In the book Das Kontinuum (1918), Hermann Weyl presents a coherent and sophisticated approach to analysis from a predicativist perspective. In the first chapter of (Weyl 1918), Weyl introduces a predicative concept of set, according to which sets are built ‘from the bottom up’ starting from the natural numbers. Weyl clearly contrasts this predicative concept of set with the concept of arbitrary set, which he finds wanting, especially when working with infinite sets. In the second chapter of Das Kontinuum, he goes on to show that large portions of 19th century analysis can be developed on the basis of his predicative concept of set.

Das Kontinuum inspired fundamental ideas in mathematical logic and beyond, such as the logical analysis of predicativity of the 1950-60’s, Solomon Feferman’s work on predicativity and Errett Bishop’s constructive mathematics. The seeds of Das Kontinuum are already visible in the early (Weyl 1910), where Weyl, among other things, offers a clarification of Zermelo’s axiom schema of Separation.

In this talk, I examine Weyl’s predicative concept of set in (Weyl 1918) and discuss its origins in (Weyl 1910).

Bibliography

  • Weyl, H., 1910, Über die Definitionen der mathematischen Grundbegriffe, Mathematischnaturwissenschaftliche Blätter, 7, pp. 93-95 and pp. 109-113.
  • Weyl, H., 1918, Das Kontinuum. Kritische Untersuchungen über die Grundlagen der Analysis, Veit, Leipzig. Translated in English, Dover Books on Mathematics, 2003.