LEADER 03675nam 22005655 450 001 9910552711503321 005 20250520153220.0 010 $a9783030897314$b(electronic bk.) 010 $z9783030897307 024 7 $a10.1007/978-3-030-89731-4 035 $a(MiAaPQ)EBC6914937 035 $a(Au-PeEL)EBL6914937 035 $a(CKB)21382871500041 035 $a(DE-He213)978-3-030-89731-4 035 $a(EXLCZ)9921382871500041 100 $a20220307d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Making of Mathematics $eHeuristic Philosophy of Mathematics /$fby Carlo Cellucci 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (457 pages) 225 1 $aSynthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science,$x2542-8292 ;$v448 311 08$aPrint version: Cellucci, Carlo The Making of Mathematics Cham : Springer International Publishing AG,c2022 9783030897307 320 $aIncludes bibliographical references and index. 327 $a1. Introduction -- Part I. Heuristic vs. Mainstream. 2. Mainstream Philosophy of Mathematics -- 3. Heuristic Philosophy of Mathematics -- Part II. Discourse on Method. 4. The Question of Method -- 5. Analytic Method -- 6. Analytic-Synthetic Method and Axiomatic Method -- 7. Rules of Discovery -- 8. Theories -- Part III. The Mathematical Process. 9. Objects -- 10. Demonstrations -- 11. Definitions -- 12. Diagrams -- 13. Notations -- Part IV. The Functionality of Mathematics. 14. Explanations -- 15. Beauty -- 16. Applicability -- Part V. Conclusion. 17. Knowledge, Mathematics, and Naturalism -- 18. Concluding Remarks -- Index. 330 $aMainstream philosophy of mathematics, namely the philosophy of mathematics that has prevailed for the past century, claims that the philosophy of mathematics cannot concern itself with the making of mathematics, in particular discovery, but only with finished mathematics, namely mathematics presented in finished form. On this basis, mainstream philosophy of mathematics argues that mathematics is theorem proving by the axiomatic method. This, however, is untenable because it is incompatible with Gödel?s incompleteness theorems, and cannot account for many features of mathematics. This book offers an alternative approach, heuristic philosophy of mathematics, according to which the philosophy of mathematics can concern itself with the making of mathematics, in particular discovery. On this basis, the book argues that mathematics is problem solving by the analytic method, and that this can account for all the main features of mathematics: mathematical method, objects, demonstrations,definitions, diagrams, notations, explanations, beauty, applicability, and knowledge. 410 0$aSynthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science,$x2542-8292 ;$v448 606 $aMathematics$xPhilosophy 606 $aMathematics 606 $aHistory 606 $aPhilosophy of Mathematics 606 $aHistory of Mathematical Sciences 615 0$aMathematics$xPhilosophy. 615 0$aMathematics. 615 0$aHistory. 615 14$aPhilosophy of Mathematics. 615 24$aHistory of Mathematical Sciences. 676 $a510.1 676 $a510.1 700 $aCellucci$b Carlo$045650 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910552711503321 996 $aThe Making of Mathematics$92803767 997 $aUNINA LEADER 01902nam0 22004333i 450 001 VAN00292294 005 20250714025312.66 017 70$2N$a9783540483229 100 $a20250505d1994 |0itac50 ba 101 $aeng 102 $aDE 105 $a|||| ||||| 181 $ai$b e 182 $ab 183 $acr 200 1 $aExistence Families, Functional Calculi and Evolution Equations$fRalph deLaubenfels 210 $aBerlin [etc.]$cSpringer-Verlag$d1994 215 $axv, 234 p.$d24 cm 461 1$1001VAN00102250$12001 $aLecture notes in mathematics$1210 $aBerlin [etc.]$cSpringer$v1570 606 $a47-XX$xOperator theory [MSC 2020]$3VANC019759$2MF 606 $a47A60$xFunctional calculus for linear operators [MSC 2020]$3VANC021617$2MF 606 $a47B06$xRiesz operators; eigenvalue distributions; approximation numbers, $s$-numbers, Kolmogorov numbers, entropy numbers, etc. of operators [MSC 2020]$3VANC022464$2MF 610 $aAbstract Cauchy problem$9KW:K 610 $aCalculus$9KW:K 610 $aEvolution equations$9KW:K 610 $aFunctional calculus$9KW:K 610 $aMaximum$9KW:K 610 $aSemigroups of operators$9KW:K 620 $dBerlin$3VANL000066 700 1$adeLaubenfels$bRalph$3VANV247948$060267 712 $aSpringer $3VANV108073$4650 801 $aIT$bSOL$c20250718$gRICA 856 4 $uhttps://doi.org/10.1007/BFb0073401$zE-book ? Accesso al full-text attraverso riconoscimento IP di Ateneo, proxy e/o Shibboleth 899 $aBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA$1IT-CE0120$2VAN08 912 $fN 912 $aVAN00292294 950 $aBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA$d08DLOAD e-Book 11547 $e08eMF11547 20250625 996 $aExistence families, functional calculi and evolution equations$978709 997 $aUNICAMPANIA