The Logic, Philosophy, and History of the Lambda-Calculus : Theory and Applications / / Levis Zerpa
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| Autore: |
Zerpa Levis
|
| Titolo: |
The Logic, Philosophy, and History of the Lambda-Calculus : Theory and Applications / / Levis Zerpa
|
| Pubblicazione: | Cham, Switzerland : , : Palgrave Macmillan, , [2024] |
| Edizione: | 1st ed. |
| Descrizione fisica: | 1 online resource (298 pages) |
| Disciplina: | 146.4 |
| Soggetto topico: | Analysis (Philosophy) |
| Logic | |
| Logic, Symbolic and mathematical | |
| Computer science | |
| Analytic Philosophy | |
| Formal Logic | |
| Mathematical Logic and Foundations | |
| Theory of Computation | |
| Nota di bibliografia: | Includes bibliographical references and index. |
| Nota di contenuto: | 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. |
| Sommario/riassunto: | 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. |
| Titolo autorizzato: | The Logic, Philosophy, and History of the Lambda-Calculus |
| ISBN: | 9783031728518 |
| 3031728513 | |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910921014103321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
History of Analytic Philosophy, . 2634-6001