/lit/ - Literature

Meh you’ll figure it out lol

>>13079610
It's symbolic logic, not math. I promise it's not that hard. You could look up translations of the formal statements into natural language online if you want, but it won't be quite the same.

Also, propositions are just Platonic forms for semantics. They're basically mythological

>>13079620
121 iq-let though

>>13079610
Hello Ramsey you qt

>>13079610
it's not math, it's logic

>>13079832
Even so, I don't understand. Take 4.27. There are other examples like that.

>>13079851
do you not know how summations work? where did you go to high school?

>>13079851
To be fair, it's not only logic

>>13079851
You can't read and understand the symbols on that page? You're never going to make it.

>>13079851
Oh I see. That's a sum of choices-- basically it outlines the number of combinations in members of a group of atomic facts are true.
Again, you can probably look up translations of the formal language.

>>13079851
That's high school-level Algebra. If you were able to pass Algebra, you should know about sums and series with an n number of terms.

>>13079862
I'm a med student in a shitty country, never studied past pre-calculus.
>>13079872
I can understand the symbols at the top easily. And yes, certainly not with that attitude.

>>13079851
just google sigma notation bruv

>>13079851
it's a summation.

>>13079884
It's probably the n choose v (I know that's a nu) bit that's fucked him.

>>13079884
I've passed calculus I and II and I still don't recognize what that symbol is next to the sum.

>>13079884
I took the o levels, they didn't teach me that in high school.

>>13079629
>Propositions are platonic forms for semantics
But they are relational

>>13079943
Oh shit. Sorry you're right

They're Platonic forms for truth-valued statements. Finals is really getting to me

>>13079610
>summation
https://www.youtube.com/watch?v=5jwXThH6fg4

>>13079961
This is why I made the thread, maybe I should learn this before reading Wittgenstein. I've read Kant, Hume and understood them tolerably well, but math is my weakness.

>>13079851
Where is he going with these truth possibilities and such? It sounds interesting

I wamt to read Wittgenstein. Whom do I read first?

>>13079982
A symbolic logic textbook
Then Kant

>>13079989
I took a Discrete Mathematics course this semester. How's that?

>>13079974
He goes on to describe that the truth possiblities of the elements in a proposition can be either true or false in varying combinations.

>>13079991
It's not the same
From my course, the treatment of logic is cursory. You need to have a pretty good grasp of how conditionals work and why

I have no idea what anyone in here is talking about. I hate being a brainless

>>13080021
Then get started

>>13080021
Don't worry, its a bunch of spooky word play meant to prove that spooky word play is bad, LOL

>>13080021
The journey of 1000 miles starts with a single step.
>>13080007
I see. Well I'll get on it then.

>>13080021
Not being able to understand is the greatest joy, for that means you are able to learn to understand.

Worth pointing out that the book is over 95 years old now and in case you want to catch up on logic (as opposed to the logic in the book, which is the same predicate logic, but super outdated in presentation), I really recommend this book

http://www.cin.ufpe.br/~mlogica/livros/Logic%20and%20Structure%20-%20Van%20Dalen.pdf

The sum on the page is actually just 2^n, via
https://en.wikipedia.org/wiki/Binomial_theorem
and 2^n is the size of the subsets of a set of size n.

E.g.
{a,b,c,d}
has size n=4 and it's subsets are
{}, {a}, {b}, {c}, {d}, {a,b}, {a,c}, ... {b,c,d}, {a,b,c,d}
Well you find that there are 16 subsets, which happens to be 2^n
The sze of subsets of size k are exactly the coefficients in
(x+y)^4 = x^4 + 4 * x^3 * y^1 + 6* x^2 * y^2 + 4 * x^1 * y^3 + y^4
i.e. they are given by the "n choose k" ratio and I suppose Wittgenstein uses a counting argument along those lines on the pages before and here doesn't bother to reduce the sum to just 2^n.

>>13080055
That explains it, they didn't use his notation in school.

>>13080055
Nigga how is a beginner supposed to read that. This is recommending spivak for babby's first calculus

>>13080021
/lit/ makes me question daily if I'm fucking retarded or if I'm just being trolled. Half the shit written on this board seem like it's just words being thrown around without any meaning or purpose just to make people think they're deep, based solely on length and complexity of reading.

>>13080073
>>13080088

I can try to cook up an explicit example for n=3 and then generalize. Take 3 proposition and let's say they are atomic (irreducible) formulas in the sense of his book.

L = "/lit/ is best board."
F = "OP is a fag."
T = "Linear type theory will take over mathematical logic eventually."

So those are our atomic propositions and we may want to count to how many different models (or "worlds", in Wittgenstein) they lead. Let's do it by hand, here are the scenairos ("worlds"):

L is false, F is false, T is false
L is true, F is false, T is false
L is false, F is true, T is false
L is false, F is false, T is true
L is true, F is true, T is false
L is true, F is false, T is true
L is false, F is true, T is true
L is true, F is true, T is true

So by hand I we find 8 options. This happens to be 2^n, i.e. 2^3.
How do we get there and how do we get there for general n? Well you may phrase it like this: If we say that the default is by convention a proposition to be false (I started with the false cases and worked my way down), then the total number is the sum of all possibilities for k<=n. In other words, rephrasing the example (with 8=2^3 total)

1 case of none of the 3 being true
3 case of none of the 3 being true
3 case of none of the 3 being true
1 case of none of the 3 being true
And 1+3+3+1 = 8.

I performed the sum over "k out of 3".
Indeed, generally, the situation is that for general n, you sum over k out of n, which is what wittgenstein writes down here?

Note: Mathematically, you can proof that this is 2^n, because
sum over "k out of n" times x^k * y^(n-k) = (x+y)^n
and if you plug in x=y=1, you get our sum on the left hand side and 2^n on the right hand side

>>13080073
>>13080088

I can try to cook up an explicit example for n=3 and then generalize. Take 3 proposition and let's say they are atomic (irreducible) formulas in the sense of his book.

L = "/lit/ is best board."
F = "OP is a fag."
T = "Linear type theory will take over mathematical logic eventually."

So those are our atomic propositions and we may want to count to how many different models (or "worlds", in Wittgenstein) they lead. Let's do it by hand, here are the scenairos ("worlds"):

L is false, F is false, T is false
L is true, F is false, T is false
L is false, F is true, T is false
L is false, F is false, T is true
L is true, F is true, T is false
L is true, F is false, T is true
L is false, F is true, T is true
L is true, F is true, T is true

So by hand I we find 8 options. This happens to be 2^n, i.e. 2^3.
How do we get there and how do we get there for general n? Well you may phrase it like this: If we say that the default is by convention a proposition to be false (I started with the false cases and worked my way down), then the total number is the sum of all possibilities for k<=n. In other words, rephrasing the example (with 8=2^3 total)

1 case of 0 of the 3 being true
3 case of 1 of the 3 being true
3 case of 2 of the 3 being true
1 case of 3 of the 3 being true
And 1+3+3+1 = 8.

I performed the sum over "k out of 3".
Indeed, generally, the situation is that for general n, you sum over k out of n, which is what wittgenstein writes down here?

Note: Mathematically, you can proof that this is 2^n, because
sum over "k out of n" times x^k * y^(n-k) = (x+y)^n
and if you plug in x=y=1, you get our sum on the left hand side and 2^n on the right hand side

>>13080155
No, I got it the first time. I was talking about the logic book you recommended, shits too advanced for me

>>13080172
Well the example is for him anyway.
The book is just good, I don't know a more verbose one that's also formal.

In any case, Wittgensteins "the world is the totality of facts" doesn't get anyone far anyway. I recommend reading the booklet to the end - and I also really liked it when I read it first, but I think Heidegger has more to give even for a rationalist.

>>13080209
Brainlet here, how did guys like you presumably become brainchads?

>>13080229
I'm old and got a degree, that's all

>>13080229
Just read stuff that's outside of your experience. I got into logic and math after I tried (and failed miserably) to read Bourbaki's Theory of Sets. Now I'm in love

>>13080285
I was there.
But even if Bourbaki was written in a more accessible way, their approach has this \tau operator to define other quantifiers from and that one is stronger than some variants of the axiom of choice - except they use it already in the logic. There's no good reason to go down that route anymore.

>>13079973
Do everything through pre-calc on Khan Academy, from the beginning, then read Stewart's "Calculus".
>t. /sci/
>pic unrelated

>>13080319
Their formal work on metamathematics isn't as important as the later work, which was to develop a unified view of the field as it emerges out of the fundamentals of set theory

Also you have to remember that the tau operator works by linkages between letters, and only replaces the letters with necessity symbols.

>>13080209
I guess I'm the guy you wrote that for. I do understand cardinality of the power set, but I don't see what Witty's trying to do with it. Is it a combination?

stick to your own lane conty

leave wittgenstein for us enlightened scientific analytic big brain niggas

>>13080425
Doesn't the example with the 3 proposition clearify it? He counts the possible options.

>>13080421
a_P := tau x. P(x)
gives you a representation of a terms that potentially has property P.
I'm saying this is a superstrong comprehension operation and it seems math can do well without any sort of strong comprehension - for the very most part. It's sort of dangerouuzz

>>13079610
Wittgenstein basically wanted to shut up all talk of spirituality. This desire was at the heart of his involvement with philosophy. "Think what you want, but at least shut up about it and spare the rest of us of your asinine claptrap." No wonder he became the poster child of the spiritually barren Anglo-Saxons.

>>13080462
But they're not really terms-- they're just letters. Read the section again more carefully.
Also you're not wrong that the way they start is sort of wonky. What I'm interested in is what they do starting with sets themselves

>>13080462
So in other words he's saying 2^n defines a number of possible worlds then given n propositions?

>>13079610
Wittgenstein is, once you have got past "that hocus-pocus of mathematical form", in which, like Spinoza, he encased and masked his philosophy — utterly exasperating. Ethics is transcendental, aesthetics is transcendental, logic is transcendental! — everything is transcendental! But all these things are in the universe, you goddamn brainless twit, how can they be transcendental! The universe is everything, nothing is transcendental! that's just a word imbeciles use to signify that they are incapable of understanding something! And sure enough, he understood neither logic, nor ethics, nor aesthetics among a great many other things, practically everything! — partly because he didn't bother reading enough of what his predecessors wrote, but mainly because he was a little man with small experiences and therefore incapable of making any progress in psychology, which is where all these "transcendental" categories begin — and end.

>>13080476

And that's why he's absolutely based

>>13079610
A comprehensive history of analytic philosophy, for OP:

1. All philosophy has been analytic, from the beginning of philosophy (quite simply because that's what all philosophy, indeed all thought, consists of: analysis).

2. Nietzsche arrives on the scene. Anglo-Saxons do not understand his analysis, ergo it is not analysis. Also, he made fun of them repeatedly for not being able to understand him. This at least they understood.

3. Anglo-Saxons: "Screw the priggish continentals: We will make our OWN philosophy." (= "The continentals are mean to us, so we won't play with them anymore.")

4. Wittgenstein's On Certainty. Illegible rubbish, but it set the tone for all future "analytic philosophy".

5. No one pays attention to the Anglo-Saxons' illegible rubbish, while book sales and star status of the continentals (many of whom are charlatans indeed but at least not boring) are soaring.

6. Finally Rorty turns around and proclaims the end of "analytic philosophy". "I wish I'd read less of our autistic bullshit and more novels instead."

7. According to the Anglo-Saxons, then, novels are the culmination and ultimate expression of philosophy.

8. And that's where Anglo-Saxon "analytic philosophy" stands to this day. Nothing more than a gigantic reaction movement to Nietzsche calling them names and making fun of them.

>>13080502
You don't understand what the term "analysis" means, do you?

>>13080209
>but I think Heidegger has more to give even for a rationalist.
This. Witty is easy peasy, just a more mystic and austere Russell. Understanding Heidegger warrants a completely new way of thinking.

>>13080461
Heidegger is harder bub

>>13080476
I am pretty sure Wittgenstein was heavily spiritual.

>>13080508
You don't understand what the term "thought" means, do you?

>>13080513
This was only a reaction to him repressing religion and spirituality throughout his career. He was raised in a very religious home.

>>13080477
>they're just letters
Yeah well all of formal math is just letters - if you want to project meaning onto them, you'll probably still want to type those expressions in some way or another. But okay I't been 8 years since I read it.

>>13080490
I can not read the last 3 sentences of the page in another way, so yeah.
But again, as I somehow implied, I doubt the value of binary logic when it come to "the real world". And I don't even mean give up logic as a whole to speak about those things - but even Relevance Logic seems more workable for me for that purpose.
There are also some other logicans going into the more exotic frameworks later, like Kripke.

>>13079610
Based Ramsey

>>13080549
What I mean is that they talk about how the meanings are assigned later on, I think.