An anthology of fundamental papers on undecidability and unsolvability, this classic reference opens with Gödel's landmark 1931 paper demonstrating that systems of logic cannot admit proofs of all true assertions of arithmetic. Subsequent papers by Gödel, Church, Turing, and Post single out the class of recursive functions as computable by finite algorithms. 1965 edition.
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43 of 43 people found the following review helpful
By T. Gwinn
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This is a great collection of seminal papers by Goedel, Church, Turing, Rosser, Kleene, and Post on the topic of undecidability. It is an extremely handy reference.
Just to note: this is certainly not a tutorial or guide to this topic for the beginner. Davis provides some prefatory comments, but these are concise and mostly set the context for the papers, rather than explaining the content of the papers. This book is more for someone interested in going back to first sources.
0 of 2 people found the following review helpful
1.0 out of 5 stars
USELESS. Mathematics is timeless. Mathematical exposition is not, which is definitively proven by this publication.
May 25, 2013
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I have to be explicit about what it is that I am reviewing. I could be reviewing many things: the mathematical content of the authors whose work is contained herein, the notation that the authors used during the time period of 1930-1941 in which they authored their papers, the editorial work that Martin Davis did on behalf of this volume in 1965, or the work that Dover did in reprinting it in 2004. Categorically, I am speaking about the last of these considerations.
The notation in this book is from an antiquated time, and is unlikely to be familiar to modern students of mathematics. Beyond that, in a treatise on logic, the lack of distinction between metamathematical and object-logic notation would be considered unacceptable in modern times. Yet in these papers, the same set of alien symbols is recycled throughout multiple contexts, which makes it very difficult to keep them straight. For example, a large tilde is used to denote both object-logic unary negation, and the metamathematical binary biconditional. The baseline dot is used to denote both metamathematical conjunction and arithmetic multiplication, which is extremely confusing in the context of a metamathematical proof of the arithmetization of syntax isomorphism between the object logic and the natural numbers. I tried to keep all of this straight by writing it down in my notes, but quickly became frustrated, and ended up searching the Internet for a version of the paper in modern notation. I found one, and I was able to digest the entire modernized paper much more quickly than my muddied forays into the beginnings of the version presented in this book. I could make similar comments about the other parts of the book which I attempted to digest.... Read more ›
The notation in this book is from an antiquated time, and is unlikely to be familiar to modern students of mathematics. Beyond that, in a treatise on logic, the lack of distinction between metamathematical and object-logic notation would be considered unacceptable in modern times. Yet in these papers, the same set of alien symbols is recycled throughout multiple contexts, which makes it very difficult to keep them straight. For example, a large tilde is used to denote both object-logic unary negation, and the metamathematical binary biconditional. The baseline dot is used to denote both metamathematical conjunction and arithmetic multiplication, which is extremely confusing in the context of a metamathematical proof of the arithmetization of syntax isomorphism between the object logic and the natural numbers. I tried to keep all of this straight by writing it down in my notes, but quickly became frustrated, and ended up searching the Internet for a version of the paper in modern notation. I found one, and I was able to digest the entire modernized paper much more quickly than my muddied forays into the beginnings of the version presented in this book. I could make similar comments about the other parts of the book which I attempted to digest.... Read more ›
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