Three beliefs that lend illusory legitimacy to Cantor's diagonal argument

Bhupinder Singh Anand

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Three beliefs that lend illusory legitimacy to Cantor's diagonal argument

Bhupinder Singh Anand

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Abstract

Whatever other beliefs there may remain for considering Cantor's diagonal argument as mathematically legitimate, there are three that, prima facie, lend it an illusory legitimacy; they need to be explicitly discounted appropriately. The first, Cantor's diagonal argument defines a non-countable Dedekind real number; the second, Goedel uses the argument to define a formally undecidable, but interpretively true, proposition; and the third, Turing uses the argument to define an uncomputable Dedekind real number.

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Bhupinder Singh Anand. 2003-05-17. Three beliefs that lend illusory legitimacy to Cantor's diagonal argument. https://arxiv.org/abs/math/0304310

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