 To sustain his critique, Quine had to revive his and Tarski’s early doubts about Carnap’s methodological apparatus and dig even deeper. (Tarski also shared Quine’s misgivings about analyticity when they discussed these issues with Carnap at Harvard; see Mancosu 2005, Frost-Arnold 2013.) Their scepticism found its target in Carnap’s ingenious measures in Logical Syntax taken to preserve the thesis that mathematics is analytic from the ravages of Gödel’s incompleteness theorems. Gödel proved that every formal system strong enough to represent number theory contains a formula that is true but neither itself or its negation is provable in that system; such formulae—known since as Gödel sentences—are provable in a still stronger system which, however, also contains a formula of its own that is true but not provable in it (and neither is its negation). Commonly, Gödel’s proof is taken to have undermined the thesis of the analyticity of arithmetic. (For discussions of this challenge to Carnap’s logical syntax project, see Friedman 1988, 1999a, 2009, Goldfarb and Ricketts 1992, Richardson 1994, Awodey and Carus 2003, 2004.) Carnap responded by stating that arithmetic demands an infinite sequence of ever richer languages and by declaring analytic statements to be provable by non-finite reasoning (1934/37, §60a-d). This looked like fitting the bill on purely technical grounds, but it is questionable whether such reasoning may still count as syntactic. Nowadays, it is computational effectiveness that is taken to distinguish purely formal from non-formal, material reasoning. (Carnap’s move highlights the tension within Logical Syntax between formal and crypto-semantic reasoning: that the rigid syntacticism officially advertised there was at the same time undermined as its failings were being compensated—illegitimately so by official standards, e.g., by considering translatability a syntactic notion—points ahead to his acceptance of semantics in 1935, only one year after the publication of Logical Syntax and contrary to his disparagement of the notion of synthetic truth there. For a discussion of Carnap’s moves, see Coffa 1978, Ricketts 1996, Goldfarb 1997, Creath 1996, 1999.) It is no criticism that Carnap’s reconstruction of arithmetic was not standard logicism, but that Carnap unduly stretched the idea of formal reasoning is. Was he saved by his shift to semantics?