [2]. Whether these two kinds of systematicity are aspects of a deeper property of cognition is hitherto unknown. The two kinds of systematicity are recalled in the remainder of this introduction before a category theory account of both is provided in the subsequent sections
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