Abstract:   Ordinals are commonly identified with particular kinds of sets. This identification is, however, highly implausible. Accordingly, in this talk I develop an “upper logicist” characterization of ordinals inspired by (i) Cantor’s view that ordinals are abstractions of well-orderings, and (ii) Russell’s view that such abstractions are higher-order entities. After reviewing important challenges to Florio & Leach-Krouse’s (2017) recent logicism about ordinals, I will show that the upper logicist characterization does not fall prey to those challenges. I will conclude by sketching how my characterization paves the way for a defense of Upper Logicism – in the sense of (Jacinto 2024) – about ordinals as well as about sets.

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Department of Mathematics 
University of Évora