The Philosophy of Mathematics


Author: Wilbur Dyre Hart

Publisher: Oxford University Press, USA

ISBN: 9780198751199

Category: Mathematics

Page: 316

View: 8266

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.

Neo-Aristotelian Perspectives in Metaphysics


Author: Daniel D. Novotný,Lukáš Novák

Publisher: Routledge

ISBN: 1134630093

Category: Philosophy

Page: 342

View: 5290

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


Author: Michele Friend

Publisher: Routledge

ISBN: 1317493796

Category: Philosophy

Page: 240

View: 2232

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.

Die Grundlagen der Arithmetik

eine logisch-mathematische untersuchung über den begriff der zahl


Author: Gottlob Frege

Publisher: Georg Olms Verlag

ISBN: 9783487400280


Page: 119

View: 4401


Die großen Fragen der Philosophie


Author: Simon Blackburn

Publisher: N.A

ISBN: 9783863120511


Page: 260

View: 7495

Québec Studies in the Philosophy of Science

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


Author: Mathieu Marion,Robert S. Cohen

Publisher: Springer Science & Business Media

ISBN: 9400915756

Category: Science

Page: 332

View: 8319

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.

Principia Mathematica.


Author: Alfred North Whitehead,Bertrand Russell

Publisher: N.A


Category: Logic, Symbolic and mathematical

Page: 167

View: 7545



Author: University of Cape Town

Publisher: N.A



Page: N.A

View: 6150

Das Wahrheitsproblem und die Idee der Semantik

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


Author: Wolfgang Stegmüller

Publisher: Springer-Verlag

ISBN: 3709136245

Category: Juvenile Nonfiction

Page: 328

View: 6185

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.

Philosophies of the Sciences

A Guide


Author: Fritz Allhoff

Publisher: John Wiley & Sons

ISBN: 9781444315585

Category: Science

Page: 368

View: 3678

A collection of essays discussing a wide range of sciences and the central philosophical issues associated with them, presenting the sciences collectively to encourage a greater understanding of their associative theoretical foundations, as well as their relationships to each other. Offers a new and unique approach to studying and comparing the philosophies of a variety of scientific disciplines Explores a wide variety of individual sciences, including mathematics, physics, chemistry, biology, psychology, sociology and economics The essays are written by leading scholars in a highly accessible style for the student audience Complements more traditional studies of philosophy of science

Scientific Inquiry

Readings in the Philosophy of Science


Author: Robert Klee

Publisher: Oxford University Press, USA


Category: Science

Page: 352

View: 2529

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.

The Oxford Companion to Philosophy


Author: Ted Honderich

Publisher: OUP Oxford

ISBN: 0191037478

Category: Philosophy

Page: 1088

View: 8461

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


Author: Patrick L. Gardiner

Publisher: Oxford University Press, USA

ISBN: 9780198750314

Category: History

Page: 224

View: 9000

Appraising Lakatos

Mathematics, Methodology, and the Man


Author: György Kampis,Ladislav Kvasz,Michael Stoeltzner

Publisher: Springer Science & Business Media

ISBN: 9401707693

Category: Science

Page: 382

View: 5227

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


Author: Greg Frost-Arnold

Publisher: Open Court

ISBN: 0812698371

Category: Philosophy

Page: 270

View: 5379

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.