Godel's Theorem Simplified

by Harry J. Gensler

This helpful volume explains and proves Godel's theorem, which states that arithmetic cannot be reduced to any axiomatic system. Written simply and directly, this book is intended for the student and general reader and presumes no specialized knowledge of mathematics or logic.

Genres: Logic, Philosophy

88 pages, Paperback

Published February 16, 1984

Reviews

[Jeff · Rating 4 out of 5]

Recommended for anyone with an interest in Gödel's Incompleteness Theorems. Note that a tolerance for formal logic is necessary.

One day i hope to paraphrase accurately and clearly Gödel's main conclusions. They have always strangely attracted me along with those of Wittgenstein's Tractatus, as though i need to figure out how they're related to each other, to myself, and to reality. I'd be happy if i satisfied the middle relationship.

As someone who eked out a passing grade in calculus in high school but hasn't used much more than simple arithmetic for >30 years, i can say that the reading level for this book suited my level of math (un)sophistication.

Nagel+Newman's Gödel's Proof was more difficult for me. Consider also:
Francesco Berto. There's Something About Gödel [highly recommended]
Torkel Franzén. Gödel's Theorem: An Incomplete Guide to Its Use and Abuse [highly recommended but scary]
S.G. Shanker. Gödel's Theorem in Focus [it might be about right for me]
Peter Smith. An Introduction to Gödel's Theorems [recommended but possibly too mathy for me]
Raymond Smullyan. Gödel's Incompleteness Theorem [highly rated]
Wish me luck! (because that might be the only thing that can help me with pure logic)

[Savino Longo · Rating 5 out of 5]

This book is a pearl, it is a few pages long, written wide, yet with its humorous style it explains Goedel's I theorem in detail, without omitting anything. It actually proposes a fully contructive demostration of the theorem using a modified Goedel's numbering which is more effective than the original one for explicative purposes, and also used by others authors, notably Smullyan. Many things that other books have tried to explain to me I understood from this book simply because the constructive context makes them clear. The typewriter style (almost, it is proportional) here is strangely suitable. The minimalistic rendering of equations is fascinating. It is the only book of logic beginning a chapter in this way "you will get headaches if you study this chapter too closely". Read it.

[readedgoods · Rating 4 out of 5]

A big-picture look at Gödel’s incompleteness theorem. I come out of this book with more questions than answers, and the material is (necessarily) dry at times.

But it’s accessibly written and conversational in tone, leaving me with a better understanding of what axiomatic systems, proofs, and incompleteness even mean.

I feel irked that, if I understand correctly, Gödel managed to shake the foundations of math by just plugging the statement “this theorem is not provable”* into a proof checker.

Idk from a layman’s perspective Gödel’s theorem just seems like some edgelord shit to me.

Anyway it’s a good first Gödel book. Up next, I’ll be reading either Journey To The Edge of Reason (a biography of him), or Gödel, Escher, Bach.

But first I need to get halfway through a bunch of other books

*crucially NOT the same thing as saying “this statement is false”