Georg Cantor’s Ordinals, Absolute Infinity&Transparent Proof of the Well-Ordering Theorem Cantor’s 1899 Letter to Dedekind

• 作者: Hermann G.W.Burchard
• 来源期刊: 哲学研究:英文版
• 学科: 教育
• 关键词: WELL ORDERING THEOREM Burali-Forti’s PARADOX Kant’s Oneness Function
• 年，卷（期）: zxyjywb_2019,（8）
• 页码范围: 435-444
• 页数: 10页
• 分类号: G633.41

摘要

Georg Cantor’s absolute infinity, the paradoxical class Ω of all ordinals, a non-entity for which being called a “class” is an undeserved dignity, must be the ultimate vexation for mathematical philosophers who hold on to some residual 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) by taking the contrapositive of his suggestion and adding Zermelo’s choice function, resulting in a concise and uncomplicated proof of the Well-Ordering Theorem.