Real Numbers Generalizations Of The Reals And Theories Of Continua
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Real Numbers Generalizations Of The Reals And Theories Of Continua
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Author : P. Ehrlich
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Real Numbers Generalizations Of The Reals And Theories Of Continua written by P. Ehrlich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
Since their appearance in the late 19th century, the Cantor--Dedekind theory of real numbers and philosophy of the continuum have emerged as pillars of standard mathematical philosophy. On the other hand, this period also witnessed the emergence of a variety of alternative theories of real numbers and corresponding theories of continua, as well as non-Archimedean geometry, non-standard analysis, and a number of important generalizations of the system of real numbers, some of which have been described as arithmetic continua of one type or another. With the exception of E.W. Hobson's essay, which is concerned with the ideas of Cantor and Dedekind and their reception at the turn of the century, the papers in the present collection are either concerned with or are contributions to, the latter groups of studies. All the contributors are outstanding authorities in their respective fields, and the essays, which are directed to historians and philosophers of mathematics as well as to mathematicians who are concerned with the foundations of their subject, are preceded by a lengthy historical introduction.
From Dedekind To G Del
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Author : Jaakko Hintikka
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
From Dedekind To G Del written by Jaakko Hintikka and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Philosophy categories.
Discussions of the foundations of mathematics and their history are frequently restricted to logical issues in a narrow sense, or else to traditional problems of analytic philosophy. From Dedekind to Gödel: Essays on the Development of the Foundations of Mathematics illustrates the much greater variety of the actual developments in the foundations during the period covered. The viewpoints that serve this purpose included the foundational ideas of working mathematicians, such as Kronecker, Dedekind, Borel and the early Hilbert, and the development of notions like model and modelling, arbitrary function, completeness, and non-Archimedean structures. The philosophers discussed include not only the household names in logic, but also Husserl, Wittgenstein and Ramsey. Needless to say, such logically-oriented thinkers as Frege, Russell and Gödel are not entirely neglected, either. Audience: Everybody interested in the philosophy and/or history of mathematics will find this book interesting, giving frequently novel insights.
Living Doubt
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Author : G. Debrock
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Living Doubt written by G. Debrock and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Philosophy categories.
Charles Sanders Peirce (1839--1914) has often been referred to as one of the most important North American philosophers, but the real extent of his philosophical importance is only now beginning to emerge. Peirce's `pragmaticism' (his own term) may provide the key to an epistemological theory which avoids both the Scylla of foundationalism and the Charybdis of relativism. Peirce's `Logic', linked to a conception of knowledge and of science, is increasingly coming to be recognised as the only possible one. In Living Doubt, 26 papers are presented by some of the world's leading philosophers, demonstrating the rich and cosmopolitan variety of approach to Peirce's epistemology. The contributions are grouped under three general headings: Knowledge, truth and the pragmatic principle; Peirce and the epistemological tradition; and Knowledge, language and semeiotic.
Apartness And Uniformity
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Author : Douglas S. Bridges
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-09-08
Apartness And Uniformity written by Douglas S. Bridges and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-08 with Computers categories.
The theory presented in this book is developed constructively, is based on a few axioms encapsulating the notion of objects (points and sets) being apart, and encompasses both point-set topology and the theory of uniform spaces. While the classical-logic-based theory of proximity spaces provides some guidance for the theory of apartness, the notion of nearness/proximity does not embody enough algorithmic information for a deep constructive development. The use of constructive (intuitionistic) logic in this book requires much more technical ingenuity than one finds in classical proximity theory -- algorithmic information does not come cheaply -- but it often reveals distinctions that are rendered invisible by classical logic. In the first chapter the authors outline informal constructive logic and set theory, and, briefly, the basic notions and notations for metric and topological spaces. In the second they introduce axioms for a point-set apartness and then explore some of the consequences of those axioms. In particular, they examine a natural topology associated with an apartness space, and relations between various types of continuity of mappings. In the third chapter the authors extend the notion of point-set (pre-)apartness axiomatically to one of (pre-)apartness between subsets of an inhabited set. They then provide axioms for a quasiuniform space, perhaps the most important type of set-set apartness space. Quasiuniform spaces play a major role in the remainder of the chapter, which covers such topics as the connection between uniform and strong continuity (arguably the most technically difficult part of the book), apartness and convergence in function spaces, types of completeness, and neat compactness. Each chapter has a Notes section, in which are found comments on the definitions, results, and proofs, as well as occasional pointers to future work. The book ends with a Postlude that refers to other constructive approaches to topology, with emphasis on the relation between apartness spaces and formal topology. Largely an exposition of the authors' own research, this is the first book dealing with the apartness approach to constructive topology, and is a valuable addition to the literature on constructive mathematics and on topology in computer science. It is aimed at graduate students and advanced researchers in theoretical computer science, mathematics, and logic who are interested in constructive/algorithmic aspects of topology.
Logic And Philosophy Of Science In Uppsala
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Author : D. Prawitz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Logic And Philosophy Of Science In Uppsala written by D. Prawitz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Philosophy categories.
The International Congresses of Logic, Methodology and Philosophy of Science, which are held every fourth year, give a cross-section of ongoing research in logic and philosophy of science. Both the invited lectures and the many contributed papers are conductive to this end. At the 9th Congress held in Uppsala in 1991 there were 54 invited lectures and around 650 contributed papers divided into 15 different sections. Some of the speakers who presented contributed papers that attracted special interest were invited to submit their papers for publication, and the result is the present volume. A few papers appear here more or less as they were presented at the Congress whereas others are expansions or elaborations of the talks given at the Congress. A selection of this kind, containing 38 papers drawn from the 650 contributed papers presented at the Uppsala Congress, cannot do justice to all facets of the field as it appeared at the Congress. But it should allow the reader to get a representative survey of contemporary research in large areas of philosophical logic and philosophy of science. About half of the papers of the volume appear in sections listed at the Congress under the heading Philosophical and Foundational Problems about the Sciences. The section Foundations of Logic, Mathematics and Computer Science is represented by three papers, Foundations of Physical Sciences by six papers, Foundations of Biological Sciences by three papers, Foundations of Cognitive Science and AI by one paper, and Foundations of Linguistics by three papers.
The Philosophy Of Michael Dummett
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Author : B.F. McGuinness
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
The Philosophy Of Michael Dummett written by B.F. McGuinness and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Philosophy categories.
The present collection of papers derives from a philosophy conference organised in the Sicilian town of M ussomeli in September 1991. The con ference aimed at providing an analysis of certain aspects of the thought of Michael Dummett, whose contributions have been very influential in several aspects of the philosophical debate continuing within the analyt ical tradition. Logic, the philosophy of mathematics, the interpretation of Frege's philosophy, and metaphysics are only some of the areas within which Dummett's ideas have been fruitful over the years. The papers contained in this book, and Dummett's replies, will, it is hoped, not merely offer a partial reconstruction of a philosopher's life work, but provide an exciting and challenging vantage point from which to look at some of the main problems of contemporary philosophy. The First International Philosophy Conference of M ussomeli - this is what the conference was called - was an extraordinary event in many ways. The quality of the papers presented, the international reputa tion of many of the participants, the venue itself, together with the unavoidable, and sometimes quite funny, organisational hiccups, made that meeting memorable. Perhaps principally memorable was the warmth and sympathy of the people of Mussomeli who strongly supported and encouraged this initia tive. A special mention is also due to the City Council Administrators, who spared no effort to make the Conference a success.
Patrick Suppes Scientific Philosopher
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Author : P. Humphreys
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-09-30
Patrick Suppes Scientific Philosopher written by P. Humphreys and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-09-30 with Language Arts & Disciplines categories.
Patrick Suppes is a philosopher and scientist whose contributions range over probability and statistics, mathematical and experimental psychology, the foundations of physics, education theory, the philosophy of language, measurement theory, and the philosophy of science. He has also been a pioneer in the area of computer assisted instruction. In each of these areas, Suppes has provided seminal ideas that in some cases led to shaping the direction of research in the field. The papers contained in this collection were commissioned with the mandate of advancing research in their respective fields rather than retrospectively surveying the contributions that Suppes himself has made. The authors form an interesting mixture of researchers in both formal philosophy of science and science itself all of whom have been inspired by his ideas. To maintain the spirit of constructive dialogue that characterizes Suppes's intellectual style, he has written individual responses to each article. In Volume 1: Probability and Probabilistic Causality, nineteen distinguished philosophers and scientists focus their attention on probabilistic issues. In Part I the contributors explore axiomatic representations of probability theory including qualitative and interval valued probabilities as well as traditional point valued probabilities. Belief structures and the dynamics of belief are also treated in detail. In Part II the rapidly growing field of probabilistic causation is assessed from both formal and empirical viewpoints. For probability theorists, statisticians, economists, philosophers of science, psychologists and those interested in the foundations of mathematical social science. In Volume 2: Philosophy of Physics, Theory Structure, and Measurement Theory, fifteen distinguished philosophers and scientists cover a wide variety of topics. Part III covers issues in quantum theory, geometry, classical mechanics, and computational physics. Part IV explores Suppes's well known set-theoretic account of scientific theories which has served him well throughout his career. Suppes's contributions to measurement theory have been widely used in mathematical psychology and elsewhere, and this material is the subject of Part V. For physicists, logicians, workers in mathematical social sicence, and philosophers of science. In Volume 3: Philosophy of Language and Logic, Learning and Action Theory, fourteen distinguished philosophers and scientists explore issues in the philosophy of language, logic, and philosophical psychology. Suppes's suggestions that quantum theory requires a rethinking of classical logic form a particularly sharp account of that controversial thesis, and Part VI deals with this issue together with topics in the philosophy of language and logic, including relational grammars and anaphora. Part VII deals with issues in psychology, action theory, and robotics, while Part VIII concludes with a general survey of Suppes's views in the philosophy of science. A comprehensive chronological and topical bibliography of Suppes's writings is included in this volume. For philosophers of language, theoretical linguists, logicians, workers in mathematical social sciences, and philosophers of science.
Language Mind And Art
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Author : D. Jamieson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Language Mind And Art written by D. Jamieson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Philosophy categories.
This book is a collection of essays in honor of Paul Ziff written by his col leagues, students, and friends. Many of the authors address topics that Ziff has discussed in his writings: understanding, rules and regularities, proper names, the feelings of machines, expression, and aesthetic experience. Paul Ziff began his professional career as an artist, went on to study painting with J. M. Hanson at Cornell, and then studied for the Ph. D. in philosophy, also at Cornell, with Max Black. Over the next three decades he produced a series of remarkable papers in philosophy of art, culminating in 1984 with the publica tion of Antiaesthetics: An Appreciation of the Cow with the Subtile Nose. In 1960 he published Semantic Analysis, his masterwork in philosophy of lan guage. Throughout his career he made important contributions to philosophy of mind in such papers as "The Simplicity of Other Minds" (1965) and "About Behaviourism" (1958). In addition to his work in these areas, his lec tures at Harvard on philosophy of religion are an underground classic; and throughout his career he has continued to make art and to search for the meaning of life in the properties of prime numbers. Although his interests are wide and deep, questions about language, art, and mind have dominated his philosophical work, and it is problems in these areas that provide the topics of most of the essays in this volume.
Other Minds
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Author : Alec Hyslop
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Other Minds written by Alec Hyslop and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Philosophy categories.
This book has been a long time in the making. Other issues have taken me away from it from time to extended time. But I kept coming back to the problem of other minds. It has remained a great issue, it is much contested still, and it is, after all, elose to us all. I like believing that the time taken has deepened my understanding of the problem and how it is to be handled. Other people, some by disagreeing vehemently, have helped greatly. I mention in particular, Brian Ellis, Robert Fox, Graeme Marshali, Tim Oakley, Ray Pinkerton and Robert Young. Robert Pargetter argued with me, and kept insisting that I write this book. John Bigelow, Michael Bradley, Keith Campbell, Frank Jackson, and William Lycan assisted by reading an earlier version and providing valued comments. Frank Jackson has been specially helpful, not just on this topic. He can be blamed for initially causing me to take the analogical inference seriously. Tbe La Trobe Philosophy Department has been a good place to do philosophy. I am grateful to Suzanne Hayster, Sandra Paul, and Betty Pritchard for struggling at various times with various recalcitrant manuscripts. Most particularly I thank Gai Larkin. She has seen the project through, with considerably more than efficiency.
Doing Worlds With Words
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Author : J. Peregrin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Doing Worlds With Words written by J. Peregrin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Philosophy categories.
Doing Worlds with Words throws light on the problem of meaning as the meeting point of linguistics, logic and philosophy, and critically assesses the possibilities and limitations of elucidating the nature of meaning by means of formal logic, model theory and model-theoretical semantics. The main thrust of the book is to show that it is misguided to understand model theory metaphysically and so to try to base formal semantics on something like formal metaphysics; rather, the book states that model theory and similar tools of the analysis of language should be understood as capturing the semantically relevant, especially inferential, structure of language. From this vantage point, the reader gains a new light on many of the traditional concepts and problems of logic and philosophy of language, such as meaning, reference, truth and the nature of formal logic.