> What I disagree with is that these observations are proof that the universe itself is rational. There are many aspects of the universe of which we're still completely oblivious, and where our understanding breaks down. The fact we can observe some degree of logic in our observations points to survivorship bias, i.e. the anthropic principle. Simply, we wouldn't be able to make sense of the universe if the conditions didn't exist for us to observe it.

Part of the problem here, is what exactly does "rational" mean in this context? Gödel never published this argument of his in a paper, only in a letter to his mother–I expect if he had ever decided to publish it, he would have expressed it more precisely. It is difficult to judge the correctness of an argument when it is an open question what exactly key terms in it mean.

> But even if I could concede this rational universe premise, my main objection is the leap of logic to then assert that humans are somehow special, and that our existence wouldn't have a meaning unless we can fulfill some sort of purpose, for which a human lifetime is not sufficient, and therefore, immortality. It's completely absurd.

That "humans are somehow special" seems to be a near-universal belief found in humanity, across time and across cultures; it is only very recently in human history that any significant proportion of people have doubted or denied it, and even today its doubters and deniers are likely a rather small percentage of the total population, especially on a global level. I don't think we should rush to dismiss as "absurd" a belief which is (arguably) a product of human evolution – doing so calls into question the reliability of our evolved belief-forming machinery, but that questioning risks becoming self-refuting, since the belief in evolution is itself a product of that machinery.

> Gödel wraps this in pseudological premises, but it reads to me like he started with the conclusion that God exists, and is trying to arrive to that conclusion with philosophical mumbo jumbo.

Although Gödel did believe in God, I don't think this particular argument of his depends on belief in God in any way. This in itself is just an argument for an afterlife, and it is entirely possible to believe in an afterlife without believing in God–that's the position of many Buddhists, and also the late 19th / early 20th century British philosopher John McTaggart (who is probably most famous for being the mentor of both Bertrand Russell and G. E. Moore).

> This is the complete opposite of the scientific method, and is therefore no different than "creation science", and all the other ontological arguments throughout history. I don't see why any _rational_ human being would give it more than the bare minimum of attention it deserves.

The scientific method deals in empirical arguments. This is not an empirical argument, so is outside the scope of the scientific method. There are many questions the scientific method, based on repeatable experiment and observation, cannot answer. For instance, it cannot answer many mathematical questions–Gödel‘s famous incompleteness theorems are not the product of the scientific method, since empirical experiments and observation are incapable of revealing to us the truth of mathematical theorems.