The Philosophy of Mathematics

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Author: Wilbur Dyre Hart

Publisher: Oxford University Press on Demand

ISBN: 9780198751205

Category: Mathematics

Page: 316

View: 6945

This volume offers a selection of the most interesting and important work from recent years in the philosophy of mathematics, which has always been closely linked to, and has exerted a significant influence upon, the main stream of analytical philosophy. The issues discussed are of interest throughout philosophy, and no mathematical expertise is required of the reader. Contributors include W.V. Quine, W.D. Hart, Michael Dummett, Charles Parsons, Paul Benacerraf, Penelope Maddy, W.W. Tait, Hilary Putnam, George Boolos, Daniel Isaacson, Stewart Shapiro, and Hartry Field.

Neo-Aristotelian Perspectives in Metaphysics

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Author: Daniel D. Novotný,Lukáš Novák

Publisher: Routledge

ISBN: 1134630093

Category: Philosophy

Page: 342

View: 357

This volume re-examines some of the major themes at the intersection of traditional and contemporary metaphysics. The book uses as a point of departure Francisco Suárez’s Metaphysical Disputations published in 1597. Minimalist metaphysics in empiricist/pragmatist clothing have today become mainstream in analytic philosophy. Independently of this development, the progress of scholarship in ancient and medieval philosophy makes clear that traditional forms of metaphysics have affinities with some of the streams in contemporary analytic metaphysics. The book brings together leading contemporary metaphysicians to investigate the viability of a neo-Aristotelian metaphysics.

Introducing Philosophy of Mathematics

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Author: Michele Friend

Publisher: Routledge

ISBN: 1317493796

Category: Philosophy

Page: 240

View: 5483

What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual accessibility and correct representation of the issues. Friend examines the standard theories of mathematics - Platonism, realism, logicism, formalism, constructivism and structuralism - as well as some less standard theories such as psychologism, fictionalism and Meinongian philosophy of mathematics. In each case Friend explains what characterises the position and where the divisions between them lie, including some of the arguments in favour and against each. This book also explores particular questions that occupy present-day philosophers and mathematicians such as the problem of infinity, mathematical intuition and the relationship, if any, between the philosophy of mathematics and the practice of mathematics. Taking in the canonical ideas of Aristotle, Kant, Frege and Whitehead and Russell as well as the challenging and innovative work of recent philosophers like Benacerraf, Hellman, Maddy and Shapiro, Friend provides a balanced and accessible introduction suitable for upper-level undergraduate courses and the non-specialist.

Erfahrung Mathematik

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Author: P.J. Davis,R. Hersh

Publisher: Springer-Verlag

ISBN: 3034850409

Category: Science

Page: 466

View: 4851

ie ältesten uns bekannten mathematischen Schriftta D feln stammen aus der Zeit um 2400 v. ehr. ; aber wir dürfen davon ausgehen, daß das Bedürfnis, Mathematik zu schaffen, ein Ausdruck der menschlichen Zivilisation an sich ist. In vier bis fünf Jahrtausenden hat sich ein gewalti ges System von Praktiken und Begriffen - die Mathematik herangebildet, die in vielfältiger Weise mit unserem Alltag verknüpft ist. Was ist Mathematik? Was bedeutet sie? Wo mit befaßt sie sich? Was sind ihre Methoden? Wie wird sie geschaffen und benützt? Wo ist ihr Platz in der Vielgestalt der menschlichen Erfahrung? Welchen Nutzen bringt sie? Was für Schaden richtet sie an? Welches Gewicht kommt ihr zu? Diese schwierigen Fragen werden noch zusätzlich kompliziert durch die Fülle des Materials und die weitver zweigten Querverbindungen, die es dem einzelnen verun möglichen, alles zu begreifen, geschweige denn, es in seiner Gesamtheit zu erfassen und zwischen den Deckeln eines normalen Buches unterzubringen. Um von dieser Material fülle nicht erdrückt zu werden, haben sich die Autoren für eine andere Betrachtungsweise entschieden. Die Mathema tik ist seit Tausenden von Jahren ein Feld menschlicher Ak tivität. In begrenztem Rahmen ist jeder von uns ein Mathe matiker und betreibt bewußt Mathematik, wenn er zum Beispiel auf dem Markt einkauft, Tapeten ausmißt oder ei nen Keramiktopf mit einem regelmäßigen Muster verziert. In bescheidenem Ausmaß versucht sich auch jeder von uns als mathematischer Denker. Schon mit dem Ausruf «Aber Zahlen lügen nicht!» befinden wir uns in der Gesellschaft von Plato oder Lakatos.

Québec Studies in the Philosophy of Science

Part I: Logic, Mathematics, Physics and History of Science

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Author: Mathieu Marion,Robert S. Cohen

Publisher: Springer Science & Business Media

ISBN: 9400915756

Category: Science

Page: 332

View: 4361

By North-American standards, philosophy is not new in Quebec: the first men tion of philosophy lectures given by a Jesuit in the College de Quebec (founded 1635) dates from 1665, and the oldest logic manuscript dates from 1679. In English-speaking universities such as McGill (founded 1829), philosophy began to be taught later, during the second half of the 19th century. The major influence on English-speaking philosophers was, at least initially, that of Scottish Empiricism. On the other hand, the strong influence of the Catholic Church on French-Canadian society meant that the staff of the facultes of the French-speaking universities consisted, until recently, almost entirely of Thomist philosophers. There was accordingly little or no work in modem Formal Logic and Philosophy of Science and precious few contacts between the philosophical communities. In the late forties, Hugues Leblanc was a young student wanting to learn Formal Logic. He could not find anyone in Quebec to teach him and he went to study at Harvard University under the supervision of W. V. Quine. His best friend Maurice L' Abbe had left, a year earlier, for Princeton to study with Alonzo Church. After receiving his Ph. D from Harvard in 1948, Leblanc started his profes sional career at Bryn Mawr College, where he stayed until 1967. He then went to Temple University, where he taught until his retirement in 1992, serving as Chair of the Department of Philosophy from 1973 until 1979.

Scientific Inquiry

Readings in the Philosophy of Science

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Author: Robert Klee

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Science

Page: 352

View: 649

Scientific Inquiry: Readings in the Philosophy of Science features an impressive collection of classical and contemporary readings on a wide range of issues in the philosophy of science. The volume is organized into six sections, each with its own introduction, and includes a general introduction that situates the philosophy of science in relation to other areas of intellectual inquiry. The selections focus on the main issues in the field, including the structure of scientific theories, models of scientific explanation, reductionism, historicist challenges to the objectivity of science, and the dispute over the ontological interpretation of mature scientific theories. Both the positivist model of science and its competitors, including contemporary social constructivist models, are included. Ideal for introductory philosophy of science courses, Scientific Inquiry strives to provide students and other readers with a thorough knowledge of the philosophical complexity of modern science and an appreciation of its authoritative intellectual standing in contemporary life.

Das Wahrheitsproblem und die Idee der Semantik

Eine Einführung in die Theorien von A. Tarski und R. Carnap

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Author: Wolfgang Stegmüller

Publisher: Springer-Verlag

ISBN: 3709136245

Category: Juvenile Nonfiction

Page: 328

View: 9060

Die vorliegende Arbeit wurde zu dem Zwecke abgefaßt, eine Einführung in die reine oder nichtempirische Semantik zu geben, die sich in den letzten Jahren zu einem eigenen Forschungszweig entwickelt hat. Immer mehr dringt in der Philosophie der Gegenwart die Erkenntnis durch, daß philosophische Untersuchungen zu einem guten Teil sprachlogischer und sprachkritischer Art sein müssen, und im Rahmen solcher Untersuchungen nehmen jene der Semantik eine zentrale Stellung ein. Während die Logikkalküle nur mit der traditionellen formalen Logik in einem gewissen historischen Zusammenhang stehen, ist der Kontakt zwischen der Semantik und den althergebrachten philosophischen Pro blemen ein viel engerer. Dort steht bloß der Begrüf der logischen Deduk tion im Vordergrund, hier hingegen der wichtigste Begriff der Erkenntnis theorie, nämlich der Begriff des wahren Urteils bzw. der wahren Aussage. Über die Bedeutung einer Explikation des Wahrheitsbegriffs braucht man wohl kaum Worte zu verlieren angesichts der Tatsache, daß unser ganzes Erkenntnisstreben darauf abzielt, zu wahren Urteilen oder Sätzen zu gelangen. Eine Beantwortung der Frage, was man unter einem wahren Urteil bzw. einer wahren Aussage zu verstehen habe, wird nicht innerhalb der Einzelwissenschaften gegeben, sondern ist seit jeher dem Philosophen überlassen worden.

Calendar

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Author: University of Cape Town

Publisher: N.A

ISBN: N.A

Category:

Page: N.A

View: 5308

Philosophies of the Sciences

A Guide

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Author: Fritz Allhoff

Publisher: John Wiley & Sons

ISBN: 9781444315585

Category: Science

Page: 368

View: 8367

A collection of essays discussing a wide range of sciences and thecentral philosophical issues associated with them, presenting thesciences collectively to encourage a greater understanding of theirassociative theoretical foundations, as well as their relationshipsto each other. Offers a new and unique approach to studying and comparing thephilosophies of a variety of scientific disciplines Explores a wide variety of individual sciences, includingmathematics, physics, chemistry, biology, psychology, sociology andeconomics The essays are written by leading scholars in a highlyaccessible style for the student audience Complements more traditional studies of philosophy ofscience

The Oxford Companion to Philosophy

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Author: Ted Honderich

Publisher: OUP Oxford

ISBN: 0191037478

Category: Philosophy

Page: 1088

View: 8135

Oxford University Press presents a major new edition of the definitive philosophical reference work for readers at all levels. For ten years the original volume has served as a stimulating introduction for general readers and as an indispensable guide for students; its breadth and depth of coverage have ensured that it is also read with pleasure and interest by those working at a higher level in philosophy and related disciplines. A distinguished international assembly of 249 philosophers contributed almost 2,000 entries, and many of these have now been considerably revised and updated; to these are added over 300 brand-new pieces on a fascinating range of current topics. This new edition offers enlightening and enjoyable discussions of all aspects of philosophy, and of the lives and work of the great philosophers from antiquity to the present day.

The philosophy of history

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Author: Patrick L. Gardiner

Publisher: Oxford University Press, USA

ISBN: 9780198750314

Category: History

Page: 224

View: 5841

Appraising Lakatos

Mathematics, Methodology, and the Man

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Author: György Kampis,L. Kvasz,Michael Stöltzner

Publisher: Springer Science & Business Media

ISBN: 9401707693

Category: Science

Page: 382

View: 9590

Imre Lakatos (1922-1974) was one of the protagonists in shaping the "new philosophy of science". More than 25 years after his untimely death, it is time for a critical re-evaluation of his ideas. His main theme of locating rationality within the scientific process appears even more compelling today, after many historical case studies have revealed the cultural and societal elements within scientific practices. Recently there has been, above all, an increasing interest in Lakatos' philosophy of mathematics, which emphasises heuristics and mathematical practice over logical justification. But suitable modifications of his approach are called for in order to make it applicable to modern axiomatised theories. Pioneering historical research in England and Hungary has unearthed hitherto unknown facts about Lakatos' personal life, his wartime activities and his involvement in the political developments of post-war Europe. From a communist activist committed to Györgyi Lukács' thinking, Lakatos developed into a staunch anti-Marxist who found his intellectual background in Popper's critical rationalism. The volume also publishes for the first time a part of his Debrecen Ph.D. thesis and it is concluded by a bibliography of his Hungarian writings.

Carnap, Tarski, and Quine at Harvard

Conversations on Logic, Mathematics, and Science

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Author: Greg Frost-Arnold

Publisher: Open Court

ISBN: 0812698371

Category: Philosophy

Page: 270

View: 3211

During the academic year 1940-1941, several giants of analytic philosophy congregated at Harvard: Bertrand Russell, Alfred Tarski, Rudlof Carnap, W. V. Quine, Carl Hempel, and Nelson Goodman were all in residence. This group held regular private meetings, with Carnap, Tarski, and Quine being the most frequent attendees. Carnap, Tarski, and Quine at Harvard allows the reader to act as a fly on the wall for their conversations. Carnap took detailed notes during his year at Harvard. This book includes both a German transcription of these shorthand notes and an English translation in the appendix section. Carnap’s notes cover a wide range of topics, but surprisingly, the most prominent question is: if the number of physical items in the universe is finite (or possibly finite), what form should scientific discourse, and logic and mathematics in particular, take? This question is closely connected to an abiding philosophical problem, one that is of central philosophical importance to the logical empiricists: what is the relationship between the logico-mathematical realm and the material realm studied by natural science? Carnap, Tarski, and Quine’s attempts to answer this question involve a number of issues that remain central to philosophy of logic, mathematics, and science today. This book focuses on three such issues: nominalism, the unity of science, and analyticity. In short, the book reconstructs the lines of argument represented in these Harvard discussions, discusses their historical significance (especially Quine’s break from Carnap), and relates them when possible to contemporary treatments of these issues. Nominalism. The founding document of twentieth-century Anglophone nominalism is Goodman and Quine’s 1947 “Steps Toward a Constructive Nominalism.” In it, the authors acknowledge that their project’s initial impetus was the conversations of 1940-1941 with Carnap and Tarski. Frost-Arnold's exposition focuses upon the rationales given for and against the nominalist program at its inception. Tarski and Quine’s primary motivation for nominalism is that mathematical sentences will be ‘unintelligible’ or meaningless, and thus perniciously metaphysical, if (contra nominalism) their component terms are taken to refer to abstract objects. Their solution is to re-interpret mathematical language so that its terms only refer to concrete entities—and if the number of concreta is finite, then portions of classical mathematics will be considered meaningless. Frost-Arnold then identifies and reconstructs Carnap’s two most forceful responses to Tarski and Quine’s view: (1) all of classical mathematics is meaningful, even if the number of concreta is finite, and (2) nominalist strictures lead to absurd consequences in mathematics and logic. The second is familiar from modern debates over nominalism, and its force is proportional to the strength of one’s commitment to preserving all of classical mathematics. The first, however, has no direct correlate in the modern debate, and turns upon the question of whether Carnap’s technique for partially interpreting a language can confer meaningfulness on the whole language. Finally, the author compares the arguments for and against nominalism found in the discussion notes to the leading arguments in the current nominalist debate: the indispensability argument and the argument from causal theories of reference and knowledge. Analyticity. Carnap, Tarski, and Quine’s conversations on finitism have a direct connection to the tenability of the analytic-synthetic distinction: under a finitist-nominalist regime, portions of arithmetic—a supposedly analytic enterprise—become empirical. Other portions of the 1940-41 notes address analyticity directly. Interestingly, Tarski’s criticisms are more sustained and pointed than Quine’s. For example, Tarski suggests that Gödel’s first incompleteness theorem furnishes evidence against Carnap’s conception of analyticity. After reconstructing this argument, Frost-Arnold concludes that it does not tell decisively against Carnap—provided that language is not treated fundamentally proof-theoretically. Quine’s points of disagreement with Carnap in the discussion notes are primarily denials of Carnap’s premises without argument. They do, however, allow us new and more precise characterizations of Carnap and Quine’s differences. Finally, the author forwards two historical conjectures concerning the radicalization of Quine’s critique of analyticity in the period between “Truth by Convention” and “Two Dogmas.” First, the finitist conversations could have shown Quine how the apparently analytic sentences of arithmetic could be plausibly construed as synthetic. Second, Carnap’s shift during his semantic period toward intensional analyses of linguistic concepts, including synonymy, perhaps made Quine, an avowed extensionalist, more skeptical of meaning and analyticity. Unity of Science. The unity of science movement originated in Vienna in the 1920s, and figured prominently in the transplantation of logical empiricism into North America in the 1940s. Carnap, Tarski, and Quine’s search for a total language of science that incorporates mathematical language into that of the natural and social sciences is a clear attempt to unify the language of science. But what motivates the drive for such a unified science? Frost-Arnold locates the answer in the logical empiricists’ antipathy towards speculative metaphysics, in contrast with meaningful scientific claims. I present evidence that, for logical empiricists over several decades, an apparently meaningful assertion or term is metaphysical if and only if that assertion or term cannot be incorporated into a language of unified science. Thus, constructing a single language of science that encompasses the mathematical and natural domains would ensure that mathematical entities are not on par with entelechies and Platonic Forms. The author explores various versions of this criterion for overcoming metaphysics, focusing on Carnap and Neurath. Finally, I consider an obstacle facing their strategy for overcoming metaphysics: there is no effective procedure to show that a given claim or term cannot be incorporated within a language.

Conceptual Roots of Mathematics

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Author: J.R. Lucas

Publisher: Routledge

ISBN: 1134622260

Category: Philosophy

Page: 472

View: 9107

The Conceptual Roots of Mathematics is a comprehensive study of the foundation of mathematics. J.R. Lucas, one of the most distinguished Oxford scholars, covers a vast amount of ground in the philosophy of mathematics, showing us that it is actually at the heart of the study of epistemology and metaphysics.

Principia Mathematica.

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Author: Alfred North Whitehead,Bertrand Russell

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: 167

View: 981

Conceptual Change

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Author: G.A. Pearce,P. Maynard

Publisher: Springer Science & Business Media

ISBN: 9401025487

Category: Science

Page: 286

View: 5801

During Hallowe'en of 1970, the Department of Philosophy of the Univer sity of Western Ontario held its annual fall colloquium at London, On tario. The general topic of the sessions that year was conceptual change. The thirteen papers composing this volume stem more or less directly from those meetings; six of them are printed here virtually as delivered, while the remaining seven were subsequently written by invitation. The programme of the colloquium was to have consisted of major papers delivered by Professors Wilfrid Sellars, Stephan Korner, Paul Ziff and Hilary Putnam, with shorter commentary thereupon by Professors Robert Binkley, Joseph Ullian, Jerry Fodor and Robert Barrett, respec tively. And that is the way it happened, with one important exception: at the eleventh hour, Sellars and Binkley exchanged roles. This gave Binkley the rather unusual and challenging task of providing a suitable Sellarsian answer to a question not of his own asking - for Binkley's paper was written under Sellars' original title. Sellars' own contribution to the vo lume is perhaps more nearly what he would have presented as main speaker than a direct response to Binkley. However, it has seemed best, on balance, to attempt no further stylistic accommodation of the one paper to the other; their mutual philosophical relevance will be evident in any case. The editors would here like to extend special thanks to both Sellars and Binkley for their extraordinary efforts under the circumstances.