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Full Idea
Elementary logic cannot characterize the usual mathematical structures, but seems to be distinguished by its completeness.
Gist of Idea
Elementary logic is complete, but cannot capture mathematics
Source
Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2)
Book Ref
'Philosophy of Logic: an anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.37