Is Godel Incompleteness nonsense?

Can somebody explain Godel to a pleb like me?

I'm a physicist, not a mathematician.

>>8455213
tl;dr some math statements (theorems) involving numbers cannot be proven or disproven under certain axiomatic systems.

>>8455352
But people say

>"There are true statements that cannot be proven"

How can it be that a statement is true and not provable?

>>8455209
>it's another "high schooler grossly misunderstands Godel" thread

>>8455412
I've never heard a satisfactory explanation.

I think almost nobody understands it. People just know how to repeat what they've read.

>>8455213
Godels's discoveries just mean semantics, impredicativities and meanings are essential to mathematics so meaning cannot simply be replaced by more syntactic rules and more lists or algorithms.

>>8455394
Natural processes exist which are fundamentally noncomputable.


https://archive.org/details/gdelsproof00nage

>>8455440
>Natural processes exist which are fundamentally noncomputable.
Like what?

>>8455440
>Godels's discoveries just mean semantics, impredicativities and meanings are essential to mathematics so meaning cannot simply be replaced by more syntactic rules and more lists or algorithms.

There must be some kind of catch to this though. If the brain is a computer that means there are rules that can be used to represent meaning.

File: hegel vaporwave.jpg (309KB, 1584x1089px) Image search: [Google]

309KB, 1584x1089px

>>8455450
https://en.wikipedia.org/wiki/Halting_problem

Our brains haven't been formalized so there's no reason to think of it as a "computer" until it is proven to be computable. Biological life is manifested in specific organisms but biology is not about those specific organisms. Biology is about what it is about those particular material systems that distinguishes them from mere inert matter i.e. we must be able to partition living organisms into two parts: their life part and the other parts that are everything else so that the life part are the same amongst all living organism while everything else varies. The notion we cannot learn anything new about matter (i.e. about physics) by studying organisms is the orthodox opinion amongst scientists I suppose but the laws of physics don't really tell us anything meaningful about the biosphere and what actually exists within it and all the actual real processes unfolding.

To clarify OP, the statement you ask about is the independence of the existence of a set between N and R in the set theory ZFC.
The statement goes by Continuum hypothesis
https://en.wikipedia.org/wiki/Continuum_hypothesis

Gödels incompleteness theorems are something much more intricate and unrelated to set theory. https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems
They are about syntactical frameworks expressing arithmetic.
Some things are shown to be unprovable. Syntactically.
If G is such a proprematic theorem, then G can't be proven, and not(G) can't be proven either.
That's what it says - it's about those formal deducation systems which lack provability power.

Finally, there are some people may write unprovable, "but true". That's when you have an intendend "model" of the natural numbers in mind. In such a model, each sentence is either true or false, so it being unprovable syntactically means there is a dissonance between the formal system and the thing in itself.
That's particualarly appealing if you're a mathematical Platonist who thinks all mathematical statements are "true" or "false" in some major sense beyond formal deducation systems.
But you can just skip this last paragraph and take Gödels theorem to just say logics of arithmetic contain sentences which are not provable, and neither their negation. Fuck "truth", provability is more accessible.

But again, what you ask about, the set issue, is just about indepdence of an axiom system (something can't be proven because some set theory axioms are not strong enough (even though the set theory is already far too strong - which make this surprising))

>>8455394
>How can it be that a statement is true and not provable?
that is not what godels incompleteness theorem states. it just says that statements exist which for a given (finite) axiom set cannot be prove right or wrong. therefore the axiom system is "incomplete" as it cannot decide all possible statements.

no axiom system therefore is complete.

>>8455551
>no axiom system therefore is complete.
https://en.wikipedia.org/wiki/Presburger_arithmetic