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Author : Lorne Szabolcsi
Publisher :
ISBN 13 :
Total Pages : 154 pages
Book Rating : 4.3/5 (91 download)
Download or read book Numerical Term Logic written by Lorne Szabolcsi and published by . This book was released on 2008 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an edited volume of the unpublished work of numerical logic pioneer, Lome Szabolcsi, who died suddenly at age 28.
Author : Neil Tennant
Publisher : Oxford University Press
ISBN 13 : 0192661981
Total Pages : 320 pages
Book Rating : 4.1/5 (926 download)
Download or read book The Logic of Number written by Neil Tennant and published by Oxford University Press. This book was released on 2022-02-10 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: In The Logic of Number, Neil Tennant defines and develops his Natural Logicist account of the foundations of the natural, rational, and real numbers. Based on the logical system free Core Logic, the central method is to formulate rules of natural deduction governing variable-binding number-abstraction operators and other logico-mathematical expressions such as zero and successor. These enable 'single-barreled' abstraction, in contrast with the 'double-barreled' abstraction effected by principles such as Frege's Basic Law V, or Hume's Principle. Natural Logicism imposes upon its account of the numbers four conditions of adequacy: First, one must show how it is that the various kinds of number are applicable in our wider thought and talk about the world. This is achieved by deriving all instances of three respective schemas: Schema N for the naturals, Schema Q for the rationals, and Schema R for the reals. These provide truth-conditions for statements deploying terms referring to numbers of the kind in question. Second, one must show how it is that the naturals sit among the rationals as themselves again, and the rationals likewise among the reals. Third, one should reveal enough of the metaphysical nature of the numbers to be able to derive the mathematician's basic laws governing them. Fourth, one should be able to demonstrate that there are uncountably many reals. Natural Logicism is realistic about the limits of logicism when it comes to treating the real numbers, for which, Tennant argues, one needs recourse to geometric intuition for deeper starting-points, beyond which logic alone will then deliver the sought results, with absolute formal rigor. The resulting program enables one to delimit, in a principled way, those parts of number theory that are produced by the Kantian understanding alone, and those parts that depend on recourse to (very simple) a priori geometric intuitions.
Author : Bertrand Russell
Publisher :
ISBN 13 :
Total Pages : 224 pages
Book Rating : 4.3/5 (91 download)
Download or read book Introduction to Mathematical Philosophy written by Bertrand Russell and published by . This book was released on 1920 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Craig DeLancey
Publisher : Open SUNY Textbooks
ISBN 13 : 9781942341437
Total Pages : pages
Book Rating : 4.3/5 (414 download)
Download or read book A Concise Introduction to Logic written by Craig DeLancey and published by Open SUNY Textbooks. This book was released on 2017-02-06 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : I. P. Hughlings
Publisher : Read Books Ltd
ISBN 13 : 1473351413
Total Pages : 81 pages
Book Rating : 4.4/5 (733 download)
Download or read book The Logic Of Names : An Introduction To Boole's Laws Of Thought.. written by I. P. Hughlings and published by Read Books Ltd. This book was released on 2016-09-06 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Logic Of Names : An Introduction To Boole's Laws Of Thought.. - By I. P. Hughlings
Author : Elliot Mendelsohn
Publisher : Springer Science & Business Media
ISBN 13 : 1461572886
Total Pages : 351 pages
Book Rating : 4.4/5 (615 download)
Download or read book Introduction to Mathematical Logic written by Elliot Mendelsohn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a compact mtroduction to some of the pnncipal tOpICS of mathematical logic . In the belief that beginners should be exposed to the most natural and easiest proofs, I have used free-swinging set-theoretic methods. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with mathematical logic has been obtained. If we are to be expelled from "Cantor's paradise" (as nonconstructive set theory was called by Hilbert), at least we should know what we are missing. The major changes in this new edition are the following. (1) In Chapter 5, Effective Computability, Turing-computabIlity IS now the central notion, and diagrams (flow-charts) are used to construct Turing machines. There are also treatments of Markov algorithms, Herbrand-Godel-computability, register machines, and random access machines. Recursion theory is gone into a little more deeply, including the s-m-n theorem, the recursion theorem, and Rice's Theorem. (2) The proofs of the Incompleteness Theorems are now based upon the Diagonalization Lemma. Lob's Theorem and its connection with Godel's Second Theorem are also studied. (3) In Chapter 2, Quantification Theory, Henkin's proof of the completeness theorem has been postponed until the reader has gained more experience in proof techniques. The exposition of the proof itself has been improved by breaking it down into smaller pieces and using the notion of a scapegoat theory. There is also an entirely new section on semantic trees.
Author : Yu. I. Manin
Publisher : Springer Science & Business Media
ISBN 13 : 1441906150
Total Pages : 389 pages
Book Rating : 4.4/5 (419 download)
Download or read book A Course in Mathematical Logic for Mathematicians written by Yu. I. Manin and published by Springer Science & Business Media. This book was released on 2009-10-13 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. The ?rst edition of this book was published in 1977. The text has been well received and is still used, although it has been out of print for some time. In the intervening three decades, a lot of interesting things have happened to mathematical logic: (i) Model theory has shown that insights acquired in the study of formal languages could be used fruitfully in solving old problems of conventional mathematics. (ii) Mathematics has been and is moving with growing acceleration from the set-theoretic language of structures to the language and intuition of (higher) categories, leaving behind old concerns about in?nities: a new view of foundations is now emerging. (iii) Computer science, a no-nonsense child of the abstract computability theory, has been creatively dealing with old challenges and providing new ones, such as the P/NP problem. Planning additional chapters for this second edition, I have decided to focus onmodeltheory,the conspicuousabsenceofwhichinthe ?rsteditionwasnoted in several reviews, and the theory of computation, including its categorical and quantum aspects. The whole Part IV: Model Theory, is new. I am very grateful to Boris I. Zilber, who kindly agreed to write it. It may be read directly after Chapter II. The contents of the ?rst edition are basically reproduced here as Chapters I–VIII. Section IV.7, on the cardinality of the continuum, is completed by Section IV.7.3, discussing H. Woodin’s discovery.
Author : Pedro Domingos
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1598296922
Total Pages : 156 pages
Book Rating : 4.5/5 (982 download)
Download or read book Markov Logic written by Pedro Domingos and published by Morgan & Claypool Publishers. This book was released on 2009 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most subfields of computer science have an interface layer via which applications communicate with the infrastructure, and this is key to their success (e.g., the Internet in networking, the relational model in databases, etc.). So far this interface layer has been missing in AI. First-order logic and probabilistic graphical models each have some of the necessary features, but a viable interface layer requires combining both. Markov logic is a powerful new language that accomplishes this by attaching weights to first-order formulas and treating them as templates for features of Markov random fields. Most statistical models in wide use are special cases of Markov logic, and first-order logic is its infinite-weight limit. Inference algorithms for Markov logic combine ideas from satisfiability, Markov chain Monte Carlo, belief propagation, and resolution. Learning algorithms make use of conditional likelihood, convex optimization, and inductive logic programming. Markov logic has been successfully applied to problems in information extraction and integration, natural language processing, robot mapping, social networks, computational biology, and others, and is the basis of the open-source Alchemy system.
Author : Alfred North Whitehead
Publisher :
ISBN 13 :
Total Pages : 688 pages
Book Rating : 4.3/5 (91 download)
Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jacob T. Schwartz
Publisher : Springer Science & Business Media
ISBN 13 : 0857298089
Total Pages : 426 pages
Book Rating : 4.8/5 (572 download)
Download or read book Computational Logic and Set Theory written by Jacob T. Schwartz and published by Springer Science & Business Media. This book was released on 2011-07-16 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This must-read text presents the pioneering work of the late Professor Jacob (Jack) T. Schwartz on computational logic and set theory and its application to proof verification techniques, culminating in the ÆtnaNova system, a prototype computer program designed to verify the correctness of mathematical proofs presented in the language of set theory. Topics and features: describes in depth how a specific first-order theory can be exploited to model and carry out reasoning in branches of computer science and mathematics; presents an unique system for automated proof verification in large-scale software systems; integrates important proof-engineering issues, reflecting the goals of large-scale verifiers; includes an appendix showing formalized proofs of ordinals, of various properties of the transitive closure operation, of finite and transfinite induction principles, and of Zorn’s lemma.
Author : Eckart Menzler-Trott
Publisher : American Mathematical Soc.
ISBN 13 : 1470428121
Total Pages : 466 pages
Book Rating : 4.4/5 (74 download)
Download or read book Logic's Lost Genius written by Eckart Menzler-Trott and published by American Mathematical Soc.. This book was released on 2016-05-05 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gerhard Gentzen (1909–1945) is the founder of modern structural proof theory. His lasting methods, rules, and structures resulted not only in the technical mathematical discipline called “proof theory” but also in verification programs that are essential in computer science. The appearance, clarity, and elegance of Gentzen's work on natural deduction, the sequent calculus, and ordinal proof theory continue to be impressive even today. The present book gives the first comprehensive, detailed, accurate scientific biography expounding the life and work of Gerhard Gentzen, one of our greatest logicians, until his arrest and death in Prague in 1945. Particular emphasis in the book is put on the conditions of scientific research, in this case mathematical logic, in National Socialist Germany, the ideological fight for “German logic”, and their mutual protagonists. Numerous hitherto unpublished sources, family documents, archival material, interviews, and letters, as well as Gentzen's lectures for the mathematical public, make this book an indispensable source of information on this important mathematician, his work, and his time. The volume is completed by two deep substantial essays by Jan von Plato and Craig Smoryński on Gentzen's proof theory; its relation to the ideas of Hilbert, Brouwer, Weyl, and Gödel; and its development up to the present day. Smoryński explains the Hilbert program in more than the usual slogan form and shows why consistency is important. Von Plato shows in detail the benefits of Gentzen's program. This important book is a self-contained starting point for any work on Gentzen and his logic. The book is accessible to a wide audience with different backgrounds and is suitable for general readers, researchers, students, and teachers.
Author : Agustín Rayo
Publisher :
ISBN 13 : 0199662622
Total Pages : 241 pages
Book Rating : 4.1/5 (996 download)
Download or read book The Construction of Logical Space written by Agustín Rayo and published by . This book was released on 2013-06-27 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our conception of logical space is the set of distinctions we use to navigate the world. Agustín Rayo argues that this is shaped by acceptance or rejection of 'just is'-statements: e.g. 'to be composed of water just is to be composed of H2O'. He offers a novel conception of metaphysical possibility, and a new trivialist philosophy of mathematics.
Author : E. Börger
Publisher : Elsevier
ISBN 13 : 008088704X
Total Pages : 618 pages
Book Rating : 4.0/5 (88 download)
Download or read book Computability, Complexity, Logic written by E. Börger and published by Elsevier. This book was released on 1989-07-01 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theme of this book is formed by a pair of concepts: the concept of formal language as carrier of the precise expression of meaning, facts and problems, and the concept of algorithm or calculus, i.e. a formally operating procedure for the solution of precisely described questions and problems.The book is a unified introduction to the modern theory of these concepts, to the way in which they developed first in mathematical logic and computability theory and later in automata theory, and to the theory of formal languages and complexity theory. Apart from considering the fundamental themes and classical aspects of these areas, the subject matter has been selected to give priority throughout to the new aspects of traditional questions, results and methods which have developed from the needs or knowledge of computer science and particularly of complexity theory.It is both a textbook for introductory courses in the above-mentioned disciplines as well as a monograph in which further results of new research are systematically presented and where an attempt is made to make explicit the connections and analogies between a variety of concepts and constructions.
Author : Mark Zegarelli
Publisher : John Wiley & Sons
ISBN 13 : 0471799416
Total Pages : 384 pages
Book Rating : 4.4/5 (717 download)
Download or read book Logic For Dummies written by Mark Zegarelli and published by John Wiley & Sons. This book was released on 2006-11-29 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: A straightforward guide to logic concepts Logic concepts are more mainstream than you may realize. There’s logic every place you look and in almost everything you do, from deciding which shirt to buy to asking your boss for a raise, and even to watching television, where themes of such shows as CSI and Numbers incorporate a variety of logistical studies. Logic For Dummies explains a vast array of logical concepts and processes in easy-to-understand language that make everything clear to you, whether you’re a college student of a student of life. You’ll find out about: Formal Logic Syllogisms Constructing proofs and refutations Propositional and predicate logic Modal and fuzzy logic Symbolic logic Deductive and inductive reasoning Logic For Dummies tracks an introductory logic course at the college level. Concrete, real-world examples help you understand each concept you encounter, while fully worked out proofs and fun logic problems encourage you students to apply what you’ve learned.
Author : Francisco Rodríguez-Consuegra
Publisher : Birkhäuser
ISBN 13 : 3034875339
Total Pages : 249 pages
Book Rating : 4.0/5 (348 download)
Download or read book The Mathematical Philosophy of Bertrand Russell: Origins and Development written by Francisco Rodríguez-Consuegra and published by Birkhäuser. This book was released on 2012-12-06 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: by Ivor Grattan-Guinness Until twenty years ago the outline history of logicism was well known. Frege had had the important ideas, until he was eclipsed by Wittgenstein. Russell was important in publicising the former and tutoring the latter, and also for working with Moore in the conversion of British philosophy from neo-Hegelianism to the new analytic tradition in the 1900s, but his own work on logic and especially logicism was very muddled. Around that time Russell, who was still alive, sold his manuscripts to McMaster University in Canada, and interest in his achievements in logic began to develop, especially after his death in 1970. Scholars found thousands of folios of unpublished holograph awaiting their attention, and also hundreds of pertinent letters (both in the Russell Archives and elsewhere in certain recipients' collections). Various facets of his work came to light for the first time, and others -which could have been gleaned from carefully reading of the published sources- gained new publicity from the evidence revealed in manuscripts. Even the technical passage work, which constitutes the unread majority of the Principia mathematica (1910-13) of Russell and Whitehead, began to receive a little respectful scrutiny. It turned out that Russell had done several pioneering things. While indeed often incoherent in reference and content, they comprised major forays into the new mathematical logic, of which he turned out to be a major founder: some are even of interest to modem studies.
Author : Roger Scruton
Publisher : Routledge
ISBN 13 : 1134792085
Total Pages : 259 pages
Book Rating : 4.1/5 (347 download)
Download or read book A Short History of Modern Philosophy written by Roger Scruton and published by Routledge. This book was released on 2002-09-11 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Short History of Modern Philosophy is a lucid, challenging and up-to-date survey of the philosophers and philosophies from the founding father of modern philosophy, René Descartes, to the most important and famous philosopher of the twentieth century, Ludwig Wittgenstein. Roger Scruton has been widely praised for his success in making the history of modern philosophy cogent and intelligible to anyone wishing to understand this fascinating subject. In this new edition, he has responded to the explosion of interest in the history of philosophy by substantially rewriting the book, taking account of recent debates and scholarship.
Author : William Stanley Jevons
Publisher :
ISBN 13 :
Total Pages : 106 pages
Book Rating : 4.0/5 (18 download)
Download or read book Pure Logic written by William Stanley Jevons and published by . This book was released on 1864 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt:
