Is there a duality in the classical acceptance of non-constructive, foundational, concepts as axiomatic?

Details Is there a duality in the classical acceptance of non-constructive, foundational, concepts as axiomatic? Is there a duality in the classical acceptance of non-constructive, foundational, concepts as axiomatic?

2003-04-21

arxiv.org/abs/math/0304308v2

Mathematics

General Mathematics

v2; introduced standardised ACI compliant notation for citations; 11 pages; an HTML version is available at http://alixcomsi

Scientific paper

We consider a philosophical question that is implicit in Selmer Bringsjord's paper, "The narrational case against Church's Thesis": If, as Mendelson argues, the classically accepted definitions of foundational concepts such as "partial recursive function", "function", "(Tarskian) truth", "set" etc. are vague and imprecise - hence possibly non-constructive and intuitionistically objectionable - then replacing one non-constructive concept by another may be psychologically unappealing, but it should be meta-mathematically valid and acceptable.

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