/lit/ - Literature

>>>/sci/

/lit/ doesn't know shit about mathematic

also, if you're just doing this to understand godel's incompleteness theorem, drop it now.

What do you mean by "learn" Gödel's Incompleteness Theorem?

>>3231299
Well, I took intro to mathematical logic, and I wanted to keep learning. I don't know where to go next. It's my last semester next spring and they aren't offering advanced, so I'm turning to studying on my own

>>3231299
>if you're just doing this to understand godel's incompleteness theorem, drop it now.
This.

>>3231310
see
>>3231303

>>3231299
>/lit/ doesn't know shit about mathematics
this
/lit/ is extremely good at mind masturbating but god forbid you introduce any formal logic into their debates, lest you want to be replied with witty arguments such as "YUO CAN'T KNOW!!1!!"

>>3231340
le Yale School Deconstructionist face

>>3231299
>>3231310
When did idiots start frequenting the board?
>nobody knows anything!
>stop being curious!

>>3231303
Wittgenstein, Russell, Cantor, Frege, Zermelo and some Husserl are all very important in the lead up to incompleteness. There's a decent book by Smullyan on the incompleteness theorems, and Chatin has written some decent stuff on the relationship between Turing and Godel's ideas (you can view the Turing machine as an answer to incompleteness) if you're looking for something a little quicker first.

>>3231362
Thank you, good sir. I know a little about Frege, Russell, and Wittgenstein already. What's a good starting point?

>>3231362
It's just not worth spending months, perhaps years of life fully comprehending a single theorem when you can easily summarize its applications to the layman in a sentence.

>>3231371
If it's your last semester, use this opportunity to collect interesting papers from places like jstor on the subject. There's been somewhat of an analytical awakening over the past few years where a lot of people have gone "These philosophers we usually deride as continental are actually pretty relevant". If you download the Smullyan book, the first chapter gives a pretty decent overview of Godel in mathematical thought, so should give you a decent idea of what you'll need to explore. When I first properly looked into it I came in the other direction through Turing, which is interesting but takes a rather blinkered view of the whole thing.

>>3231396
Out Demons Out. Stop spreading your fear of learning.

>>3231415
this is like trying to learn greek just to read a minor socratic dialogue, it's pointless and you'll give up halfway.

>>3231415
On the contrary, I don't think what OP is talking about is authentic efforts to learn. He's saying "Hey guys I just "finished" an introduction (whatever that is) to mathematical logic and I want to "learn" Gödel's Incompleteness Theorem." I think you're redirecting him to topics he probably won't understand just judging by how he has used terminology. You shouldn't be sending him to postgraduate textbooks when you don't have an inkling about his abilities.

>>3231270
I did an independent study with a the math theory prof at my campus and we still couldn't fully get to the guts of incompleteness in a full semester. If you want to understand it without going through the formal proof and basically learning the theory of computing and shit like that, then get an intro text off amazon.

>>3231436
If their last semester is coming up, any of the Oxford logic guides should be the appropriate level. Smullyan certainly is. Chaitin tends to write a sort of high brow, somewhat biased form of pop-maths, and I can't see he wouldn't be fine for anyone smart enough to go to a university. A lot of people like you tend to be scared of the whole thing, partly because it's tied to the analytic/continental divide, but there's nothing massively difficult in there.

If you want something easier, here's a nice radio programme and reading list: http://www.bbc.co.uk/programmes/b00dshx3
And OP, IOT is often a good intro if they have a show about it.

>>3231270
Don't ask /lit/ about logic. They are the most uninformed group to ask. You should really ask /sci/. However, you need to realize it is going to take about a year of dedication to learn the incompleteness theorem itself (and this is assuming you already know how to write complex mathematical proofs). Assuming you have a good background in mathematics, I suggest Enderton's classic "A Mathematical Introduction to Logic". Almost every university uses this book and it covers all the essential material. However, if you don't know how to write a proof, then I suggest not buying it because it will be a waste of time. If you need an introduction to proofs I suggest "Sets, Functions and Logic" by K. Devlin. I would forget about it unless you are mathematically inclined. I don't want to sound like a dick, I just don't want you to waste your time.

>>3231471
>but there's nothing massively difficult in there
Yeah, if you learn your shit sequentially.

>>3231541
>Yeah, if you learn your shit sequentially.
Which is why a secondary text has been recommended.

>>3231270
Tarski's Introduction to Logic. Dover sells it for ten dolla'.
Kind of the obvious choice... not sure why it hasn't been recommended yet. I guess we're too busy showing off our e-peen.

Thanks /lit/, I love you for you guidance and wisdom

godel escher bach

>>3231598
This is not what he is looking for if he wants to learn the theorems. Tarski's book regards a deductive calculus, not a mathematical calculus that is necessary for the model theory involved in Godel's proofs. This would be a rubbish suggestion if the man really wants to learn the theorems and why they work.

>>3232059
This is a good intro to the ideas but this does not serve the purpose that OP probably wants.

>>3232171
Okay whatever.

>>3232169
Okay whatever.

>>3232059
This.

Why did this post take so long to materialize?

>>3232169
>>3232171
It's a good introduction to formal logic even if it isn't all written in the same notation. People have to start somewhere. Y'all are just the math version of those faggots who tell people that Being and Time is a good introduction to phenomenology.

tfw I have't read mayonnaise or horseradish

>>3232689
What...?