The Logic, Philosophy, and History of the Lambda-Calculus
Springer International Publishing (Verlag)
978-3-031-72850-1 (ISBN)
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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.
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 -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): Viète'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.
| Erscheint lt. Verlag | 27.1.2025 |
|---|---|
| Reihe/Serie | History of Analytic Philosophy |
| Zusatzinfo | X, 358 p. 10 illus. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 148 x 210 mm |
| Themenwelt | Geisteswissenschaften ► Philosophie ► Allgemeines / Lexika |
| Geisteswissenschaften ► Philosophie ► Logik | |
| Geisteswissenschaften ► Philosophie ► Philosophie der Neuzeit | |
| Geisteswissenschaften ► Philosophie ► Sprachphilosophie | |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| Schlagworte | Alonzo Church • Analytic philosophy • Lambda-Calculus • Linguistics • symbolic logic |
| ISBN-10 | 3-031-72850-5 / 3031728505 |
| ISBN-13 | 978-3-031-72850-1 / 9783031728501 |
| Zustand | Neuware |
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