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

2025-12-09

AI Summary

This paper addresses the relationship between large language models (LLMs) and the symbol grounding problem, arguing that LLMs do not solve but systematically *bypass* it. Method: We develop a unified semantic framework grounded in category theory to formally characterize the distinction between human and LLM meaning-making: specifically, how each maps content into truth-conditional propositions over a possible-world state space *W*. The framework models the absence of perceptual–symbol coupling in LLMs, showing they rely solely on statistical associations to generate higher-order propositions without intrinsic reference. Contribution/Results: First, we provide the first category-theoretic formalization of the full semantic generation process. Second, we advance the novel theoretical claim that LLMs *bypass*, rather than resolve, symbol grounding. Third, we rigorously prove that LLM inference is independent of real-world anchoring. This framework establishes a formal foundation for delineating the semantic boundaries of LLMs.

Technology Category

• Natural Language Processing: (Large) Language Models
• Machine Learning: Large Multimodal Models (LMMs)
• Cognitive Modeling & Cognitive Systems: Symbolic Representations

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

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.

Problem

• Analyzes how LLMs transform content into truth propositions
• Argues LLMs circumvent the symbol grounding problem
• Uses categorical framework to compare humans and LLMs

Innovation

• Categorical framework analyzes LLM content transformation
• Compares human and LLM proposition formation processes
• Argues LLMs circumvent symbol grounding problem