Philosophy of Mathematics Seminar


Philosophy of Mathematics seminar


Anna Bellomo, Vienna

Bolzano’s Measurable Numbers  

In section VII of his Reine Zahlenlehre, Bernard Bolzano (1781-1848) introduces a special class of infinitary numbers which he calls measurable. Bolzano’s text is dense and difficult to interpret, thus, despite several excellent attempts in the literature at coming to terms with its mathematical and conceptual import, there are still several points of his construction that deserve further scrutiny. In this talk I will focus on one such point, namely, the theorem in § 107 (see Steve Russ (ed.), The Mathematical Works of Bernard Bolzano, Oxford University Press, 2004, pp. 412-415), and evaluate its significance for regarding Bolzano’s measurable numbers as an instance of the ‘arithmetization of analysis’ he has contributed to in other writings.