 Gödel himself developed an argument against the conventionalist philosophy of mathematics of logical positivism, and of Carnap’s in particular, based on the incompleteness results (Gödel 1953/9). It is discussed in Goldfarb and Ricketts 1992; Ricketts 1995; Goldfarb 1995; Crocco 2003; Awodey &amp; Carus 2003, 2004; Tennant 2008. 