Classical Theism, Philosophy, and Religion Forum / Books for Gödel's Incompleteness Theorems

**Posted by Greg** 9/22/2015 3:08 pm

Does anyone have recommendations for books expositing Gödel's incompleteness theorems? I am looking for something mathematically rigorous.

**Posted by Scott** 9/22/2015 6:29 pm

Nagel and Newman's Gödel's Proof is rightly regarded as a classic and I'm not aware of any others that compare to it.

Of course if it's mathematical rigor you want, you can always go straight to the horse's mouth and read Gödel's own On Formally Undecidable Propositions of Principia Mathematica and Other Formal Systems.

(I originally put those in as live links to Amazon pages, but they got swapped out for links to textbooks.com and Walmart.com. I've seen that happen before with links others have posted as well; I suspect some jiggery-pokery from the forum server.)

EDIT: Here's a test. The URL I'm pasting in is unquestionably to Amazon; let's see what comes out.

Last edited by Scott (9/22/2015 6:37 pm)

**Posted by Scott** 9/22/2015 6:38 pm

That worked fine, so maybe the URL is altered upon editing. Here's another test.

EDIT: It still works in the preview.

EDIT: But it was altered to a Walmart link when I saved the edit.

EDIT: . . . and then back to Amazon when I saved another edit.

Well, I'll stop wasting bandwidth with tests, but something funny is going on. It's not a browser-redirect issue; the altered link is (was) actually in the saved page code.

Last edited by Scott (9/22/2015 6:43 pm)

**Posted by Greg** 9/22/2015 6:45 pm

Thanks Scott.

The Nagel and Newman book looks very good. I'll take a look. I imagine I will consult Gödel's paper itself, but someone suggested to me that it's not the best place to start. I am expositing the theorems for a math course, which is why I need mathematical rigor. I have also seen some good things about Gödel's Theorem: An Incomplete Guide to Its Use and Abuse, though that might not have everything I am looking for.

**Posted by Mysterious Brony** 9/22/2015 9:54 pm

Well, if you want mathematical rigor, try a book that introduces you to mathematical proofs. Take a look at "A Transition to Advanced Mathematics" by Smith, Eggen and Andre. If you want to go straight to mathematical rigor try any Real Analysis book.

**Posted by Greg** 9/22/2015 11:13 pm

I am pretty familiar with analysis. I'm just looking for rigorous treatments of Gödel's theorem in particular (since I know that there are also lots of non-technical accounts of it, which wouldn't be helpful to me).