Seminar Series in Analytic Philosophy 2025-26: Session 3

Upper Logicist Ordinals

Bruno Jacinto (LanCog, University of Lisbon)

10 October 2025, 16:00 (Lisbon Time – WET)

Faculdade de Letras de Lisboa

Sala Mattos Romão [C201.J] (Departamento de Filosofia)

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 abstractionist characterizations of ordinals, and 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.