Good book for Gödel's incompleteness theorems

[phaser88]

Can anyone recommend a good textbook that would include Gödel's incompleteness theorems?

Also I have some basic questions:

From the stuff I read on the web it seems that Gödel's incompleteness theorem, basically just created a statement which is unprovable by its nature of being self-referential. as explained http://www.scienceforums.net/topic/29955-godels-theorem-for-dummies/"

Godel found a way of encoding a statement to the effect of "This statement is unprovable" into the symbolic logic system defined in Principia Mathematica (PM). The notable aspect of the statement is that it is self-referential, which Godel managed to accomplish by encoding statements in PM into "Godel Numbers." Thus the actual statement in PM refers to its own Godel Number.

To boil it down into a nutshell, I'd say it means that any system which is expressive enough to be consistent and complete is also expressive enough to contain self-referential statements which doom it to incompleteness.

Is that really all there is to it? In other words, do all of the unprovable statements take the form of a self-referential paradox? In which case, why do people think it is so deep? If that is the case, then it is trivial, because obviously if you construct a self-referential statement designed to paradoxical, then you won't be able to prove it, but so what?

 

[micromass]

Hi phaser88!

Try the following excellent book: "Godels theorem simplified" by Harry Gensler.

The rest of your questions are answered in the thread https://www.physicsforums.com/showthread.php?t=500713