 In a footnote, Ramsey adds that \(\omega_1\) must imply \(p\), and \(\omega_3\) must imply \(\neg{p}\). The definition makes sense in light of the background assumptions (6.1)–(6.3) above: the world \(\omega_2\) has the same utility as the gamble ‘\(\omega_1\) if \(p\), \(\omega_3\) otherwise’ just in case