LEADER 04365nam 2200649Ia 450 001 9910807368103321 005 20240418100157.0 010 $a1-283-39828-1 010 $a9786613398284 010 $a3-11-021186-6 024 7 $a10.1515/9783110211863 035 $a(CKB)1000000000692131 035 $a(EBL)370733 035 $a(OCoLC)476206249 035 $a(SSID)ssj0000178860 035 $a(PQKBManifestationID)11156074 035 $a(PQKBTitleCode)TC0000178860 035 $a(PQKBWorkID)10230081 035 $a(PQKB)11113112 035 $a(MiAaPQ)EBC370733 035 $a(DE-B1597)35484 035 $a(OCoLC)1013939216 035 $a(OCoLC)774131973 035 $a(DE-B1597)9783110211863 035 $a(Au-PeEL)EBL370733 035 $a(CaPaEBR)ebr10693579 035 $a(CaONFJC)MIL339828 035 $a(EXLCZ)991000000000692131 100 $a20080617d2008 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt 182 $cc 183 $acr 200 00$aInfinitesimal differences $econtroversies between leibniz and his contemporaries /$fedited by Ursula Goldenbaum and Douglas Jesseph 210 $aBerlin ;$aNew York $cWalter De Gruyter$dc2008 215 $a1 online resource (336 p.) 300 $a"This volume had its beginnings in a conference entitled The Metaphysical and Mathematical Discussion os the Status of Infinitesimals in Leibniz's Time held in April 2006 at Emory University"--Introd. 311 $a3-11-020216-6 320 $aIncludes bibliographical references (p. [309]-323) and index. 327 $t Frontmatter -- $tTable of Contents -- $tIntroduction -- $tLeery Bedfellows: Newton and Leibniz on the Status of Infinitesimals -- $tInfinity, Infinitesimals, and the Reform of Cavalieri: John Wallis and his Critics -- $tIndivisibilia Vera - How Leibniz Came to Love Mathematics -- $tIndivisibles and Infinitesimals in Early Mathematical Texts of Leibniz -- $tArchimedes, Infinitesimals and the Law of Continuity: On Leibniz's Fictionalism -- $tAn Enticing (Im)Possibility: Infinitesimals, Differentials, and the Leibnizian Calculus -- $tProductive Ambiguity in Leibniz's Representation of Infinitesimals -- $tGenerality and Infinitely Small Quantities in Leibniz's Mathematics - The Case of his Arithmetical Quadrature of Conic Sections and Related Curves -- $tLeibniz's Calculation with Compendia -- $tNieuwentijt, Leibniz, and Jacob Hermann on Infinitesimals -- $tTruth in Fiction: Origins and Consequences of Leibniz's Doctrine of Infinitesimal Magnitudes -- $tRule of Continuity and Infinitesimals in Leibniz's Physics -- $tLeibniz on Infinitesimals and the Reality of Force -- $tDead Force, Infinitesimals, and the Mathematicization of Nature -- $t Backmatter 330 $aThe essays offer a unified and comprehensive view of 17th century mathematical and metaphysical disputes over status of infinitesimals, particularly the question whether they were real or mere fictions. Leibniz's development of the calculus and his understanding of its metaphysical foundation are taken as both a point of departure and a frame of reference for the 17th century discussions of infinitesimals, that involved Hobbes, Wallis, Newton, Bernoulli, Hermann, and Nieuwentijt. Although the calculus was undoubtedly successful in mathematical practice, it remained controversial because its procedures seemed to lack an adequate metaphysical or methodological justification. The topic is also of philosophical interest, because Leibniz freely employed the language of infinitesimal quantities in the foundations of his dynamics and theory of forces. Thus, philosophical disputes over the Leibnizian science of bodies naturally involve questions about the nature of infinitesimals. The volume also includes newly discovered Leibnizian marginalia in the mathematical writings of Hobbes. 606 $aPhysics$xPhilosophy$vCongresses 606 $aMathematics$xPhilosophy$vCongresses 615 0$aPhysics$xPhilosophy 615 0$aMathematics$xPhilosophy 676 $a193 686 $aCF 5517$2rvk 701 $aGoldenbaum$b Ursula$066156 701 $aJesseph$b Douglas Michael$059803 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910807368103321 996 $aInfinitesimal differences$93977707 997 $aUNINA