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About the Author

Kurt Godel was probably the most outstanding logician of the first half of the twentieth century. Born in Czechoslovakia, Godel studied and taught in Vienna and then came to the United States in 1940 as a member of the Institute for Advanced Study at Princeton University. In 1953 he was made a show more professor at the institute, where he remained until his death in 1978. Godel is especially well known for his studies of the completeness of logic, the incompleteness of number theory, the consistency of the axiom of choice and the continuum hypothesis. Godel is also known for his work on constructivity, the decision problem, and the foundations of computation theory, as well as his views on the philosophy of mathematics; especially his support of a strong form of Platonism in mathematics. (Bowker Author Biography) show less

Series

Works by Kurt Gödel

Obras completas (1989) 19 copies
Scritti scelti (2011) 7 copies
Collected works 4 copies

Associated Works

Reflections on Kurt Gödel (1987) — Associated Name — 70 copies
Principia Mathematica. Vorwort und Einleitungen. (2002) — Foreword, some editions — 8 copies

Tagged

Common Knowledge

Canonical name
Gödel, Kurt
Legal name
Gödel, Kurt Friedrich
Other names
GÖDEL, Kurt Friedrich
GÖDEL, Kurt
Birthdate
1906-04-28
Date of death
1978-01-14
Gender
male
Nationality
Austria (birth)
Czechoslovakia
Germany
USA
Cause of death
death certificate stated "malnutrition and inanition caused by personality disturbance"
Education
University of Vienna
Occupations
mathematician
logician
philosopher
Awards and honors
Albert Einstein Award (1951)
National Medal of Science (Mathematics and Computer Science, 1974)
Short biography
One of the most significant logicians of all time, Gödel's work has had immense impact upon scientific and philosophical thinking in the 20th century, a time when many, such as Bertrand Russell, A. N. Whitehead and David Hilbert, were pioneering the use of logic and set theory to understand the foundations of mathematics.

Gödel is best known for his two incompleteness theorems, published in 1931 when he was 25 years of age, one year after finishing his doctorate at the University of Vienna. The more famous incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (Peano arithmetic), there are true propositions about the naturals that cannot be proved from the axioms. To prove this theorem, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers.

He also showed that the continuum hypothesis cannot be disproved from the accepted axioms of set theory, if those axioms are consistent. He made important contributions to proof theory by clarifying the connections between classical logic, intuitionistic logic, and modal logic.

Members

Reviews

Does what it says on the tin, and contains only one typo that I spotted, so that's good.

However, this really *is* just an annotation of Gödel's paper, with very little added. In particular, there are no proper worked-through examples to provide a context for all the logic proofs, so at the end of the day, unless the reader is already familiar with the subject, he or she is likely to be left wondering, "OK, but so what?".

And one minor nitpick: for reasons that are unstated, the author has chosen to replace Gödel's original multiplication operator (.) with a centred dot; this leads to places where, for those of us who are from a country that use the same convention as Germany, and a centred dot has quite a different meaning, the text is harder to follow than it should be. I can't imagine why, if he felt the need to change the glyph used for the multiplication operator, he didn't use the ordinary "times" symbol (×) instead, since, as far as I know, that is unambiguous, at least in the relevant context.

Perhaps I'm being unfair: the author does a great job of rendering the original paper into comprehensible English, including switching Gödel's idiosyncratic naming into something much more accessible to an English speaker. Maybe that was all that he intended to do. But the subtitle if the book is "A Reader's Guide...", and this particular reader was expecting something rather less arcane, bridging the gap between the original paper and a hypothetical non-expert reader who wasn't already familiar with the subject.
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Flagged
N7DR | Mar 25, 2024 |
I thought it was quite interesting, but I don't feel I have the necessary background in math to completely appreciate this work. Gödel makes up his own notations, but follows some standards for mathematical logic. It helped that the book had references to what it was talking about in the book itself though, and it is also extensively footnoted. I though it was a very interesting paper, but like I said, I need a more thorough grounding in logic to fully appreciate it.

I will be reading this again when I can understand it better. Five out of five for turning the establishment on it's head though. Before this paper, mathematicians assumed it was possible to go and explain everything in math. But you can't explain everything in math using math, so there are some things that are just unexplainable. I probably didn't really get that right, but it matters not.… (more)
 
Flagged
Floyd3345 | Jun 15, 2019 |
The Horror!

I thought I should post a brief note to prevent other potential buyers from being misled by the editorial reviews the way I was. _Choice_ says that the editors "deserve the highest praise for the design of the edition." _Mind_ says it is "beautifully produced". _The Journal of Symbolic Logic_ calls it "beautifully prepared". _Zentralblatt_ says that it "was published in a very nice and careful way".

It is reasonable to interpret these statements as referring, at least in part, to the physical appearance of the book; under that interpretation, it is my opinion that these statements couldn't be more wrong. It looks like the volume was printed in the cheapest way possible, and the page layout is amateurish at best.

It is a pity that Oxford University Press hasn't seen fit to publish an edition whose physical beauty is commensurate with the beauty of Godel's ideas.
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Flagged
cpg | Oct 14, 2017 |

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