05484nam a22005655i 4500 978-3-031-72851-8 DE-He213 20251030114920.0 cr nn 008mamaa 250107s2024 sz | s |||| 0|eng d 9783031728518 978-3-031-72851-8 10.1007/978-3-031-72851-8 doi B808.5.A-Z HPCF5 bicssc PHI039000 bisacsh QDHR9 thema Zerpa, Levis. author. aut http://id.loc.gov/vocabulary/relators/aut 90177 The Logic, Philosophy, and History of the Lambda-Calculus [electronic resource] : Theory and Applications / by Levis Zerpa. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Palgrave Macmillan, 2024. XXXI, 255 p. 10 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda History of Analytic Philosophy, 2634-6001 Part 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. This 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. Analysis (Philosophy). 71325 Logic. 70674 Mathematical logic. 66195 Computer science. 58552 Analytic Philosophy. 71326 Formal Logic. 76707 Mathematical Logic and Foundations. 66198 Theory of Computation. 67552 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031728501 Printed edition: 9783031728525 Printed edition: 9783031728532 History of Analytic Philosophy, 2634-6001 71329 https://doi.org/10.1007/978-3-031-72851-8 ZDB-2-REP ZDB-2-SXPR 66351 66351