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The quote by S. C. Kleene, from Metamathematics, (New York:
van Nostrand, 1952):
"(Formalization) will not be finished until all the properties or
undefined terms which matter for the decutction of theorems have been expressed
by axioms. Then is should be possible to perform the deductions treating the
technical terms as words in themselves without meaning. For to say that they
have meanings necessary to the deduction of the theorems, other than what they
derive from the axioms which govern them, amount to saying that not all of their
properties which matter for the deductions have been expressed by axioms. When
the meanings of the technical terms are thus left out of account, we have
arrived at the standpoint of formal axiomatics."
Judith
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