1 March 2022, Philmath / EXPRESS Seminar, Anna Bellomo

Section VII of Bolzano’s Reine Zahlenlehre (RZ) introduces a special class of numbers, the measurable numbers, which constitute an early attempt at a rigorous treatment of the real number continuum. It remains to be settled, however, whether the RZ VII treatment is an instance of the ‘arithmetization of analysis’ Bolzano is often considered a pioneer of. In this talk I will offer a detailed analysis of Bolzano's RZ VII which leads me to conclude that Bolzano's measurable numbers cannot fully be described as an attempt at arithmetizing analysis – rather, they are still very much part of a traditional picture of mathematics as the science of quantity.

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