|
Showing 1 - 16 of
16 matches in All Departments
'A wealth of examples to which solutions are given permeate the
text so the reader will certainly be active.'The Mathematical
GazetteThis is the final book written by the late great puzzle
master and logician, Dr. Raymond Smullyan.This book is a sequel to
my Beginner's Guide to Mathematical Logic.The previous volume deals
with elements of propositional and first-order logic, contains a
bit on formal systems and recursion, and concludes with chapters on
Goedel's famous incompleteness theorem, along with related
results.The present volume begins with a bit more on propositional
and first-order logic, followed by what I would call a 'fein'
chapter, which simultaneously generalizes some results from
recursion theory, first-order arithmetic systems, and what I dub a
'decision machine.' Then come five chapters on formal systems,
recursion theory and metamathematical applications in a general
setting. The concluding five chapters are on the beautiful subject
of combinatory logic, which is not only intriguing in its own
right, but has important applications to computer science. Argonne
National Laboratory is especially involved in these applications,
and I am proud to say that its members have found use for some of
my results in combinatory logic.This book does not cover such
important subjects as set theory, model theory, proof theory, and
modern developments in recursion theory, but the reader, after
studying this volume, will be amply prepared for the study of these
more advanced topics.
'A wealth of examples to which solutions are given permeate the
text so the reader will certainly be active.'The Mathematical
GazetteThis is the final book written by the late great puzzle
master and logician, Dr. Raymond Smullyan.This book is a sequel to
my Beginner's Guide to Mathematical Logic.The previous volume deals
with elements of propositional and first-order logic, contains a
bit on formal systems and recursion, and concludes with chapters on
Goedel's famous incompleteness theorem, along with related
results.The present volume begins with a bit more on propositional
and first-order logic, followed by what I would call a 'fein'
chapter, which simultaneously generalizes some results from
recursion theory, first-order arithmetic systems, and what I dub a
'decision machine.' Then come five chapters on formal systems,
recursion theory and metamathematical applications in a general
setting. The concluding five chapters are on the beautiful subject
of combinatory logic, which is not only intriguing in its own
right, but has important applications to computer science. Argonne
National Laboratory is especially involved in these applications,
and I am proud to say that its members have found use for some of
my results in combinatory logic.This book does not cover such
important subjects as set theory, model theory, proof theory, and
modern developments in recursion theory, but the reader, after
studying this volume, will be amply prepared for the study of these
more advanced topics.
This is an exciting if not rambling account of events of Raymond
Smullyan's four lives - as a mathematical logician, musician,
magician, and author - together with thoughts that come to his mind
as he recalls them. This book includes topics from some of
Smullyan's twenty-six books, as well as many of his favorite
anecdotes and jokes. It also presents some generalizations of
theorems of the great logicians Goedel and Tarski, and discusses
logic in general, and how he won his wife with a logic trick!
Smullyan also relates some of his teaching experiences, and
expresses his views on mathematical education, and how our present
textbooks are primarily responsible for its decline! About his life
as a pianist, Smullyan relates a good deal about his experiences
with the Piano Society - a wonderful organization to which he is a
staunch contributor, and how he has had such delightful relations
with many of its members. Last but not least, Smullyan recounts how
he has known some lovely ladies over the years.
This is an exciting if not rambling account of events of Raymond
Smullyan's four lives - as a mathematical logician, musician,
magician, and author - together with thoughts that come to his mind
as he recalls them. This book includes topics from some of
Smullyan's twenty-six books, as well as many of his favorite
anecdotes and jokes. It also presents some generalizations of
theorems of the great logicians Goedel and Tarski, and discusses
logic in general, and how he won his wife with a logic trick!
Smullyan also relates some of his teaching experiences, and
expresses his views on mathematical education, and how our present
textbooks are primarily responsible for its decline! About his life
as a pianist, Smullyan relates a good deal about his experiences
with the Piano Society - a wonderful organization to which he is a
staunch contributor, and how he has had such delightful relations
with many of its members. Last but not least, Smullyan recounts how
he has known some lovely ladies over the years.
Raymond Smullyan presents a bombshell puzzle so startling that it
seems incredible that there could be any solution at all! But there
is indeed a solution - moreover, one that requires a chain of
lesser puzzles to be solved first. The reader is thus taken on a
journey through a maze of subsidiary problems that has all the
earmarks of an entertaining detective story.This book leads the
unwary reader into deep logical waters through seductively
entertaining logic puzzles. One example is Boolean algebra with
such weird looking equations as 1+1=0 - a subject which today plays
a vital role, not only in mathematical systems, but also in
computer science and artificial intelligence.
Raymond Smullyan presents a bombshell puzzle so startling that it
seems incredible that there could be any solution at all! But there
is indeed a solution - moreover, one that requires a chain of
lesser puzzles to be solved first. The reader is thus taken on a
journey through a maze of subsidiary problems that has all the
earmarks of an entertaining detective story.This book leads the
unwary reader into deep logical waters through seductively
entertaining logic puzzles. One example is Boolean algebra with
such weird looking equations as 1+1=0 - a subject which today plays
a vital role, not only in mathematical systems, but also in
computer science and artificial intelligence.
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.
Characters from "Wonderland" and "Through the Looking-Glass"
populate these 88 puzzles involving word play, logic and metalogic,
and philosophical paradoxes. The charmingly illustrated challenges
range from easy to difficult and include solutions.
"Another scintillating collection of brilliant problems and
paradoxes by the most entertaining logician and set theorist who
ever lived." -- Martin Gardner
"Smullyan is not your run-of-the-mill puzzlemeister; he polishes up
old chestnuts, spins variations on a theme, and peoples his logical
world with a delightful cast of characters." -- "Science 82"
"I believe Ray Smullyan to be the Lewis Carroll of our times. His
little books of logic puzzles will be remembered long after most of
us are forgotten." -- Peter Denning, Chairman of the Computer
Science Department, Naval Postgraduate School
"You may experience small frissons of delight as you follow
Smullyan into the dizzying heights of Godel's proof and the very
nature of proof, truth, and logic in mathematics." -- "Kirkus
Reviews
"Discover scintillating new perspectives on the principles of
mathematical logic with this puzzle treasury. Inspired by the
classic tale of a prisoner's choice between two doors, these
whimsically themed challenges allow readers to base their decisions
on logic rather than luck. Nineteen chapters advance from
relatively simple puzzles and meta-puzzles to highly complex
paradoxes involving probability, time, and change. The author, a
well-known philosopher and magician as well as a celebrated
mathematician and logician, was acclaimed by "The New York Times"
as "a master at translating difficult ideas into stories and
puzzles that require no formal background, only patience and a
passion to learn."
This work is a sequel to the author's Gödel's Incompleteness Theorems, though it can be read independently by anyone familiar with Gödel's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.
"The most original, most profound, and most humorous collection of
recreational logic and math problems ever written." -- Martin
Gardner, "Scientific American
""The value of the book lies in the wealth of ingenious puzzles.
They afford amusement, vigorous exercise, and instruction." --
Willard Van Orman Quine, "The New York Times Book Review
"If you're intrigued by puzzles and paradoxes, these 200
mind-bending logic puzzles, riddles, and diversions will thrill you
with challenges to your powers of reason and common sense. Raymond
M. Smullyan -- a celebrated mathematician, logician, magician, and
author -- presents a logical labyrinth of more than 200
increasingly complex problems. The puzzles delve into Godel's
undecidability theorem and other examples of the deepest paradoxes
of logic and set theory. Detailed solutions follow each puzzle.
This book contains 50 elegant, witty chess problems concerned with
deducing events in a game's past. Holmes instructs Watson in the
intricacies of retrograde analysis, leading to increasingly
difficult self-contained mysteries.
This book serves both as a completely self-contained introduction
and as an exposition of new results in the field of recursive
function theory and its application to formal systems.
In his most popular book since THE LADY OR THE TIGER? the grand
vizier of the puzzle world gives us 1001 hours of brain-teasing
fun. Smullyan includes wonderful old chestnuts and some fiendishly
original puzzles, 225 in all. An absolute must for all puzzle fans
from the middle-school whiz to the sophisticated matematician or
computer scientist.
Is there really a God, and if so, what is God actually like? Is
there an afterlife, and if so, is there such a thing as eternal
punishment for unrepentant sinners, as many orthodox Christians and
Muslims believe? And is it really true that our unconscious minds
are connected to a higher spiritual reality, and if so, could this
higher spiritual reality be the very same thing that religionists
call "God"? In his latest book. Raymond M. Smullyan invites the
reader to explore some beautiful and some horrible ideas related to
religious and mystical thought. In Part One, Smullyan uses the
writings on religious by fellow polymath Martin Gardner as the
starting point for some inspired ideas about religion and belief.
Part Two focuses on the doctrine of Hell and its justification,
with Smullyan presenting powerful arguments on both sides of the
controversy. "If God asked you to vote on the retention or
abolition of Hell, " he asks, "how would you vote?" Smullyan has
posed this question to many believers and received some surprising
answers. In the last part of his treasurable triptych, Smullyan
takes up the "beautiful and inspiring" ideas of Richard Bucke and
Edward Carpenter on Cosmic Consciousness. Readers will delight in
Smullyan's observations on religion and in his clear-eyed
presentation of many new and startling ideas about this most
wonderful product of human consciousness. A witty and stimulating
inquiry into religion and mysticism by the best-selling
philosopher.
|
You may like...
Loot
Nadine Gordimer
Paperback
(2)
R398
R330
Discovery Miles 3 300
Loot
Nadine Gordimer
Paperback
(2)
R398
R330
Discovery Miles 3 300
Top Five
Rosario Dawson, Cedric The Entertainer, …
Blu-ray disc
R40
Discovery Miles 400
|