GEB will take you from superficial knowledge to full grok.
A word of caution: there is a risk when reading popular science/math books like GEB of coming away feeling like one understands something at a higher level than one actually does, particularly if one hasn’t already studied the subject formally.
If one has formally studied incompleteness before, it’s easy to wave away standard primitive recursive derivations (e.g. the proof predicate) as tedious and trivial and beside the main point, but having this attitude the first time around could be dangerous.
I read GEB years ago, and recall liking it quite a bit, though I disagree with Louie Helm’s endorsement of GEB as a course reference, at least not without supplementation from a “standard” source like these notes (or any formal logic textbook).
I agree that GEB should be supplemented with formal study for a deeper understanding.
To clarify my anecdote, my “formal study” of incompleteness allowed me to manipulate the symbols, follow the proofs, pass a test, and conclude that incompleteness is something I have to believe.
By contrast, GEB showed me incompleteness intuitively. It made incompleteness seem natural and inevitable. It convinced me, instead of forcing my beliefs.
(“There’s a difference between a proof and a why”, as I like to say.)
This is likely due in part to the fact that my “formal study” of incompleteness was part of university courses, and was not self-motivated. I like to think I could have gleaned a “why” from the formal proofs—but I didn’t. It wasn’t high priority.
GEB makes it fun and relatively easy, which is a huge part of its appeal. That said, reading about something is rarely a substitute for hands-on experience.
A word of caution: there is a risk when reading popular science/math books like GEB of coming away feeling like one understands something at a higher level than one actually does, particularly if one hasn’t already studied the subject formally.
If one has formally studied incompleteness before, it’s easy to wave away standard primitive recursive derivations (e.g. the proof predicate) as tedious and trivial and beside the main point, but having this attitude the first time around could be dangerous.
I read GEB years ago, and recall liking it quite a bit, though I disagree with Louie Helm’s endorsement of GEB as a course reference, at least not without supplementation from a “standard” source like these notes (or any formal logic textbook).
I agree that GEB should be supplemented with formal study for a deeper understanding.
To clarify my anecdote, my “formal study” of incompleteness allowed me to manipulate the symbols, follow the proofs, pass a test, and conclude that incompleteness is something I have to believe.
By contrast, GEB showed me incompleteness intuitively. It made incompleteness seem natural and inevitable. It convinced me, instead of forcing my beliefs.
(“There’s a difference between a proof and a why”, as I like to say.)
This is likely due in part to the fact that my “formal study” of incompleteness was part of university courses, and was not self-motivated. I like to think I could have gleaned a “why” from the formal proofs—but I didn’t. It wasn’t high priority.
GEB makes it fun and relatively easy, which is a huge part of its appeal. That said, reading about something is rarely a substitute for hands-on experience.