Georg Cantor’s Ordinals, Absolute Infinity & Transparent Proof of the Well-Ordering Theorem

Philosophy Study 9 (8) (2019)
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Abstract

Georg Cantor's absolute infinity, the paradoxical Burali-Forti class Ω of all ordinals, is a monstrous non-entity for which being called a "class" is an undeserved dignity. This must be the ultimate vexation for mathematical philosophers who hold on to some residual sense of realism in set theory. By careful use of Ω, we can rescue Georg Cantor's 1899 "proof" sketch of the Well-Ordering Theorem––being generous, considering his declining health. We take the contrapositive of Cantor's suggestion and add Zermelo's choice function. This results in a concise and uncomplicated proof of the Well-Ordering Theorem.

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