LEADER 05413nam 22006615 450 001 9910921014103321 005 20250404222159.0 010 $a9783031728518 010 $a3031728513 024 7 $a10.1007/978-3-031-72851-8 035 $a(CKB)37156281400041 035 $a(MiAaPQ)EBC31875768 035 $a(Au-PeEL)EBL31875768 035 $a(DE-He213)978-3-031-72851-8 035 $a(OCoLC)1485005345 035 $a(EXLCZ)9937156281400041 100 $a20250107d2024 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Logic, Philosophy, and History of the Lambda-Calculus $eTheory and Applications /$fLevis Zerpa 205 $a1st ed. 210 1$aCham, Switzerland :$cPalgrave Macmillan,$d[2024] 215 $a1 online resource (298 pages) 225 1 $aHistory of Analytic Philosophy,$x2634-6001 311 08$a9783031728501 311 08$a3031728505 320 $aIncludes bibliographical references and index. 327 $aPart I Introduction -- 1 General Introduction and Motivation -- Part II: The Logic and Philosophy of the Lambda-Calculus: Lambda-Philosophy -- 2 Lambda-Philosophy: The General Program -- 3 The ?-Calculus as a Solution to a Problem of Philosophical Analysis -- 4 The ?-Calculus as a Formal System of Symbolic Logic and the Container Notation -- Part III: Two Applications: Arithmetic and Propositional Logic -- 5 The Container Notation in the ?-Calculus (1): Arithmetic -- 6 The Container Notation in the ?-Calculus (2): Propositional Logic -- Part IV: The Philosophy of Computer Science and Computability Theory in Lambda-Philosophy -- 7 Questioning a Dogma of Algorithmic Thinking in Our Time -- Part V: Ontology in Lambda-Philosophy -- 8 The Criterion of Ontological Commitment as a Logical Tester in Ontology -- 9 Church's Ontological Development -- 10 Compiler Output as a Programming Tester in Ontology -- Part VI: The History of The Lambda-Calculus: Three Comparative Studies -- 11 Comparative Historical Studies (0): Introduction -- 12 Comparative Historical Studies (1): Vičte's Analytic Art in ?-Philosophy -- 13 Comparative Historical Studies (2): A Brief Analysis of Descartes' Correlation-Hypothesis and Church's Thesis -- 14 Comparative Historical Studies (3): Wittgenstein Anticipation of Church Numerals. 330 $aThis is the first book focused on the logico-philosophical aspects of the lambda-calculus since the inception of the field in 1932 in the pioneering work of Alonzo Church. The book starts a new field called "lambda-philosophy": a branch of logic-based analytic philosophy in the tradition of Frege and Russell, directly constructed from the lambda-calculus. Another innovation of the book is a new graphical and intuitive logico-mathematical notation for the lambda-calculus called "the container notation". The book covers in detail some episodes of the history of the subject, including three comparative studies of the lambda-calculus with Vičte's algebra, Descartes' analytic geometry, and Wittgenstein's Tractatus. A didactic approach to the logico-mathematical aspects of the lambda-calculus, partially based on cognitive science, provides the technical basis for the analysis. In this way, the book provides a systematic and coherent treatment of diverse logico-philosophical aspects and applications of the lambda-calculus as part of the platform offered by lambda-philosophy. The book includes the following: a detailed treatment of the ambiguities of the concept of function (under the traditional or Euler's notation); an elucidation of the notion of transformative philosophical analysis; an account of Church's methodology which shows that the lambda-calculus is an adequate solution to the problem of a philosophical analysis of functions as rules of computation; a didactic treatment of the formal aspects of the lambda-calculus through the container notation; and diverse arithmetical and logical examples of the container notation. The book questions a dogma of algorithmic thinking by arguing that the lambda-calculus is more intuitive and natural than Turing machines. The Logic, Philosophy, and History of the Lambda-Calculus is essential reading for all scholars and researchers of the history of analytic philosophy and especially those focussing on logic-based analytic philosophy. Levis Zerpa is Researcher-Professor at Yachay Tech University, Ecuador. 410 0$aHistory of Analytic Philosophy,$x2634-6001 606 $aAnalysis (Philosophy) 606 $aLogic 606 $aLogic, Symbolic and mathematical 606 $aComputer science 606 $aAnalytic Philosophy 606 $aFormal Logic 606 $aMathematical Logic and Foundations 606 $aTheory of Computation 615 0$aAnalysis (Philosophy) 615 0$aLogic. 615 0$aLogic, Symbolic and mathematical. 615 0$aComputer science. 615 14$aAnalytic Philosophy. 615 24$aFormal Logic. 615 24$aMathematical Logic and Foundations. 615 24$aTheory of Computation. 676 $a146.4 700 $aZerpa$b Levis$01782313 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910921014103321 996 $aThe Logic, Philosophy, and History of the Lambda-Calculus$94308398 997 $aUNINA