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＜電子ブック＞
Axiomatic Thinking I / edited by Fernando Ferreira, Reinhard Kahle, Giovanni Sommaruga

版	1st ed. 2022.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2022
大きさ	XIV, 205 p. 9 illus., 4 illus. in color : online resource
著者標目	Ferreira, Fernando editor Kahle, Reinhard editor Sommaruga, Giovanni editor SpringerLink (Online service)
件　名	LCSH:Mathematical logic LCSH:Mathematics—Philosophy LCSH:Mathematics LCSH:History FREE:Mathematical Logic and Foundations FREE:Philosophy of Mathematics FREE:History of Mathematical Sciences
一般注記	Volume 1: History and Philosophy -- Axiomatisches Denken -- Part I: History and Philosophy -- Hilbert's Axiomatisches Denken -- Scope and Limits of Axiomatics -- The Semantic Function of the Axiomatic Method -- Aristotle's Relations: An Interpretation in Combinatory Logic -- The Two Sides of Modern Axiomatics: Dedekind and Peano, Hilbert and Bourbaki -- Notes for a Seminar in Axiomatic Reasoning -- Axiomatic Thinking, Identity of Proofs and the Quest for an Intensional Proof-Theoretic Semantics -- Proofs as Objects -- Where Do Axioms Come From? -- Panel Discussion on the Foundations of Mathematics. In this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert's axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics, computer science and elsewhere. The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of Hilbert's return to his foundational studies, which ultimately resulted in the establishment of proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used the opportunity to bring Paul Bernays back to Göttingen as his main collaborator in foundational studies in the years to come. The contributions are addressed to mathematical and philosophical logicians, but also to philosophers of science as well as physicists and computer scientists with an interest in foundations. Chapter 8 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com HTTP:URL=https://doi.org/10.1007/978-3-030-77657-2

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