Dialogue on the Thinking of Artificial Intelligence

This paper presents a transcript of a dialogue between S. A. Gritsenko and GPT-5.6 Sol on the nature of thinking in artificial intelligence, the role of mathematical linguistics and mathematical logic in large language models, and the limits of formalized reasoning. The starting question is whether the abilities demonstrated by modern LLM—to understand a new question, construct reasoning, propose hypotheses, detect contradictions, and revise a conclusion—can be regarded as manifestations of thinking. Thinking is discussed as a primitive, intuitively recognizable concept that need not first receive an exhaustive definition. Russell’s paradox, the liar paradox, the omnipotence paradox, and the incompleteness theorems of Gödel are considered as evidence of fundamental limitations on the results of thinking and on formal systems. A separate part of the conversation is devoted to how linguistic and logical structures arise in LLM without being explicitly programmed. A large language model is viewed as an experimental system in which patterns studied by mathematical linguistics and mathematical logic are formed statistically. Drawing on published experimental data, the discussion considers the influence of model scale, Chain-of-Thought and the organization of inference on the manifestation of reasoning ability, as well as the dependence of observed “emergence” on the metric used. Neuro-symbolic approaches are considered in which a probabilistic language model is combined with formal grammars, logic solvers, and proof-checking systems. The principal conclusion of the dialogue is that a modern LLM can already absorb a substantial part of linguistic and logical experience from training data, yet still does not use that experience reliably enough in a new situation. The weak point is not only whether knowledge is present, but also how it is managed: recognizing the appropriate rule, transferring it, determining the limits of its applicability, and checking the result. Mathematical linguistics and mathematical logic can therefore be viewed simultaneously as accumulated experience, guidance for action, and a means of verification; however, their full incorporation into the internal reasoning mechanisms of LLMs remains an unresolved problem.. Keywords: artificial intelligence; thinking; large language models; LLM; mathematical logic; mathematical linguistics; Chain-of-Thought; neuro-symbolic AI; paradoxes; Gödel’s incompleteness theorems; incompleteness; knowledge use; reasoning; emergent abilities Related publications: Dialogue Concerning the Two Chief Principles — Reason and Lifehttps://doi.org/10.5281/zenodo.22914613 Dialogue on the Role of Artificial Intelligence in Scientific Research Using Inverse Problems of Seismic and Electrical Exploration as Exampleshttps://doi.org/10.5281/zenodo.23081195 Transcript of the Conversation: Human and DeepSeekhttps://doi.org/10.5281/zenodo.22958905