A Philosophical Introduction To Higher Order Logics
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A Philosophical Introduction To Higher Order Logics
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Author : Andrew Bacon
language : en
Publisher: Taylor & Francis
Release Date : 2023-09-29
A Philosophical Introduction To Higher Order Logics written by Andrew Bacon and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-29 with Philosophy categories.
This is the first comprehensive textbook on higher-order logic that is written specifically to introduce the subject matter to graduate students in philosophy. The book covers both the formal aspects of higher-order languages—their model theory and proof theory, the theory of λ-abstraction and its generalizations—and their philosophical applications, especially to the topics of modality and propositional granularity. The book has a strong focus on non-extensional higher-order logics, making it more appropriate for foundational metaphysics than other introductions to the subject from computer science, mathematics, and linguistics. A Philosophical Introduction to Higher-order Logics assumes only that readers have a basic knowledge of first-order logic. With an emphasis on exercises, it can be used as a textbook though is also ideal for self-study. Author Andrew Bacon organizes the book's 18 chapters around four main parts: I. Typed Language II. Higher-Order Languages III. General Higher-Order Languages IV. Higher-Order Model Theory In addition, two appendices cover the Curry-Howard isomorphism and its applications for modeling propositional structure. Each chapter includes exercises that move from easier to more difficult, strategically placed throughout the chapter, and concludes with an annotated suggested reading list providing graduate students with most valuable additional resources. Key Features: Is the first comprehensive introduction to higher-order logic as a grounding for addressing problems in metaphysics Introduces the basic formal tools that are needed to theorize in, and model, higher-order languages Offers an abundance of - Simple exercises throughout the book, serving as comprehension checks on basic concepts and definitions - More difficult exercises designed to facilitate long-term learning Contains annotated sections on further reading, pointing the reader to related literature, learning resources, and historical context
Introduction To Higher Order Categorical Logic
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Author : J. Lambek
language : en
Publisher: Cambridge University Press
Release Date : 1988-03-25
Introduction To Higher Order Categorical Logic written by J. Lambek and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-03-25 with Mathematics categories.
Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.
Philosophical Introduction To Set Theory
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Author : Stephen Pollard
language : en
Publisher: Courier Dover Publications
Release Date : 2015-07-15
Philosophical Introduction To Set Theory written by Stephen Pollard and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-15 with Mathematics categories.
This unique approach maintains that set theory is the primary mechanism for ideological and theoretical unification in modern mathematics, and its technically informed discussion covers a variety of philosophical issues. 1990 edition.
An Introduction To The Philosophy Of Logic
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Author : Daniel Cohnitz
language : en
Publisher: Cambridge University Press
Release Date : 2019-05-16
An Introduction To The Philosophy Of Logic written by Daniel Cohnitz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-16 with Philosophy categories.
Philosophy of logic is a fundamental part of philosophical study, and one which is increasingly recognized as being immensely important in relation to many issues in metaphysics, metametaphysics, epistemology, philosophy of mathematics, and philosophy of language. This textbook provides a comprehensive and accessible introduction to topics including the objectivity of logical inference rules and its relevance in discussions of epistemological relativism, the revived interest in logical pluralism, the question of logic's metaphysical neutrality, and the demarcation between logic and mathematics. Chapters in the book cover the state of the art in contemporary philosophy of logic, and allow students to understand the philosophical relevance of these debates without having to contend with complex technical arguments. This will be a major new resource for students working on logic, as well as for readers seeking a better understanding of philosophy of logic in its wider context.
Higher Order Metaphysics
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Author : Peter Fritz
language : en
Publisher: Oxford University Press
Release Date : 2024-03-06
Higher Order Metaphysics written by Peter Fritz 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 2024-03-06 with Philosophy categories.
This volume explores the use of higher-order logics in metaphysics. Higher-order logics are natural extensions of the common systems of predicate logic, with a history going back to the very beginnings of formal logic. Such logics are well suited to formalize metaphysical views and arguments. Over the last decade, there has been a resurgence of interest in higher-order metaphysics. Seventeen original essays are grouped under five headings. Three introductory chapters present higher-order languages and motivate their use in metaphysics. Three chapters on pure higher-order metaphysics discuss different options of higher-order languages and logics which may be used in metaphysics. Three chapters on applied higher-order metaphysics consider the application of higher-order logic to various central topics of metaphysics. Three historical chapters trace the development of higher-order logic as it relates to metaphysics over the last 150 years. The volume concludes with a discussion, containing two chapters criticizing the use of higher-order logic in metaphysics, as well as responses to these criticisms by two authors.
Philosophical Logic
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Author : John MacFarlane
language : en
Publisher: Routledge
Release Date : 2020-11-29
Philosophical Logic written by John MacFarlane and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-29 with Philosophy categories.
Introductory logic is generally taught as a straightforward technical discipline. In this book, John MacFarlane helps the reader think about the limitations of, presuppositions of, and alternatives to classical first-order predicate logic, making this an ideal introduction to philosophical logic for any student who already has completed an introductory logic course. The book explores the following questions. Are there quantificational idioms that cannot be expressed with the familiar universal and existential quantifiers? How can logic be extended to capture modal notions like necessity and obligation? Does the material conditional adequately capture the meaning of 'if'—and if not, what are the alternatives? Should logical consequence be understood in terms of models or in terms of proofs? Can one intelligibly question the validity of basic logical principles like Modus Ponens or Double Negation Elimination? Is the fact that classical logic validates the inference from a contradiction to anything a flaw, and if so, how can logic be modified to repair it? How, exactly, is logic related to reasoning? Must classical logic be revised in order to be applied to vague language, and if so how? Each chapter is organized around suggested readings and includes exercises designed to deepen the reader's understanding. Key Features: An integrated treatment of the technical and philosophical issues comprising philosophical logic Designed to serve students taking only one course in logic beyond the introductory level Provides tools and concepts necessary to understand work in many areas of analytic philosophy Includes exercises, suggested readings, and suggestions for further exploration in each chapter
Propositional Quantifiers
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Author : Peter Fritz
language : en
Publisher: Cambridge University Press
Release Date : 2024-05-16
Propositional Quantifiers written by Peter Fritz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-16 with Philosophy categories.
Propositional quantifiers are quantifiers binding proposition letters, understood as variables. This Element introduces propositional quantifiers and explains why they are especially interesting in the context of propositional modal logics. It surveys the main results on propositionally quantified modal logics which have been obtained in the literature, presents a number of open questions, and provides examples of applications of such logics to philosophical problems.
Simple Type Theory
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Author : William M. Farmer
language : en
Publisher: Springer Nature
Release Date : 2025-04-23
Simple Type Theory written by William M. Farmer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-23 with Computers categories.
This unique textbook, in contrast to a standard logic text, provides the reader with a logic that can be used in practice to express and reason about mathematical ideas. The book is an introduction to simple type theory, a classical higher-order version of predicate logic that extends first-order logic. It presents a practice-oriented logic called Alonzo that is based on Alonzo Church's formulation of simple type theory known as Church's type theory. Unlike traditional predicate logics, Alonzo admits undefined expressions. The book illustrates using Alonzo how simple type theory is suited ideally for reasoning about mathematical structures and constructing libraries of mathematical knowledge. For this second edition, more than 400 additions, corrections, and improvements have been made, including a new chapter on inductive sets and types. Topics and features: !-- [if !supportLists]--· !--[endif]--Offers the first book-length introduction to simple type theory as a predicate logic !-- [if !supportLists]--· !--[endif]--Provides the reader with a logic that is close to mathematical practice !-- [if !supportLists]--· !--[endif]--Includes a module system for building libraries of mathematical knowledge !-- [if !supportLists]--· !--[endif]--Employs two semantics, one for mathematics and one for logic !-- [if !supportLists]--· !--[endif]--Emphasizes the model-theoretic view of predicate logic !-- [if !supportLists]--· !--[endif]--Presents several important topics, such as definite description and theory morphisms, not usually found in standard logic textbooks Aimed at students of mathematics and computing at the graduate or upper-undergraduate level, this book is well suited for mathematicians, computing professionals, engineers, and scientists who need a practical logic for expressing and reasoning about mathematical ideas. William M. Farmer is a Professor in the Department of Computing and Software at McMaster University in Hamilton, Ontario, Canada.
Philosophy Of Logic
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Author :
language : en
Publisher: Elsevier
Release Date : 2006-11-29
Philosophy Of Logic written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-29 with Mathematics categories.
The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert's program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights.- Written by leading logicians and philosophers- Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic- Clear, in-depth expositions of technical detail- Progressive organization from general considerations to informal to symbolic logic to nonclassical logics- Presents current work in symbolic logic within a unified framework- Accessible to students, engaging for experts and professionals- Insightful philosophical discussions of all aspects of logic- Useful bibliographies in every chapter
Philosophy Of Logics
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Author : Susan Haack
language : en
Publisher: Cambridge University Press
Release Date : 1978-07-27
Philosophy Of Logics written by Susan Haack and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978-07-27 with Philosophy categories.
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