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The distinction between hallucinations (false perceptions) and delusions (false beliefs) is reflected in the various theories about these positive symptoms. I have been particularly interested in the idea (from B Maher) that the fundamental problem is a disorder of perception, which patients try to understand using normal processes of belief formation. I shall review evidence that symptoms, such as delusions of control, can be understood in terms of a failure of self-monitoring, that is, a failure to predict the sensory consequences of our own actions, linked to disorders of long range connectivity. However, further experiments suggest that this perceptual disorder is not enough. There seems to be an additional abnormality of belief formation such that beliefs about abnormal sensations are accepted, despite their implausibility and rejection by other people. Finally I shall consider recent computational models of brain function derived from Bayes’ theorem (e.g. predictive coding), which suggest that there are no essential differences between mechanisms of perception and belief. In both cases the problem is to decide whether or not incoming evidence (e.g. sensations) requires that we should change our model of the world. This insight has important implications for our understanding of the positive symptoms of schizophrenia.