LEADER 03727nam 22006015 450 001 9910731462303321 005 20240619121706.0 010 $a3-031-27304-4 024 7 $a10.1007/978-3-031-27304-9 035 $a(MiAaPQ)EBC30591730 035 $a(Au-PeEL)EBL30591730 035 $a(DE-He213)978-3-031-27304-9 035 $a(PPN)272261408 035 $a(CKB)26895859000041 035 $a(EXLCZ)9926895859000041 100 $a20230610d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPhilosophy of Mathematics in Antiquity and in Modern Times /$fby Ulrich Felgner 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2023. 215 $a1 online resource (314 pages) 225 1 $aScience Networks. Historical Studies,$x2296-6080 ;$v62 311 08$aPrint version: Felgner, Ulrich Philosophy of Mathematics in Antiquity and in Modern Times Cham : Springer International Publishing AG,c2023 9783031273032 327 $aThe concept of mathematics -- Plato's philosophy of mathematics -- The Aristotelian conception of mathematics -- The axiomatic method of Euclid -- Finitism in Greek mathematics -- The paradoxes of Zeno -- On certainty in mathematics -- The Cartesian nativism, the Prometheus myth, Augustinian illuminism, and Cartesian rationalism -- John Locke's thoughts on mathematics -- Rationalism -- Empiricism in mathematics -- Immanuel Kant's conception of mathematics -- Psychologism in mathematics -- Logicism -- The concept of "set" -- Contemporary Platonism -- The problem of non-constructive proofs of existence -- The formal and the contentual position -- Dedekind and the emergence of structuralism -- Hilbert's critical philosophy -- Epilogue -- Index of names -- Index of subjects -- Index of abbreviations. 330 $a»Philosophy of Mathematics« is understood, in this book, as an effort to clarify such questions that mathematics itself raises but cannot answer with its own methods. These include, for example, questions about the ontological status of mathematical objects (e.g., what is the nature of mathematical objects?) and the epistemological status of mathematical theorems (e.g., from what sources do we draw when we prove mathematical theorems?). The answers given by Plato, Aristotle, Euclid, Descartes, Locke, Leibniz, Kant, Cantor, Frege, Dedekind, Hilbert and others will be studied in detail. This will lead us to deep insights, not only into the history of mathematics, but also into the conception of mathematics as it is commonly held in the present time. The book is a translation from the German, however revised and considerably expanded. Various chapters have been completely rewritten. 410 0$aScience Networks. Historical Studies,$x2296-6080 ;$v62 606 $aLogic, Symbolic and mathematical 606 $aGeometry 606 $aMathematical Logic and Foundations 606 $aGeometry 606 $aFilosofia de la matemàtica$2thub 606 $aHistòria de la matemàtica$2thub 608 $aLlibres electrònics$2thub 615 0$aLogic, Symbolic and mathematical. 615 0$aGeometry. 615 14$aMathematical Logic and Foundations. 615 24$aGeometry. 615 7$aFilosofia de la matemàtica 615 7$aHistòria de la matemàtica 676 $a510.1 676 $a510.1 700 $aFelgner$b Ulrich$056790 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910731462303321 996 $aPhilosophy of Mathematics in Antiquity and in Modern Times$93395580 997 $aUNINA