 As noted above, historically, the primary interest in the epsilon calculus was as a means to obtaining consistency proofs. Hilbert’s lectures from 1917–1918 already note that one can easily prove the consistency of propositional logic, by taking propositional variables and formulae to range over truth values 0 and 1, and interpreting the logical connectives as the corresponding arithmetic operations. Similarly, one can prove the consistency of predicate logic (or the pure epsilon calculus), by specializing to interpretations where the universe of discourse has a single element. These considerations suggest the following more general program for proving consistency: