Logic, Semantics, Metamathematics PDF Download
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Author: Alfred Tarski
Publisher: Hackett Publishing
ISBN: 9780915144761
Category : Philosophy
Languages : en
Pages : 542
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Book Description
Author: Alfred Tarski
Publisher: Hackett Publishing
ISBN: 9780915144761
Category : Philosophy
Languages : en
Pages : 542
Get Book Here
Book Description
Author: Alfred Tarski
Publisher: American Mathematical Soc.
ISBN: 0821810413
Category : Mathematics
Languages : en
Pages : 342
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Book Description
Culminates nearly half a century of the late Alfred Tarski's foundational studies in logic, mathematics, and the philosophy of science. This work shows that set theory and number theory can be developed within the framework of a new, different and simple equational formalism, closely related to the formalism of the theory of relation algebras.
Author: Peter B. Andrews
Publisher: Springer Science & Business Media
ISBN: 9781402007637
Category : Computers
Languages : en
Pages : 416
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Book Description
In case you are considering to adopt this book for courses with over 50 students, please contact
[email protected] for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.
Author: Alfred Tarski
Publisher: Dover Books on Mathematics
ISBN: 9780486477039
Category : Mathematics
Languages : en
Pages : 0
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Book Description
This well-known book by the famed logician consists of three treatises: A General Method in Proofs of Undecidability, Undecidability and Essential Undecidability in Mathematics, and Undecidability of the Elementary Theory of Groups. 1953 edition.
Author: Sten Lindström
Publisher: Springer Science & Business Media
ISBN: 1402089260
Category : Mathematics
Languages : en
Pages : 509
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Book Description
This anthology reviews the programmes in the foundations of mathematics from the classical period and assesses their possible relevance for contemporary philosophy of mathematics. A special section is concerned with constructive mathematics.
Author: Rudolf Carnap
Publisher: Routledge
ISBN: 1317830601
Category : Philosophy
Languages : en
Pages : 369
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Book Description
This is IV volume of eight in a series on Philosophy of the Mind and Language. For nearly a century mathematicians and logicians have been striving hard to make logic an exact science. But a book on logic must contain, in addition to the formulae, an expository context which, with the assistance of the words of ordinary language, explains the formulae and the relations between them; and this context often leaves much to be desired in the matter of clarity and exactitude. Originally published in 1937, the purpose of the present work is to give a systematic exposition of such a method, namely, of the method of " logical syntax".
Author: Robert R. Stoll
Publisher: Courier Corporation
ISBN: 0486139646
Category : Mathematics
Languages : en
Pages : 516
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Book Description
Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.
Author: Gil Sagi
Publisher: Cambridge University Press
ISBN: 1108529828
Category : Mathematics
Languages : en
Pages : 316
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Book Description
This collection of new essays presents cutting-edge research on the semantic conception of logic, the invariance criteria of logicality, grammaticality, and logical truth. Contributors explore the history of the semantic tradition, starting with Tarski, and its historical applications, while central criticisms of the tradition, and especially the use of invariance criteria to explain logicality, are revisited by the original participants in that debate. Other essays discuss more recent criticism of the approach, and researchers from mathematics and linguistics weigh in on the role of the semantic tradition in their disciplines. This book will be invaluable to philosophers and logicians alike.
Author: Theodore Hailperin
Publisher: Lehigh University Press
ISBN: 9780934223454
Category : Mathematics
Languages : en
Pages : 316
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Book Description
This study presents a logic in which probability values play a semantic role comparable to that of truth values in conventional logic. The difference comes in with the semantic definition of logical consequence. It will be of interest to logicians, both philosophical and mathematical, and to investigators making use of logical inference under uncertainty, such as in operations research, risk analysis, artificial intelligence, and expert systems.
Author: Andrew Aberdein
Publisher: Springer Science & Business Media
ISBN: 9400765347
Category : Philosophy
Languages : en
Pages : 392
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Book Description
Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics.
