Earlier accounts of belief typically presupposed a subject — an "I" — who stands in a relation to a proposition. Russell, having dissolved the Cartesian subject, must give a different account. A belief is a disposition of the organism: to believe that p is to be disposed to behave in ways that would be appropriate if p were true. This behaviourist strain in Russell's account is qualified by his recognition that dispositions involve internal states — that there are neurological or psychological facts that ground the behavioural dispositions — but the outer behaviour is what provides the evidential basis for belief attribution.
Desire, similarly, is analysed in terms of goal-directed behaviour: to desire something is to be in a state that causes behaviour aimed at producing that thing, and that is extinguished when the thing is obtained. Russell insists that we often do not know what we desire until we have obtained it and noticed that the behaviour stops — a point that anticipates debates about the opacity of mental states. He also notes that introspective reports of desire are unreliable: the reasons we give for our actions are often post-hoc rationalisations rather than accurate reports of their causes.
The most technically demanding part of Russell's account concerns the content of beliefs: what makes a belief a belief about something in particular. He analyses beliefs not as simple two-term relations (subject believes proposition) but as multiple-relation facts involving the believing subject and the several constituents of what is believed. This "multiple relation theory of judgment" was attacked by Wittgenstein, who pointed out that it failed to explain how the constituents of a belief are unified into something that is true or false — a criticism that forced Russell to significantly revise his account.
The analysis of belief and desire occupies Chapters 12–14 of The Analysis of Mind (1921). Wittgenstein's criticism of the multiple-relation theory is recorded in Russell's own notebooks and in his correspondence; it contributed to his abandonment of the theory in his later work.
