Title: Frege's Frege Arithmetic

Speaker: Francesca Boccuni (University Vita-Salute San Raffaele)

Time: May 29th (Friday), 15:00 - 18:00

Location: Room 109, Lee Shau Kee Humanities Buildings No.3 (李兆基人文学苑3号楼109)

Abstract:

In recent articles, Richard Kimberly Heck argues that a significant conceptual gap separates (Neologicist) Frege Arithmetic (FA) from ordinary arithmetic. The latter concerns finite cardinals employed in everyday contexts, whereas FA exceeds the conceptual resources required for ordinary arithmetical reasoning. This article investigates whether a consistent system of Frege's Basic Law V, and maximally faithful to Frege's original project—termed Frege's Frege Arithmetic (FFA)—is better suited than FA to capture ordinary arithmetic. By analysing the proof-theoretic strength (in Heck’s sense) of FFA, I will argue that FFA is in fact conceptually stronger than FA, because of Frege's definition of cardinals as equivalence classes closed under equinumerosity. On the basis of Heck's considerations, the article suggests that Frege's original project offers less justification for our knowledge of ordinary arithmetic than Neologicism.