Foundational Studies Selected Works
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Foundational Studies Selected Works
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Author : Lev D. Beklemishev
language : en
Publisher: Elsevier
Release Date : 2000-04-01
Foundational Studies Selected Works written by Lev D. Beklemishev and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-01 with Computers categories.
Foundational Studies Selected Works
Andrzej Mostowski And Foundational Studies
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Author : A. Ehrenfeucht
language : en
Publisher: IOS Press
Release Date : 2008-03-06
Andrzej Mostowski And Foundational Studies written by A. Ehrenfeucht and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-06 with Mathematics categories.
Andrzej Mostowski was one of the leading 20th century logicians. His legacy is examined in this volume of papers devoted both to his extraordinary scientific heritage and to the memory of him as a great researcher, teacher, organizer of science and human. Professor Mostowski pioneered and mastered many areas of mathematical logic. His contributions spanned set theory, recursion theory, and model theory - the backbone of foundations of mathematics. He is best known of the Kleene-Mostowski and Davis-Mostowski hierarchies of properties of integers reflecting the complexity of their definitions, and of the very elegant concept of a generalized quantifier which inspired and keeps stimulating a stream of deep work on fundamental issues of logics, deduction and reasoning both in mathematics and in computer science, and also of the contributions and excellent lectures on undecidability, unprovability, consistency and independence of various statements in set theory and arithmetic following Gödel, Tarski and Cohen. The overall content of the volume is designed to cover the current main streams in the field. For many years after WWII, especially in the late sixties, till his untimely death in 1975, Warsaw - where he led the centre of foundational studies - was a place where many leading logicians visited, studied, and started their career. Their memories form an important part of this volume, attempting to bring back the extraordinary achievements and personality of Mostowski.
Quantifiers Quantifiers And Quantifiers Themes In Logic Metaphysics And Language
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Author : Alessandro Torza
language : en
Publisher: Springer
Release Date : 2015-07-23
Quantifiers Quantifiers And Quantifiers Themes In Logic Metaphysics And Language written by Alessandro Torza and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-23 with Philosophy categories.
This volume covers a wide range of topics that fall under the 'philosophy of quantifiers', a philosophy that spans across multiple areas such as logic, metaphysics, epistemology and even the history of philosophy. It discusses the import of quantifier variance in the model theory of mathematics. It advances an argument for the uniqueness of quantifier meaning in terms of Evert Beth’s notion of implicit definition and clarifies the oldest explicit formulation of quantifier variance: the one proposed by Rudolf Carnap. The volume further examines what it means that a quantifier can have multiple meanings and addresses how existential vagueness can induce vagueness in our modal notions. Finally, the book explores the role played by quantifiers with respect to various kinds of semantic paradoxes, the logicality issue, ontological commitment, and the behavior of quantifiers in intensional contexts.
Philosophy Of Mathematics
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Author :
language : en
Publisher: Elsevier
Release Date : 2009-07-08
Philosophy Of Mathematics written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-08 with Philosophy categories.
One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathematics have been developed and it is these positions (both historical and current) that are surveyed in the current volume. Traditional theories (Platonism, Aristotelianism, Kantianism), as well as dominant modern theories (logicism, formalism, constructivism, fictionalism, etc.), are all analyzed and evaluated. Leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) is also discussed. The result is a handbook that not only provides a comprehensive overview of recent developments but that also serves as an indispensable resource for anyone wanting to learn about current developments in the philosophy of mathematics.-Comprehensive coverage of all main theories in the philosophy of mathematics-Clearly written expositions of fundamental ideas and concepts-Definitive discussions by leading researchers in the field-Summaries of leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) are also included
Mereology
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Author : A. J. Cotnoir
language : en
Publisher: Oxford University Press
Release Date : 2021
Mereology written by A. J. Cotnoir and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Mathematics categories.
Aaron Cotnoir and Achille Varzi present a comprehensive and up-to-date guide to mereology, the study of relations between parts and wholes. They introduce a variety of theories and offer all the tools needed to engage in this ever-evolving field of inquiry, for readers at all levels, from newcomers to experts.
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.
Handbook Of Philosophical Logic
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Author : Dov M. Gabbay
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Handbook Of Philosophical Logic written by Dov M. Gabbay 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.
This volume presents a number of systems of logic which can be considered as alternatives to classical logic. The notion of what counts as an alternative is a somewhat problematic one. There are extreme views on the matter of what is the 'correct' logical system and whether one logical system (e. g. classical logic) can represent (or contain) all the others. The choice of the systems presented in this volume was guided by the following criteria for including a logic as an alternative: (i) the departure from classical logic in accepting or rejecting certain theorems of classical logic following intuitions arising from significant application areas and/or from human reasoning; (ii) the alternative logic is well-established and well-understood mathematically and is widely applied in other disciplines such as mathematics, physics, computer science, philosophy, psychology, or linguistics. A number of other alternatives had to be omitted for the present volume (e. g. recent attempts to formulate so-called 'non-monotonic' reason ing systems). Perhaps these can be included in future extensions of the Handbook of Philosophical Logic. Chapter 1 deals with partial logics, that is, systems where sentences do not always have to be either true or false, and where terms do not always have to denote. These systems are thus, in general, geared towards reasoning in partially specified models. Logics of this type have arisen mainly from philo sophical and linguistic considerations; various applications in theoretical computer science have also been envisaged.
The Higher Infinite
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Author : Akihiro Kanamori
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-23
The Higher Infinite written by Akihiro Kanamori 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 2008-11-23 with Mathematics categories.
Over the years, this book has become a standard reference and guide in the set theory community. It provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contemporary research, with open questions and speculations throughout.
In The Intermissions Collected Works On Research Into The Essentials Of Theoretical Physics In R
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Author : Yuri A Trutnev
language : en
Publisher: World Scientific
Release Date : 1998-11-23
In The Intermissions Collected Works On Research Into The Essentials Of Theoretical Physics In R written by Yuri A Trutnev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-23 with Science categories.
This book gives an account of the creative work of theorists at the largest Soviet secret laboratory, now the Russian Federal Nuclear Center at Arzamas-16, and concrete situations where some famous results on the essentials of theoretical physics emerged, so to speak, in the intermissions of the quest for bombs. The collection contains about 30 papers with brief comments. Some of them have received international recognition. But few people can conceive where they were written, since the publication of a paper by a secret physicist in a Soviet journal was supported by fictitious affiliations. Other papers are less well known, particularly because Soviet journals were not always translated into European languages. However, pioneer results contained in them merit more attention.
Ernst Zermelo Collected Works Gesammelte Werke
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Author : Ernst Zermelo
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-20
Ernst Zermelo Collected Works Gesammelte Werke written by Ernst Zermelo 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 2010-01-20 with Mathematics categories.
Ernst Zermelo (1871-1953) is regarded as the founder of axiomatic set theory and best-known for the first formulation of the axiom of choice. However, his papers include also pioneering work in applied mathematics and mathematical physics. This edition of his collected papers will consist of two volumes. Besides providing a biography, the present Volume I covers set theory, the foundations of mathematics, and pure mathematics and is supplemented by selected items from his Nachlass and part of his translations of Homer's Odyssey. Volume II will contain his work in the calculus of variations, applied mathematics, and physics. The papers are each presented in their original language together with an English translation, the versions facing each other on opposite pages. Each paper or coherent group of papers is preceded by an introductory note provided by an acknowledged expert in the field which comments on the historical background, motivations, accomplishments, and influence.