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

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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.
v2; introduced standardised ACI compliant notation for citations; 11 pages; an HTML version is available at http://alixcomsi.com/CTG_06_Consequences_Bringsjord.htm

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General Mathematics, 03B10

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http://salesiana.dossiersoluciones.com/handle/123456789/67171

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0304308
 http://arxiv.org/abs/math/0304308

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arXiv