Language models (LMs) can exhibit human-like behaviour, but it is unclear how to describe this behaviour without undue anthropomorphism. We formalise a behaviourist view of LM character traits: qualities such as truthfulness, sycophancy, and coherent beliefs and intentions, which may manifest as consistent patterns of behaviour. Our theory is grounded in empirical demonstrations of LMs exhibiting different character traits, such as accurate and logically coherent beliefs and helpful and harmless intentions. We infer belief and intent from LM behaviour, finding their consistency varies with model size, fine-tuning, and prompting. In addition to characterising LM character traits, we evaluate how these traits develop over the course of an interaction. We find that traits such as truthfulness and harmfulness can be stationary, i.e., consistent over an interaction, in certain contexts but may be reflective in different contexts, meaning they mirror the LM’s behaviour in the preceding interaction. Our formalism enables us to describe LM behaviour precisely and without undue anthropomorphism.