Kurt Gödel's Philosophical Remarks

[Humanista]

1. The world is rational.
2. Human reason can, in principle, be developed more highly (through certain techniques).
3. There are systematic methods for the solution of all problems (also art, etc).
4. There are other worlds and rational beings, who are of the other and higher kind.
5. The world in which we now live is not the only one in which we live or have lived.
6. Incomparably more is knowable a priori than is currently known.
7. The development of human thought since the Renaissance is thoroughly one-sided.
8. Reason in mankind will be developed on every side.
9. The formally correct is a science of reality.
10. Materialism is false.
11. The higher beings are connected to the other beings by analogy, not by composition.
12. Concepts have an objective existence (likewise mathematical theorems).
13. There is a scientific (exact) philosophy {and theology} (this is also most fruitful for science), which deals with the concepts of the highest abstractness.
14. Religions are, for the most part, bad, but Religion is not.

[eremita]

Já que o OP só tá copiando-e-colando a tradução da Eva-Maria Engelen, direta ou indiretamente, sem sequer dar-se ao trabalho de compartilhar o troço na metalíngua do lugar (português), então vou usar inglês mesmo. Assim não preciso re-traduzir nada; e dá menos margem para "ackshyually" e outras falácias de olha-o-aviãozinho. Caso outros foristas queiram, traduzo excertos do que escrevi, ou do que o Gödel escreveu no alemão.

Also, OP is "conveniently" omitting that those are axioms. Axioms are shit you're supposed to take as true without questioning, because they're either obviously true or already shown to be true. Neither is the case here so I'm not playing along — instead I'm showing the axioms themselves are a slopfest (easy to dispute, ungrounded) on the same level as the plot of Skibidi Toilet.

1. The world is rational.

The original (Die Welt ist vernünftig) is already bad, and the translation follows fashion.
Does the world follow consistent rules? Most likely, yes.
Do those rules have "existence"? Hard to say, probably not. It's more like we interpret certain patterns as if they were rules.
Can humans comprehend those rules partially? It's more like we're forging the rules, but if you pretend they're inherent to reality, likely yes.
Can humans comprehend those rules completely? Most likely, no.

2. Human reason can, in principle, be developed more highly (through certain techniques).

"Human reason" is just an abstraction dammit. A convenient one, like algorithm, but it shouldn't be confused with something real.
That said you can, at least in principle, develop human reason "more highly", if "more highly" means at least one of those two things:

• less likely to follow incorrect or poorly formed premises
• less likely to output an fallacious conclusion out of true premises

Note one thing does not automatically lead to the other.

3. There are systematic methods for the solution of all problems (also art, etc).

Emphasis mine. I'm calling bullshit on that "all".

4. There are other worlds and rational beings, who are of the other and higher kind.
5. The world in which we now live is not the only one in which we live or have lived.

Those two axioms are on the same tier as "let's assume the tooth fairy exists, and she lives in her castle".

6. Incomparably more is knowable a priori than is currently known.

Emphasis mine, again. That's qualia-like babble.

7. The development of human thought since the Renaissance is thoroughly one-sided.

I'm not digging through the original to know WTF this muppet is referring to, when he says the development was one-sided (einseitig). But it's likely something like "waaah, they developed that thing that really matters, instead of that thing that ⟨blink⟩I⟨/blink⟩ want it to!"

8. Reason in mankind will be developed on every side.

Please tell me this is a translation error, and Gödel isn't vomiting certainty about the future. Pleeeeease. /me checks original Nah, he is. *rolls eyes*
This axiom is exactly on the same level as "trust me" = "you're gullible rubbish, aren't you? If I smear anything on your snout you'll swallow it. Open your mouth, aaaah~". Yes, it's that bad; not only he's vomiting certainty on something he cannot show to the reader, but that he himself cannot know for sure.

9. The formally correct is a science of reality.

Okay, this one is on Engelen. The original is a wee bit clearer: "Das formal Richtige ist eine Wirklichkeitwissenschaft." He's basically saying formal thought is a science dealing with real things.
Still heavily contestable, though. Refer to what I said under #1 and #2.

10. Materialism is false.

You know what's false? This whole list of axioms.

11. The higher beings are connected to the other beings by analogy, not by composition.

You can argue cosmic coxinha is connected to mundane coxinha by analogy (as in, both are structured the same way) instead of composition (as in, both contain shredded chicken), but this still begs the question:
Does cosmic coxinha exist? (Probably not.)
Same deal with "higher beings" (höheren Wesen).

12. Concepts have an objective existence (likewise mathematical theorems).

You know what has objective existence? Dirty toilet paper. Like the one Gödel wrote this shite on. But unlike the shite he wrote on it.

13. There is a scientific (exact) philosophy {and theology} (this is also most fruitful for science), which deals with the concepts of the highest abstractness.

{and nihilogy, and centaurology, and santaklauslogy} — srry, I couldn't resist.
This one was already shown to be heavily disputable, given previous ones.

14. Religions are, for the most part, bad, but Religion is not.

First off, note how every single other axiom in this list is epistemic (claims something is true or false), but this one is deontic (claims something is good or bad). You could translate this crap as "I dun liek relijunz lol but I luuuuv teh religion lmao " and it would be still semantically equivalent to the original (die Religionen sind zum größten Teil schlecht, aber nicht die Religion).
Probably an artefact of how this list of axioms is compiled, but this creates an implicit fallacy called "wishful thinking" — "it's good so it's true lol lmao haha". (It goes without saying "X is not bad" +> "X is good" is not the same as "X is not false" +> "X is true".)
But even if we disregard this crap (we shouldn't), the axiom is still used toilet paper. It's creating one of those meaningless distinctions between "religions" and "religion".

*yawn*