LEADER 04430nam 22007095 450 001 9910484659703321 005 20230810184400.0 010 $a3-319-17109-7 024 7 $a10.1007/978-3-319-17109-8 035 $a(CKB)3710000000436814 035 $a(EBL)2096187 035 $a(SSID)ssj0001524911 035 $a(PQKBManifestationID)11845558 035 $a(PQKBTitleCode)TC0001524911 035 $a(PQKBWorkID)11484934 035 $a(PQKB)11046208 035 $a(DE-He213)978-3-319-17109-8 035 $a(MiAaPQ)EBC2096187 035 $a(PPN)186399898 035 $a(EXLCZ)993710000000436814 100 $a20150624d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFunctions and Generality of Logic $eReflections on Dedekind's and Frege's Logicisms /$fby Hourya Benis-Sinaceur, Marco Panza, Gabriel Sandu 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (145 p.) 225 1 $aLogic, Epistemology, and the Unity of Science,$x2214-9783 ;$v37 300 $aDescription based upon print version of record. 311 $a3-319-17108-9 320 $aIncludes bibliographical references. 327 $aChapter 1: Is Dedekind a logicist?; Hourya Benis Sinaceur -- Chapter 2: Functions and Expressions; Marco Panza -- Chapter 3: Frege, Russell, Ramsey on arbitrary functions; Gabriel Sandu. 330 $aThis book examines three connected aspects of Frege?s logicism: the differences between Dedekind?s and Frege?s interpretation of the term ?logic? and related terms and reflects on Frege?s notion of function, comparing its understanding and the role it played in Frege?s and Lagrange?s foundational programs. It concludes with an examination of the notion of arbitrary function, taking into account Frege?s, Ramsey?s and Russell?s view on the subject. Composed of three chapters, this book sheds light on important aspects of Dedekind?s and Frege?s logicisms. The first chapter explains how, although he shares Frege?s aim at substituting logical standards of rigor to intuitive imports from spatio-temporal experience into the deductive presentation of arithmetic, Dedekind had a different goal and used or invented different tools. The chapter highlights basic dissimilarities between Dedekind?s and Frege?s actual ways of doing and thinking. The second chapter reflects on Frege?s notion of a function, in comparison with the notions endorsed by Lagrange and the followers of the program of arithmetization of analysis. It remarks that the foundational programs pursued by Lagrange  and Frege are crucially different and based on a different idea of what the foundations of mathematics should be like. However, despite this contrast, the notion of function plays similar roles in the two programs, and this chapter emphasizes the similarities. The third chapter traces the development of thinking about Frege?s program in the foundations of mathematics, and includes comparisons of Frege?s, Russell?s and Ramsey?s views. The chapter discusses earlier papers written by Hintikka, Sandu, Demopoulos and Trueman. Although the chapter?s main focus is on the notion of arbitrary correlation, it starts out by discussing some aspects of the connection between this notion and Dedekind Theorem. 410 0$aLogic, Epistemology, and the Unity of Science,$x2214-9783 ;$v37 606 $aLogic 606 $aMathematics 606 $aHistory 606 $aScience$xPhilosophy 606 $aLogic 606 $aHistory of Mathematical Sciences 606 $aPhilosophy of Science 615 0$aLogic. 615 0$aMathematics. 615 0$aHistory. 615 0$aScience$xPhilosophy. 615 14$aLogic. 615 24$aHistory of Mathematical Sciences. 615 24$aPhilosophy of Science. 676 $a511.324 700 $aBenis-Sinaceur$b Hourya$4aut$4http://id.loc.gov/vocabulary/relators/aut$01216443 702 $aPanza$b Marco$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSandu$b Gabriel$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484659703321 996 $aFunctions and generality of logic$92812249 997 $aUNINA