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Author: Geoffrey Hunter Publisher: Univ of California Press ISBN: 9780520023567 Category : Mathematics Languages : en Pages : 306
Book Description
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.
Author: Geoffrey Hunter Publisher: Univ of California Press ISBN: 9780520023567 Category : Mathematics Languages : en Pages : 306
Book Description
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.
Author: Aladdin M. Yaqub Publisher: Broadview Press ISBN: 1554811716 Category : Philosophy Languages : en Pages : 346
Book Description
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.
Author: Richard Zach Publisher: ISBN: Category : Languages : en Pages : 418
Book Description
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.
Author: Theodore Sider Publisher: Oxford University Press ISBN: 0192658816 Category : Philosophy Languages : en Pages : 305
Book Description
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.
Author: Aladdin M. Yaqub Publisher: Broadview Press ISBN: 1460402448 Category : Philosophy Languages : en Pages : 346
Book Description
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.
Author: Geoffrey Hunter Publisher: Univ of California Press ISBN: 0520023560 Category : Mathematics Languages : en Pages : 304
Book Description
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.
Author: Michael L. O'Leary Publisher: John Wiley & Sons ISBN: 1118548019 Category : Mathematics Languages : en Pages : 464
Book Description
A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts Numerous examples that illustrate theorems and employ basic concepts such as Euclid’s lemma, the Fibonacci sequence, and unique factorization Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Löwenheim–Skolem, Burali-Forti, Hartogs, Cantor–Schröder–Bernstein, and König An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis.
Author: Jens Lemanski Publisher: Springer Nature ISBN: 3030330907 Category : Mathematics Languages : en Pages : 318
Book Description
The chapters in this timely volume aim to answer the growing interest in Arthur Schopenhauer’s logic, mathematics, and philosophy of language by comprehensively exploring his work on mathematical evidence, logic diagrams, and problems of semantics. Thus, this work addresses the lack of research on these subjects in the context of Schopenhauer’s oeuvre by exposing their links to modern research areas, such as the “proof without words” movement, analytic philosophy and diagrammatic reasoning, demonstrating its continued relevance to current discourse on logic. Beginning with Schopenhauer’s philosophy of language, the chapters examine the individual aspects of his semantics, semiotics, translation theory, language criticism, and communication theory. Additionally, Schopenhauer’s anticipation of modern contextualism is analyzed. The second section then addresses his logic, examining proof theory, metalogic, system of natural deduction, conversion theory, logical geometry, and the history of logic. Special focus is given to the role of the Euler diagrams used frequently in his lectures and their significance to broader context of his logic. In the final section, chapters discuss Schopenhauer’s philosophy of mathematics while synthesizing all topics from the previous sections, emphasizing the relationship between intuition and concept. Aimed at a variety of academics, including researchers of Schopenhauer, philosophers, historians, logicians, mathematicians, and linguists, this title serves as a unique and vital resource for those interested in expanding their knowledge of Schopenhauer’s work as it relates to modern mathematical and logical study.
Author: Richard Milton Martin Publisher: ISBN: Category : Philosophy Languages : en Pages : 402
Book Description
The philosophical papers collected together in this volume cover a variety of topics centering around the three items of the title. Mereology, the theory of part-whole, appears and reappears throughout as a kind of basso ostinato for much that is said. For its full effect, however, mereology must be combined with various items treated in metalogic or logical semiotics, the modern trivium of syntax, semantics, and pragmatics. When pressed for their total philosophic richness, all of these subjects flow over into topics of perennial interest in metaphysics, including even metaphysical theology. It is thought that the treatment here brings these various subjects together in a new light and in an exact way. As a result, they are seen to gain in richness, scope, and depth, and a basis provided for the study of how intimately they "interanimate" each other. Each paper here is a critical and/or constructive adventure of ideas, not necessarily agreeing in all details with every other. Even though they are concerned with a considerable variety of philosophical topics, there is nonetheless a common methodology throughout, namely, the logica utens of first order quantification theory - or its algebraic surrogate - together with the first-order metalogic based on it, which are thought to provide the bedrock of sound philosophical method. This view has been spelled out in considerable detail in the author's previous publications and is further develop here in important ways. "Richard M. Martin's work display a wealth of ideas, proposals, and formal analyses, always on top of the ideal of precision and rigour which were so important to him" Lingua e Stile, 1988 Of interest to: Philosophers, linguists, logicians
Author: Geoffrey Hunter
Author: Geoffrey Hunter
Author: 
Author: Aladdin M. Yaqub
Author: Richard Zach
Author: Theodore Sider
Author: Aladdin M. Yaqub
Author: Geoffrey Hunter
Author: Michael L. O'Leary
Author: Jens Lemanski
Author: Richard Milton Martin