Paradoxes of Early Set Theory
Paradoxes of Early Set Theory

Summary/Abstract: The paradoxes of set theory, usually connected with the names of Russell, Zermelo, or Burali-Forti, are concerned with the contradictory notion of ‘the set of all sets’. A further consideration of the topic, going back to the mathematical and even philosophical investigations of Cantor himself, could prompt interesting historical reassessments and reveal new insights into the configuration of set theory. I will show that Cantor’s adherence to some concepts such as absolute actual infinite or consistent and inconsistent multiplicities, together with the rejection of the principle of comprehension are fundamentally connected with his outlook on the paradoxes and also with the way he introduced and configured the basic concepts of set theory - the primitive notion of set, the transfinite numbers, the future principle of well-ordering - and their role as the foundations of mathematics.

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