Dark Bilious Vapors

But how could I deny that I possess these hands and this body, and withal escape being classed with persons in a state of insanity, whose brains are so disordered and clouded by dark bilious vapors....
--Rene Descartes, Meditations on First Philosophy: Meditation I

Home » Archives » January 2005 » New draft of Gödel's Theorems

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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.

January 2005

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