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| Author | : Charles D. Parsons |
| Publisher | : Cornell University Press |
| Total Pages | : 367 |
| Release | : 2018-08-06 |
| Genre | : Mathematics |
| ISBN | : 1501729322 |
Download Mathematics in Philosophy Book in PDF, ePub and Kindle
This important book by a major American philosopher brings together eleven essays treating problems in logic and the philosophy of mathematics. A common point of view, that mathematical thought is central to our thought in general, underlies the essays. In his introduction, Parsons articulates that point of view and relates it to past and recent discussions of the foundations of mathematics. Mathematics in Philosophy is divided into three parts. Ontology—the question of the nature and extent of existence assumptions in mathematics—is the subject of Part One and recurs elsewhere. Part Two consists of essays on two important historical figures, Kant and Frege, and one contemporary, W. V. Quine. Part Three contains essays on the three interrelated notions of set, class, and truth.
| Author | : Geoffrey Hellman |
| Publisher | : Cambridge University Press |
| Total Pages | : 296 |
| Release | : 2021-02-04 |
| Genre | : Science |
| ISBN | : 1316999602 |
Download Mathematics and Its Logics Book in PDF, ePub and Kindle
In these essays Geoffrey Hellman presents a strong case for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite what appear to be contradictions between different systems, and positing different frameworks serving different legitimate purposes. The essays refine and extend Hellman's modal-structuralist account of mathematics, developing a height-potentialist view of higher set theory which recognizes indefinite extendability of models and stages at which sets occur. In the first of three new essays written for this volume, Hellman shows how extendability can be deployed to derive the axiom of Infinity and that of Replacement, improving on earlier accounts; he also shows how extendability leads to attractive, novel resolutions of the set-theoretic paradoxes. Other essays explore advantages and limitations of restrictive systems - nominalist, predicativist, and constructivist. Also included are two essays, with Solomon Feferman, on predicative foundations of arithmetic.
| Author | : Jaakko Hintikka |
| Publisher | : |
| Total Pages | : 462 |
| Release | : 1976 |
| Genre | : Logic |
| ISBN | : |
Download Essays on mathematical and philosophical logic Book in PDF, ePub and Kindle
| Author | : Åsa Hirvonen |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 385 |
| Release | : 2015-03-10 |
| Genre | : Philosophy |
| ISBN | : 1614519323 |
Download Logic Without Borders Book in PDF, ePub and Kindle
In recent years, mathematical logic has developed in many directions, the initial unity of its subject matter giving way to a myriad of seemingly unrelated areas. The articles collected here, which range from historical scholarship to recent research in geometric model theory, squarely address this development. These articles also connect to the diverse work of Väänänen, whose ecumenical approach to logic reflects the unity of the discipline.
| Author | : David DeVidi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 487 |
| Release | : 2011-03-23 |
| Genre | : Philosophy |
| ISBN | : 9400702140 |
Download Logic, Mathematics, Philosophy, Vintage Enthusiasms Book in PDF, ePub and Kindle
The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic (William Lawvere, Peter Aczel, Graham Priest, Giovanni Sambin); analytical philosophy (Michael Dummett, William Demopoulos), philosophy of science (Michael Redhead, Frank Arntzenius), philosophy of mathematics (Michael Hallett, John Mayberry, Daniel Isaacson) and decision theory and foundations of economics (Ken Bimore). Most articles are contributions to current philosophical debates, but contributions also include some new mathematical results, important historical surveys, and a translation by Wilfrid Hodges of a key work of arabic logic.
| Author | : John P. Burgess |
| Publisher | : Cambridge University Press |
| Total Pages | : 253 |
| Release | : 2008-02-21 |
| Genre | : Science |
| ISBN | : 113947054X |
Download Mathematics, Models, and Modality Book in PDF, ePub and Kindle
John Burgess is the author of a rich and creative body of work which seeks to defend classical logic and mathematics through counter-criticism of their nominalist, intuitionist, relevantist, and other critics. This selection of his essays, which spans twenty-five years, addresses key topics including nominalism, neo-logicism, intuitionism, modal logic, analyticity, and translation. An introduction sets the essays in context and offers a retrospective appraisal of their aims. The volume will be of interest to a wide range of readers across philosophy of mathematics, logic, and philosophy of language.
| Author | : Jaakko Hintikka |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 459 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 9400998252 |
Download Essays on Mathematical and Philosophical Logic Book in PDF, ePub and Kindle
The Fourth Scandinavian Logic Symposium and the First Soviet-Finnish Logic Conference were held in JyvaskyIa, Finland, June 29-July 6, 1976. The Conferences were organized by a committee which consisted of the editors of the present volume. The Conferences were supported financially by the Ministry of Education of Finland, by the Academy of Finland, and by the Division of Logic, Methodology, and Philosophy of Science of the International Union of History of Science. The Philosophical Society of Finland and the Jyvaskyla Summer Festival gave valuable help in various practicalities. 35 papers by authors representing 10 countries were presented at the two meetings. Of those papers 24 appear here. THE EDITORS v TABLE OF CONTENTS PREFACE v PART 1/ PROOF THEORY GEORG KREISEL / Some Facts from the Theory of Proofs and Some Fictions from General Proof Theory 3 DAG PRAWITZ / Proofs and the Meaning and Completeness of the Logical Constants 25 v. A. SMIRNOV / Theory of Quantification and tff-calculi 41 LARS SVENONIUS/Two Kinds of Extensions of Primitive Recursive Arithmetic 49 DIRK VAN DALEN and R. STATMAN / Equality in the Presence of Apartness 95 PART II / INFINITARY LANGUAGES VEIKKO RANTALA / Game-Theoretical Semantics and Back-and- Forth 119 MAARET KAR TTUNEN / Infinitary Languages N oo~.
| Author | : Jaakko Hintikka |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 494 |
| Release | : 1979 |
| Genre | : Gardening |
| ISBN | : 9789027708793 |
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Proceedings of the Fourth Scandinavian Logic Symposium and of the First Soviet-Finnish Logic Conference, Jyväskylä, Finland, June 29-July 6, 1976.
| Author | : Roman Murawski |
| Publisher | : BRILL |
| Total Pages | : 327 |
| Release | : 2015-06-29 |
| Genre | : Philosophy |
| ISBN | : 9042030917 |
Download Essays in the Philosophy and History of Logic and Mathematics Book in PDF, ePub and Kindle
The book is a collection of the author’s selected works in the philosophy and history of logic and mathematics. Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. Part II contains essays in the history of logic and mathematics. They address such issues as the philosophical background of the development of symbolism in mathematical logic, Giuseppe Peano and his role in the creation of contemporary logical symbolism, Emil L. Post's works in mathematical logic and recursion theory, the formalist school in the foundations of mathematics and the algebra of logic in England in the 19th century. The history of mathematics and logic in Poland is also considered. This volume is of interest to historians and philosophers of science and mathematics as well as to logicians and mathematicians interested in the philosophy and history of their fields.
| Author | : Erich H Reck |
| Publisher | : |
| Total Pages | : 326 |
| Release | : 2018-11-16 |
| Genre | : Mathematics |
| ISBN | : 9781848902879 |
Download Logic, Philosophy of Mathematics, and Their History Book in PDF, ePub and Kindle
In a career that spans 60 years so far, W.W. Tait has made many highly influential contributions to logic, the philosophy of mathematics, and their history. The present collection of new essays - contributed by former students, colleagues, and friends - is a Festschrift, i.e., a celebration of his life and work. The essays address a variety of themes prominent in his work or related to it. The collection starts with an introduction in which Tait's contributions are sketched and put into context. The eleven essays that follow are arranged in three parts: Part I. Proof Theory and its History; Part II. Logic and Philosophy of Mathematics; and Part III. History of Logic and Philosophy of Mathematics. Each of the essays contributes substantially to one or several of these areas. The authors included are: Steve Awodey, Solomon Feferman, Michael Friedman, Warren Goldfarb, Geoffrey Hellman, William Howard, Stephen Menn, Rebecca Morris, Charles Parsons, Erich Reck, Thomas Ricketts, and Wilfried Sieg. The editor, Erich H. Reck is Professor of Philosophy at the University of California at Riverside.
