Enterprise AI Analysis

A Categorical Analysis of Large Language Models and Why LLMs Circumvent the Symbol Grounding Problem

This paper presents a formal, categorical framework for analysing how humans and large language models (LLMs) transform content into truth-evaluated propositions about a state space of possible worlds W, in order to argue that LLMs do not solve but circumvent the symbol grounding problem. Operating at an epistemological level of abstraction within the category of relations (Rel), we model the human route (H → C → Pred(W))-consultation and interpretation of grounded content-and the artificial route (H → C' → G × C' → O → Pred(W))—prompting a trained LLM and interpreting its outputs together with the training pipeline (C → C' → D(C') → G). The framework distinguishes syntax from semantics, represents meanings as propositions within Pred(W) (the power set of W), and defines success as soundness (entailment): the success set He where the AI's output set PAI(h) is a subset of the human ground-truth set Phuman (h). We then locate failure modes at tokenisation, dataset construction, training generalisation, prompting ambiguity, inference stochasticity, and interpretation. On this basis, we advance the central thesis that LLMs lack unmediated access to W and therefore do not solve the symbol grounding problem. Instead, they circumvent it by exploiting pre-grounded human content. We further argue that apparent semantic competence is derivative of human experience, causal coupling, and normative practices, and that hallucinations are entailment failures (PAI(h) Z Phuman(h)), which are intrinsic to this architecture, not mere implementation bugs. The categorical perspective clarifies debates clouded by anthropomorphic language, connects to extensions (e.g., probabilistic morphisms, partiality for refusals), and delineates the boundaries within which LLMs can serve as reliable epistemic interfaces. We discuss idealisations and scope limits, and conclude with some methodological guidance: expand He through curation, tooling, and verification, while avoiding attributing any understanding to stochastic, pattern-completing systems.