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＜電子ブック＞
Axiomatic Thinking II / 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
本文言語	英語
大きさ	XIV, 287 p. 45 illus., 9 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  全ての件名で検索 LCSH:Mathematics LCSH:History FREE:Mathematical Logic and Foundations FREE:Philosophy of Mathematics FREE:History of Mathematical Sciences
一般注記	Volume 2: Logic, Mathematics, and other Sciences -- Part II: Logic -- A Framework for Metamathematics -- Simplified Cut Elimination for Kripke-Platek Set Theory -- On the Performance of Axiom Systems -- Well-Ordering Priciples in Proof Theory and Reverse Mathematics -- Part III: Mathematics -- Reflections on the Axiomatic Approach to Continuity -- Abstract Generality, Simplicity, Forgetting, and Discovery -- Varieties of Infiniteness in the Existence of Infinitely Many Primes -- Axiomatics as a Functional Strategy for Complex Proofs: the Case of Riemann Hypothesis -- Part IV: Other Sciences -- What is the Church-Turing Thesis? -- Axiomatic Thinking in Physics--Essence or Useless Ornament? -- Axiomatic Thinking--Applied to Religion. 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 HTTP:URL=https://doi.org/10.1007/978-3-030-77799-9

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