Bradley insists that appearances are real — they are facts, they happen, they matter. The sensory world of colours, sounds, and textures; the social world of persons, institutions, and histories; the inner world of thoughts, feelings, and desires — all of these are genuinely real. What they are not is ultimate: they do not exist in the mode they present themselves as existing, as independent, self-subsistent items standing in external relations. They are appearances of the Absolute — aspects or manifestations of the one experiential whole that, when taken as independently real, generate contradictions.
Bradley's test for ultimate reality is self-consistency: what is real must be able to be thought without contradiction. Applied to the categories of appearance — things, qualities, relations, space, time, the self — the test consistently fails: each generates contradictions when examined carefully. The self, for instance, seems to require both that it is unified (the same self over time) and that it changes (it has different states at different times), and Bradley argues that no adequate account can be given of how it can be both. The Absolute alone — the undifferentiated, non-relational whole — survives the test.
One of Bradley's most interesting claims is that truth and reality come in degrees. No finite judgment is simply true or simply false: every judgment captures some aspect of the Absolute from a particular, partial perspective, and is therefore partly true and partly false. Mathematical truths are more adequate to reality than perceptual judgments; perceptual judgments are more adequate than mere feelings; but none is absolutely true, because none captures the Absolute in its completeness. Absolute truth would be the complete judgment that is identical with the Absolute itself — and no finite mind can make that judgment.
The relationship between appearance and reality is the organising theme of the entire book. The doctrine of degrees of truth is developed in Chapter XXIV of Part II and was extensively discussed by Harold Joachim in The Nature of Truth (1906).