The Principles of Mathematics Revisited

Author: Jaakko Hintikka

Publisher: Cambridge University Press

ISBN: 9780521624985

Category: Mathematics

Page: 288

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This book, written by one of philosophy's pre-eminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. It is therefore a book of critical importance to logical theory. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. The famous impossibility results by Gödel and Tarski that have dominated the field for the last sixty years turn out to be much less significant than has been thought. All of ordinary mathematics can in principle be done on this first-order level, thus dispensing with the existence of sets and other higher-order entities.

Logic, Epistemology, and the Unity of Science

Author: Shahid Rahman,John Symons,Dov M. Gabbay,Jean Paul van Bendegem

Publisher: Springer Science & Business Media

ISBN: 1402028083

Category: Philosophy

Page: 626

View: 714

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The first volume in this new series explores, through extensive co-operation, new ways of achieving the integration of science in all its diversity. The book offers essays from important and influential philosophers in contemporary philosophy, discussing a range of topics from philosophy of science to epistemology, philosophy of logic and game theoretical approaches. It will be of interest to philosophers, computer scientists and all others interested in the scientific rationality.

Lingua Universalis vs. Calculus Ratiocinator:

An Ultimate Presupposition of Twentieth-Century Philosophy

Author: Jaakko Hintikka

Publisher: Springer Science & Business Media

ISBN: 9401586012

Category: Philosophy

Page: 270

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R. G. Collingwood saw one of the main tasks of philosophers and of historians of human thought in uncovering what he called the ultimate presuppositions of different thinkers, of different philosophical movements and of entire eras of intellectual history. He also noted that such ultimate presuppositions usually remain tacit at first, and are discovered only by subsequent reflection. Collingwood would have been delighted by the contrast that constitutes the overall theme of the essays collected in this volume. Not only has this dichotomy ofviews been one ofthe mostcrucial watersheds in the entire twentieth-century philosophical thought. Not only has it remained largely implicit in the writings of the philosophers for whom it mattered most. It is a truly Collingwoodian presupposition also in that it is not apremise assumed by different thinkers in their argumentation. It is the presupposition of a question, an assumption to the effect that a certain general question can be raised and answered. Its role is not belied by the fact that several philosophers who answered it one way or the other seem to be largely unaware that the other answer also makes sense - if it does. This Collingwoodian question can be formulated in a first rough approximation by asking whether language - our actual working language, Tarski's "colloquiallanguage" - is universal in the sense of being inescapable. This formulation needs all sorts of explanations, however.

Formen der Anschauung

Eine Philosophie der Mathematik

Author: Pirmin Stekeler-Weithofer

Publisher: Walter de Gruyter

ISBN: 3110212218

Category: Philosophy

Page: 411

View: 8645

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What are pure geometric forms? In what sense are there an infinite number of points on a line? What is the relationship between empirically correct statements about real bodily figures (or movements) and the ideal truths of a pure mathematical geometry (also in space-time)? Starting from Kant and Wittgenstein, the book demonstrates how our dealings with figures and symbols is to be understood beyond the technical mastery of forms of calculation and proof.

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

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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.

Dictionary Of Modern American Philosophers

Author: John R. Shook

Publisher: Bloomsbury Publishing

ISBN: 1847144705

Category: Philosophy

Page: 2000

View: 3183

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The Dictionary of Modern American Philosophers includes both academic and non-academic philosophers, and a large number of female and minority thinkers whose work has been neglected. It includes those intellectuals involved in the development of psychology, pedagogy, sociology, anthropology, education, theology, political science, and several other fields, before these disciplines came to be considered distinct from philosophy in the late nineteenth century. Each entry contains a short biography of the writer, an exposition and analysis of his or her doctrines and ideas, a bibliography of writings, and suggestions for further reading. While all the major post-Civil War philosophers are present, the most valuable feature of this dictionary is its coverage of a huge range of less well-known writers, including hundreds of presently obscure thinkers. In many cases, the Dictionary of Modern American Philosophers offers the first scholarly treatment of the life and work of certain writers. This book will be an indispensable reference work for scholars working on almost any aspect of modern American thought.

Quantification: Transcending Beyond Frege’s Boundaries

A Case Study In Transcendental-Metaphysical Logic

Author: Aleksy Molczanow

Publisher: BRILL

ISBN: 9004224173

Category: Philosophy

Page: 252

View: 9843

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Drawing on the original conception of Kant’s synthetic a priori and the relevant related developments in philosophy, this book presents a reconstruction of the intellectual history of the conception of quantity and offers an entirely novel transcendental-metaphysical account of quantification.

Counterfactuals and Scientific Realism

Author: Michael J. Shaffer

Publisher: Springer

ISBN: 1137271582

Category: Science

Page: 209

View: 8163

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The author attempts to show that scientific realism is compatible with the presence of idealization in the sciences. His main contention is that idealized theories can be treated as counterfactuals about how things are in worlds that are similar to but simpler than the actual world.

Russell Revisited

Critical Reflections on the Thought of Bertrand Russell

Author: Alan Schwerin under the auspices of the Bertrand Russell Society

Publisher: Cambridge Scholars Publishing

ISBN: 1443806897

Category: Philosophy

Page: 165

View: 7535

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Bertrand Russell has played a central role in the development of modern western philosophy, especially analytic philosophy. An appreciation of the main themes and arguments of the thinkers who contributed to this modern movement in philosophy must include references to and analyses of Russell’s important contributions. It would seem that many do recognize the significance of his thought and have shown this in a somewhat dramatic manner. Russell’s Google number, for instance, is about 2.35 million. If the number of entries listed in this search engine is any indication of the level of interest online in Russell, we can surely conclude that the thought and life of this aristocratic English philosopher, logician and humanist still captures the imagination of tens of thousands, if not millions around the globe – even some thirty-seven years after his death. How do we account for this abiding interest in Russell? In a word it is accessibility. Whether it is the complex epistemological issue of the veracity of sense-data, the conundrums associated with the possibility of non-existent objects, the intricacies of the debates on the nature of language or the interminable search of a clear understanding of happiness, Russell inevitably has something profound and clear to say on the matter. Readers of Russell Revisited: Critical Reflections on the Thought of Bertrand Russell will be reminded of this fact time and time again as they explore the analyses here. Representing some of the best of the most recent scholarship on Russell, the articles gathered in this collection serve as a testament to the value of Russell’s diverse contributions to a wide range of challenging philosophical issues.

The Autonomy of Mathematical Knowledge

Hilbert's Program Revisited

Author: Curtis Franks

Publisher: Cambridge University Press

ISBN: 0521514371

Category: Mathematics

Page: 213

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This study reconstructs, analyses and re-evaluates the programme of influential mathematical thinker David Hilbert, presenting it in a new light.

Conservation Equations And Modeling Of Chemical And Biochemical Processes

Author: Said S.E.H. Elnashaie,Parag Garhyan

Publisher: CRC Press

ISBN: 9780203911501

Category: Science

Page: 636

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Presenting strategies in control policies, this text uses a systems theory approach to predict, simulate and streamline plant operation, conserve fuel and resources, and increase workplace safety in the manufacturing, chemical, petrochemical, petroleum, biochemical and energy industries. Topics of discussion include system theory and chemical/biochemical engineering systems, steady state, unsteady state, and thermodynamic equilibrium, modeling of systems, fundamental laws governing the processes in terms of the state variables, different classifications of physical models, the story of chemical engineering in relation to system theory and mathematical modeling, overall heat balance with single and multiple chemical reactions and single and multiple reactions.

Philosophie im Geiste Bolzanos

anlässlich des 222. Geburtstages von Bernard Bolzano ; Edgar Morscher gewidmet

Author: Alexander Hieke,Otto Neumaier

Publisher: N.A

ISBN: N.A

Category: Knowledge, Theory of

Page: 392

View: 1741

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Encyclopedia of Philosophy: Price - Sextus Empiricus

Author: Donald M. Borchert

Publisher: Thomson Gale/MacMillan Reference USA

ISBN: N.A

Category: Philosophy

Page: 10

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Containing material from hundreds of highly distinguished contributors representing the world's top universities and institutions, the second edition has a truly global perspective. It contains more than 2,100 entries -- including more than 450 new articles. Among the many topics covered are African, Islamic, Jewish, Russian, Chinese, and Buddhist philosophies; bioethics and biomedical ethics; art and aesthetics; epistemology; metaphysics; peace and war; social and political philosophy; the Holocaust; feminist thought; and much more. Additionally, the second edition also features 1,000 biographical entries on major figures in philosophical thought throughout history.

The Future of Arid Lands-Revisited

A Review of 50 Years of Drylands Research

Author: Charles F. Hutchinson,Stefanie M. Herrmann

Publisher: Springer Science & Business Media

ISBN: 9781402066894

Category: Science

Page: 228

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The Future of Arid Lands, edited by Gilbert White and published in 1956, comprised papers delivered at the "International Arid Lands Meetings" held in New Mexico in 1955. At these meetings, experts considered the major issues then confronting the world’s arid lands and developed a research agenda to address these issues. This book reexamines this earlier work and explores changes in the science and management of arid lands over the past 50 years within their historical contexts.

Making Music with Computers

Creative Programming in Python

Author: Bill Manaris,Andrew R. Brown

Publisher: CRC Press

ISBN: 1482222213

Category: Computers

Page: 502

View: 8823

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Teach Your Students How to Use Computing to Explore Powerful and Creative Ideas In the twenty-first century, computers have become indispensable in music making, distribution, performance, and consumption. Making Music with Computers: Creative Programming in Python introduces important concepts and skills necessary to generate music with computers. It interweaves computing pedagogy with musical concepts and creative activities, showing students how to integrate the creativity and design of the arts with the mathematical rigor and formality of computer science. The book provides an introduction to creative software development in the Python programming language. It uses innovative music-creation activities to illustrate introductory computer programming concepts, including data types, algorithms, operators, iteration, lists, functions, and classes. The authors also cover GUIs, event-driven programming, big data, sonification, MIDI programming, client–server programming, recursion, fractals, and complex system dynamics. Requiring minimal musical or programming experience, the text is designed for courses in introductory computer science and computing in the arts. It helps students learn computer programming in a creative context and understand how to build computer music applications. Also suitable for self-study, the book shows musicians and digital music enthusiasts how to write music software and create algorithmic music compositions. Web Resource A supplementary website (http://jythonMusic.org) provides a music library and other software resources used in the text. The music library is an extension of the jMusic library and incorporates other cross-platform programming tools. The website also offers example course and associated media resources.

Teaching Mathematics to Able Children

Author: Valsa Koshy

Publisher: Routledge

ISBN: 1136626131

Category: Education

Page: 148

View: 4164

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This book enables teachers to effectively meet the needs of their most able mathematicians. Using a tried and tested set of principles developed and used by The Able Children's Education Unit at Brunel University, the author demonstrates how to: identify high mathematical ability in a pupil, plan suitably challenging activities and teach them most effectively within the existing National Numeracy framework, make the most of the classroom resources available, including ICT and external agencies, implement strategies for differentiation, illustrated with real-life classroom examples. Accessible in style and featuring practical case studies throughout, this book will give teachers and student teachers the confidence and knowledge to effectively challenge and develop the skills of the most able mathematician.

Varieties of Constructive Mathematics

Author: Douglas Bridges,Fred Richman

Publisher: Cambridge University Press

ISBN: 9780521318020

Category: Mathematics

Page: 149

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A survey of constructive approaches to pure mathematics emphasizing the viewpoint of Errett Bishop's school. Considers intuitionism, Russian constructivism, and recursive analysis, with comparisons among the various approaches included where appropriate.