Author: Rebecca Goldstein
Publisher: W. W. Norton & Company
ISBN: 0393327604
Category : Biography & Autobiography
Languages : en
Pages : 299
Book Description
"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.
Incompleteness
Author: Rebecca Goldstein
Publisher: W. W. Norton & Company
ISBN: 0393327604
Category : Biography & Autobiography
Languages : en
Pages : 299
Book Description
"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.
Publisher: W. W. Norton & Company
ISBN: 0393327604
Category : Biography & Autobiography
Languages : en
Pages : 299
Book Description
"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.
Proving the Unprovable
Author: Christopher Slobogin
Publisher: Oxford University Press
ISBN: 0198040962
Category : Psychology
Languages : en
Pages : 209
Book Description
This book is written for researchers, scholars, advanced graduate students, and clinicians who work in risk assessment and criminal responsibility. It addresses the question of admitting expert testimony from behavioral health experts in determining matters of culpability and dangerousness by examining a number of factors, including the source of the expert testimony, whether juries need it, and whether it is presented as proven or informed in the court. It argues that the question cannot be understood as a dualistic matter of being for or against expert testimony; rather, its highly nuanced arguments show that determining who should be punished and who should be preventively detained must happen through an interdisciplinary process that looks at the specific circumstances of each case. It offers an analytic framework for making these determinations that treats culpability and dangerousness not as static, ontologically-complete entities, but rather as socially-constructed concepts that cannot be determined solely through the scientific method. The book makes the intriguing argument throughout that although expert testimony cannot be considered scientifically reliable or proven, it should nevertheless be included as long as it can be classified and understood as informed speculation because it makes legal factfinders attend more closely to the matters that the law considers pertinent to past mental states. It seeks to reconcile the tension between the law's demand for accuracy and the inability of behavioral science to provide more than speculative answers for most questions raised by the insanity defense and related doctrines and by sentencing, commitment and sex offender statutes that require determinations of risk.
Publisher: Oxford University Press
ISBN: 0198040962
Category : Psychology
Languages : en
Pages : 209
Book Description
This book is written for researchers, scholars, advanced graduate students, and clinicians who work in risk assessment and criminal responsibility. It addresses the question of admitting expert testimony from behavioral health experts in determining matters of culpability and dangerousness by examining a number of factors, including the source of the expert testimony, whether juries need it, and whether it is presented as proven or informed in the court. It argues that the question cannot be understood as a dualistic matter of being for or against expert testimony; rather, its highly nuanced arguments show that determining who should be punished and who should be preventively detained must happen through an interdisciplinary process that looks at the specific circumstances of each case. It offers an analytic framework for making these determinations that treats culpability and dangerousness not as static, ontologically-complete entities, but rather as socially-constructed concepts that cannot be determined solely through the scientific method. The book makes the intriguing argument throughout that although expert testimony cannot be considered scientifically reliable or proven, it should nevertheless be included as long as it can be classified and understood as informed speculation because it makes legal factfinders attend more closely to the matters that the law considers pertinent to past mental states. It seeks to reconcile the tension between the law's demand for accuracy and the inability of behavioral science to provide more than speculative answers for most questions raised by the insanity defense and related doctrines and by sentencing, commitment and sex offender statutes that require determinations of risk.
Logically Fallacious
Author: Bo Bennett
Publisher: eBookIt.com
ISBN: 1456607375
Category : Education
Languages : en
Pages : 429
Book Description
This book is a crash course in effective reasoning, meant to catapult you into a world where you start to see things how they really are, not how you think they are. The focus of this book is on logical fallacies, which loosely defined, are simply errors in reasoning. With the reading of each page, you can make significant improvements in the way you reason and make decisions. Logically Fallacious is one of the most comprehensive collections of logical fallacies with all original examples and easy to understand descriptions, perfect for educators, debaters, or anyone who wants to improve his or her reasoning skills. "Expose an irrational belief, keep a person rational for a day. Expose irrational thinking, keep a person rational for a lifetime." - Bo Bennett This 2021 Edition includes dozens of more logical fallacies with many updated examples.
Publisher: eBookIt.com
ISBN: 1456607375
Category : Education
Languages : en
Pages : 429
Book Description
This book is a crash course in effective reasoning, meant to catapult you into a world where you start to see things how they really are, not how you think they are. The focus of this book is on logical fallacies, which loosely defined, are simply errors in reasoning. With the reading of each page, you can make significant improvements in the way you reason and make decisions. Logically Fallacious is one of the most comprehensive collections of logical fallacies with all original examples and easy to understand descriptions, perfect for educators, debaters, or anyone who wants to improve his or her reasoning skills. "Expose an irrational belief, keep a person rational for a day. Expose irrational thinking, keep a person rational for a lifetime." - Bo Bennett This 2021 Edition includes dozens of more logical fallacies with many updated examples.
On Formally Undecidable Propositions of Principia Mathematica and Related Systems
Author: Kurt Gödel
Publisher: Courier Corporation
ISBN: 0486158403
Category : Mathematics
Languages : en
Pages : 82
Book Description
First English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.
Publisher: Courier Corporation
ISBN: 0486158403
Category : Mathematics
Languages : en
Pages : 82
Book Description
First English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.
An Introduction to Gödel's Theorems
Author: Peter Smith
Publisher: Cambridge University Press
ISBN: 1139465937
Category : Mathematics
Languages : en
Pages : 376
Book Description
In 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Gödel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.
Publisher: Cambridge University Press
ISBN: 1139465937
Category : Mathematics
Languages : en
Pages : 376
Book Description
In 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Gödel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.
Forever Undecided
Author: Raymond M. Smullyan
Publisher: Knopf
ISBN: 0307962466
Category : Mathematics
Languages : en
Pages : 286
Book Description
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!
Publisher: Knopf
ISBN: 0307962466
Category : Mathematics
Languages : en
Pages : 286
Book Description
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!
Roads to Infinity
Author: John Stillwell
Publisher: CRC Press
ISBN: 1439865507
Category : Mathematics
Languages : en
Pages : 202
Book Description
Winner of a CHOICE Outstanding Academic Title Award for 2011!This book offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. The treatment is h
Publisher: CRC Press
ISBN: 1439865507
Category : Mathematics
Languages : en
Pages : 202
Book Description
Winner of a CHOICE Outstanding Academic Title Award for 2011!This book offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. The treatment is h
Principia Mathematica
Author: Alfred North Whitehead
Publisher:
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 688
Book Description
Publisher:
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 688
Book Description
Gödel's Proof
Author: Ernest Nagel
Publisher: Psychology Press
ISBN: 041504040X
Category : Gödel's theorem
Languages : en
Pages : 118
Book Description
In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system and had radical implications that have echoed throughout many fields. A gripping combination of science and accessibility, Godel’s Proofby Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity.
Publisher: Psychology Press
ISBN: 041504040X
Category : Gödel's theorem
Languages : en
Pages : 118
Book Description
In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system and had radical implications that have echoed throughout many fields. A gripping combination of science and accessibility, Godel’s Proofby Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity.
Metamathematics of First-Order Arithmetic
Author: Petr Hájek
Publisher: Cambridge University Press
ISBN: 1107168414
Category : Mathematics
Languages : en
Pages : 475
Book Description
A much-needed monograph on the metamathematics of first-order arithmetic, paying particular attention to fragments of Peano arithmetic.
Publisher: Cambridge University Press
ISBN: 1107168414
Category : Mathematics
Languages : en
Pages : 475
Book Description
A much-needed monograph on the metamathematics of first-order arithmetic, paying particular attention to fragments of Peano arithmetic.