Can a listener recover what a speaker means from the form of an utterance alone? We answer this question information-theoretically, and for a listener given by any featurizer of text, including the hidden states of contemporary large language models. Modeling language use as a joint distribution over meanings, contexts, and utterances, we derive upper bounds on the probability that a decoder recovers a speaker's intended meaning from a representation of the utterance. The bounds are governed by the uncertainty that form leaves about meaning, which splits into an irreducible part and a part that only (extralinguistic) context, but never the utterance alone, can resolve. Because these quantities are intrinsic to language, no representation, however much text or supervision produced it, can surpass them; the bounds hold whether the space of meanings is discrete or continuous. Experiments on artificial languages, Mandarin zero-pronoun resolution, and color reference provide empirical evidence in support of the theory.
We discuss the nature of chatbots as conversation partners in problem-solving. What can chatbots do and what can't they do? We develop hypotheses on how this can this be explained. Our argument draws on insights from Aggregation Dynamics, Cognitive Linguistics, Neuropsychology and Psychology. We establish that chatbots are multifaceted and composite systems. Our argument focuses on basic chatbots in the hope of thereby making statements about the core functionality of more advanced chatbots. Basic chatbots are assumed to consist of a Large Language Model (LLM) with a simple interface. The main results of our research are: a description of human imagination, understanding and thinking based on so-called metaphorical problem propagations; the hypothesis that the texts in the text dataset used for training LLMs have specific characteristics and that these texts only partially imitate human thinking and understanding; the hypothesis that the LLM training process encodes artificial metaphorical problem propagations into an LLM from these text datasets. Our conclusions are that a basic chatbot cannot be a thinking partner capable of matching the cognitive flexibility of humans, and that further development of the Large Language Model will not lead to this either. But chatbots exist, they are being used on a massive scale, by both individuals and organisations. It is therefore socially and politically important to understand them. Our article aims to contribute to the discussion on the functioning, benefits and drawbacks of chatbots. Cognitive Linguistics shows how the use of metaphor is an expression of our thinking. Aggregation Dynamics, is an attempt at a comprehensive systems theory. We believe that the concept of metaphorical problem propagation could provide an interesting addition for both. Chatbots a solution? For what?