 In this passage we find an early version of a representation theorem argument for probabilistic norms on partial belief and for expected utility theory, of the kind later made popular by Savage. (See also Skyrms 1987, and the entry on  normative theories   of rational choice: expected utility, §2.2). It is dubious,  however, that Ramsey really proved that the stated laws must be true of any consistent set of partial beliefs. Amongst the axioms of his representation theorem for utilities are several non-necessary conditions, as well as conditions (like those regarding the ethically neutral proposition) which are not plausible as conditions of consistency on preferences. More importantly, Ramsey’s ‘proof’ is grounded in strong theoretical assumptions about the connection between degrees of belief and preferences, which Ramsey admits are idealizations.