Dedekind’s Analysis of Number: Systems and Axioms
Wilfried Sieg,Dirk Schlimm +1 more
TLDR
In 1888 Hilbert made his Rundreise from Königsberg to other German university towns, he arrived in Berlin just as Dedekind’s Was sind und was sollen die Zahlen?About:
This article is published in Synthese.The article was published on 2005-10-01 and is currently open access. It has received 51 citations till now. The article focuses on the topics: Western philosophy & Formal epistemology.read more
Citations
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Chains of Life: Turing, Lebensform, and the Emergence of Wittgenstein’s Later Style
TL;DR: The notion of Lebensform in Wittgenstein's later philosophy is discussed in this paper, where it is argued that this constituted a substantive step forward in his attitude toward the notion of simplicity.
Methodology and metaphysics in the development of Dedekind's theory of ideals
TL;DR: In this article, a mathematician is asked to turn to the counsel of philosophers, in much the same way as a nation considering an action of dubious international legality is called upon to turning to the United Nations for guidance.
Journal ArticleDOI
Hilbert, logicism, and mathematical existence
TL;DR: David Hilbert’s early foundational views, especially those corresponding to the 1890s, are analysed here, and strong evidence is considered for the fact that Hilbert was a logicist at that time, following upon Dedekind's footsteps in his understanding of pure mathematics.
Journal ArticleDOI
On the creative role of axiomatics. The discovery of lattices by Schröder, Dedekind, Birkhoff, and others
TL;DR: Three different ways in which systems of axioms can contribute to the discovery of new notions are presented and they are illustrated by the various Ways in which lattices have been introduced in mathematics by Schröder et al.
References
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Book ChapterDOI
Was sind und was sollen die Zahlen
TL;DR: In this paper, the author verstehe unter einem Ding jeden Gegenstand unseres Denkens, and verstehen den Denkens unter den Dingen sprechen.
Book
Modern Algebra and the Rise of Mathematical Structures
TL;DR: The notion of mathematical structure is among the most pervasive ones in twentieth century mathematics as mentioned in this paper, and it has been widely adopted in other mathematical domains since the 1930s. But, what is a mathematical structure and what is the place of this notion within the whole fabric of mathematics?
Book ChapterDOI
Stetigkeit und irrationale Zahlen
TL;DR: In this paper, the authors present Betrachtungen, welche den Gegenstand dieser kleine Schrift bilden, stammen aus dem Herbst des Jahres 1858, and fuhlte dabei empfindlicher als jemals fruher den Mangel einer wissenschaftlichen Begrundung der Arithmetik.