 At exactly the same time there appeared Carnap (1934), Logische Syntax der Sprache, which offered an account of analyticity for languages in which all logico-mathematical operators could make similar contributions to the status of a sentence as analytically true (or analytically false). Carnap, however, did this by employing axiomatizations involving all the various logico-mathematical operators, co-functioning in grammatically complex axioms. His approach was therefore quite unlike the more ‘natural’ one of Gentzen, which was single-operator focused. Moreover, the unnatural approach was still Carnap’s preferred choice in work as late as his Foundations of Logic and Mathematics (Carnap  1939).[44]  We mention Carnap in contrast with Gentzen here because of Gentzen’s tragic early death at the end of the Second World War. Who knows how Gentzen might have extended his exquisitely conceived inferentialist techniques to items on the broad logicist agenda? His writings appeared in English translation only in 1969 (see Gentzen 1934/1935 [1969]). Carnap, however, did survive to exert considerable influence on the thinking of a new generation of philosophers of mathematics on the problems and prospects for logicism; and he was able to do so from the mid-1930s, in the USA, writing in English. 