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45A Reassessment of Cantorian Abstraction based on the $$\varepsilon $$ ε -operatorSynthese 200 (5): 1-26. 2022.Cantor’s abstractionist account of cardinal numbers has been criticized by Frege as a psychological theory of numbers which leads to contradiction. The aim of the paper is to meet these objections by proposing a reassessment of Cantor’s proposal based upon the set theoretic framework of Bourbaki—called BK—which is a First-order set theory extended with Hilbert’s \-operator. Moreover, it is argued that the BK system and the \-operator provide a faithful reconstruction of Cantor’s insights on card…Read more
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52A Reassessment of Cantorian Abstraction based on the ε-operatorSynthese. forthcoming.Cantor's abstractionist account of cardinal numbers has been criticized by Frege as a psychological theory of numbers which leads to contradiction. The aim of the paper is to meet these objections by proposing a reassessment of Cantor's proposal based upon the set theoretic framework of Bourbaki - called BK - which is a First-order set theory extended with Hilbert's ε-operator. Moreover, it is argued that the BK system and the ε-operator provide a faithful reconstruction of Cantor's insights on …Read more
Munich, Bayern, Germany
Areas of Specialization
Logic and Philosophy of Logic |
Philosophy of Mathematics |