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Gödel’s Incompleteness Theorems

Anonymous Tue 15 Sep 03:38:07 2020 No.12122210 View Reply Original Report

Quoted By: >>12122259 >>12122364 >>12122414 >>12123102 >>12123116

What are the philosophical implications?

Anonymous

Anonymous Tue 15 Sep 2020 03:44:00 No.12122226 Report

Quoted By:

Anekantavada

Anonymous

Anonymous Tue 15 Sep 2020 03:55:23 No.12122259 Report

Quoted By: >>12122452 >>12123038 >>12123103

>>12122210
None. The theorem is strictly confined to formal systems equipped with a sufficient amount of arithmetic. If you create a TOE that contains that sufficient amount of arithmetic, the theorems' consequences are restricted only to the arithmetical components and do not apply to the theory as a whole.

See Torkel Franzen's "Godel's Theorem: An Incomplete Guide to its Use and Abuse"

Anonymous

Anonymous Tue 15 Sep 2020 04:02:07 No.12122275 Report

Quoted By:

we'll never be able to comprehend God

Anonymous

Anonymous Tue 15 Sep 2020 04:13:22 No.12122303 Report

Quoted By:

The boundary between the known and unknown, the knowable and unknowable, is not a simple line, it’s more like a recursive fractal. We csn never know everything because any sufficiently robust system of knowledge creates manifold new unknowns.

Logicism is dead, logical postivism is double-dead, mechanism has been shot full of holes.
There exist unsolvable problems.

Anonymous

Anonymous Tue 15 Sep 2020 04:47:34 No.12122364 Report

Quoted By: >>12122368

>>12122210
This universe was made specifically for us to suffer in.

Anonymous

Anonymous Tue 15 Sep 2020 04:50:02 No.12122368 Report

Quoted By:

>>12122364
>ptsd mathematician going wtf at every level conceivable.

Anonymous

Anonymous Tue 15 Sep 2020 05:16:08 No.12122414 Report

Quoted By:

>>12122210
Pi is a lie?

Anonymous

Anonymous Tue 15 Sep 2020 05:23:47 No.12122425 Report

Quoted By: >>12123162

why do people consider this man the greatest logician of the 20th century (some say the greatest logician since Aristotle) when he was a theist?

Anonymous

Anonymous Tue 15 Sep 2020 05:33:00 No.12122452 Report

Quoted By:

>>12122259
Uh? Since when the arithmetical component doesn't interact with the rest of the theory? You can indeed craft systems designed to work around Gödelian limitations that way, but it's going to be crappy.

"Recursive, consistent logical systems capable of arithmetic are incomplete". I'd rather remove the recursivity requirement (resulting in an "empirical" proof system based on experiments), or even the consistency one (you get a programming language).

Anonymous

Anonymous Tue 15 Sep 2020 09:02:41 No.12123038 Report

Quoted By:

stop reading these pseuds, the only one with any intelligence and understanding is this nigger here >>12122259

Anonymous

Anonymous Tue 15 Sep 2020 09:46:46 No.12123102 Report

Quoted By:

>>12122210
Practically speaking, it means we’ll always be searching for stronger and stronger axioms, even to prove facts about just the natural numbers.

Anonymous

Anonymous Tue 15 Sep 2020 09:48:00 No.12123103 Report

Quoted By:

>>12122259
>restricted only to the arithmetical components
what is this in opposition to?

Anonymous

Anonymous Tue 15 Sep 2020 09:52:40 No.12123116 Report

Quoted By:

>>12122210
I think many people confuse the implications of incompleteness and those of the munchhausen trilemma. I think you are asking about the latter.

Anonymous

Anonymous Tue 15 Sep 2020 10:15:54 No.12123162 Report

Quoted By:

>>12122425
Wow, you're so much smarter than Godel for not believing in God, special snowflake.

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