Functions And Generality Of Logic
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Functions And Generality Of Logic
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Author : Hourya Benis-Sinaceur
language : en
Publisher: Springer
Release Date : 2015-06-24
Functions And Generality Of Logic written by Hourya Benis-Sinaceur and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-24 with Philosophy categories.
This book examines three connected aspects of Frege’s logicism: the differences between Dedekind’s and Frege’s interpretation of the term ‘logic’ and related terms and reflects on Frege’s notion of function, comparing its understanding and the role it played in Frege’s and Lagrange’s foundational programs. It concludes with an examination of the notion of arbitrary function, taking into account Frege’s, Ramsey’s and Russell’s view on the subject. Composed of three chapters, this book sheds light on important aspects of Dedekind’s and Frege’s logicisms. The first chapter explains how, although he shares Frege’s aim at substituting logical standards of rigor to intuitive imports from spatio-temporal experience into the deductive presentation of arithmetic, Dedekind had a different goal and used or invented different tools. The chapter highlights basic dissimilarities between Dedekind’s and Frege’s actual ways of doing and thinking. The second chapter reflects on Frege’s notion of a function, in comparison with the notions endorsed by Lagrange and the followers of the program of arithmetization of analysis. It remarks that the foundational programs pursued by Lagrange and Frege are crucially different and based on a different idea of what the foundations of mathematics should be like. However, despite this contrast, the notion of function plays similar roles in the two programs, and this chapter emphasizes the similarities. The third chapter traces the development of thinking about Frege’s program in the foundations of mathematics, and includes comparisons of Frege’s, Russell’s and Ramsey’s views. The chapter discusses earlier papers written by Hintikka, Sandu, Demopoulos and Trueman. Although the chapter’s main focus is on the notion of arbitrary correlation, it starts out by discussing some aspects of the connection between this notion and Dedekind Theorem.
Logic Form And Function
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Author : John Alan Robinson
language : en
Publisher: North Holland
Release Date : 1979
Logic Form And Function written by John Alan Robinson and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Philosophy categories.
Logic: form and content; Formulas: syntax and intuitive semantics; Boolean analysis of sentences; Infinitive finitary trees and boolean compactness; Semantic analysis of sentences and terms; Logical consequence: sequents and proofs; Logical equivalence: substitutivity and variants; Normal forms of sentences and sequents; Herbrand models and maps; Quad notation for clausal sequents; Unification; Resolution; Resolution on the computer; Historical notes; Appedix; Index.
Computability
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Author : Richard L Epstein
language : en
Publisher: Advanced Reasoning Forum
Release Date : 2018-10-24
Computability written by Richard L Epstein and has been published by Advanced Reasoning Forum this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-24 with Mathematics categories.
Now in a new edition!--the classic presentation of the theory of computable functions in the context of the foundations of mathematics. Part I motivates the study of computability with discussions and readings about the crisis in the foundations of mathematics in the early 20th century while presenting the basic ideas of whole number, function, proof, and real number. Part II starts with readings from Turing and Post leading to the formal theory of recursive functions. Part III presents sufficient formal logic to give a full development of Gödel's incompleteness theorems. Part IV considers the significance of the technical work with a discussion of Church's Thesis and readings on the foundations of mathematics. This new edition contains the timeline "Computability and Undecidability" as well as the essay "On mathematics".
Reference And Generality
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Author : Peter Thomas Geach
language : en
Publisher:
Release Date : 1980
Reference And Generality written by Peter Thomas Geach and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Language Arts & Disciplines categories.
Logic From A To Z
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Author : John B. Bacon
language : en
Publisher: Routledge
Release Date : 2013-09-05
Logic From A To Z written by John B. Bacon and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-05 with Philosophy categories.
First published in the most ambitious international philosophy project for a generation; the Routledge Encyclopedia of Philosophy. Logic from A to Z is a unique glossary of terms used in formal logic and the philosophy of mathematics. Over 500 entries include key terms found in the study of: * Logic: Argument, Turing Machine, Variable * Set and model theory: Isomorphism, Function * Computability theory: Algorithm, Turing Machine * Plus a table of logical symbols. Extensively cross-referenced to help comprehension and add detail, Logic from A to Z provides an indispensable reference source for students of all branches of logic.
Wittgenstein On Logic As The Method Of Philosophy
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Author : Oskari Kuusela
language : en
Publisher: Oxford University Press
Release Date : 2019-01-03
Wittgenstein On Logic As The Method Of Philosophy written by Oskari Kuusela and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-03 with Philosophy categories.
In Wittgenstein on Logic as the Method of Philosophy, Oskari Kuusela examines Wittgenstein's early and late philosophies of logic, situating their philosophical significance in early and middle analytic philosophy with particular reference to Frege, Russell, Carnap, and Strawson. He argues that not only the early but also the later Wittgenstein sought to further develop the logical-philosophical approaches of his contemporaries. Throughout his career Wittgenstein's aim was to resolve problems with and address the limitations of Frege's and Russell's accounts of logic and their logical methodologies so as to achieve the philosophical progress that originally motivated the logical-philosophical approach. By re-examining the roots and development of analytic philosophy, Kuusela seeks to open up covered up paths for the further development of analytic philosophy. Offering a novel interpretation of the philosopher, he explains how Wittgenstein extends logical methodology beyond calculus-based logical methods and how his novel account of the status of logic enables one to do justice to the complexity and richness of language use and thought while retaining rigour and ideals of logic such as simplicity and exactness. In addition, this volume outlines the new kind of non-empiricist naturalism developed in Wittgenstein's later work and explaining how his account of logic can be used to dissolve the long-standing methodological dispute between the ideal and ordinary language schools of analytic philosophy. It is of interest to scholars, researchers, and advance students of philosophy interested in engaging with a number of scholarly debates.
Logic
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Author : Alexander BAIN (Professor of Logic in the University of Aberdeen.)
language : en
Publisher:
Release Date : 1870
Logic written by Alexander BAIN (Professor of Logic in the University of Aberdeen.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1870 with categories.
Logic
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Author : Alexander Bain
language : en
Publisher:
Release Date : 1889
Logic written by Alexander Bain and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1889 with Logic categories.
The Oxford Handbook Of Generality In Mathematics And The Sciences
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Author : Karine Chemla
language : en
Publisher: Oxford University Press
Release Date : 2016-08-25
The Oxford Handbook Of Generality In Mathematics And The Sciences written by Karine Chemla and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-25 with Mathematics categories.
Generality is a key value in scientific discourses and practices. Throughout history, it has received a variety of meanings and of uses. This collection of original essays aims to inquire into this diversity. Through case studies taken from the history of mathematics, physics and the life sciences, the book provides evidence of different ways of understanding the general in various contexts. It aims at showing how collectives have valued generality and how they have worked with specific types of "general" entities, procedures, and arguments. The books connects history and philosophy of mathematics and the sciences at the intersection of two of the most fruitful contemporary lines of research: historical epistemology, in which values (e.g. "objectivity", "accuracy") are studied from a historical viewpoint; and the philosophy of scientific practice, in which conceptual developments are seen as embedded in networks of social, instrumental, and textual practices. Each chapter provides a self-contained case-study, with a clear exposition of the scientific content at stake. The collection covers a wide range of scientific domains - with an emphasis on mathematics - and historical periods. It thus allows a comparative perspective which suggests a non-linear pattern for a history of generality. The introductory chapter spells out the key issues and points to the connections between the chapters.
Logic By Alexander Bain
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Author : Alexander Bain
language : en
Publisher:
Release Date : 1870
Logic By Alexander Bain written by Alexander Bain and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1870 with categories.