  In two of his last papers, ‘Principles of Finitist Mathematics’ and ‘The Formal Structure of Intuitionist Mathematics’ ([NP] 197–200), Ramsey sided with Weyl. It appears that he wanted to obtain arithmetic by adding quantifiers, with Weyl’s rules, to Skolem’s primitive recursive arithmetic. But he did not provide a rule of existential elimination and rules that he proposed in these papers appear to restrict formulas with quantifiers to those that can be converted to prenex normal form (with quantifiers prefixed on the left, followed with a quantifier-free matrix). In intuitionism, the law of the excluded middle applies to atomic formulas and, if quantifiers are in prenex normal form, the theory remains constructive. This is what Ramsey captured, but the result is not the full intuitionistic arithmetic, as not all intuitionistic formulas are equivalent to prenex formulas. In ‘Principles of Finitist Mathematics’, he stated that his rules provide “all the logical modes allowed by the finitists” ([NP] 201), but if he meant ‘intuitionism’, the claim was inaccurate.