I recently heard some speculation on the origin of the term “Hilbert system” for the axiomatic systems that are used to inflict pain on logic students, particularly at the start of proof theory classes. A long time ago, at least when Gentzen wrote, they were called logistic systems. The first publication in which they were called “Hilbert systems” seems to have been Entailment, vol. 1. Does anyone know if there are earlier uses? I’d be quite happy if that turned out to be the origin of the term.

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