Structuralism and Isomorphism

Philosophia Mathematica (1):nkt024 (2013)
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Abstract

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 classical second-order arithmetic is a correct report, and structures on which intuitionistic second-order arithmetic is correct. An argument due to Dedekind then proves that structures and structures are isomorphic. Consequently, first- and second-order statements true in structures must hold in , and conversely. Since instances of the general law of the excluded third fail in structures but hold in , a contradiction ensues

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