If structuralism is a true view of mathematics on which the statements of mathematicians are taken 'at face value', then there are both structures on which (1) classical second-order arithmetic is a correct report, and structures on which (2) intuitionistic second-order arithmetic is correct. An argument due to Dedekind then proves that structures (1) and structures (2) are isomorphic. Consequently, first- and second-order statements true in structures (1) must hold in (2), and conversely. Since instances of the general law of the excluded third fail in structures (2) but hold in (1), a contradiction ensues.
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