05277nam a22005175i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001500172072001800187072002300205072001700228100008200245245013100327250001800458264007900476300004500555336002600600337002600626338003600652347002400688490004700712505133900759520209702098650003404195650001804229650003104247650002904278650003204307650002504339650004704364650003404411710003404445773002604479776003604505776003604541776003604577830005404613856004604667912001404713912001504727999001704742978-3-031-72851-8DE-He21320251030114920.0cr nn 008mamaa250107s2024    sz |    s    |||| 0|eng d  a97830317285189978-3-031-72851-87 a10.1007/978-3-031-72851-82doi 4aB808.5.A-Z 7aHPCF52bicssc 7aPHI0390002bisacsh 7aQDHR92thema1 aZerpa, Levis.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut99017714aThe Logic, Philosophy, and History of the Lambda-Calculush[electronic resource] :bTheory and Applications /cby Levis Zerpa.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Palgrave Macmillan,c2024.  aXXXI, 255 p. 10 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aHistory of Analytic Philosophy,x2634-60010 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 λ-Calculus as a Solution to a Problem of Philosophical Analysis -- 4 The λ-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 λ-Calculus (1): Arithmetic -- 6 The Container Notation in the λ-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): Viète’s Analytic Art in λ-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.  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 Viète'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. 0aAnalysis (Philosophy).971325 0aLogic.970674 0aMathematical logic.966195 0aComputer science.95855214aAnalytic Philosophy.97132624aFormal Logic.97670724aMathematical Logic and Foundations.96619824aTheory of Computation.9675522 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303172850108iPrinted edition:z978303172852508iPrinted edition:z9783031728532 0aHistory of Analytic Philosophy,x2634-600197132940uhttps://doi.org/10.1007/978-3-031-72851-8  aZDB-2-REP  aZDB-2-SXPR  c66351d66351