The Incompleteness Phenomenon

The Incompleteness Phenomenon
Author: Martin Goldstern
Publisher: CRC Press
Total Pages: 218
Release: 2018-10-08
Genre: Mathematics
ISBN: 1439863539

Download The Incompleteness Phenomenon Book in PDF, Epub and Kindle

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.

Incompleteness

Incompleteness
Author: Rebecca Goldstein
Publisher: W. W. Norton & Company
Total Pages: 299
Release: 2006-01-31
Genre: Biography & Autobiography
ISBN: 0393327604

Download Incompleteness Book in PDF, Epub and Kindle

"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.

Paideia

Paideia
Author: Anna-Teresa Tymieniecka
Publisher: Springer Science & Business Media
Total Pages: 516
Release: 2000-08-31
Genre: Philosophy
ISBN: 9780792363194

Download Paideia Book in PDF, Epub and Kindle

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

Intelligent Design and Religion as a Natural Phenomenon
Author: John S. Wilkins
Publisher: Routledge
Total Pages: 559
Release: 2017-03-02
Genre: Science
ISBN: 1351927108

Download Intelligent Design and Religion as a Natural Phenomenon Book in PDF, Epub and Kindle

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.

Incomplete Nature: How Mind Emerged from Matter

Incomplete Nature: How Mind Emerged from Matter
Author: Terrence W. Deacon
Publisher: W. W. Norton & Company
Total Pages: 625
Release: 2012
Genre: Medical
ISBN: 0393049914

Download Incomplete Nature: How Mind Emerged from Matter Book in PDF, Epub and Kindle

Examines the emergent processes that bridge the gap between organisms that think and have consciousness and those that do not and discusses the origins of life, information, and free will.

Gödel's Theorem

Gödel's Theorem
Author: Torkel Franzén
Publisher: CRC Press
Total Pages: 182
Release: 2005-06-06
Genre: Mathematics
ISBN: 1439876924

Download Gödel's Theorem Book in PDF, Epub and Kindle

"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

Mathematical Undecidability, Quantum Nonlocality and the Question of the Existence of God

Mathematical Undecidability, Quantum Nonlocality and the Question of the Existence of God
Author: A. Driessen
Publisher: Springer Science & Business Media
Total Pages: 234
Release: 2012-12-06
Genre: Science
ISBN: 9401154287

Download Mathematical Undecidability, Quantum Nonlocality and the Question of the Existence of God Book in PDF, Epub and Kindle

On January 22, 1990, the late John Bell held at CERN (European Laboratory for Particle Physics), Geneva a seminar organized by the Center of Quantum Philosophy, that at this time was an association of scientists interested in the interpretation of quantum mechanics. In this seminar Bell presented once again his famous theorem. Thereafter a discussion took place in which not only physical but also highly speculative epistemological and philosophical questions were vividly debated. The list of topics included: assumption of free will in Bell's theorem, the understanding of mind, the relationship between the mathematical and the physical world, the existence of unobservable causes and the limits of human knowledge in mathematics and physics. Encouraged by this stimulating discussion some of the participants decided to found an Institute for Interdisciplinary Studies (lIS) to promote philosoph ical and interdisciplinary reflection on the advances of science. Meanwhile the lIS has associated its activities with the Swiss foundation, Fondation du Leman, and the Dutch foundation, Stichting Instudo, registered in Geneva and Amsterdam, respectively. With its activities the lIS intends to strengthen the unity between the professional activities in science and the reflection on fun damental philosophical questions. In addition the interdisciplinary approach is expected to give a contribution to the progress of science and the socio economic development. At present three working groups are active within the lIS, i. e. : - the Center for Quantum Philosophy, - the Wealth Creation and Sustainable Development Group, - the Neural Science Group.

The Philosopher's Handbook

The Philosopher's Handbook
Author: Stanley Rosen
Publisher: Random House Reference
Total Pages: 656
Release: 2009-02-19
Genre: Philosophy
ISBN: 0307559076

Download The Philosopher's Handbook Book in PDF, Epub and Kindle

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.

Can Mathematics Be Proved Consistent?

Can Mathematics Be Proved Consistent?
Author: Jan von Plato
Publisher: Springer
Total Pages: 263
Release: 2021-07-26
Genre: Mathematics
ISBN: 9783030508784

Download Can Mathematics Be Proved Consistent? Book in PDF, Epub and Kindle

Kurt Gödel (1906–1978) shook the mathematical world in 1931 by a result that has become an icon of 20th century science: The search for rigour in proving mathematical theorems had led to the formalization of mathematical proofs, to the extent that such proving could be reduced to the application of a few mechanical rules. Gödel showed that whenever the part of mathematics under formalization contains elementary arithmetic, there will be arithmetical statements that should be formally provable but aren’t. The result is known as Gödel’s first incompleteness theorem, so called because there is a second incompleteness result, embodied in his answer to the question "Can mathematics be proved consistent?" This book offers the first examination of Gödel’s preserved notebooks from 1930, written in a long-forgotten German shorthand, that show his way to the results: his first ideas, how they evolved, and how the jewel-like final presentation in his famous publication On formally undecidable propositions was composed.The book also contains the original version of Gödel’s incompleteness article, as handed in for publication with no mentioning of the second incompleteness theorem, as well as six contemporary lectures and seminars Gödel gave between 1931 and 1934 in Austria, Germany, and the United States. The lectures are masterpieces of accessible presentations of deep scientific results, readable even for those without special mathematical training, and published here for the first time.

Gödel's Disjunction

Gödel's Disjunction
Author: Leon Horsten
Publisher: Oxford University Press
Total Pages: 288
Release: 2016-09-09
Genre: Mathematics
ISBN: 0191077682

Download Gödel's Disjunction Book in PDF, Epub and Kindle

The logician Kurt Gödel 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 Gödel's disjunction in these frameworks. The contributions in this volume have been written by world leading experts in the field.