Science and art have long recognized that perceptual experience depends on the involvement of the experiencer. In art history, this idea is captured by Ernst Gombrich’s ‘beholder’s share’. In neuroscience, it traces to Helmholtz’s concept of ‘perception as inference’, which is enjoying renewed prominence in the guise of ‘prediction error minimization’ (PEM) or the ‘Bayesian brain’. The shared idea is that our perceptual experience – whether of the world, of ourselves, or of an artwork – depends on the active ‘top-down’ interpretation of sensory input. Perception becomes a generative act, in which perceptual, cognitive, affective, and sociocultural expectations conspire to shape the brain’s ‘best guess’ of the causes of sensory signals. In this article, I explore the parallels between the Bayesian brain and the beholders’ share, illustrated, somewhat informally, with examples from Impressionist, Expressionist, and Cubist art. By connecting phenomenological insights from these traditions with the cognitive neuroscience of predictive perception, I outline a reciprocal relationship in which art reveals phenomenological targets for neurocognitive accounts of subjectivity, while the concepts of predictive perception may in turn help make mechanistic sense of the beholder’s share. This is not standard neuroaesthetics – the attempt to discover the brain basis of aesthetic experience – nor is it any kind of neuro-fangled ‘theory of art’. It is instead an examination of one way in which art and brain science can be equal partners in revealing deep truths about human experience.