Set Theory Logic And Their Limitations
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Set Theory Logic And Their Limitations
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Author : Moshe Machover
language : en
Publisher: Cambridge University Press
Release Date : 1996-05-23
Set Theory Logic And Their Limitations written by Moshe Machover and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-05-23 with Mathematics categories.
This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations. A rigorous axiomatic presentation of Zermelo-Fraenkel set theory is given, demonstrating how the basic concepts of mathematics have apparently been reduced to set theory. This is followed by a presentation of propositional and first-order logic. Concepts and results of recursion theory are explained in intuitive terms, and the author proves and explains the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics or philosophy this book provides an excellent introduction to logic and set theory.
Set Theory Logic And Their Limitations
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Author : Moshé Machover
language : en
Publisher:
Release Date : 1998
Set Theory Logic And Their Limitations written by Moshé Machover and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
The Limits Of Logic
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Author : Stewart Shapiro
language : en
Publisher: Routledge
Release Date : 2016-12-05
The Limits Of Logic written by Stewart Shapiro and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-05 with Philosophy categories.
The International research Library of Philosophy collects in book form a wide range of important and influential essays in philosophy, drawn predominantly from English-language journals. Each volume in the library deals with a field of enquiry which has received significant attention in philosophy in the last 25 years and is edited by a philosopher noted in that field.
A Course On Set Theory
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Author : Ernest Schimmerling
language : en
Publisher: Cambridge University Press
Release Date : 2011-07-28
A Course On Set Theory written by Ernest Schimmerling and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-28 with Mathematics categories.
Set theory is the mathematics of infinity and part of the core curriculum for mathematics majors. This book blends theory and connections with other parts of mathematics so that readers can understand the place of set theory within the wider context. Beginning with the theoretical fundamentals, the author proceeds to illustrate applications to topology, analysis and combinatorics, as well as to pure set theory. Concepts such as Boolean algebras, trees, games, dense linear orderings, ideals, filters and club and stationary sets are also developed. Pitched specifically at undergraduate students, the approach is neither esoteric nor encyclopedic. The author, an experienced instructor, includes motivating examples and over 100 exercises designed for homework assignments, reviews and exams. It is appropriate for undergraduates as a course textbook or for self-study. Graduate students and researchers will also find it useful as a refresher or to solidify their understanding of basic set theory.
Logic And Relational Theory
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Author : C. J. Date
language : en
Publisher: Technics Publications
Release Date : 2020-06-06
Logic And Relational Theory written by C. J. Date and has been published by Technics Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-06 with Computers categories.
This book is a revised, upgraded, and hugely improved version of an earlier one called Logic and Databases. Although it’s effectively a brand new book, therefore, the following remarks from that earlier book are still relevant here. First, logic and databases are inextricably intertwined. The relational model itself is essentially just elementary logic, tailored to database needs. Now, if you’re a database professional, this won’t be news to you—but you still might not realize just how much everything we do in the database world is (or should be!) affected by logic. Logic is fundamental, and everywhere. As a database professional, therefore, you owe it to yourself to understand the basics of formal logic, and you ought to be able to explain (and perhaps defend) the connections between formal logic and database technology. And that’s what this book is about. What it does is show, through a series of partly independent, partly interrelated essays, just how various crucial aspects of database technology—some of them very familiar, others maybe less so—are solidly grounded in formal logic. Overall, the goal is to help you realize the importance of logic in everything you do, and also, I hope, to help you see that logic can be fun.
The Outer Limits Of Reason
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Author : Noson S. Yanofsky
language : en
Publisher: MIT Press
Release Date : 2013-08-23
The Outer Limits Of Reason written by Noson S. Yanofsky and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-23 with Science categories.
This exploration of the scientific limits of knowledge challenges our deep-seated beliefs about our universe, our rationality, and ourselves. “A must-read for anyone studying information science.” —Publishers Weekly, starred review Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own intuitions about the world—including our ideas about space, time, and motion, and the complex relationship between the knower and the known. Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve: • perfectly formed English sentences that make no sense • different levels of infinity • the bizarre world of the quantum • the relevance of relativity theory • the causes of chaos theory • math problems that cannot be solved by normal means • statements that are true but cannot be proven Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.
A Book Of Set Theory
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Author : Charles C Pinter
language : en
Publisher: Courier Corporation
Release Date : 2014-07-23
A Book Of Set Theory written by Charles C Pinter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-23 with Mathematics categories.
"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--
Hume S Problem
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Author : Colin Howson
language : en
Publisher: Clarendon Press
Release Date : 2000-11-02
Hume S Problem written by Colin Howson and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-11-02 with Philosophy categories.
Colin Howson offers a solution to one of the central, unsolved problems of Western philosophy, the problem of induction. In the mid-eighteenth century David Hume argued that successful prediction tells us nothing about the truth of the predicting theory. No matter how many experimental tests a hypothesis passes, nothing can be legitimately inferred about its truth or probable truth. But physical theory routinely predicts the values of observable magnitudes to many small places of decimals and within very small ranges of error. The chance of this sort of predictive success without a true theory seems so remote that the possibility should be dismissed. This suggests that Hume's argument must be wrong; but there is still no consensus on where exactly this flaw lies. Howson argues that there is no flaw, and examines the implications of this disturbing conclusion for relation between science and its empirical base.
Proofs And Fundamentals
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Author : Ethan D. Bloch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Proofs And Fundamentals written by Ethan D. Bloch 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 2013-12-01 with Mathematics categories.
In an effort to make advanced mathematics accessible to a wide variety of students, and to give even the most mathematically inclined students a solid basis upon which to build their continuing study of mathematics, there has been a tendency in recent years to introduce students to the for mulation and writing of rigorous mathematical proofs, and to teach topics such as sets, functions, relations and countability, in a "transition" course, rather than in traditional courses such as linear algebra. A transition course functions as a bridge between computational courses such as Calculus, and more theoretical courses such as linear algebra and abstract algebra. This text contains core topics that I believe any transition course should cover, as well as some optional material intended to give the instructor some flexibility in designing a course. The presentation is straightforward and focuses on the essentials, without being too elementary, too exces sively pedagogical, and too full to distractions. Some of features of this text are the following: (1) Symbolic logic and the use of logical notation are kept to a minimum. We discuss only what is absolutely necessary - as is the case in most advanced mathematics courses that are not focused on logic per se.
Models And Theories
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Author : Roman Frigg
language : en
Publisher: Taylor & Francis
Release Date : 2022-06-28
Models And Theories written by Roman Frigg and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-28 with Philosophy categories.
Models and theories are of central importance in science, and scientists spend substantial amounts of time building, testing, comparing and revising models and theories. It is therefore not surprising that the nature of scientific models and theories has been a widely debated topic within the philosophy of science for many years. The product of two decades of research, this book provides an accessible yet critical introduction to the debates about models and theories within analytical philosophy of science since the 1920s. Roman Frigg surveys and discusses key topics and questions, including: What are theories? What are models? And how do models and theories relate to each other? The linguistic view of theories (also known as the syntactic view of theories), covering different articulations of the view, its use of models, the theory-observation divide and the theory-ladenness of observation, and the meaning of theoretical terms. The model-theoretical view of theories (also known as the semantic view of theories), covering its analysis of the model-world relationship, the internal structure of a theory, and the ontology of models. Scientific representation, discussing analogy, idealisation and different accounts of representation. Modelling in scientific practice, examining how models relate to theories and what models are, classifying different kinds of models, and investigating how robustness analysis, perspectivism, and approaches committed to uncertainty-management deal with multi-model situations. Models and Theories is the first comprehensive book-length treatment of the topic, making it essential reading for advanced undergraduates, researchers, and professional philosophers working in philosophy of science and philosophy of technology. It will also be of interest to philosophically minded readers working in physics, computer sciences and STEM fields more broadly.