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Anonymous Fri 04 Dec 17:52:23 2020 No.12419717 View Reply Original Report

Quoted By: >>12421019 >>12421038 >>12421056 >>12421065 >>12422698

can someone explain to me what is Gödel's incompleteness theorems?

Anonymous

Anonymous Fri 04 Dec 2020 18:00:22 No.12419742 Report

Quoted By:

Wikipedia is already extremely low level, considering it's a theorem with a kinda complicated proof

Anonymous

Anonymous Sat 05 Dec 2020 01:42:05 No.12420994 Report

Quoted By:

https://www.youtube.com/watch?v=V49i_LM8B0E
1:26:50

Anonymous

Anonymous Sat 05 Dec 2020 01:49:59 No.12421019 Report

Quoted By: >>12421060

>>12419717
Basically the Munchhausen trilemma and pre-socratic philosophy conveyed in mathematics. Nothing new. It's always been known that man cannot both penetrate to the absolute basis and prove with certainty that he has done so.

Anonymous

Anonymous Sat 05 Dec 2020 01:57:55 No.12421038 Report

Quoted By:

>>12419717
There's always more math to discover.

Anonymous

Anonymous Sat 05 Dec 2020 02:05:42 No.12421056 Report

Quoted By:

>>12419717
Holy shit, these answers...

All it says is that for any (consistent) axiomatic system there are some statements which are true but can't be proven in that system (or equivalently, are false but can't be proven false)

So for example, the Riemann Hypothesis might be true but it also might be impossible to prove that within the axioms commonly accepted by mathematicians (called ZFC)

Anonymous

Anonymous Sat 05 Dec 2020 02:06:58 No.12421060 Report

Quoted By: >>12421061

>>12421019
not what the incompleteness theorems are about retard

Anonymous

Anonymous Sat 05 Dec 2020 02:07:53 No.12421061 Report

Quoted By: >>12421080

>>12421060
Why not retard?

Anonymous

Anonymous Sat 05 Dec 2020 02:08:09 No.12421065 Report

Quoted By:

>>12419717
just read it. the proof isn't that long

Anonymous

Anonymous Sat 05 Dec 2020 02:11:06 No.12421080 Report

Quoted By: >>12421098

>>12421061
the incompleteness theorems aren't concerned with whether axioms are "provable" (the dogmatic argument from the munchhausen trilemma). they show that regardless of what axioms you choose (provided that they satisfy a few things important for arithmetic) that there are true statements (true *given the dogmatically assumed axioms*) that cannot be proved from those axioms

Anonymous

Anonymous Sat 05 Dec 2020 02:15:56 No.12421098 Report

Quoted By:

>>12421080
I see. Interesting, thanks.

Anonymous

Anonymous Sat 05 Dec 2020 11:44:45 No.12422417 Report

Quoted By:

For any interesting map, there are places that exist even though you can't get there via legal roads.

Anonymous

Anonymous Sat 05 Dec 2020 13:44:26 No.12422653 Report

Quoted By:

He started some theorems but left them incomplete and that's really profound or something.

Anonymous

Anonymous Sat 05 Dec 2020 14:04:22 No.12422698 Report

Quoted By:

>>12419717
All his theorem shows is that given a set of axioms there are some statements that can't be proved. Even if you create a new axion to prove that statement you can then create a new statement that is unprovable given that new set of axioms. That's it. It doesn't say which statements can't be proved give a set of axioms. It's more a thought exercise that has no has application to the real world.

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