Reviews (1)

The most concise work on the philosophy of mathematics
Anyone looking for a synopsis on collected essays on this subject need look no further. This is not only because of the relative scarcity of books on this subject. I would say this book will become (if it is not already) the bible of the philosophy of maths, like the book of Hardy is on number theory.
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Subjects:  1. General    2. History & Philosophy    3. Logic    4. Logic, Symbolic and mathematic    5. Logic, Symbolic and mathematical    6. Mathematics    7. Philosophy    8. Religion - Socialissues    9. Mathematical logic    10. Mathematics / History    11. Philosophy of mathematics    12. Philosophy | Logic & Mathematics   

Reviews (9)

Classical Foundations of Formal Logic
S. Wuest, M.S. in Computer Science, AI, Data Fusion
Warm Place in my Fireplace
This book has a warm place in my fireplace.I cannot believe anyone who thinks this book is fun.If you like sticking forks into your eyes, or drinking battery acid, you will love this book.I used this book in my college logic class 11 years ago, and I have been in therapy ever since to rid my nights of the awful dreams.This book was terribly written, the exercises were impossible, and the answers in the back of the book were wrong (was this some kind of sick joke?).
Solid introduction to the study
Copi's textbook lays out all of the basic concepts in symbolic logic necessary for progressing on to more advanced work and understanding many of the fundamentals of discrete mathematics. Some people have commented that his treatment is outdated, but a thorough understanding of chapters 6, 8, and 10 should equip anyone to understand the newer forms of notation. Chapter 7 is notably excellent but seemed out of place. As the most advanced of the whole book, it relates more than later chapters to the "further reading" topics. Proof of the redundancy of "indirect proof" (chapter 3?) and multi-modal logic beyond binary values were other very notable highlights.
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Subjects:  1. General    2. Logic    3. Logic, Symbolic and mathematic    4. Mathematics    5. Philosophy    6. Mathematical logic    7. Philosophy / General   

Subjects:  1. Logic    2. Logic, Symbolic and mathematic    3. Logic, Symbolic and mathematical    4. Mathematical And Symbolic Logic    5. Mathematics    6. Philosophy Of Mathematics    7. Science/Mathematics    8. Calculus & mathematical analysis    9. MSC: 03-XX    10. Mathematics / Logic   

Reviews (11)

the heuristic of mathematical discovery
In a footnote to chapter 2 (much of the content of "Proofs and Refutations" is in the footnotes) Lakatos writes: "Until the seventeenth century, Euclidians approved the Platonic method of analysis as the method of heuristic; later they replaced it by the stroke of luck and/or genius." That stroke of luck and/or genius is a slight of hand that hides much of the story of the unfolding of mathematical research. nice reading for the general public
Very nice book if you are in high school or in college and would like to see how mathematics evolves. It makes a very pleasant reading although the mathematical ideas behind are not trivial. a study in mathematical thought
I want to add a few words to the brief comment by the reader in Monroe (who gave this book one star). I tend to agree that "Proofs and Refutations" isn't a primer in mathematical proof-writing; it's certainly not a textbook for beginning mathematicians wanting to know how to practice their craft.Read more

Subjects:  1. General    2. Logic    3. Logic, Symbolic and mathematic    4. Logic, Symbolic and mathematical    5. Mathematics    6. Philosophy    7. Philosophy / General    8. Proof theory   

Editorial Review

Kurt Gödel is often held up as an intellectual revolutionary whose incompleteness theorem helped tear down the notion that there was anything certain about the universe. Philosophy professor, novelist, and MacArthur Fellow Rebecca Goldstein reinterprets the evidence and restores to Gödel's famous idea the meaning he claimed he intended: that there is a mathematical truth--an objective certainty--underlying everything and existing independently of human thought. Gödel, Goldstein maintains, was an intellectual heir to Plato whose sense of alienation from the positivists and postmodernists of the 1940s was only ameliorated by his friendship with another intellectual giant, Albert Einstein. As Goldstein writes, "That his work, like Einstein's, has been interpreted as not only consistent with the revolt against objectivity but also as among its most compelling driving forces is ... more than a little ironic."Read more

Reviews (49)

Ironic
Unlike some previous reviewers I think Rebecca Goldstein does an admirable job showing us a glimpse of the inner world of probably the finest logician that ever lived. She does so in an entertaining style, and the way she describes the odd friendship between Gödel and Einstein is very touching in a `novelish' kind of way.
The Paradox of Kurt Godel.
_Incompleteness:The Proof and Paradox of Kurt Godel_ in the Great Discoveries Series by MacArthur Fellow and philosopher Rebecca Goldstein is a decent biography of the logician Kurt Godel.The fascinating, eccentric, and brilliant Kurt Godel is best known for his incompleteness theorem which showed that any sufficiently strong axiomatic theory is either incomplete or inconsistent.This book reviews Godel's life, attempts to provide an outline of his theorem, and provides a discussion of the philosophical foundations of mathematics.Godel was a Platonic realist for most of his life and believed that mathematical objects were real and that mathematical propositions were true independent of humans.Godel's incompleteness theorem has been misinterpreted by postmodernists who use it to argue that there is no truth, contrary to Godel's own interpretations.As has been pointed out by other reviewers there are problems with Goldstein's discussion of the foundations of mathematics and her attempted outline of Godel's theorem.Nevertheless, the book is fairly interesting for its recollections of Godel.In particular, the author follows Godel from his early career as part of the Vienna circle (as a "Platonist among the positivists"), the distinctions between the thought of Godel and that of Wittgenstein, to his eventual emigration to the United States and his role as a logician at the Institute for Advanced Study in Princeton, New Jersey.Particularly interesting is the emerging relationship between Godel and Einstein (Einstein claiming that the only reason why he went to his office at all was to be able to walk home with Godel).In addition, Godel was to derive a solution to Einstein's field equations making use of a rotating universe with cyclical time which he presented to Einstein as a gift.Among other things we learn that Godel did not accept the theory of evolution (though his remark that Stalin didn't believe in the theory either may seem peculiar); the author suggests that as a rationalist Godel sought to excise chance and contingency and thus the theory of evolution would appear anathema to him.In addition, we are told that Godel believed a form of the ontological proof for the existence of God to be valid.Furthermore, Godel also believed that his theories had much to say about the nature of the human mind.For example, in a recent series of books the mathematician and physicist Roger Penrose has suggested that the human mind cannot be understood using the analogy of a computer because of Godel's famous result.Godel also was interested in the subject of the afterlife and believed in the reality of the immortal soul.Philosophically, Godel was inspired by both Plato and especially Leibniz.In fact, Godel was believed to have read every book available by and about Leibniz at the Firestone Library at Princeton.During one of his bouts of paranoia, Godel maintained that there existed a conspiracy to keep men stupid by suppressing Leibniz's greatest works.Throughout most of his life Godel was oddly reticent and prone to paranoia and fearfulness.He suffered from some sort of delusion that his food was being poisoned and had very peculiar dietary habits.This ultimately led to his starvation and death after his wife was hospitalized.Godel's position in the mathematics department was also peculiar, and as the author notes in many ways he was extremely isolated.Some of the best books on Godel explicating his philosophy have been written by his fellow logician and friend Hao Wang.Godel's theorems have played an enormous role in the development of Twentieth century mathematics and in the theory of artificial intelligence.He was very clearly a man of unsurpassed genius but also great eccentricity.For example, when Godel was attempting to become a United States citizen he claimed to have uncovered a logical flaw in the United States Constitution which would enable the establishment of tyranny in this country.While the author does not know what this alleged flaw was, this story provides an interesting anecdote revealing Godel's logical mind.While this book must be reservedly recommended for what it has to say on the philosophical underpinnings of mathematics and Godel's theorem, it nevertheless provides an interesting account of the life of this great logician.
Incomplete -- butInteresting
Ms. Goldstein's inter-related aims are several. She wants to provideinsights into the personal life of Godel(why, for example, he and Einstein were close friends), provide a descriptive tour of his incompleteness theorems and convey their significance in the history of modern thought. The result is a somewhat choppy text.One of her central arguments -- that Godel is wrongfully construed as a non-Platonist -- would itself, it seems, justify a book of this length. The central part of the Incompleteness provides a description of Godel's theorem, but I"m afraid it falls short of the mark.In the end, it seems to have a surplus of symbolism, all of which results in something like the statement, -Pr(g)(iff G is not provable). Little was gained from following her argument that could not have been realized with her earlier statements and examples to the effect that Godel demonstrated that any consistent system will generate true, but not provable statements.
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Subjects:  1. Austria    2. Biography    3. Biography / Autobiography    4. General    5. Godel, Kurt    6. History & Philosophy    7. Logic    8. Logicians    9. Mathematics    10. Proof theory    11. Science/Mathematics    12. Scientists - General    13. United States    14. Science: General Issues   

Editorial Review

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Reviews (11)

A Good Book for a Tough Subject
Abstract language theory is hard, but Languages and Machines does a very good job of explaining the subject step by step. The topics are covered extremely thoroughly and with just the right amount of rigor.As for those who claim it's not exciting enough, you can't get blood out of a stone.Only the most dedicated computer scientist and mathematicians will find this topic interesting.Even so, this book does a superb job of tying theory to application (e.g., the machines one can use language theory to build) for even the most obscure concepts (like the Greibach Normal Form).
emphasises the Turing machine
[A review of the 3RD EDITION, 2005.]
horrified
The book is incredibly boring.If you're condemned to read it (say, it's required reading for your qualifiers), I strongly recommend that you find a group of people to study w/ and pool your resources to only buy a single copy.The lack of answers at the back of the book makes self study difficult, and groupwork might be the only way to stay awake.
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Subjects:  1. Computational complexity    2. Computer Books: General    3. Computer Science    4. Computers    5. Formal Language Theory    6. Formal languages    7. Logic    8. Machine theory    9. Mathematics    10. Computers / Computer Science    11. Databases & data structures    12. Mathematical theory of computation   

Editorial Review

Even those with little mathematical background will be able to understand this user-friendly book, which focuses on formal languages and models of computation. (The author devotes an entire chapter to induction and recursive definitions.) Read more

Reviews (20)

Lacks educational value
During the course this book has been anything but helpful. The introductory part is a laugh as it takes for given you as a reader is very deep into mathematical lingo and proofs. Indeed the poofs are some of the worst written, many of them using statements as "Clearly it is..." and "It is now easy to see...", well, no, it isn't easy and mostly seems like a shortcut from the author to excuse himself from actual explanations. Breadth Of Information
I normally don't write reviews. Couple of not very positive reviews could not stop me writing one for this title. In my opinion, this book really presents a breadth of information Terrible book
This book is awful. Hard to follow along with the reading. Poor examples, lacking and skipping many steps when there actually is an example. Answers to a few of the questions would have been nice, to know if the problems were done correctly. Must be a master of discrete mathmatics to have any understanding what is going on. I have seen many better books. ... Read more

Subjects:  1. Computable functions    2. Computer Science    3. Computers    4. Logic    5. Mathematics    6. Programming - General    7. Programming Languages - General    8. Science/Mathematics    9. Sequential Machine Theory    10. Computers / Computer Science    11. General Theory of Computing    12. Programming languages   

Reviews (1)

Helpful overview
Process algebra is not only of interest in mathematics, theoretical computer science, and mathematical logic but is of enormous importance in applications. Most of these applications have been in business process modeling, models of concurrent processing, and computational biology. This book gives a fairly comprehensive overview of the main approaches to process algebra, but emphasizing theoretical foundations and not practical applications. One of the process algebras discussed in the book is the pi-calculus, this discussion appearing in Part 3 of the book by Joachim Parrow. This article was the only one read by this reviewer, so the commentary here will deal with it exclusively.
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Subjects:  1. Algebra - General    2. Boolean Algebra    3. Data Modeling & Design    4. Data Processing - Parallel Processing    5. Information Theory    6. Logic    7. Machine theory    8. Mathematics    9. Parallel Processing    10. Parallel processing (Electroni    11. Parallel processing (Electronic computers)    12. Programming - Parallel Programming    13. Science/Mathematics    14. Algebra    15. Computers / Information Theory   

Reviews (4)

unlike any other probability text
Unlike standard books on probability, Hacking gives a strong introduction to the basic concepts, drawn from his background in philosophy. Several passages discuss writers like Hume and Popper. I've never seen a probability text like this one!
Hacking gets everything right except for Keynes
Hacking's book is a job well done.He blends history,philosophy,logic,mathematics,statistics and science with wit and judicious scrutiny in general.Unfortunately,the book is slightly marred by inaccurate and/or incorrect statements about J. M. Keynes and/or his logical theory of probability.Describing Keynes as a"belief dogmatist"is way off the mark given Keynes's penchant for changing his mind as new and/or relevant information and analysis became available over his lifetime.Secondly,it is bizarre for Hacking to claim that Keynes had no use for frequency-type probability theories and jeered at the idea of relative frequency holding in the long run because in the long run we are all dead.(Hacking,pp.146-151).The only frequency theory Keynes ever rejected was that of John Venn.Keynes always considered frequency theories to be accurate and correct for some cases.However,they were not general in scope but limited in their applicability.The interested reader should consult chapter 8 of Keynes's A Treatise on Probability(1921).Finally, Keynes rejected the fallacy of long runism or conditional apriorism because of its unsound argument.The fact that in the long run some process may converge to a particular outcome in the limit offers no support to a do-nothing policy in the present.If the only available relevant evidence bearing on the probability of a proposition is frequency data then the logical probability is the same as the relative frequency estimate.The only caveat Keynes would add would be that the frequency data should have passed the Lexis Q Test for stability.

For anyone, anythinker
I would HIGHLY recommend this book for anyone (including business men) who must make decisions with incomplete information and under uncertainty.Instead of focusing on the mechanics of statistics, it focuses on how to think about risky propositions.Read more

Subjects:  1. Induction (Logic)    2. Logic    3. Mathematics    4. Philosophy    5. Probabilities    6. Probability & Statistics - General    7. Science/Mathematics    8. Philosophy / General   

Reviews (7)

Biggest return for the biggest investment
This was the second-hardest book I ever read.Honestly, it took me years and years to get through it.I even had to buy a 2nd copy, because I kept getting frustrated and throwing the first copy across the room until it was destroyed.So yes, this book requires a substantial effort to read.
A must
The book provides all the tools needed for a productive use of the theory. Written by leading experts in the field, the book is both a fascinating introduction as well as a comprehensive reference for experts. Excellent if you have the math...
to understand it.This book is intended for serious students of computer science or those who have some similar training - it is definitely set up as a textbook.However, that being said, if you have the background the authors' delivery is fist-class and very clear.Read more

Subjects:  1. Computer Mathematics    2. Computer Science    3. Computers    4. Computers - General Information    5. Kolmogorov complexity    6. Logic    7. Reference - General    8. Science/Mathematics    9. Applied mathematics    10. Mathematical theory of computation    11. Mathematics / Statistics   

Reviews (6)

A must have
A must have for set theorists. Does a better job than Jech. It's a little weird how you get a sense of the set theorists as people, but the historical stuff is otherwise really great.

Interesting but too much reading
Assumes set theory through forcing and some model theory. He integrates a lot of historical information which is interesting but greatly adds to the reading without adding to the mathematical understanding. The semester is short and I want to learn what I need and get on with life. While it does have more details than Jech, I like Jech's style better and not just because it is shorter. (The 2e is just a corrected reprint of 1e.)

Excellent as a follow-up to Kunen
I'm a graduate student in set theory and I'm finding Kanamori an excellent follow-up to Kunen.The book manages to combine detailed technical exposition with historical insight which is actually useful to understanding the material (not just a list of dates) and gives one a "feel" for the subject.
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Subjects:  1. General    2. Geometry - General    3. Large cardinals (Mathematics)    4. Logic    5. Mathematics    6. Science/Mathematics    7. Set Theory    8. Mathematics / Logic    9. Mathematics / Set Theory    10. Mathematics-Geometry - General    11. Mathematics-Logic    12. infinitary combinatorics    13. large cardinals    14. new axioms for set theory     15. relative consistency results    

Reviews (6)

Basic crib sheet for category theory
Anyone coming to this book from Pierce's "Types and Programming Languages" will be disappointed. While his "Types ..." book is a model of clear exposition, this book reads like a set of notes jotted down on the back on an envelope. The extensive bibliographic sections are more than fifteen years out of date. Much of the material referenced is no longer in print, and recent developments are, of course, not mentioned. Those seeking a very gentle introduction to category theory would do better with the book by Lawvere and Schanuel, who cover more of category theory than Pierce. Mathematically mature computer science readers will find everything they need to know about the subject in Mac Lane's book.

The problem isn't the book...
Nothing wrong with this book *per se*.But it doesn't go far enough, and it's too expensive.I find Barr and Wells easier to read and more complete.And Meertens, Fokkinga, and Van Oosten are cheaper.
Too terse
This is a very short book: 70 pages of text + a bibliography.The first 50 pages are about general category theory, and the last 20 pages are specifically for computer scientists.My interest is in general category theory, and I bought this because I have a BS in CS and thought I'd find plenty of familiar examples.Unfortunately this book doesn't have nearly enough examples.I found it easier to skim some undergrad abstract algebra books in the library (groups, rings, vector spaces) and then continuing with category theory intros written for math students. ... Read more

Subjects:  1. Categories (Mathematics)    2. Computer Books: General    3. Computer Mathematics    4. Computer Science    5. Computers    6. Logic    7. Mathematics    8. Category theory    9. Computer Programming    10. Computers / Computer Science    11. Mathematical theory of computation    12. Mathematics for scientists & engineers   

Reviews (4)

Actually proves the theorem
The book is wonderful because it actually proves the theorem in a way that a non-expert in mathematical foundations can actually understand.I wish all popular mathematics books were written at this level where the goal is to educate and entertain.Now as I suggested to the author all we need is a book like this one that will explain Godel's and Cohen's results on the independence of the continuum hypothesis.

A fascinating introduction to the Banach-Tarski Paradox
The Pea And The Sun: A Mathematical Paradox is a fascinating introduction to the Banach-Tarski Paradox, a mathematical riddle that asserts it could be possible to create something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again. Written to be accessible to lay readers and non-mathematicians, The Pea And The Sun outlines the history of the paradox, introduces readers to the basics of such matters as set theory, isometrics, scissors congruence and equidecomposability, and walks the reader through the theorem and proof that object duplication is indeed mathematically possible. But just because it is mathematically possible, is it physically possible? The highly counterintuitive nature of the mathematical theorem demands a critical response. A final chapter dwells on speculation as to how the Banach-Tarski Paradox may apply to the modern and future world. Written in a fresh, captivating, friendly style, The Pea And The Sun is remarkably engaging and will appeal to any reader with a discerning, inquisitive mind into the nature of the so-called impossible, regardless of their particular mathematical background.
Perfect blend of math, humor, and information for the layman as well as the math professional
This book gives an incisive look at a fascinating area of science. It is technical enough to hold the attention of the math whiz, while "gentle" enough to carry a complete layman along. I personally learned a great deal about this amazing paradox, and also about the world of higher mathamatics in general. Fascinating, but light hearted reading. Highly recommended for anyone with any interest in this type of field. ... Read more

Subjects:  1. Banach-Tarski paradox    2. History    3. Logic    4. Mathematics    5. Science/Mathematics    6. Set Theory    7. Mathematical logic   

Subjects:  1. Logic    2. Mathematical Analysis    3. Mathematics    4. Number Theory    5. Science/Mathematics    6. Mathematics / Number Theory    7. Mathematics and Science   

Reviews (9)

Good Introduction to Mathematics, Historically and Philosophically
Though originally published in 1958, Howard Eves' book was a completely new find for me. Fortunately this classic text has found extended life through Dover Publications, which is making many great, older volumes available for newer generations. I am not a mathematician by vocation or training and I am usually only interested in more philosophically focused books concerning logic or meta-logical issues. But I found this book extremely enlightening, showing the interrelations of (what had previously been to my mind) unrelated historical streams of thought. In the following I will give a brief summary and point out some of, what I consider, the highlights of Eves' volume. Fundamental yes.... but is a very demanding introduction
Back in the days when I thought that mathematics could be understood by a through understanding of fundamental logic, I thought this book would help me on that.. well it did, by showing me that is not the path to take... the book is a good historical developments of fundamental concepts with many exercises which makes you review your calculus again.

india and china
in answer to the reviewer who stated:
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Subjects:  1. General    2. History    3. Logic    4. Mathematics    5. Philosophy    6. Philosophy Of Mathematics    7. Science/Mathematics    8. Mathematics / General   

Subjects:  1. General    2. History & Philosophy    3. History & Surveys - Ancient & Classical    4. Logic    5. Mathematics    6. Philosophy    7. Science/Mathematics    8. Ancient Greece    9. Ancient Western philosophy to c 500    10. History of ideas, intellectual history    11. History of mathematics    12. History of science    13. Mathematics / General    14. Mathematics, Greek    15. Philosophy of science   

Reviews (10)

Excellent Resource!
The Theory of Gambling and Statistical Logic is a superbly written book comtaining much knowledge about gambling and assessing the odds for specific games.Epstein begins with an overview of statistics and gambling, followed by chapters on specific items, like dic and coins, and specific games, like blackjack, bridge, and even chess.One caveat:you need more than a rudimentary knowledge of statistics to fully appreciate this book.Also, the book was written in the 1970's before poker (in general) and hold 'em (in specific) became popular.If you are buying The Theory of Gambling and Statistical Logic to analyze poker, I would recommend looking elsewhere.

Disappointing and Often Uninsightful
Some parts are interesting, and the writing can be entertaining, but the book is short on insight and clarity and long on tedious tables and uninterpreted computations. Very Hard to Find Info
Don't read this book if you're a poker player who knows how to divide your outs by number of unseen cards but never took any serious math courses.This is a serious mathematical treatment of gambling.Read more

Subjects:  1. Differential Equations    2. Economics - General    3. Game theory    4. Games of chance (Mathematics)    5. Logic    6. Mathematics    7. Probabilities    8. Probability & Statistics - General    9. Science/Mathematics    10. Statistical decision    11. Gambling    12. Mathematics / Differential Equations   

Subjects:  1. Geometry - General    2. History & Philosophy    3. Literary Criticism    4. Logic    5. Mathematics    6. Reference    7. Geometry    8. Hilbert    9. MSC (2000): 01A55, 01A60, 01A75, 03-03, 51-03, 03A05, 00A30    10. Mathematics / History    11. analysis    12. foundations    13. philosophy of mathematics   

Editorial Review

Gödel's incompleteness theorem--which showed that any robust mathematical system contains statements that are true yet unprovable within the system--is an anomaly in 20th-century mathematics. Its conclusions are as strange as they are profound, but, unlike other recent theorems of comparable importance, grasping the main steps of the proof requires little more than high school algebra and a bit of patience. Ernest Nagel and James Newman's original text was one of the first (and best) to bring Gödel's ideas to a mass audience. With brevity and clarity, the volume described the historical context that made Gödel's theorem so paradigm-shattering. Where the first edition fell down, however, was in the guts of the proof itself; the brevity that served so well in defining the problem made their rendering of Gödel's solution so dense as to be nearly indigestible.Read more

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Reviews (25)

Great Description of DifficultWork - An Excellent Introduction
I had read "On Formally Undecidable Propositions of Principia Mathematica and Related Systems" By the mathermatician himself and then found Ernest Nagel's "Godel's Proof" nearly by accident.The titles of the work are examples of the main diffeernce of the two: the latter is far more simple and comprehensible.Diving right into Goedels work with a some decent understanding of mathematics and a thourough reading of "Principia Mathematica" by Russel and Whitehead, I thought I would be able to handle it.I was able to comprehend Goedel but found it gave me a headache to read more than a few pages at a time. Getting through after far too many hours and little true understanding.It seemed that while I could grasp the concepts I wasnt so clear on the subtlties of Goedel's theorem. I was more than happy to read Nagel's Work which is very approachable and exemplifies the important points that the average person might breeze through in Goedel's work.This being said the work of Nagel should be considered an introduction to Goedel's work and both have their place as excellent works.
Thoroughness in Explaining Background and Context as well as Gödel's Proof Itself
I redid my review (now July 2006) after your 50:50 votes on helpfulness.I think you needed more content to the review and less ebullience.So here it is...In the interim, I have read other treatments of Gödel's proof (including the Dover book of Gödel's article itself also with an introduction, Beyond Numeracy, The Advent of the Algorithm [ref below], and several others).What stands out in THIS book, though, is the extreme thoroughness of explaining to you the context in which Gödel was working at the time.This book is unique in its dedication to getting you to a concrete understanding of -- and appreciation for -- the background and context.In fact making sure you get the context appreciation takes up about 2/3rd's of the book!Of course the book is thorough on the Proof itself too.Is that part easy?No, it's still not.But you won't be left at all vague on what the proof is like.The only other book that is as good on the CONTEXT of Gödel's proof is The Advent of the Algorithm.The Advent of the Algorithm is also excellent on how others took, and "ran-with", Gödel's results.As for which edition of this book (Gödel's Proof) to get, the new addition has Hofstaddter's introduction.That intro adds value for sentimentality (if you should so find his story about his reading the book and his subsequent friendship with Nagel) and Hofstadter's own ebullience, but the book is virtually identical otherwise with its 1959 edition.It would be perfectly good -- you'll miss nothing -- if you bought a cheap 1959 edition.For a good complimentary book, get also The Advent of the Algorithm by David Berlinski (2000) ISBN 0 15 100338 6 or ISBN 0 15 601391 6 (pbk).You can read my review on that book too if you like.

It's like "Brief History of Time" in Mathematics
It gives me the same feeling after reading "Brief History of Time". They both explain some very fundamental thing in Science in layman's term. But the difference from "Brief History of Time" is that I can fully understand what the authors are trying to convey.
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Subjects:  1. General    2. Godel's theorem    3. Gèodel's theorem    4. Logic    5. Mathematical And Symbolic Logic    6. Mathematics    7. Science/Mathematics    8. GOEDEL'S THEOREM    9. Mathematical logic    10. Mathematics / Logic   

Reviews (5)

Within the reach of determined general readers
This excellent collection has introductions which help immensely. With only a math major from the 50's and no advanced degree I was still able to develop my own fairly rigorous single page synopsis of Godel's theorems.

Oops
"Philosophical and Mathematical Correspondence" was published 13 years after Heijenoort's.

Just a comment.
In response to Jay Miller's question below there is a book titled "Philosophical and Mathematical Correspondence. Gottlob Frege" that has 21 letters between Russell and Frege over a period of 10 years beginning with Russell's observation of his famous paradox in 1902. This wonderful collection of correspondence was published 20 years before "From Frege to Godel" and includes letters from many of the same mathematicians and logicians. ... Read more

Subjects:  1. General    2. History & Surveys - General    3. Logic    4. Mathematics    5. Philosophy    6. 20th century    7. Mathematical logic    8. Philosophy / General    9. c 1800 to c 1900