The Incompleteness Phenomenon
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The Incompleteness Phenomenon
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Author : Martin Goldstern
language : en
Publisher: CRC Press
Release Date : 2018-10-08
The Incompleteness Phenomenon written by Martin Goldstern and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-08 with Mathematics categories.
This introduction to mathematical logic takes Gödel's incompleteness theorem as a starting point. It goes beyond a standard text book and should interest everyone from mathematicians to philosophers and general readers who wish to understand the foundations and limitations of modern mathematics.
Understanding And Conscious Experience
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Author : Andrei Ionuț Mărăşoiu
language : en
Publisher: Taylor & Francis
Release Date : 2024-09-02
Understanding And Conscious Experience written by Andrei Ionuț Mărăşoiu and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-02 with Philosophy categories.
This volume explores how understanding relates to conscious experience. In doing so, it builds bridges between different philosophical disciplines and provides a metaphysically robust characterization of understanding, both in and beyond science. The past two decades have witnessed growing interest from epistemologists, philosophers of science, philosophers of mind and ethicists in the nature and value of intellectual understanding. This volume features original essays on understanding and the phenomenal experiences that underlie it. The chapters are divided into three thematic sections. Part 1 provides theoretical characterizations of understanding, including Henk de Regt’s defense of a contextual theory of scientific understanding and a debate on whether scientific inference and explanatory power are necessary or central features of understanding. Part 2 explores how conscious experience and understanding are related. The chapters articulate a phenomenal theory of understanding and address themes that are connected to understanding, including awareness, transformative experiences and exemplification. Finally, Part 3 is devoted to domain-specific inquiries about understanding, such as logical proofs, particle physics and moral understanding. Understanding and Conscious Experience will be of interest to scholars and advanced students working in the philosophy of science, epistemology, philosophy of mind, ethics and phenomenology.
The Tarskian Turn
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Author : Leon Horsten
language : en
Publisher: MIT Press
Release Date : 2011-07-15
The Tarskian Turn written by Leon Horsten and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-15 with Philosophy categories.
A philosopher proposes a new deflationist view of truth, based on contemporary proof-theoretic approaches. In The Tarskian Turn, Leon Horsten investigates the relationship between formal theories of truth and contemporary philosophical approaches to truth. The work of mathematician and logician Alfred Tarski (1901–1983) marks the transition from substantial to deflationary views about truth. Deflationism—which holds that the notion of truth is light and insubstantial—can be and has been made more precise in multiple ways. Crucial in making the deflationary intuition precise is its relation to formal or logical aspects of the notion of truth. Allowing that semantical theories of truth may have heuristic value, in The Tarskian Turn Horsten focuses on axiomatic theories of truth developed since Tarski and their connection to deflationism. Arguing that the insubstantiality of truth has been misunderstood in the literature, Horsten proposes and defends a new kind of deflationism, inferential deflationism, according to which truth is a concept without a nature or essence. He argues that this way of viewing the concept of truth, inspired by a formalization of Kripke's theory of truth, flows naturally from the best formal theories of truth that are currently available. Alternating between logical and philosophical chapters, the book steadily progresses toward stronger theories of truth. Technicality cannot be altogether avoided in the subject under discussion, but Horsten attempts to strike a balance between the need for logical precision on the one hand and the need to make his argument accessible to philosophers.
Paideia
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Author : Anna-Teresa Tymieniecka
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-08-31
Paideia written by Anna-Teresa Tymieniecka 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 2000-08-31 with Education categories.
The education of humanity is the key to the next century's culture, its social and practical life. The main concerns of education are perennial, but the continuous flood of inventions, the technological innovations that re-shape life, calls for a radically new appraisal of the situation, such as only philosophy can provide. Answering the call of humanity for the measure, sense of proportion and direction that could re-orient present and future education, the phenomenology of life - integral and scientific, in a dialogue with the arts, the sciences, and the humanities - proposes an ontopoietic model of life's unfolding as the universal paradigm for this re-orientation. Taking the Human Creative Condition as its Archimedean point, it offers a unique context for a fresh investigation of the concerns of education, both perennial and immediate.
Intelligent Design And Religion As A Natural Phenomenon
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Author : John S. Wilkins
language : en
Publisher: Routledge
Release Date : 2017-03-02
Intelligent Design And Religion As A Natural Phenomenon written by John S. Wilkins and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-02 with Religion categories.
Over the past decade a strident public debate has arisen about the nature and origin of religions. Controversies include how exactly religion evolved, whether by individual or group selection, if it is adaptive, and if not, whether and how it is a side effect of evolution. This volume focuses on the issue of naturalizing religion: on the ways in which cognitive science and social sciences have treated religion as a natural phenomenon. It questions whether religious behaviour, institutions, and experiences can be explained in natural terms. The editor brings together some of the best published work on the definition of 'religion', intelligent design and the evolution of religion.
Handbook Of Practical Logic And Automated Reasoning
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Author : John Harrison
language : en
Publisher: Cambridge University Press
Release Date : 2009-03-12
Handbook Of Practical Logic And Automated Reasoning written by John Harrison 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 2009-03-12 with Computers categories.
The sheer complexity of computer systems has meant that automated reasoning, i.e. the ability of computers to perform logical inference, has become a vital component of program construction and of programming language design. This book meets the demand for a self-contained and broad-based account of the concepts, the machinery and the use of automated reasoning. The mathematical logic foundations are described in conjunction with practical application, all with the minimum of prerequisites. The approach is constructive, concrete and algorithmic: a key feature is that methods are described with reference to actual implementations (for which code is supplied) that readers can use, modify and experiment with. This book is ideally suited for those seeking a one-stop source for the general area of automated reasoning. It can be used as a reference, or as a place to learn the fundamentals, either in conjunction with advanced courses or for self study.
G Del S Disjunction
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Author : Leon Horsten
language : en
Publisher: Oxford University Press
Release Date : 2016
G Del S Disjunction written by Leon Horsten 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 2016 with Mathematics categories.
The logician Kurt Godel in 1951 established a disjunctive thesis about the scope and limits of mathematical knowledge: either the mathematical mind is not equivalent to a Turing machine (i.e., a computer), or there are absolutely undecidable mathematical problems. In the second half of the twentieth century, attempts have been made to arrive at a stronger conclusion. In particular, arguments have been produced by the philosopher J.R. Lucas and by the physicist and mathematician Roger Penrose that intend to show that the mathematical mind is more powerful than any computer. These arguments, and counterarguments to them, have not convinced the logical and philosophical community. The reason for this is an insufficiency if rigour in the debate. The contributions in this volume move the debate forward by formulating rigorous frameworks and formally spelling out and evaluating arguments that bear on Godel's disjunction in these frameworks. The contributions in this volume have been written by world leading experts in the field.
The Philosopher S Handbook
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Author : Stanley Rosen
language : en
Publisher: Random House Reference
Release Date : 2009-02-19
The Philosopher S Handbook written by Stanley Rosen and has been published by Random House Reference this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-19 with Philosophy categories.
An ideal introduction for the casual reader and a beneficial reference for the student, The Philosopher's Handbook features the writings of some of the world's most influential philosophers. Based on the premise that all human beings are curious about their existence, Rosen's collection brings together primary excerpts from the works of prominent thinkers such as Plato, Nietzsche, Descartes, Machiavelli, and Kant. Experts in each field have carefully selected the sources and provided brief introductions to help readers gain insight into the readings. Newly revised in order to emphasize its broad appeal, The Philosopher's Handbook is a solid introduction to Western philosophy for all inquiring minds.
Information And Randomness
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Author : Cristian S. Calude
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Information And Randomness written by Cristian S. Calude 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 Mathematics categories.
The first edition of the monograph Information and Randomness: An Algorithmic Perspective by Crist ian Calude was published in 1994. In my Foreword I said: "The research in algorithmic information theory is already some 30 years old. However, only the recent years have witnessed a really vigorous growth in this area. . . . The present book by Calude fits very well in our series. Much original research is presented. . . making the approach richer in consequences than the classical one. Remarkably, however, the text is so self-contained and coherent that the book may also serve as a textbook. All proofs are given in the book and, thus, it is not necessary to consult other sources for classroom instruction. " The vigorous growth in the study of algorithmic information theory has continued during the past few years, which is clearly visible in the present second edition. Many new results, examples, exercises and open prob lems have been added. The additions include two entirely new chapters: "Computably Enumerable Random Reals" and "Randomness and Incom pleteness". The really comprehensive new bibliography makes the book very valuable for a researcher. The new results about the characterization of computably enumerable random reals, as well as the fascinating Omega Numbers, should contribute much to the value of the book as a textbook. The author has been directly involved in these results that have appeared in the prestigious journals Nature, New Scientist and Pour la Science.
G Del S Theorem
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Author : Torkel Franzén
language : en
Publisher: CRC Press
Release Date : 2005-06-06
G Del S Theorem written by Torkel Franzén and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-06 with Mathematics categories.
"Among the many expositions of Gödel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franzén gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstandings and abuses of the incompleteness theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incompleteness in theological, anti-mechanist and post-modernist debates, it is a valuable addition to the literature." --- John W. Dawson, author of Logical Dilemmas: The Life and Work of Kurt Gödel