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Author : Jaakko Hintikka,Ilkka Niiniluoto,Esa Saarinen
Publisher : Unknown
Page : 462 pages
File Size : 41,9 Mb
Release : 1976
Category : Logic
ISBN : LCCN:78014736
Author : Åsa Hirvonen,Juha Kontinen,Roman Kossak,Andrés Villaveces
Publisher : Walter de Gruyter GmbH & Co KG
Page : 438 pages
File Size : 51,8 Mb
Release : 2015-03-10
Category : Philosophy
ISBN : 9781614519324
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,Michael Hallett,Peter Clark
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 45,8 Mb
Release : 2011-03-23
Category : Philosophy
ISBN : 9789400702141
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 : Jaakko Hintikka,I. Niiniluoto,Esa. Saarinen
Publisher : Springer Science & Business Media
Page : 459 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400998254
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 : Roman Murawski
Publisher : BRILL
Page : 327 pages
File Size : 50,6 Mb
Release : 2015-06-29
Category : Philosophy
ISBN : 9789042030916
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 : Geoffrey Hellman
Publisher : Cambridge University Press
Page : 0 pages
File Size : 49,9 Mb
Release : 2022-11-10
Category : Science
ISBN : 1108714005
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 : Charles D. Parsons
Publisher : Cornell University Press
Page : 367 pages
File Size : 52,6 Mb
Release : 2018-08-06
Category : Mathematics
ISBN : 9781501729324
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
Page : 295 pages
File Size : 52,7 Mb
Release : 2021-02-04
Category : Mathematics
ISBN : 9781108494182
The essays in this volume present a sustained case for a healthy pluralism in mathematics and its logics.
Author : Wang Hao
Publisher : Springer Science & Business Media
Page : 394 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400923560
~Et moi ... si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non· The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Author : Willard Van Orman Quine
Publisher : Harvard University Press
Page : 201 pages
File Size : 47,6 Mb
Release : 1980-05-15
Category : Philosophy
ISBN : 9780674254442
These nine essays are largely concerned with the theory of meaning and references—semantics. At the same time adjacent portions of philosophy and logic are discussed. To the existence of what objects may a given scientific theory be said to be committed? And what considerations may suitably guide us in accepting or revising such ontological commitments? These are among the questions dealt with in this book, particular attention being devoted to the role of abstract entities in mathematics. There is speculation on the mechanism whereby objects of one sort or another come to be posited, a process in which the notion of identity plays an important part.
Author : Giandomenico Sica
Publisher : Polimetrica s.a.s.
Page : 353 pages
File Size : 43,5 Mb
Release : 2005
Category : Mathematics
ISBN : 9788876990144
Author : John P. Burgess
Publisher : Cambridge University Press
Page : 253 pages
File Size : 47,7 Mb
Release : 2008-02-21
Category : Science
ISBN : 9781139470544
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 : Karel Lambert
Publisher : Cambridge University Press
Page : 207 pages
File Size : 49,7 Mb
Release : 2002-10-31
Category : Science
ISBN : 9781139436465
Free logic is an important field of philosophical logic that first appeared in the 1950s. J. Karel Lambert was one of its founders and coined the term itself. The essays in this collection (written over a period of 40 years) explore the philosophical foundations of free logic and its application to areas as diverse as the philosophy of religion and computer science. Amongst the applications on offer are those to the analysis of existence statements, to definite descriptions and to partial functions. The volume contains a proof that free logics of any kind are non-extensional and then uses that proof to show that Quine's theory of predication and referential transparency must fail. The purpose of this collection is to bring an important body of work to the attention of a new generation of professional philosophers, computer scientists and mathematicians.
Author : Ian Rumfitt
Publisher : Oxford University Press, USA
Page : 369 pages
File Size : 42,7 Mb
Release : 2015
Category : Philosophy
ISBN : 9780198733638
Classical logic has been attacked by adherents of rival, anti-realist logical systems: Ian Rumfitt comes to its defence. He considers the nature of logic, and how to arbitrate between different logics. He argues that classical logic may dispense with the principle of bivalence, and may thus be liberated from the dead hand of classical semantics.
Author : Jaakko Hintikka,I. Niiniluoto,Esa Saarinen
Publisher : Springer Science & Business Media
Page : 494 pages
File Size : 51,9 Mb
Release : 1979
Category : Gardening
ISBN : 9027708797
Proceedings of the Fourth Scandinavian Logic Symposium and of the First Soviet-Finnish Logic Conference, Jyväskylä, Finland, June 29-July 6, 1976.
