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- Title
BOLZANO'S MATHEMATICAL INFINITE.
- Authors
BELLOMO, ANNA; MASSAS, GUILLAUME
- Abstract
Bernard Bolzano (1781–1848) is commonly thought to have attempted to develop a theory of size for infinite collections that follows the so-called part–whole principle, according to which the whole is always greater than any of its proper parts. In this paper, we develop a novel interpretation of Bolzano's mature theory of the infinite and show that, contrary to mainstream interpretations, it is best understood as a theory of infinite sums. Our formal results show that Bolzano's infinite sums can be equipped with the rich and original structure of a non-commutative ordered ring, and that Bolzano's views on the mathematical infinite are, after all, consistent.
- Subjects
NONCOMMUTATIVE rings; NINETEENTH century
- Publication
Review of Symbolic Logic, 2023, Vol 16, Issue 1, p59
- ISSN
1755-0203
- Publication type
Article
- DOI
10.1017/S1755020321000010