People often form polarized beliefs about others. In a clinical setting this is referred to as a dichotomous or ‘split’ representation of others, whereby others are not imbued with possessing mixtures of opposing properties. Here, we formalise these accounts as an oversimplified categorical model of others’ internal, intentional, states. We show how a resulting idealization and devaluation of others can be stabilized by attributing unexpected behaviour to fictive external factors. For example, under idealization, less-than-perfect behaviour is attributed to unfavourable external conditions, thereby maintaining belief in the other’s goodness. This feature of the model accounts for how extreme beliefs are buffered against counter-evidence, while at the same time being prone to precipitous changes of polarity. Equivalent inference applied to the self creates an oscillation between self-aggrandizement and self-deprecation, capturing oscillatory relational and affective dynamics. Notably, such oscillatory dynamics arise out of the Bayesian nature of the model, wherein a subject arrives at the most plausible explanation for their observations, given their current expectations. Thus, the model we present accounts for aspects of splitting that appear ‘defensive’, without the need to postulate a specific defensive intention. By contrast, we associate psychological health with a fine-grained representation of internal states, constrained by an integrated prior, corresponding to notions of ‘character’. Finally, the model predicts that extreme appraisals of self or other are associated with causal attribution errors.