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01/30/2005: New draft of Gödel's Theorems
Prof. Peter Smith of Cambridge has posted a
new draft of the first thirteen chapters of his upcoming book An
Introduction to Gödel's Theorems, with promises of more to come.
(I blogged about a previous
draft at Signifying Nothing.)
You'll need a background in symbolic logic to follow the work. If you have
the logic background, you're interested in mathematics, and you've never
worked your way through proofs of Gödel's theorems (or if you have
worked your way through the proofs, but have forgotten how they go, or if
you've only read the hand-waving proof in Hofstadter's Gödel,
Escher, Bach), I highly recommend reading Prof. Smith's work.
Brock on 01.30.05 @ 09:43 PM CST
Replies: 3 comments
on Monday, January 31st, 2005 at 10:15 AM CST, Len Cleavelin said
How severe a background in symbolic logic is required? I've got one semester junior level symbolic logic (the required logic course for philosophy majors at my uni), plus a semester of modal logic. Think that's enough?
on Monday, January 31st, 2005 at 3:51 PM CST, Karen McLauchlan said
Mathematics on that level is severely beyond my limited ken. That's why I thought you'd appreciate Dr. Wolfram's stuff atleast on a technical basis...I can only follow the premise and "oooh-and-aaah" at the results.
on Monday, January 31st, 2005 at 6:13 PM CST, Brock said
As I said on my previous post on the subject at SN, you'll need to know your ∀s from your ∃s. Basically, you'll need to be capable of following a symbolic proof.
Karen, if you want the layman's picture, read Hofstader's book. The first fifteen chapters anyway, which take you through Gödel's first incompleteness theorem. As I said, there's a lot of handwaving in Hofstadter's book, but you don't really need to be bogged down in the technical details of proving that "every primitive recursive function is representable-in-Q."
Hofstadter's book is very entertaining. There's a reason it won a Pulitzer.