Gödel himself wrote, but did not publish, a searching critique of Carnap’s position (Gödel, 1953–9). Gödel focuses not on his first incompleteness theorem but on the corollary he drew in his second theorem: that, under a certain natural characterization of the property of consistency, a characterization which can be given mathematically via his arithmetization of syntax, no formal theory of the type Gödel considered could prove its own consistency. He argued that Carnap, in order to make good hi