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 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 Mathematical Logic and the Foundations of Mathematics written by G. T. Kneebone and published by . This book was released on 1963 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Foundations of Mathematical Logic written by Haskell Brooks Curry and published by . This book was released on 1963 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive account of the constructive theory of the first-order predicate calculus, which is central to modern mathematical logic and important for mathematicians, philosophers and scientists whose work impinges upon logic. The first half of the book gives the basic principles and outlines of the field. After a general introduction, the author discusses formal methods including algorithms and epitheory. A brief treatment of the Markov treatment of algorithms is included. The elementary facts about lattices and similar algebraic systems are then covered. In the second half of the book Curry investigates the possibility for a formulation which expresses the meaning to be attached to the logical connectives and to develop the properties which follow from the assumptions so motivated. Written by a man considered by many to be one of the major pioneers in the field of mathematical logic, this book avoids a doctrinaire stance, presenting various interpretations of logical systems.--From publisher description. NOTE 505 0 Formal systems -- Epitheory -- Relational logical algebra -- The theory of implication -- Negation -- Quantification -- Modality.
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 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 Mathematical Logic written by Heinz-Dieter Ebbinghaus and published by Springer Nature. This book was released on 2021-05-28 with total page 304 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 Micha? Walicki and published by World Scientific. This book was released on 2012 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 does not presuppose any previous knowledge 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, in which careful presentation of concepts, results and examples is accompanied by the informal analogies and illustrations. 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 mathematical logic.
Download or read book The Algebra of Logic written by Louis Couturat and published by Prabhat Prakashan. This book was released on 2015-06-14 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from The Algebra of Logic Mathematical Logic is a necessary preliminary to logical Mathematics. "Mathematical Logic" is the name given by Peano to what is also known (after Venn) as "Symbolic Logic"; and Symbolic Logic is, in essentials, the Logic of Aristotle, given new life and power by being dressed up in the wonderful - almost magical - armour and accoutrements of Algebra. In less than seventy years, logic, to use an expression of De Morgan's, has so thriven upon symbols and, in consequence, so grown and altered that the ancient logicians would not recognize it, and many old-fashioned logicians will not recognize it. The metaphor is not quite correct: Logic has neither grown nor altered, but we now see more of it and more into it. The primary significance of a symbolic calculus seems to lie in the economy of mental effort which it brings about, and to this is due the characteristic power and rapid development of mathematical knowledge. Attempts to treat the operations of formal logic in an analogous way had been made not in frequently by some of the more philosophical mathematicians, such as Leibniz and Lambert; but their labors remained little known, and it was Boole and De Morgan, about the middle of the nineteenth century, to whom a mathematical - though of course non-quantitative - way of regarding logic was due. By this, not only was the traditional or Aristotelian doctrine of logic reformed and completed, but out of it has developed, in course of time, an instrument which deals in a sure manner with the task of investigating the fundamental concepts of mathematics - a task which philosophers have repeatedly taken in hand, and in which they have as repeatedly failed. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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 Logic and Foundations of Mathematics written by Andrea Cantini and published by . This book was released on 2014-01-15 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Foundations of Logic and Mathematics written by Yves Nievergelt and published by . This book was released on 2002 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Logic and Foundations of Mathematics written by Raymond Klibansky and published by . This book was released on 1968 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Logic and Foundations of Mathematics written by Arend Heyting and published by . This book was released on 1969 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt:
