LEADER 03759nam 22006615 450 001 9910595053703321 005 20240221142827.0 010 $a3-030-77799-5 024 7 $a10.1007/978-3-030-77799-9 035 $a(MiAaPQ)EBC7097823 035 $a(Au-PeEL)EBL7097823 035 $a(CKB)24866013600041 035 $a(DE-He213)978-3-030-77799-9 035 $a(PPN)264958632 035 $a(EXLCZ)9924866013600041 100 $a20220917d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAxiomatic Thinking II /$fedited by Fernando Ferreira, Reinhard Kahle, Giovanni Sommaruga 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (293 pages) 311 08$aPrint version: Ferreira, Fernando Axiomatic Thinking II Cham : Springer International Publishing AG,c2023 9783030777982 320 $aIncludes bibliographical references. 327 $aVolume 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. . 330 $aIn 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. 606 $aMathematical logic 606 $aMathematics$xPhilosophy 606 $aMathematics 606 $aHistory 606 $aMathematical Logic and Foundations 606 $aPhilosophy of Mathematics 606 $aHistory of Mathematical Sciences 606 $aAxiomes$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematical logic. 615 0$aMathematics$xPhilosophy. 615 0$aMathematics. 615 0$aHistory. 615 14$aMathematical Logic and Foundations. 615 24$aPhilosophy of Mathematics. 615 24$aHistory of Mathematical Sciences. 615 7$aAxiomes 676 $a516 676 $a516 702 $aFerreira$b Fernando$f1958- 702 $aKahle$b Reinhard 702 $aSommaruga-Rosolemos$b Giovanni 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910595053703321 996 $aAxiomatic thinking II$93027980 997 $aUNINA