Beyond and Below Cognitive Space: A Framework for Perfecting Conceptual Spaces

Peter Gärdenfors’ conceptual spaces framework represents a significant advance in cognitive science by proposing a geometric model of cognition that fills in gaps of symbolic and associationist accounts in explaining prototypical categorization and similarity judgment. This paper argues that in developing this framework, Gärdenfors has independently recovered something very similar to the cognitive structure of Aristotle. Surveying the Aristotelian-Thomistic cognitive hierarchy pinpoints where the conceptual spaces framework can be ontologically grounded and expanded. The paper concludes with preliminary observations on the implications of this analysis for Large Language Models (LLMs), arguing that better philosophical accounts of cognition may inform better LLM architectures, and that the Aristotelian-Thomistic framework provides the most complete account currently available of both what cognitive geometry correctly models and what lies irreducibly beyond it.