Incompleteness In The Land Of Sets

Incompleteness In The Land Of Sets Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Incompleteness In The Land Of Sets book. This book definitely worth reading, it is an incredibly well-written.

Incompleteness in the Land of Sets

Melvin Fitting
Incompleteness in the Land of Sets Book PDF

Author : Melvin Fitting
Publisher : Unknown
Page : 0 pages
File Size : 48,8 Mb
Release : 2007
Category : Incompleteness theorems
ISBN : 1904987346

Get Book

Incompleteness in the Land of Sets by Melvin Fitting Pdf

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

Raymond M. Smullyan
Forever Undecided Book PDF

Author : Raymond M. Smullyan
Publisher : Knopf
Page : 286 pages
File Size : 40,5 Mb
Release : 2012-07-04
Category : Mathematics
ISBN : 9780307962461

Get Book

Forever Undecided by Raymond M. Smullyan Pdf

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 Gödel

Carlo Cellucci
The Theory of G del Book PDF

Author : Carlo Cellucci
Publisher : Springer Nature
Page : 164 pages
File Size : 48,6 Mb
Release : 2022-11-21
Category : Philosophy
ISBN : 9783031134173

Get Book

The Theory of Gödel by Carlo Cellucci Pdf

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

Melvin Fitting,Brian Rayman
Raymond Smullyan on Self Reference Book PDF

Author : Melvin Fitting,Brian Rayman
Publisher : Springer
Page : 195 pages
File Size : 49,8 Mb
Release : 2018-01-11
Category : Philosophy
ISBN : 9783319687322

Get Book

Raymond Smullyan on Self Reference by Melvin Fitting,Brian Rayman Pdf

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

Manuel Bremer
Universality in Set Theories Book PDF

Author : Manuel Bremer
Publisher : Walter de Gruyter
Page : 125 pages
File Size : 52,7 Mb
Release : 2013-05-02
Category : Philosophy
ISBN : 9783110326109

Get Book

Universality in Set Theories by Manuel Bremer Pdf

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?

Canada's Odyssey

Peter H. Russell
Canada s Odyssey Book PDF

Author : Peter H. Russell
Publisher : University of Toronto Press
Page : 544 pages
File Size : 41,5 Mb
Release : 2017-05-08
Category : History
ISBN : 9781487514488

Get Book

Canada's Odyssey by Peter H. Russell Pdf

150 years after Confederation, Canada is known around the world for its social diversity and its commitment to principles of multiculturalism. But the road to contemporary Canada is a winding one, a story of division and conflict as well as union and accommodation. In Canada’s Odyssey, renowned scholar Peter H. Russell provides an expansive, accessible account of Canadian history from the pre-Confederation period to the present day. By focusing on what he calls the "three pillars" of English Canada, French Canada, and Aboriginal Canada, Russell advances an important view of our country as one founded on and informed by "incomplete conquests". It is the very incompleteness of these conquests that have made Canada what it is today, not just a multicultural society but a multinational one. Featuring the scope and vivid characterizations of an epic novel, Canada’s Odyssey is a magisterial work by an astute observer of Canadian politics and history, a perfect book to commemorate the 150th anniversary of Confederation.

Logic, Logic, and Logic

George Boolos
Logic Logic and Logic Book PDF

Author : George Boolos
Publisher : Harvard University Press
Page : 458 pages
File Size : 44,7 Mb
Release : 1998
Category : Mathematics
ISBN : 067453767X

Get Book

Logic, Logic, and Logic by George Boolos Pdf

George Boolos was one of the most prominent and influential logician-philosophers of recent times. This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; on Frege, Dedekind, Cantor, and Russell; and on miscellaneous topics in logic and proof theory, including three papers on various aspects of the Gödel theorems. Boolos is universally recognized as the leader in the renewed interest in studies of Frege's work on logic and the philosophy of mathematics. John Burgess has provided introductions to each of the three parts of the volume, and also an afterword on Boolos's technical work in provability logic, which is beyond the scope of this volume.

A Concise Introduction to Mathematical Logic

Wolfgang Rautenberg
A Concise Introduction to Mathematical Logic Book PDF

Author : Wolfgang Rautenberg
Publisher : Springer
Page : 337 pages
File Size : 51,7 Mb
Release : 2010-07-01
Category : Mathematics
ISBN : 9781441912213

Get Book

A Concise Introduction to Mathematical Logic by Wolfgang Rautenberg Pdf

Mathematical logic developed into a broad discipline with many applications in mathematics, informatics, linguistics and philosophy. This text introduces the fundamentals of this field, and this new edition has been thoroughly expanded and revised.

Godel's Incompleteness Theorems

Raymond M. Smullyan
Godel s Incompleteness Theorems Book PDF

Author : Raymond M. Smullyan
Publisher : Oxford University Press
Page : 156 pages
File Size : 45,6 Mb
Release : 1992-08-20
Category : Mathematics
ISBN : 9780190281441

Get Book

Godel's Incompleteness Theorems by Raymond M. Smullyan Pdf

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.

Fundamentals of Mathematical Logic

Peter G. Hinman
Fundamentals of Mathematical Logic Book PDF

Author : Peter G. Hinman
Publisher : CRC Press
Page : 894 pages
File Size : 53,8 Mb
Release : 2018-10-08
Category : Mathematics
ISBN : 9781439864272

Get Book

Fundamentals of Mathematical Logic by Peter G. Hinman Pdf

This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.

Gödel's Theorem

Torkel Franzén
G del s Theorem Book PDF

Author : Torkel Franzén
Publisher : Unknown
Page : 128 pages
File Size : 43,9 Mb
Release : 2017-08-09
Category : Electronic
ISBN : 1138427268

Get Book

Gödel's Theorem by Torkel Franzén Pdf

"Among the many expositions of G�del's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franz�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 G�del

Elements of Set Theory

Herbert B. Enderton
Elements of Set Theory Book PDF

Author : Herbert B. Enderton
Publisher : Academic Press
Page : 279 pages
File Size : 46,6 Mb
Release : 1977-05-23
Category : Mathematics
ISBN : 9780080570426

Get Book

Elements of Set Theory by Herbert B. Enderton Pdf

This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.

Godel's Incompleteness Theorems

Raymond M. Smullyan
Godel s Incompleteness Theorems Book PDF

Author : Raymond M. Smullyan
Publisher : Oxford University Press
Page : 156 pages
File Size : 54,8 Mb
Release : 1992-08-20
Category : Mathematics
ISBN : 9780195364378

Get Book

Godel's Incompleteness Theorems by Raymond M. Smullyan Pdf

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

Amnon Lehavi
The Construction of Property Book PDF

Author : Amnon Lehavi
Publisher : Cambridge University Press
Page : 361 pages
File Size : 55,7 Mb
Release : 2013-06-20
Category : Law
ISBN : 9781107035386

Get Book

The Construction of Property by Amnon Lehavi Pdf

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

Colin Toffelmire
A Discourse and Register Analysis of the Prophetic Book of Joel Book PDF

Author : Colin Toffelmire
Publisher : BRILL
Page : 242 pages
File Size : 41,7 Mb
Release : 2016-07-11
Category : Religion
ISBN : 9789004325074

Get Book

A Discourse and Register Analysis of the Prophetic Book of Joel by Colin Toffelmire Pdf

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.