Download or read book Le Niewski s Systems of Logic and Foundations of Mathematics written by Rafal Urbaniak and published by . This book was released on 2013-10-31 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Le niewski s Systems of Logic and Foundations of Mathematics written by Rafal Urbaniak and published by Springer Science & Business Media. This book was released on 2013-09-24 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This meticulous critical assessment of the ground-breaking work of philosopher Stanislaw Leśniewski focuses exclusively on primary texts and explores the full range of output by one of the master logicians of the Lvov-Warsaw school. The author’s nuanced survey eschews secondary commentary, analyzing Leśniewski's core philosophical views and evaluating the formulations that were to have such a profound influence on the evolution of mathematical logic. One of the undisputed leaders of the cohort of brilliant logicians that congregated in Poland in the early twentieth century, Leśniewski was a guide and mentor to a generation of celebrated analytical philosophers (Alfred Tarski was his PhD student). His primary achievement was a system of foundational mathematical logic intended as an alternative to the Principia Mathematica of Alfred North Whitehead and Bertrand Russell. Its three strands—‘protothetic’, ‘ontology’, and ‘mereology’, are detailed in discrete sections of this volume, alongside a wealth other chapters grouped to provide the fullest possible coverage of Leśniewski’s academic output. With material on his early philosophical views, his contributions to set theory and his work on nominalism and higher-order quantification, this book offers a uniquely expansive critical commentary on one of analytical philosophy’s great pioneers.
Download or read book The Logical Foundations of Mathematics written by William S. Hatcher and published by Pergamon. This book was released on 1982 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: First-order logic. The origin of modern foundational studies. Frege's system and the paradoxes. The teory of types. Zermelo-Fraenkel set theory. Hilbert's program and Godel's incompleteness theorems. The foundational systems of W.V. Quine. Categorical algebra.
Download or read book Classical Mathematical Logic written by Richard L. Epstein and published by Princeton University Press. This book was released on 2011-12-18 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Classical Mathematical Logic, Richard L. Epstein relates the systems of mathematical logic to their original motivations to formalize reasoning in mathematics. The book also shows how mathematical logic can be used to formalize particular systems of mathematics. It sets out the formalization not only of arithmetic, but also of group theory, field theory, and linear orderings. These lead to the formalization of the real numbers and Euclidean plane geometry. The scope and limitations of modern logic are made clear in these formalizations. The book provides detailed explanations of all proofs and the insights behind the proofs, as well as detailed and nontrivial examples and problems. The book has more than 550 exercises. It can be used in advanced undergraduate or graduate courses and for self-study and reference. Classical Mathematical Logic presents a unified treatment of material that until now has been available only by consulting many different books and research articles, written with various notation systems and axiomatizations.
Download or read book Foundations of Set Theory written by A.A. Fraenkel and published by Elsevier. This book was released on 1973-12-01 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there been such extensive, almost revolutionary, developments. This book tries to avoid a detailed discussion of those topics which would have required heavy technical machinery, while describing the major results obtained in their treatment if these results could be stated in relatively non-technical terms. This book comprises five chapters and begins with a discussion of the antinomies that led to the reconstruction of set theory as it was known before. It then moves to the axiomatic foundations of set theory, including a discussion of the basic notions of equality and extensionality and axioms of comprehension and infinity. The next chapters discuss type-theoretical approaches, including the ideal calculus, the theory of types, and Quine's mathematical logic and new foundations; intuitionistic conceptions of mathematics and its constructive character; and metamathematical and semantical approaches, such as the Hilbert program. This book will be of interest to mathematicians, logicians, and statisticians.
Download or read book Fundamentals of Mathematical Logic written by Samuel Parkers and published by . This book was released on 2022-09-20 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The sub-field of mathematics that focuses on identifying the applications of formal logic to mathematics is known as mathematical logic. It is also known as symbolic logic or formal logic. It is concerned with the study of expressive and deductive power of formal systems. Some of the formal logical systems are first-order logic, nonclassical and modal logic, algebraic logic and other classical logics. The discipline is divided into four areas. These are model theory, proof theory, set theory and recursion theory. The field is closely related to theoretical computer science and foundations of mathematics. The field finds its applications in other disciplines such as physics, biology, economics, metaphysics, law and morals, and psychology. This book explores all the important aspects of related to this discipline in the present day scenario. Different approaches, evaluations, methodologies and studies on mathematical logic have been included herein. As this field is emerging at a rapid pace, the contents of this book will help the readers understand the modern concepts and applications of the subject.
Download or read book Philosophy and Ideology written by Z.A. Jordan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 778 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this study is to describe the development of philosophy in Poland since the end of the Second World War and the development of Marxist-Leninist philosophy which, owing to international political events, has assumed an impor tant role in the intellectual life of contemporary Poland. This task could not have been accomplished without relating post-war developments to those of the inter war period. Consequently, the period studied covers the years 1918-1958. Yet another extension was necessary. Marxism-Leninism regards sociology as a part of philosophy. Moreover, Marxism-Leninism often resorts to sociology to support or justify some of its philosophical views. Finally, its criticism of 'bourgeois philosophy' is often concerned with social philosophy and socio logical theories which supposedly are implicit or explicit in 'bourgeois philoso phy'. For this reason it was desirable to consider in this study some theoretical and methodological problems of the social sciences. They are taken into ac count when they illuminate philosophical controversies or the evolution of Marxist-Leninist philosophy. Marxism-Leninism is not only a new line of development but also a new point of departure in Polish philosophy. It provides a striking contrast with the established philosophical tradition which originated roughly at the time when G. E. Moore and Bertrand Russell initiated the analytical trend in English philosophy. The contrast can be epitomised by the contradistinction of philoso phy and ideology, chosen as the title of this study.
Download or read book Studies in Logic and the Foundations of Mathematics written by and published by . This book was released on 1965 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Logic written by H.-D. Ebbinghaus and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.
Download or read book Introduction to Mathematical Logic written by Agustin Willmott and published by Larsen and Keller Education. This book was released on 2019-06-20 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical logic is a subfield of mathematics that is concerned with the application of formal logic to mathematics. It is closely associated with the foundations of mathematics, metamathematics and theoretical computer science. The study of the deductive power of formal proof systems and the expressive power of formal systems are the unifying themes in mathematical logic. Set theory, recursion theory, proof theory and model theory are the primary subfields in mathematical logic. Each of these fields has a distinct focus. The systems of propositional logic and first-order logic are widely explored for application in the foundations of mathematics. The classical logic systems such as second-order logic or infinitary logic and nonclassical logic systems such as intuitionistic logic are also studied in this field. This book provides comprehensive insights into the field of mathematical logic. It presents the complex subject of mathematical logic in the most comprehensible and easy to understand language. In this book, constant effort has been made to make the understanding of the difficult concepts as easy and informative as possible, for the readers.
Download or read book Introduction to Mathematical Logic written by Michał Walicki and published by World Scientific Publishing Company. This book was released on 2011-12-13 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a systematic and well-paced introduction to mathematical logic. Excellent as a course text, the book presupposes only elementary background and can be used also for self-study by more ambitious students. Starting with the basics of set theory, induction and computability, it covers propositional and first-order logic — their syntax, reasoning systems and semantics. Soundness and completeness results for Hilbert's and Gentzen's systems are presented, along with simple decidability arguments. The general applicability of various concepts and techniques is demonstrated by highlighting their consistent reuse in different contexts. Unlike in most comparable texts, presentation of syntactic reasoning systems precedes the semantic explanations. The simplicity of syntactic constructions and rules — of a high, though often neglected, pedagogical value — aids students in approaching more complex semantic issues. This order of presentation also brings forth the relative independence of syntax from the semantics, helping to appreciate the importance of the purely symbolic systems, like those underlying computers. An overview of the history of logic precedes the main text, while informal analogies precede introduction of most central concepts. These informal aspects are kept clearly apart from the technical ones. Together, they form a unique text which may be appreciated equally by lecturers and students occupied with mathematical precision, as well as those interested in the relations of logical formalisms to the problems of computability and the philosophy of logic. Contents:A History of Logic:Patterns of ReasoningA Language and Its MeaningA Symbolic Language1850–1950 — Mathematical LogicModern Symbolic LogicSummaryElements of Set Theory:Sets, Functions, RelationsInductionTuring Machines:Computability and DecidabilityPropositional Logic:Syntax and Proof SystemsSemantics of PLSoundness and CompletenessFirst-Order Logic:Syntax and Proof Systems of FOLSemantics of FOLMore SemanticsSoundness and CompletenessWhy is First Order Logic “First Order”? Readership: Undergraduates learning logic, lecturers teaching logic, any professionals who are non-experts in the subject but wish to learn and understand more about logic.
Download or read book The Foundations of Mathematics in the Theory of Sets written by John P. Mayberry and published by Cambridge University Press. This book was released on 2000 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2001 book will appeal to mathematicians and philosophers interested in the foundations of mathematics.
Download or read book Introduction to Elementary Mathematical Logic written by Abram Aronovich Stolyar and published by Courier Corporation. This book was released on 1984-01-01 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lucid, non-intimidating presentation by a Russian scholar explores propositional logic, propositional calculus, and predicate logic. Topics include computer science and systems analysis, linguistics, and problems in the foundations of mathematics. Accessible to high school students, it also constitutes a valuable review of fundamentals for professionals. 1970 edition.
Download or read book Mathematical Logic in Asia written by Rod G. Downey and published by World Scientific. This book was released on 2006 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to the main areas of mathematical logic and applications to computer science. There are articles on weakly o-minimal theories, algorithmic complexity of relations, models within the computable model theory, hierarchies of randomness tests, computable numberings, and complexity problems of minimal unsatisfiable formulas. The problems of characterization of the deduction-detachment theorem, ?1-induction, completeness of Le?niewski's systems, and reduction calculus for the satisfiability problem are also discussed.The coverage includes the answer to Kanovei's question about the upper bound for the complexity of equivalence relations by convergence at infinity for continuous functions. The volume also gives some applications to computer science such as solving the problems of inductive interference of languages from the full collection of positive examples and some negative data, the effects of random negative data, methods of formal specification and verification on the basis of model theory and multiple-valued logics, interval fuzzy algebraic systems, the problems of information exchange among agents on the base topological structures, and the predictions provided by inductive theories.
Download or read book Polish Logic 1920 1939 written by Storrs McCall and published by OUP Oxford. This book was released on 1967-08 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polish Logic 1920-1939
Download or read book Logic Foundations of Mathematics written by A. Heyting and published by Gordon & Breach Science Pub. This book was released on 1968-05 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Development of Mathematical Logic written by P. H. Nidditch and published by Burns & Oates. This book was released on 1998 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a clear and straightforward summary of the history of formal logic from the time of Aristotle to that of Godel. Nidditch discusses the four main trends at the root of modern logic: Aristotle's theory of the syllogism; the idea of a universal language; the idea of the parts of mathematics forming deductive systems; and the discoveries in mathematics in the early nineteenth century. He goes on to outline the chief ideas and theories of the main writers on mathematical logic, including Jevons, Peirce, Boole, Russell, and Whitehead. The text is easy to read and gives the beginning student a valuable perspective on mathematical logic.
