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At the core of attitudes to the axiomatic method that may be called realist is the view that ‘undefined’ does not entail ‘meaningless’ and so it may be possible to provide a meaning for the primitive terms of our theory in advance of laying down the axioms: perhaps they are previously understood terms of ordinary language; or, if not, we may be able to establish the intended meanings by means of what Frege calls elucidations — informal explanations which suffice to indicate the intended meanings of terms. But elucidation, Frege says, is inessential. It merely serves the purpose of mutual understanding among investigators, as well as of the communication of science to others. We may relegate it to a propaedeutic. It has no place in the system of a science; no conclusions are based on it. Someone who pursued research only by himself would not need it
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