/sci/ - Science & Math

But..but...I...

>>5380759
>strang thurry reeel

I wish string theory was real

Dude how can you claim you know more than the scientist who have speculated about string theory? This is why everyone at Reddit hates this place so fucking smug, not just in this board.

>>5380775
You can't deny string theory is a mess right now.
At the same time you can't deny the standard mode is more elegant.
I guess it's one of those things that just point in the general direction until someone figures it out.

>gravity
>understood

Pick one, retard OP

sage in all fields just to be safe

>>5380835
saved

>>5380878

What?

What does inconsistency have to do with being real? If it was consistent it still wouldnt be real.

ANYWAY, I always felt the kind of word Godel did was more controversial than we treat it. The kind of paradox's that show up with Godel, or Russell's paradox exist only within the framework that those philosophers came up with. There are alternatives yet to be explored, like Wittgenstein's work.

>>5380878
>implying Platonism is bad

>>5380925

Yeah!

Anyway, Godel was a plantonist. Which is the most "Nummers r reel" perspective there is.

>>5380930
Exactly. And Platonism resolves incompleteness. All possible mathematical structures exist. Therefore no undecidable statements, QED.

>>5380922
Well, can you derive arithmetic in first order logic with equality and elements of set theory, rather than second order logic and axiom upon unjustified axiom? If so, then you bypassed Godel's proof. Wittgenstein did not understand the significance of Godel's work and really did not know much logic outside of Russell and Whitehead. His comments on the foundations of mathematics should be forgotten. His real work was on the philosophy of logic and language. I do not want to downplay Witty's work, I just do not think it is worthy of reflection considering modern advancements in the philosophy of mathematics.

>>5380934

Cool! Thats a really concise way of stating that.

Argument time:

Plantonism is kind of dumb.

>>5380939

Interesting.

Yeah, I am getting very interested in Wittgenstein, I read his tractatus, and "Culture and Value." I plan on reading his writing on math , after all, Wittgenstein considered it his most important contribution.

I dont know, maybe he wasnt well versed in the relevant philosophy of his time. But it still seems really suspicious to me that we rely on the mathematical foundations that we do.

I heard Wittgenstein only read the introduction to Godel's work. Didnt even bother reading the actual proof.

>>5380934
>implying you even need that

Infinity doesn't exist. Godel is useless when applied to the existence of mathematical objects that can actually be described by finite rules. There is a very clear class of questions - which contains e.g. all questions that anyone would ever care in geometry, calculus, algebra, or physics - that simply have to be decidable. Everything else is unmathematical garbage.

Do you agree that even before the proof of Fermat's Last Theorem was known, it was unthinkable that the proposition of the theorem was undecidable? I think that it obviously had to be decidable. Now, someone could choose different (weaker) axioms about integers where FLT would be undecidable. But I would have trouble classifying him as a mathematician - he would perhaps be a generalized logician but not mathematician in my counting. All mathematicians must agree about the narrow class of propositions about integers.

Consider a prototypical example of incompleteness: the continuum hypothesis. The question whether the real numbers are countable or not is already unmathematical. The set of those real numbers whose existence we can take "really seriously" - those that can actually and accurately be described by a finite rule, a finite algorithm - is clearly countable. When looking at the hard core of mathematics, I am convinced that every meaningful statement in mathematics can be pretty much boil down to solid, surely decidable statements about integers. We can also imagine things based on larger sets that are "not" integers but that's just a helpful trick for our intuition. Real maths can work with the "linguistic" description of all these objects in terms of finite sequences of math symbols. And with these rules, everything we care about has to be decidable.

>>5380955
>finitism

>>5380971
Why laughing whores? What do you not like about it?

>>5380922
But Godel never said that arithmetic is inconsistent. That's just nonsense made up by whoever made that comic. Before making pretentious statements about Wittgenstein, you should probably like... learn the basic meanings of Godel's theorems.

Fucking /sci/, man...

I am not qualified to judge the validity of strang thurry, but I think considering that nowadays most of physics community is into it, then it must have some merit.

>>5380778
>you can't deny the standard mode is more elegant
It isn't. String theory at least has a mathematical foundation and it is based on weaker assumptions.

>>5381025

I thought he did right?

I thought the whole point of Godel's theorems were that a theory could not be both complete and consistent? Am I wrong? His second theorem was just the same idea applied to arithmetic.

I admit I dont understand his second theorem.

>Netownian
>Credible

>>5381085
No...

So, we have a bunch of axioms for arithmetic, and a bunch of allowed inferences, with which we deduce new theorems from those axioms.

We hope that, from the axioms of arithmetic

1. we can deduce every true statement about arithmetic, 'completeness'

2. we don't deduce false statements, 'consistency'.

the first theorem tell us that, if our axioms of arithmetic are consistent, which we assume they are, then our system is incomplete. there are true statements of arithmetic we cannot deduce.

we assume that the axioms are consistent, but can we be sure? the second incompleteness theorem tells us 'no', if a system is consistent, it can't prove that it is consistent.

neither of these things say that our system of arithmetic is inconsistent.