Hilbert’s second problem was different from the others, because it was not so much a mathematical question as a question about mathematics itself. He began with a full-throated endorsement of the formalist approach to mathematics: When we are engaged in investigating the foundations of a science, we must set up a system of axioms which contains an exact and complete description of the relations subsisting between the elementary ideas of that science. The axioms so set up are at the same time the definitions of those elementary ideas; and no statement within the realm of the science whose
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