Analogy as the Basic Operator: Limits of Language Models and the Nature of Doxa

Abstract

Large language models (LLMs) demonstrate the ability to solve tasks that until recently were considered the prerogative of human intelligence, but they are not particularly good at generating something fundamentally new. This paper shows that this gap is not accidental: it is rooted in the architecture itself. We formalize the self-attention mechanism as an operator of geometric analogy: attention computes a weighted sum of values, where the weights are proportional to the geometric similarity of queries and keys. This is neither logical inference nor the generation of something new, but the transfer of structure by geometric proximity. From this formalization we derive structural limits: abduction in Peirce's sense - the generation of a new explanation from an observation - is inaccessible to attention. We introduce the distinction between doxa and logos: doxa is a source of proposals that does not possess truth; logos is a formal system that accepts or rejects these proposals. We show that LLMs satisfy all the characteristics of doxa, and that the interface between doxa and logos is asymmetric. The analysis implies that an LLM is insufficient on its own, and that further development lies in building hybrid systems in which the proposals of doxa are verified by logos.