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Bolzano’s Theory of .i.meßbare Zahlen./i.. Insights and Uncertainties Regarding the Number Continuum
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SYSNO ASEP 0561783 Document Type E - Electronic Document R&D Document Type R&D Presentation (audio-visual, electronic documents. Documents released only in a form readable by a computer (eg . documents released on CD only), available only via the Internet, WEB presentation. Title Bolzano’s Theory of meßbare Zahlen. Insights and Uncertainties Regarding the Number Continuum Author(s) Fuentes Guillén, Elías (FLU-F) ORCID, RID, SAI Issue data Cham: Springer, 2022 Number of pages 38 s. Publication form Online - E Language eng - English Country NL - Netherlands Issue 2 Keywords Bernard Bolzano ; measurable numbers ; number continuum ; real numbers ; nineteenth-century mathematics Subject RIV AA - Philosophy ; Religion OECD category Philosophy, History and Philosophy of science and technology R&D Projects GJ19-03125Y GA ČR - Czech Science Foundation (CSF) Institutional support FLU-F - RVO:67985955 DOI https://doi.org/10.1007/978-3-030-19071-2_96-2 Annotation During the first half of the 1830s, and as part of his project for a Größenlehre, Bernard Bolzano worked on a manuscript entitled Reine Zahlenlehre in which he introduced the notion of what he called “meßbare Zahlen”. The various additions and corrections to its three extant versions are evidence of an unfinished work, the definitive edition of which was not published until 1976. The present chapter casts light upon the links between, on the one hand, his theory of “measurable numbers” and its conceptual framework, and, on the other hand, his insights and uncertainties with regard to the notions of number and quantity prior to the writing of that work. While Bolzano’s proposal has usually been considered as an attempt at a theory of what nowadays is called the real-number continuum, this chapter shows that a more faithful reading must consider it as a pioneering and transitional theory of the number continuum which provided relevant insights into this latter but which remained, nonetheless, still bound to a not-yet-modern conception of mathematics and numbers. Workplace Institute of Philosophy Contact Chlumská Simona, chlumska@flu.cas.cz ; Tichá Zuzana, asep@flu.cas.cz Tel: 221 183 360 Year of Publishing 2023 Electronic address https://doi.org/10.1007/978-3-030-19071-2_96-2
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