Four views of arithmetical truth

Philosophical Quarterly 40 (159):155-168 (1990)
Charles Sayward
University of Nebraska, Lincoln
Four views of arithmetical truth are distinguished: the classical view, the provability view, the extended provability view, the criterial view. The main problem with the first is the ontology it requires one to accept. Two anti-realist views are the two provability views. The first of these is judged to be preferable. However, it requires a non-trivial account of the provability of axioms. The criterial view is gotten from remarks Wittgenstein makes in Tractatus 6.2-6.22 . It is judged to be the best of four views. It is also defended against objections.
Keywords Wittgenstein  Dummett  mathematical truth
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DOI 10.2307/2219808
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