Introduction To Metalogic

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Metalogic

Geoffrey Hunter
Metalogic Book PDF

Author : Geoffrey Hunter
Publisher : Univ of California Press
Page : 306 pages
File Size : 53,5 Mb
Release : 1973-06-26
Category : Mathematics
ISBN : 0520023560

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Metalogic by Geoffrey Hunter Pdf

This work makes available to readers without specialized training in mathematics complete proofs of the fundamental metatheorems of standard (i.e., basically truth-functional) first order logic. Included is a complete proof, accessible to non-mathematicians, of the undecidability of first order logic, the most important fact about logic to emerge from the work of the last half-century. Hunter explains concepts of mathematics and set theory along the way for the benefit of non-mathematicians. He also provides ample exercises with comprehensive answers.

An Introduction to Metalogic

Aladdin M. Yaqub
An Introduction to Metalogic Book PDF

Author : Aladdin M. Yaqub
Publisher : Broadview Press
Page : 346 pages
File Size : 49,9 Mb
Release : 2014-10-24
Category : Philosophy
ISBN : 9781554811717

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An Introduction to Metalogic by Aladdin M. Yaqub Pdf

An Introduction to Metalogic is a uniquely accessible introduction to the metatheory of first-order predicate logic. No background knowledge of logic is presupposed, as the book is entirely self-contained and clearly defines all of the technical terms it employs. Yaqub begins with an introduction to predicate logic and ends with detailed outlines of the proofs of the incompleteness, undecidability, and indefinability theorems, covering many related topics in between.

Sets, Logic, Computation

Richard Zach
Sets Logic Computation Book PDF

Author : Richard Zach
Publisher : Unknown
Page : 418 pages
File Size : 51,9 Mb
Release : 2021-07-13
Category : Electronic
ISBN : 9798536395509

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Sets, Logic, Computation by Richard Zach Pdf

A textbook on the semantics, proof theory, and metatheory of first-order logic. It covers naive set theory, first-order logic, sequent calculus and natural deduction, the completeness, compactness, and Löwenheim-Skolem theorems, Turing machines, and the undecidability of the halting problem and of first-order logic. It is based on the Open Logic project, and available for free download at slc.openlogicproject.org.

An Introduction to Logical Theory

Aladdin M. Yaqub
An Introduction to Logical Theory Book PDF

Author : Aladdin M. Yaqub
Publisher : Broadview Press
Page : 438 pages
File Size : 40,6 Mb
Release : 2013-03-22
Category : Philosophy
ISBN : 9781551119939

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An Introduction to Logical Theory by Aladdin M. Yaqub Pdf

This book reclaims logic as a branch of philosophy, offering a self-contained and complete introduction to the three traditional systems of classical logic (term, sentence, and predicate logic) and the philosophical issues that surround those systems. The exposition is lucid, clear, and engaging. Practical methods are favored over the traditional, and creative approaches over the merely mechanical. The author’s guiding principle is to introduce classical logic in an intellectually honest way, and not to shy away from difficulties and controversies where they arise. Relevant philosophical issues, such as the relation between the meaning and the referent of a proper name, logical versus metaphysical possibility, and the conceptual content of an expression, are discussed throughout. In this way, the book is not only an introduction to the three main systems of classical logic, but also an introduction to the philosophy of classical logic.

Logic for Philosophy

Theodore Sider
Logic for Philosophy Book PDF

Author : Theodore Sider
Publisher : Oxford University Press
Page : 305 pages
File Size : 53,6 Mb
Release : 2010-01-07
Category : Philosophy
ISBN : 9780192658814

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Logic for Philosophy by Theodore Sider Pdf

Logic for Philosophy is an introduction to logic for students of contemporary philosophy. It is suitable both for advanced undergraduates and for beginning graduate students in philosophy. It covers (i) basic approaches to logic, including proof theory and especially model theory, (ii) extensions of standard logic that are important in philosophy, and (iii) some elementary philosophy of logic. It emphasizes breadth rather than depth. For example, it discusses modal logic and counterfactuals, but does not prove the central metalogical results for predicate logic (completeness, undecidability, etc.) Its goal is to introduce students to the logic they need to know in order to read contemporary philosophical work. It is very user-friendly for students without an extensive background in mathematics. In short, this book gives you the understanding of logic that you need to do philosophy.

An Introduction to Proof Theory

Paolo Mancosu,Sergio Galvan,Richard Zach
An Introduction to Proof Theory Book PDF

Author : Paolo Mancosu,Sergio Galvan,Richard Zach
Publisher : Oxford University Press
Page : 431 pages
File Size : 50,8 Mb
Release : 2021
Category : Philosophy
ISBN : 9780192895936

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An Introduction to Proof Theory by Paolo Mancosu,Sergio Galvan,Richard Zach Pdf

An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics.

Logic with Trees

Colin Howson
Logic with Trees Book PDF

Author : Colin Howson
Publisher : Routledge
Page : 234 pages
File Size : 47,7 Mb
Release : 2005-10-11
Category : Philosophy
ISBN : 9781134785506

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Logic with Trees by Colin Howson Pdf

Logic With Trees is a new and original introduction to modern formal logic. Unlike most texts, it also contains discussions on more philosophical issues such as truth, conditionals and modal logic. It presents the formal material with clarity, preferring informal explanations and arguments to intimidatingly rigorous development. Worked examples and excercises enable the readers to check their progress. Logic With Trees equips students with * a complete and clear account of the truth-tree system for first order logic * the importance of logic and its relevance to many different disciplines * the skills to grasp sophisticated formal reasoning techniques necessary to explore complex metalogic * the ability to contest claims that `ordinary' reasoning is well represented by formal first order logic The issues covered include a thorough discussion of truth-functional and full first order logic, using the truth-tree or semantic tableau approach. Completeness and Soundness proofs are given for both truth-functional and first order trees. Much use is made of induction, which is presented in a clear and consistent manner. There is also discussion of alternative deductive systems, an introduction to transfinite numbers and categoricity, the Lowenhein-Skolem theories and the celebrated findings of Godel and Church. The book concludes with an account of Kripke's attempted solution of the liar paradox and a discussion of the weakness of truth-functional account of conditionals. Particularly useful to those who favour critical accounts of formal reasoning, it will be of interest to students of philosophy at first level and beyond and also students of mathematics and computer science.

Introduction to Logic

Harry J Gensler
Introduction to Logic Book PDF

Author : Harry J Gensler
Publisher : Routledge
Page : 589 pages
File Size : 48,8 Mb
Release : 2012-08-06
Category : Philosophy
ISBN : 9781136994524

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Introduction to Logic by Harry J Gensler Pdf

Introduction to Logic combines likely the broadest scope of any logic textbook available with clear, concise writing and interesting examples and arguments. Its key features, all retained in the Second Edition, include: • simpler ways to test arguments than those available in competing textbooks, including the star test for syllogisms • a wide scope of materials, making it suitable for introductory logic courses (as the primary text) or intermediate classes (as the primary or supplementary book) • engaging and easy-to-understand examples and arguments, drawn from everyday life as well as from the great philosophers • a suitability for self-study and for preparation for standardized tests, like the LSAT • a reasonable price (a third of the cost of many competitors) • exercises that correspond to the LogiCola program, which may be downloaded for free from the web. This Second Edition also: • arranges chapters in a more useful way for students, starting with the easiest material and then gradually increasing in difficulty • provides an even broader scope with new chapters on the history of logic, deviant logic, and the philosophy of logic • expands the section on informal fallacies • includes a more exhaustive index and a new appendix on suggested further readings • updates the LogiCola instructional program, which is now more visually attractive as well as easier to download, install, update, and use.

Elementary Logic

Brian Garrett
Elementary Logic Book PDF

Author : Brian Garrett
Publisher : Routledge
Page : 190 pages
File Size : 42,5 Mb
Release : 2014-09-12
Category : Philosophy
ISBN : 9781317547495

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Elementary Logic by Brian Garrett Pdf

Elementary Logic explains what logic is, how it is done, and why it can be exciting. The book covers the central part of logic that all students have to learn: propositional logic. It aims to provide a crystal-clear introduction to what is often regarded as the most technically difficult area in philosophy. The book opens with an explanation of what logic is and how it is constructed. Subsequent chapters take the reader step-by-step through all aspects of elementary logic. Throughout, ideas are explained simply and directly, with the chapters packed with overviews, illustrative examples, and summaries. Each chapter builds on previous explanation and example, with the final chapters presenting more advanced methods. After a discussion of meta-logic and logical systems, the book closes with an exploration of how paradoxes can exist in the world of logic. Elementary Logic's clarity and engagement make it ideal for any reader studying logic for the first time.

Principia Mathematica

Alfred North Whitehead,Bertrand Russell
Principia Mathematica Book PDF

Author : Alfred North Whitehead,Bertrand Russell
Publisher : Cambridge University Press
Page : 524 pages
File Size : 55,9 Mb
Release : 1927
Category : Mathematics
ISBN : 052106791X

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Principia Mathematica by Alfred North Whitehead,Bertrand Russell Pdf

The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century.

An Introduction to Metalogic

Aladdin M. Yaqub
An Introduction to Metalogic Book PDF

Author : Aladdin M. Yaqub
Publisher : Broadview Press
Page : 346 pages
File Size : 49,8 Mb
Release : 2014-10-24
Category : Philosophy
ISBN : 9781770483811

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An Introduction to Metalogic by Aladdin M. Yaqub Pdf

An Introduction to Metalogic is a uniquely accessible introduction to the metatheory of first-order predicate logic. No background knowledge of logic is presupposed, as the book is entirely self-contained and clearly defines all of the technical terms it employs. Yaqub begins with an introduction to predicate logic and ends with detailed outlines of the proofs of the incompleteness, undecidability, and indefinability theorems, covering many related topics in between.

Logic for Computer Science

Jean H. Gallier
Logic for Computer Science Book PDF

Author : Jean H. Gallier
Publisher : Courier Dover Publications
Page : 532 pages
File Size : 49,5 Mb
Release : 2015-06-18
Category : Mathematics
ISBN : 9780486780825

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Logic for Computer Science by Jean H. Gallier Pdf

This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in first-order logic; SLD-resolution, logic programming, and the foundations of PROLOG; and many-sorted first-order logic. Numerous problems appear throughout the book, and two Appendixes provide practical background information.

Classical and Nonclassical Logics

Eric Schechter
Classical and Nonclassical Logics Book PDF

Author : Eric Schechter
Publisher : Princeton University Press
Page : 530 pages
File Size : 50,5 Mb
Release : 2005-08-28
Category : Mathematics
ISBN : 0691122792

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Classical and Nonclassical Logics by Eric Schechter Pdf

Classical logic is traditionally introduced by itself, but that makes it seem arbitrary and unnatural. This text introduces classical alongside several nonclassical logics (relevant, constructive, quantative, paraconsistent).

Modal Logic

Brian F. Chellas
Modal Logic Book PDF

Author : Brian F. Chellas
Publisher : Cambridge University Press
Page : 316 pages
File Size : 40,7 Mb
Release : 1980-02-29
Category : Mathematics
ISBN : 0521295157

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Modal Logic by Brian F. Chellas Pdf

An introductory textbook on modal logic the logic of necessity and possibility.

The Logic Book

Merrie Bergmann,James Moor,Jack Nelson
The Logic Book Book PDF

Author : Merrie Bergmann,James Moor,Jack Nelson
Publisher : McGraw-Hill Humanities/Social Sciences/Languages
Page : 0 pages
File Size : 40,5 Mb
Release : 2008-07-30
Category : Philosophy
ISBN : 007353563X

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The Logic Book by Merrie Bergmann,James Moor,Jack Nelson Pdf

This leading text for symbolic or formal logic courses presents all techniques and concepts with clear, comprehensive explanations, and includes a wealth of carefully constructed examples. Its flexible organization (with all chapters complete and self-contained) allows instructors the freedom to cover the topics they want in the order they choose.