Incompleteness In The Land Of Sets
DOWNLOAD
READ ONLINE
Download Incompleteness In The Land Of Sets PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Incompleteness In The Land Of Sets book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Incompleteness In The Land Of Sets
DOWNLOAD
READ ONLINE
Author : Melvin Fitting
language : en
Publisher:
Release Date : 2007
Incompleteness In The Land Of Sets written by Melvin Fitting and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Incompleteness theorems categories.
Russell's paradox arises when we consider those sets that do not belong to themselves. The collection of such sets cannot constitute a set. Step back a bit. Logical formulas define sets (in a standard model). Formulas, being mathematical objects, can be thought of as sets themselves-mathematics reduces to set theory. Consider those formulas that do not belong to the set they define. The collection of such formulas is not definable by a formula, by the same argument that Russell used. This quickly gives Tarski's result on the undefinability of truth. Variations on the same idea yield the famous results of Gödel, Church, Rosser, and Post. This book gives a full presentation of the basic incompleteness and undecidability theorems of mathematical logic in the framework of set theory. Corresponding results for arithmetic follow easily, and are also given. Gödel numbering is generally avoided, except when an explicit connection is made between set theory and arithmetic. The book assumes little technical background from the reader. One needs mathematical ability, a general familiarity with formal logic, and an understanding of the completeness theorem, though not its proof. All else is developed and formally proved, from Tarski's Theorem to Gödel's Second Incompleteness Theorem. Exercises are scattered throughout.
Forever Undecided
DOWNLOAD
READ ONLINE
Author : Raymond M. Smullyan
language : en
Publisher: Knopf
Release Date : 2012-07-04
Forever Undecided written by Raymond M. Smullyan and has been published by Knopf this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-04 with Mathematics categories.
Forever Undecided is the most challenging yet of Raymond Smullyan’s puzzle collections. It is, at the same time, an introduction—ingenious, instructive, entertaining—to Gödel’s famous theorems. With all the wit and charm that have delighted readers of his previous books, Smullyan transports us once again to that magical island where knights always tell the truth and knaves always lie. Here we meet a new and amazing array of characters, visitors to the island, seeking to determine the natives’ identities. Among them: the census-taker McGregor; a philosophical-logician in search of his flighty bird-wife, Oona; and a regiment of Reasoners (timid ones, normal ones, conceited, modest, and peculiar ones) armed with the rules of propositional logic (if X is true, then so is Y). By following the Reasoners through brain-tingling exercises and adventures—including journeys into the “other possible worlds” of Kripke semantics—even the most illogical of us come to understand Gödel’s two great theorems on incompleteness and undecidability, some of their philosophical and mathematical implications, and why we, like Gödel himself, must remain Forever Undecided!
The Theory Of G Del
DOWNLOAD
READ ONLINE
Author : Carlo Cellucci
language : en
Publisher: Springer Nature
Release Date : 2022-11-21
The Theory Of G Del written by Carlo Cellucci and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-21 with Philosophy categories.
This book presents Gödel’s incompleteness theorems and the other limitative results which are most significant for the philosophy of mathematics. Results are stated in the form most relevant for use in the philosophy of mathematics. An appendix considers their implications for Hilbert’s Program for the foundations of mathematics. The text is self-contained, all notions being explained in full detail, but of course previous exposure to the very first rudiments of mathematical logic will help.
Raymond Smullyan On Self Reference
DOWNLOAD
READ ONLINE
Author : Melvin Fitting
language : en
Publisher: Springer
Release Date : 2018-01-11
Raymond Smullyan On Self Reference written by Melvin Fitting and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-11 with Philosophy categories.
This book collects, for the first time in one volume, contributions honoring Professor Raymond Smullyan’s work on self-reference. It serves not only as a tribute to one of the great thinkers in logic, but also as a celebration of self-reference in general, to be enjoyed by all lovers of this field. Raymond Smullyan, mathematician, philosopher, musician and inventor of logic puzzles, made a lasting impact on the study of mathematical logic; accordingly, this book spans the many personalities through which Professor Smullyan operated, offering extensions and re-evaluations of his academic work on self-reference, applying self-referential logic to art and nature, and lastly, offering new puzzles designed to communicate otherwise esoteric concepts in mathematical logic, in the manner for which Professor Smullyan was so well known. This book is suitable for students, scholars and logicians who are interested in learning more about Raymond Smullyan's work and life.
Universality In Set Theories
DOWNLOAD
READ ONLINE
Author : Manuel Bremer
language : en
Publisher: Walter de Gruyter
Release Date : 2013-05-02
Universality In Set Theories written by Manuel Bremer and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-02 with Philosophy categories.
The book discusses the fate of universality and a universal set in several set theories. The book aims at a philosophical study of ontological and conceptual questions around set theory. Set theories are ontologies. They posit sets and claim that these exhibit the essential properties laid down in the set theoretical axioms. Collecting these postulated entities quantified over poses the problem of universality. Is the collection of the set theoretical entities itself a set theoretical entity? What does it mean if it is, and what does it mean if it is not? To answer these questions involves developing a theory of the universal set. We have to ask: Are there different aspects to universality in set theory, which stand in conflict to each other? May inconsistency be the price to pay to circumvent ineffability? And most importantly: How far can axiomatic ontology take us out of the problems around universality?
Godel S Incompleteness Theorems
DOWNLOAD
READ ONLINE
Author : Raymond M. Smullyan
language : en
Publisher: Oxford University Press
Release Date : 1992-08-20
Godel S Incompleteness Theorems written by Raymond M. Smullyan 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 1992-08-20 with Mathematics categories.
Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists.
The Construction Of Property
DOWNLOAD
READ ONLINE
Author : Amnon Lehavi
language : en
Publisher: Cambridge University Press
Release Date : 2013-06-20
The Construction Of Property written by Amnon Lehavi 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 2013-06-20 with Law categories.
Presents a structural and institutional theory of property and examines property regimes, protagonists of property and the challenges of globalisation.
A Discourse And Register Analysis Of The Prophetic Book Of Joel
DOWNLOAD
READ ONLINE
Author : Colin Toffelmire
language : en
Publisher: BRILL
Release Date : 2016-07-11
A Discourse And Register Analysis Of The Prophetic Book Of Joel written by Colin Toffelmire and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-11 with Religion categories.
In A Discourse and Register Analysis of the Prophetic Book of Joel, Colin M. Toffelmire presents a thorough analysis of the text of Joel from the perspective of Systemic Functional Linguistics.
Fratricide In The Holy Land
DOWNLOAD
READ ONLINE
Author : Avner Falk
language : en
Publisher: Terrace Books
Release Date : 2005-02-17
Fratricide In The Holy Land written by Avner Falk and has been published by Terrace Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-17 with History categories.
This is the first English-language book ever to apply psychoanalytic knowledge to the understanding of the most intractable international struggle in our world today—the Arab-Israeli conflict. Two ethnic groups fight over a single territory that both consider to be theirs by historical right—essentially a rational matter. But close historical examination shows that the two parties to this tragic conflict have missed innumerable opportunities for a rational partition of the territory between them and for a permanent state of peace and prosperity rather than perennial bloodshed and misery. Falk suggests that a way to understand and explain such irrational matters is to examine the unconscious aspects of the conflict. He examines large-group psychology, nationalism, group narcissism, psychogeography, the Arab and Israeli minds, and suicidal terrorism, and he offers psychobiographical studies of Ariel Sharon and Yasser Arafat, two key players in this tragic conflict today.
Agricultural Land Redistribution And Land Administration In Sub Saharan Africa
DOWNLOAD
READ ONLINE
Author : Frank F. K. Byamugisha
language : en
Publisher: World Bank Publications
Release Date : 2014-05-05
Agricultural Land Redistribution And Land Administration In Sub Saharan Africa written by Frank F. K. Byamugisha and has been published by World Bank Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-05 with Social Science categories.
Agricultural Land Redistribution and Land Administration in Sub-Saharan Africa: Case Studies of Recent Reforms focuses on “how” to undertake land reforms in Sub-Saharan Africa, but with relevant lessons for other developing countries. It provides details, with case studies, on how reforms were undertaken to address a pressing and controversial development challenge in Africa – land ownership inequality – and an intransigent development issue – inefficiency and corruption in land administration. An equally important contribution of the book is assessing reforms and highlighting valuable lessons for other countries contemplating reforms. The six case studies collectively cover two main areas of land governance: reforms in redistributing agricultural land and reforms in land administration. The first two case studies discuss reforms in redistributing agricultural land in Malawi and South Africa, part of the southern Africa region where land ownership inequalities rival those in Latin America. The remaining case studies, four in number, are focused on addressing corruption and inefficiency in land administration in a variety of contexts of governance including stable and post-conflict countries. The case studies cover: • Decentralizing land administration with demonstrations from Uganda, Ethiopia, Tanzania, and Ghana; • Developing post-conflict land administration systems with examples from Liberia and Rwanda; • Re-engineering and computerizing land information systems with examples from Ghana and Uganda; and • Improving management of government land through land inventories with examples drawn from Ghana and Uganda. The common elements between sometimes disparate experiences provide lessons of relevance to African and other developing countries contemplating similar reforms. The rigorous analysis and yet down-to-earth lessons of experience are a reflection of the authors’ deep global experience underpinned by personal participation in the reforms covered by the book. This volume will be of interest to a wide audience including land specialists and practitioners, African policy makers, experts and managers in the international development community, and the academia.