03759nam 22006615 450 991059505370332120240221142827.03-030-77799-510.1007/978-3-030-77799-9(MiAaPQ)EBC7097823(Au-PeEL)EBL7097823(CKB)24866013600041(DE-He213)978-3-030-77799-9(PPN)264958632(EXLCZ)992486601360004120220917d2022 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierAxiomatic Thinking II /edited by Fernando Ferreira, Reinhard Kahle, Giovanni Sommaruga1st ed. 2022.Cham :Springer International Publishing :Imprint: Springer,2022.1 online resource (293 pages)Print version: Ferreira, Fernando Axiomatic Thinking II Cham : Springer International Publishing AG,c2023 9783030777982 Includes bibliographical references.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.Mathematical logicMathematicsPhilosophyMathematicsHistoryMathematical Logic and FoundationsPhilosophy of MathematicsHistory of Mathematical SciencesAxiomesthubLlibres electrònicsthubMathematical logic.MathematicsPhilosophy.Mathematics.History.Mathematical Logic and Foundations.Philosophy of Mathematics.History of Mathematical Sciences.Axiomes516516Ferreira Fernando1958-Kahle ReinhardSommaruga-Rosolemos GiovanniMiAaPQMiAaPQMiAaPQBOOK9910595053703321Axiomatic thinking II3027980UNINA