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Author : David Hilbert
Publisher : Springer
ISBN 13 :
Total Pages : 210 pages
Book Rating : 4.F/5 ( download)
Download or read book Grundzüge der Theoretischen Logik written by David Hilbert and published by Springer. This book was released on 1972-09-25 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : D. Hilbert
Publisher :
ISBN 13 :
Total Pages : 172 pages
Book Rating : 4.:/5 (867 download)
Download or read book Principles of Mathematical Logic written by D. Hilbert and published by . This book was released on 1950 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : D. Hilbert
Publisher : American Mathematical Society
ISBN 13 : 147047056X
Total Pages : 187 pages
Book Rating : 4.4/5 (74 download)
Download or read book Principles of Mathematical Logic written by D. Hilbert and published by American Mathematical Society. This book was released on 2022-05-11 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: David Hilbert was particularly interested in the foundations of mathematics. Among many other things, he is famous for his attempt to axiomatize mathematics. This now classic text is his treatment of symbolic logic. This translation is based on the second German edition and has been modified according to the criticisms of Church and Quine. In particular, the authors' original formulation of Gödel's completeness proof for the predicate calculus has been updated. In the first half of the twentieth century, an important debate on the foundations of mathematics took place. Principles of Mathematical Logic represents one of Hilbert's important contributions to that debate. Although symbolic logic has grown considerably in the subsequent decades, this book remains a classic.
Author : David Hilbert
Publisher : American Mathematical Soc.
ISBN 13 : 0821820249
Total Pages : 186 pages
Book Rating : 4.8/5 (218 download)
Download or read book Principles of Mathematical Logic written by David Hilbert and published by American Mathematical Soc.. This book was released on 1999 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: David Hilbert was particularly interested in the foundations of mathematics. Among many other things, he is famous for his attempt to axiomatize mathematics. This now classic text is his treatment of symbolic logic. It lays the groundwork for his later work with Bernays. This translation is based on the second German edition, and has been modified according to the criticisms of Church and Quine. In particular, the authors' original formulation of Gödel's completeness proof for the predicate calculus has been updated. In the first half of the twentieth century, an important debate on the foundations of mathematics took place. Principles of Mathematical Logic represents one of Hilbert's important contributions to that debate. Although symbolic logic has grown considerably in the subsequent decades, this book remains a classic.
Author : William Ewald
Publisher : Springer-Verlag
ISBN 13 : 3540694447
Total Pages : 1062 pages
Book Rating : 4.5/5 (46 download)
Download or read book David Hilbert's Lectures on the Foundations of Arithmetic and Logic 1917-1933 written by William Ewald and published by Springer-Verlag. This book was released on 2013-05-14 with total page 1062 pages. Available in PDF, EPUB and Kindle. Book excerpt: The core of Volume 3 consists of lecture notes for seven sets of lectures Hilbert gave (often in collaboration with Bernays) on the foundations of mathematics between 1917 and 1926. These texts make possible for the first time a detailed reconstruction of the rapid development of Hilbert’s foundational thought during this period, and show the increasing dominance of the metamathematical perspective in his logical work: the emergence of modern mathematical logic; the explicit raising of questions of completeness, consistency and decidability for logical systems; the investigation of the relative strengths of various logical calculi; the birth and evolution of proof theory, and the parallel emergence of Hilbert’s finitist standpoint. The lecture notes are accompanied by numerous supplementary documents, both published and unpublished, including a complete version of Bernays’s Habilitationschrift of 1918, the text of the first edition of Hilbert and Ackermann’s Grundzüge der theoretischen Logik (1928), and several shorter lectures by Hilbert from the later 1920s. These documents, which provide the background to Hilbert and Bernays’s monumental Grundlagen der Mathematik (1934, 1938), are essential for understanding the development of modern mathematical logic, and for reconstructing the interactions between Hilbert, Bernays, Brouwer, and Weyl in the philosophy of mathematics.
Author : Rudolf Carnap
Publisher : Courier Corporation
ISBN 13 : 048614349X
Total Pages : 272 pages
Book Rating : 4.4/5 (861 download)
Download or read book Introduction to Symbolic Logic and Its Applications written by Rudolf Carnap and published by Courier Corporation. This book was released on 2012-07-12 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Clear, comprehensive, and rigorous treatment develops the subject from elementary concepts to the construction and analysis of relatively complex logical languages. Hundreds of problems, examples, and exercises. 1958 edition.
Author : Steve Awodey
Publisher : Oxford University Press
ISBN 13 : 0198907443
Total Pages : 528 pages
Book Rating : 4.1/5 (989 download)
Download or read book Rudolf Carnap: Studies in Semantics written by Steve Awodey and published by Oxford University Press. This book was released on 2024-05-07 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains Carnap's Studies in Semantics, a series of three interlocking books: Introduction to Semantics (1942), Formalization of Logic (1942), and Meaning and Necessity (1947). They were extremely influential in their time, especially the third, and shaped the direction of analytic philosophy during the 1950s and 1960s. They constitute the background to a number of celebrated controversies of that period, especially those between Carnap and Quine. Most of the philosophical debates today in philosophical logic and the philosophy of language ultimately had their origins here. This new edition situates these works in their context, both within Carnap's philosophical development and within the philosophical debates they responded to and influenced. The editors' introduction explains how Carnap arrived at the project of semantics in the 1930s and how it developed into these three successive publications, how the three books fit together, and how the project developed and changed in the course of the 1940s. It also describes the reception of the books as they appeared, as well as Carnap's response. The editorial and textual notes give variant readings, Carnap's own marginal notes on these texts in his personal copies, and elucidatory commentary where Carnap's terminology or notation are no longer familiar. This will be an indispensable volume for anyone interested in the origins and preoccupations of present-day analytic philosophy, especially philosophical logic and philosophy of language.
Author : Joan Roselló
Publisher : Cambridge Scholars Publishing
ISBN 13 : 152752762X
Total Pages : 295 pages
Book Rating : 4.5/5 (275 download)
Download or read book Hilbert, Göttingen and the Development of Modern Mathematics written by Joan Roselló and published by Cambridge Scholars Publishing. This book was released on 2019-02-01 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: David Hilbert is one of the outstanding mathematicians of the twentieth century and probably the most influential. This book highlights Hilbert’s contributions to mathematics, putting them in their historical, social and cultural context. In doing so, particular attention is paid to Hilbert’s axiomatic method and his proposal for the foundations of mathematics, the so-called Hilbert’s program. The book also discusses the development of algebraic number theory, the theory of integral equations, modern algebra and the structural image of mathematics. In addition, it considers the famous list of Mathematical Problems presented in Paris in 1900, the mathematical tradition of the University of Göttingen, the great debate on the foundations of mathematics in the twenties between formalists and intuitionists, and, finally, Hilbert’s work on the theory of relativity and the foundations of quantum mechanics. The book will primarily appeal to an academic audience, although it will also be of interest to general-interest science readers.
Author : Phillip Herdina
Publisher : Routledge
ISBN 13 : 1136605061
Total Pages : 436 pages
Book Rating : 4.1/5 (366 download)
Download or read book Dict Philos Terms Germ-Eng V1 written by Phillip Herdina and published by Routledge. This book was released on 2013-01-11 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Available on its own, or as part of a two-volume set, this German-English dictionary is the first comprehensive work in the field and an indispensible companion for students, academics, translators and linguists concerned with almost any area of philosophy.
Author : Paolo Mancosu
Publisher : Oxford University Press
ISBN 13 : 0192649299
Total Pages : 336 pages
Book Rating : 4.1/5 (926 download)
Download or read book An Introduction to Proof Theory written by Paolo Mancosu and published by Oxford University Press. This book was released on 2021-08-12 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics.
Author : P. Lorenzen
Publisher : Springer Science & Business Media
ISBN 13 : 9401715823
Total Pages : 131 pages
Book Rating : 4.4/5 (17 download)
Download or read book Formal Logic written by P. Lorenzen and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Logic", one of the central words in Western intellectual history, compre hends in its meaning such diverse things as the Aristotelian syllogistic, the scholastic art of disputation, the transcendental logic of the Kantian critique, the dialectical logic of Hegel, and the mathematical logic of the Principia Mathematica of Whitehead and Russell. The term "Formal Logic", following Kant is generally used to distinguish formal logical reasonings, precisely as formal, from the remaining universal truths based on reason. (Cf. SCHOLZ, 1931). A text-book example of a formal-logical inference which from "Some men are philosophers" and "All philosophers are wise" concludes that "Some men are wise" is called formal, because the validity of this inference depends only on the form ofthe given sentences -in particular it does not depend on the truth or falsity of these sentences. (On the dependence of logic on natural language, English, for example, compare Section 1 and 8). The form of a sentence like "Some men are philosophers", is that which remains preserved when the given predicates, here "men" and "philosophers" are replaced by arbitrary ones. The form itself can thus be represented by replacing the given predicates by variables. Variables are signs devoid of meaning, which may serve merely to indicate the place where meaningful constants (here the predicates) are to be inserted. As variables we shall use - as did Aristotle - letters, say P, Q and R, as variables for predicates.
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 : Md. Aquil Khan
Publisher : Springer
ISBN 13 : 3662587718
Total Pages : 210 pages
Book Rating : 4.6/5 (625 download)
Download or read book Logic and Its Applications written by Md. Aquil Khan and published by Springer. This book was released on 2019-02-13 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the refereed proceedings of the 8th Indian Conference on Logic and Its Applications, ICLA 2019, held in Delhi, India, in March 2019. The volume contains 13 full revised papers along with 6 invited talks presented at the conference. The aim of this conference series is to bring together researchers from a wide variety of fields in which formal logic plays a significant role. Areas of interest include mathematical and philosophical logic, computer science logic, foundations and philosophy of mathematics and the sciences, use of formal logic in areas of theoretical computer science and artificial intelligence, logic and linguistics, and the relationship between logic and other branches of knowledge. Of special interest are studies in systems of logic in the Indian tradition, and historical research on logic.
Author : Willard Van Orman Quine
Publisher : Harvard University Press
ISBN 13 : 9780674802070
Total Pages : 384 pages
Book Rating : 4.8/5 (2 download)
Download or read book Set Theory and Its Logic written by Willard Van Orman Quine and published by Harvard University Press. This book was released on 1969 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an extensively revised edition of W. V. Quine’s introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before. Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.
Author : Willard Van O QUINE
Publisher : Harvard University Press
ISBN 13 : 0674042425
Total Pages : 381 pages
Book Rating : 4.6/5 (74 download)
Download or read book Set Theory and Its Logic, Revised Edition written by Willard Van O QUINE and published by Harvard University Press. This book was released on 2009-06-30 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an extensively revised edition of Mr. Quine's introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before. Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.
Author : Anna-Teresa Tymieniecka
Publisher : Elsevier
ISBN 13 : 1483274888
Total Pages : 346 pages
Book Rating : 4.4/5 (832 download)
Download or read book Contributions to Logic and Methodology written by Anna-Teresa Tymieniecka and published by Elsevier. This book was released on 2014-05-12 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributions to Logic and Methodology in Honor of J. M. Boche?ski focuses on the influence, contributions, and legacy of J. M. Boche?ski in the fields of logic and methodology. The selection first offers information on some remarks on inferential deduction, modal logic with eight modalities, and method and logic in presocratic explanation. Discussions focus on inference, evidence, hypothesis, generalization, semantical discussion, proof of necessity, multiple dialogues, and construction trees. The text then elaborates on reification, quotation, and nominalization, logic of preference and choice, and sense, denotation, and the context of sentences. Topics include axioms of preference and of choice, economic context, methodological remarks, reification, nominalization, and quotation. The manuscript examines conjectural inference and phenomenological analysis, including anticipatory evidence and choice of method, conjecture of the universal order, conjectural requirement of the architectonic project, and outline of the program of conjectural inquiry. The selection is a dependable source of information for philosophers and researchers interested in the influence and contributions of J. M. Boche?ski to logic and methodology.
Author : Stefania Centrone
Publisher : Springer
ISBN 13 : 9402411321
Total Pages : 526 pages
Book Rating : 4.4/5 (24 download)
Download or read book Essays on Husserl's Logic and Philosophy of Mathematics written by Stefania Centrone and published by Springer. This book was released on 2017-09-07 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: Essays on Husserl’s Logic and Philosophy of Mathematics sets out to fill up a lacuna in the present research on Husserl by presenting a precise account of Husserl’s work in the field of logic, of the philosophy of logic and of the philosophy of mathematics. The aim is to provide an in-depth reconstruction and analysis of the discussion between Husserl and his most important interlocutors, and to clarify pivotal ideas of Husserl’s by considering their reception and elaboration by some of his disciples and followers, such as Oskar Becker and Jacob Klein, as well as their influence on some of the most significant logicians and mathematicians of the past century, such as Luitzen E. J. Brouwer, Rudolf Carnap, Kurt Gödel and Hermann Weyl. Most of the papers consider Husserl and another scholar – e.g. Leibniz, Kant, Bolzano, Brentano, Cantor, Frege – and trace out and contextualize lines of influence, points of contact, and points of disagreement. Each essay is written by an expert of the field, and the volume includes contributions both from the analytical tradition and from the phenomenological one.
