LEADER 00982nam--2200349---450- 001 990000380740203316 005 20080603162817.0 035 $a0038074 035 $aUSA010038074 035 $a(ALEPH)000038074USA01 035 $a0038074 100 $a20010329d1983----km-y0itay0103----ba 101 $ait 102 $aITA 105 $a||||||||001yy 200 1 $aRaffaele Baldi$el'uomo, il poeta, il critico$fAgnello Baldi 210 $aCava dei Tirreni$cMitilia$d1983 215 $a30 p.$d22 cm 410 $12001 676 $a851.912 700 1$aBALDI,$bAgnello$0208397 801 0$aIT$bsalbc$gISBD 912 $a990000380740203316 951 $aXV.1.A. Misc. 247(V G MISC. 4/22)$b15410 LM$cXV.1 959 $aBK 969 $aUMA 979 $aPATTY$b90$c20010329$lUSA01$h1010 979 $c20020403$lUSA01$h1646 979 $aPATRY$b90$c20040406$lUSA01$h1626 979 $aCAPRIOLO$b90$c20080603$lUSA01$h1628 996 $aRaffaele Baldi$9875579 997 $aUNISA LEADER 05834nam 22007335 450 001 9910349545203321 005 20200701034346.0 010 $a3-030-18707-1 024 7 $a10.1007/978-3-030-18707-1 035 $a(CKB)4100000009191151 035 $a(MiAaPQ)EBC5894506 035 $a(DE-He213)978-3-030-18707-1 035 $a(EXLCZ)994100000009191151 100 $a20190909d2019 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics /$fby John L. Bell 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (320 pages) 225 1 $aThe Western Ontario Series in Philosophy of Science, A Series of Books in Philosophy of Science, Methodology, Epistemology, Logic, History of Science, and Related Fields,$x1566-659X ;$v82 311 $a3-030-18706-3 320 $aIncludes bibliographical references and index. 327 $aPart I: The Continuous, the Discrete, and the Infinitesimal in the History of Thought -- Chapter 1. The Continuous and the Discrete in Ancient Greece, the Orient, and the European Middle Ages -- Chapter 2. The 16th and 17th Centuries: The Founding of the Infinitesimal Calculus -- Chapter 3. The 18th and Early 19th Centuries: The Age of Continuity -- Chapter 4. The Reduction of the Continuous to the Discrete in the 19th and early 20th Centuries -- Chapter 5. Dissenting Voices: Divergent Conceptions of the Continuum in the 19th and Early 20th Centuries -- Part II: Continuity and Infinitesimals in Today?s Mathematics -- Chapter 6. Topology -- Chapter 7. Category/Topos Theory -- Chapter 8. Nonstandard Analysis -- Chapter 9. The Constructive and Intuitionistic Continua -- Chapter 10. Smooth Infiniteimal Analysis/Synthetic Geometry. 330 $aThis book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled ?The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,? reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,? discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincaré, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal. . 410 0$aThe Western Ontario Series in Philosophy of Science, A Series of Books in Philosophy of Science, Methodology, Epistemology, Logic, History of Science, and Related Fields,$x1566-659X ;$v82 606 $aMathematics?Philosophy 606 $aPhilosophy 606 $aLogic, Symbolic and mathematical 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aGeometry, Differential 606 $aMathematics 606 $aHistory 606 $aPhilosophy of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/E34020 606 $aHistory of Philosophy$3https://scigraph.springernature.com/ontologies/product-market-codes/E15000 606 $aMathematical Logic and Formal Languages$3https://scigraph.springernature.com/ontologies/product-market-codes/I16048 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aHistory of Mathematical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M23009 615 0$aMathematics?Philosophy. 615 0$aPhilosophy. 615 0$aLogic, Symbolic and mathematical. 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 0$aGeometry, Differential. 615 0$aMathematics. 615 0$aHistory. 615 14$aPhilosophy of Mathematics. 615 24$aHistory of Philosophy. 615 24$aMathematical Logic and Formal Languages. 615 24$aAnalysis. 615 24$aDifferential Geometry. 615 24$aHistory of Mathematical Sciences. 676 $a190 676 $a510.1 700 $aBell$b John L$4aut$4http://id.loc.gov/vocabulary/relators/aut$0119420 906 $aBOOK 912 $a9910349545203321 996 $aThe Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics$92218345 997 $aUNINA