  Wittgenstein had hinted in the Tractatus at a logic-free equational calculus for arithmetic (6.02–6.031 &amp; 6.241), but Ramsey thought this to be a “ridiculously narrow view of mathematics” (1925a, [PP] 180), and wanted the convenience afforded by quantifiers. He assessed two alternatives to Wittgenstein, Thoralf Skolem’s proposal simply to do away with the quantifiers, in a paper where he introduced primitive recursive arithmetic (Skolem 1923 [1967]) and Hermann Weyl’s suggestion in ‘Über die neue Grundlagenkrise der Mathematik’ (Weyl 1921 [1998]) – the very paper in which he joined Brouwer in his critique of classical mathematics, – that universality should be understood in analogy with bank drafts, as ‘instructions for judgements’, while existence would be a ‘judgment abstract’, classical existence being compared to a treasure map that does not tell us where to find the treasure (Weyl 1921 [1998], 97–98). These explanations happen to justify (1.1) and (1.2) above. Weyl claimed further that (1.1) and (1.2) cannot be negated since one could not, say, survey infinitely many disjuncts, so the law of excluded middle would not hold. 