LEADER 04344nam 22006735 450 001 9910999778503321 005 20251204210800.0 010 $a9783031623875$b(eBook) 024 7 $a10.1007/978-3-031-62387-5 035 $a(CKB)38485066500041 035 $a(DE-He213)978-3-031-62387-5 035 $a(MiAaPQ)EBC32013217 035 $a(Au-PeEL)EBL32013217 035 $a(EXLCZ)9938485066500041 100 $a20250417h20252025 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 04$aThe Palgrave companion to the philosophy of set theory /$feditors, Carolin Antos, Neil Barton, Giorgio Venturi 210 1$aCham :$cSpringer,$d[2025] 210 4$dİ2025 215 $a1 online resource (xv, 393 pages) 225 1 $aPalgrave Companions,$x3004-9180 311 08$a9783031623868 320 $aIncludes bibliographical references and index. 327 $aChapter 1. Introduction -- Part I Epistemology -- Chapter 2.The Problem of Existence forDescriptivism About the Reference of Set-Theoretic Expressions -- Chapter 3. Intuition and Observation -- Chapter 4. Arealism, ThinRealism, and the Problem of Extrinsic Evidence -- Chapter 5. The Hidden Use of New Axioms -- Part II Formal Theories -- Chapter 6. The Iterative Notion of Function and the Iterative Notion of Set -- Chapter 7. What Set Theory Could Not Be About -- Chapter 8. Hamkins? Analogy Between Set Theory and Geometry: Pluralism by Leveling Up? -- Chapter 9. Basic Mathematics Beyond Classicality -- Part III Ontology -- Chapter 10. Iteration and Dependence Again -- Chapter 11. What Is Forcing Potentialism? -- Chapter 12. On the Consistency of Height and Width Potentialism -- Chapter 13. Higher-Order Platonism and Multiversism -- Chapter 14. Language, Models, and Reality: Weak Existence and a Threefold Correspondence. 330 $aThis volume showcases some of the up-and-coming voices of an emerging field - the philosophy of set theory - which in recent years has gained prominence in the philosophy of mathematics. The chapters in this volume both present new topics and propose solutions to old problems. It contains a broad picture of the philosophy of set theory, examining questions from epistemology and ontology, whilst touching on the use of formal theories in the study of mathematical infinity. Key features of this volume: ? Explores new and interesting connections between philosophy, set theory, and the study of infinity.? Considers questions intended to appeal to a wider audience in both philosophy and mathematical logic.? Examines three key areas of study: Epistemology, Formal Theories, and Ontology. The book provides a key reference text for future debates and is ideal for both newcomers to the philosophy of set theory and established researchers in the field. Carolin Antos, PhD, is an Assistant Professor for Theoretical Philosophy at the University of Konstanz. Neil Barton, PhD, is a Lecturer in the Department of Philosophy at the National University of Singapore. Giorgio Venturi, PhD, is a tenure-track Associate Professor at the Department of Civilization and Forms of Knowledge at the University of Pisa. 410 0$aPalgrave companions.$x3004-9180 606 $aSet theory$xPhilosophy 606 $aMathematics$xPhilosophy 606 $aLogic 606 $aKnowledge, Theory of 606 $aMetaphysics 606 $aPhilosophy of Mathematics 606 $aFormal Logic 606 $aEpistemology 606 $aMetaphysics 615 0$aSet theory$xPhilosophy. 615 0$aMathematics$xPhilosophy. 615 0$aLogic. 615 0$aKnowledge, Theory of. 615 0$aMetaphysics. 615 14$aPhilosophy of Mathematics. 615 24$aFormal Logic. 615 24$aEpistemology. 615 24$aMetaphysics. 676 $a510.1 702 $aAntos$b Carolin$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aBarton$b Neil$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aVenturi$b Giorgio$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910999778503321 996 $aThe Palgrave Companion to the Philosophy of Set Theory$94374959 997 $aUNINA