LEADER 05256nam 2200769 a 450 001 9910780054903321 005 20200520144314.0 010 $a9786613017758 010 $a1-283-01775-X 010 $a1-4008-2404-4 010 $a1-4008-1430-8 024 7 $a10.1515/9781400824045 035 $a(CKB)111056486505706 035 $a(EBL)662362 035 $a(OCoLC)705539244 035 $a(SSID)ssj0000242700 035 $a(PQKBManifestationID)11194796 035 $a(PQKBTitleCode)TC0000242700 035 $a(PQKBWorkID)10310678 035 $a(PQKB)10264233 035 $a(DE-B1597)446689 035 $a(OCoLC)979741812 035 $a(DE-B1597)9781400824045 035 $a(Au-PeEL)EBL662362 035 $a(CaPaEBR)ebr10453194 035 $a(CaONFJC)MIL301775 035 $a(MiAaPQ)EBC662362 035 $a(PPN)170254860 035 $a(EXLCZ)99111056486505706 100 $a20000322d2000 uy 0 101 0 $aeng 135 $aurcn||||||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe search for mathematical roots, 1870-1940$b[electronic resource] $elogics, set theories and the foundations of mathematics from Cantor through Russell to Go?del /$fI. Grattan-Guinness 205 $aCourse Book 210 $aPrinceton, N.J. $cPrinceton University Press$dc2000 215 $a1 online resource (705 p.) 300 $aDescription based upon print version of record. 311 $a0-691-05858-X 311 $a0-691-05857-1 320 $aIncludes bibliographical references (p. [594]-669) and index. 327 $tFront matter --$tCONTENTS --$tCHAPTER 1. Explanations --$tCHAPTER 2. Preludes: Algebraic Logic and Mathematical Analysis up to 1870 --$tCHAPTER 3. Cantor: Mathematics as Mengenlehre --$tCHAPTER 4. Parallel Processes in Set Theory, Logics and Axiomatics, 1870's-1900's --$tCHAPTER 5. Peano: the Formulary of Mathematics --$tCHAPTER 6. Russell's Way In: From Certainty to Paradoxes, 1895-1903 --$tCHAPTER 7. Russell and Whitehead Seek the Principia Mathematica, 1903-1913 --$tCHAPTER 8. The Influence and Place of Logicism, 1910-1930 --$tCHAPTER 9. Postludes: Mathematical Logic and Logicism in the 1930's --$tCHAPTER 10. The Fate of the Search --$tCHAPTER 11. Transcription of Manuscripts --$tBIBLIOGRAPHY --$tINDEX 330 $aWhile many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the first comprehensive history of the mathematical background, content, and impact of the mathematical logic and philosophy of mathematics that Russell developed with A. N. Whitehead in their Principia mathematica (1910-1913). ? This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. Substantial surveys are provided of many related topics and figures of the late nineteenth century: the foundations of mathematical analysis under Weierstrass; the creation of algebraic logic by De Morgan, Boole, Peirce, Schröder, and Jevons; the contributions of Dedekind and Frege; the phenomenology of Husserl; and the proof theory of Hilbert. The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and Gödel. A strong American theme runs though the story, beginning with the mathematician E. H. Moore and the philosopher Josiah Royce, and stretching through the emergence of Church and Quine, and the 1930's immigration of Carnap and GödeI. Grattan-Guinness draws on around fifty manuscript collections, including the Russell Archives, as well as many original reviews. The bibliography comprises around 1,900 items, bringing to light a wealth of primary materials. Written for mathematicians, logicians, historians, and philosophers--especially those interested in the historical interaction between these disciplines--this authoritative account tells an important story from its most neglected point of view. Whitehead and Russell hoped to show that (much of) mathematics was expressible within their logic; they failed in various ways, but no definitive alternative position emerged then or since. 606 $aArithmetic$xFoundations$xHistory$y19th century 606 $aArithmetic$xFoundations$xHistory$y20th century 606 $aSet theory$xHistory$y19th century 606 $aSet theory$xHistory$y20th century 606 $aLogic, Symbolic and mathematical$xHistory$y19th century 606 $aLogic, Symbolic and mathematical$xHistory$y20th century 615 0$aArithmetic$xFoundations$xHistory 615 0$aArithmetic$xFoundations$xHistory 615 0$aSet theory$xHistory 615 0$aSet theory$xHistory 615 0$aLogic, Symbolic and mathematical$xHistory 615 0$aLogic, Symbolic and mathematical$xHistory 676 $a510 686 $aCC 2000$2rvk 700 $aGrattan-Guinness$b I$066910 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910780054903321 996 $aThe search for mathematical roots, 1870-1940$93674508 997 $aUNINA