Hermann Weyl and the roots of mathematical logic
Hermann Weyl’s book Das Kontinuum [2] presents a coherent and sophisticated approach to analysis from a predicativist perspective. In the first chapter of [2], Weyl introduces a system of predicative sets, built “from the bottom up” starting from the natural numbers. He then goes on to show that large portions of 19th century analysis can be developed on that predicative basis. Das Kontinuum anticipated and inspired fundamental ideas in mathematical logic, ideas that we find in the logical analysis of predicativity of the 1950-60’s, in Solomon Feferman’s work on predicativity and in Errett Bishop’s constructive mathematics. The seeds of Das Kontinuum are already visible in the early [1], where Weyl, among other things, offers a clarification of Zermelo’s axiom schema of Separation. In this talk, I examine key intriguing ideas in [1], ideas that witness important debates among mathematicians at the beginning of the 20th century. I then argue that aspects of [1] foreshadow fundamental features of Das Kontinuum. This allows us to consider [2] under the new light offered by [1].
References
- [1]
- Weyl, H., 1910, Über die Definitionen der mathematischen Grundbegriffe, Mathematisch-naturwissenschaftliche Blätter, 7, pp. 93–95 and pp. 109–113.
- [2]
- Weyl, H., 1918, Das Kontinuum. Kritische Untersuchungen über die Grundlagen der Analysis, Veit, Leipzig. Translated in English, Dover Books on Mathematics, 2003. (Page references are to the translation).
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