Harvard Logic Colloquium: Donald Martin (UCLA)

Donald Martin (UCLA): Cantor's Grundlagen

Cantor’s early (1883) Grundlagen einer allgemeinen Mannigfaltigkeitslehre is badly organized and has
important errors and omissions. Nevertheless it is rich in content, and its concepts are in some ways
superior to Cantor’s later ones.

I will mainly concentrate on a few aspects of Grundlagen: (1) what might be called Cantor’s quasiaxiomatic,
iterative account of ordinal numbers; (2) the role that something like a Replacement Axiom
plays in this account; (3) the relation between the Grundlagen notion of absolute infinity and Cantor’s
later notion of inconsistent multiplicities.