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<p>We bring together foundational theories of meaning and a mathematical formalism of artificial general intelligence to provide a mechanistic explanation of meaning, communication and symbol emergence. We establish circumstances under which a machine might mean what we think it means by what it says, or comprehend what we mean by what we say. We conclude that a language model such as ChatGPT does not comprehend or engage in meaningful communication with humans, though it may exhibit complex behaviours such as theory of mind.</p>

<p>If <em>A</em> and <em>B</em> are sets such that <em>A</em> is a subset of <em>B</em>, generalisation may be understood as the inference from <em>A</em> of a hypothesis sufficient to construct <em>B</em>. One might infer any number of hypotheses from <em>A</em>, yet only some of those may generalise to <em>B</em>. How can one know which are likely to generalise? One strategy is to choose the shortest, equating the ability to compress information with the ability to generalise (a ``proxy for intelligence”). We examine this in the context of a mathematical formalism of enactive cognition. We show that compression is neither necessary nor sufficient to maximise performance (measured in terms of the probability of a hypothesis generalising). We formulate a proxy unrelated to length or simplicity, called weakness. We show that if tasks are uniformly distributed, then there is no choice of proxy that performs at least as well as weakness maximisation in all tasks while performing strictly better in at least one. In other words, weakness is the pareto optimal choice of proxy. In experiments comparing maximum weakness and minimum description length in the context of binary arithmetic, the former generalised at between <em>1.1</em> and <em>5</em> times the rate of the latter. We argue this demonstrates that weakness is a far better proxy, and explains why Deepmind's Apperception Engine is able to generalise effectively.</p>

<p>To make accurate inferences in an interactive setting, an agent must not confuse passive observation of events with having participated in causing those events. The ``do'' operator formalises interventions so that we may reason about their effect. Yet there exist at least two pareto optimal mathematical formalisms of general intelligence in an interactive setting which, presupposing no explicit representation of intervention, make maximally accurate inferences. We examine one such formalism. We show that in the absence of an operator, an intervention can still be represented by a variable. Furthermore, the need to explicitly represent interventions in advance arises only because we presuppose abstractions. The aforementioned formalism avoids this and so, initial conditions permitting, representations of relevant causal interventions will emerge through induction. These emergent abstractions function as representations of one’s self and of any other object, inasmuch as the interventions of those objects impact the satisfaction of goals. We argue (with reference to theory of mind) that this explains how one might reason about one's own identity and intent, those of others, of one's own as perceived by others and so on. In a narrow sense this describes what it is to be aware, and is a mechanistic explanation of aspects of consciousness.</p>