I disagree with everything is religious and think this actually doesn't differentiate between religion, politics, philosophy, .. and some more things. However, I think the topic is quite interesting.

My initial reaction was that the discussion would evolve around rather aggressive games like playing Jihad or the Crusades or whatever. I cannot really imagine what playing a religious game would even mean? Would it mean that the game is full of a specific ideology?

I don't think I have such a game. But I want to look at my GOG library and search for games that I find more ambitious regarding philosophic or spiritual content. .. I finished looking and to my surprise out of ~200 games none really qualifies for this category. Maybe there is indeed a market gap, i.e. games with a philosophic or spiritual deepness.

Most of the games I own are rather plain wordly entertainment (strategy, RPG, adventures, simulations).

Excuse me, OP didn't say everything, but everyone. As in "everyone has own core beliefs and protects those beliefs with utmost passion (sometimes even zeal)". That doesn't mean, however that every action of that person is dictated by those beliefs. Not everything is religious, yes.

Again, the topic was only not about "religious games", but any games that feature religion and it's adepts depicting them with significant depth. Since I can't to look up games in your library, I can't say anything for sure, but it's quite probable that you can have games that deal with religion.

Witcher series does, Blackwell series does, there are some strategy games (heck, there is even "god simulator" genre).

That's not what the theorem stats; in fact, your statement doesn't really say much.

What it says is that there are statements that can't either be proven or disproven. A statement like 1=1 is easily provable, and 1=2 is easily disprovable (or, rather, its negation is provable), but the theorem says that there are statements that don't fit into either category.

Furthermore, there are a couple of other requirements for the theorem to hold:
1. The system must be sufficiently powerful. A system of arithmetic that only handles basic mathematical operations but doesn't have any logic, free variables, or quantifiers, is not powerful enough. (In other words, we need to say "there exists" if we want to say something like "there does not exist a proof of this statement".)
2. The system must be consistent. In an inconsistent system, *everything* is provable, including statements that would claim to be provable. (I'd actually consider this a reasonable definition of consistency; a formal system is consistent iff there exists at least one well-formed non-theorem.) (Easy example of an inconsistent system; take a formalization of arithmetic that includes conventional logic, and add the negation of 1=1 as an option; we can then prove everything by the closest counterpart to proof by contradiction.)

(Incidentally, annother theorem by Godel says that consistency can't be proven within the system, but that's another theorem with a proof that isn't as easy to understand.)

If I remember correctly the post this is a reply to, all I did was divide by zero. (The transformation on each side of the equation, mainly cancelling the zero (equivalent to dividing by it), is the same; it's just that this particular transformation isn't something that can be consistently defined without violating the axioms of arithmetic.)

In the Japanese version, this particular figure is called Megami, which simply translates to "Goddess". So, we can conclude that this being is just a nameless goddess, like the goddess of a matriarchal monotheistic religion would be.

SaGa 1 also has a god in it (though his name was translated as "Creator" in the US version).

Doing it manually is no help here; if a statement has no proof, there is no way, manual or otherwise, to derive the proofless statement from the axioms and rules of inference.

In fact, one could write an algorithm to enumerate every theorem of a formal system, and since the statements and theorems of the system are countable, one could write an algorithm that will find a proof or disproof of any statement if there is one; that algorithm is guaranteed to terminate if (and I believe only if) the statement is decidable.

Besides, truth is relative to the specific system of axioms in use. Case in point:

True or False: There exist non-degenerate triangles with two right angles. (A degenerate triangle is one where (at least) one of the angles is 0.)

Sort of. The axioms are invented, in some way, and every other property is then discovered; those properties are only "true" relative to the system of axioms (and rules of inference) in use.

This reminds me of one thing: The imaginary numbers are no less real than the real numbers. In fact, the real numbers have enough counter-intuitive properties that they don't *really* seem that real.

I'd argue that they do mix, provided the people involved are rational.

Politics and religion, on the other hand, don't mix, and the result of trying to mix them is rather explosive.
This fails to account for vacuously true statemens.

For example, it is true that every even prime except 2 is divisible by 0 (in other words, if p is said even prime, there exists x such that 0 * x = p). However, this statement fails to be analytic because the predicate doesn't affirm any such subject. Furthermore, we can't verify it experimentially because we can't even find an even prime bigger than 2 (and it should be obvious why there are none).

I'd go even further to argue even pol/religion can be mixed well if both parties are rational/open minded. It's when one tries to influence/control the other(or use the other for one's own gain/that of their ideology) that things get iffy.

And provided goals of politics and science are aligned.

Both provisions are, obviously, false.

I agree that democracy, despite being kind of shit, is still the best system around so far.

However, with respect to wits etc. - it all comes down to ones advisors. If a dictator surrounds themselves with intelligent people that are good in their fields, listens to their advice, and can discern the facts from the self-interest crap, then they will do well.

Likewise, a democracy where the people in power are useless, and surround themselves with useless people, won't do too well.

Unfortunately the measure of "doing well" is these days only relevant within an election cycle - sometimes not even that, since we've had our Prime Minister usurped from their own party while in power due to bad polls that were years away from an election.

But I digress.

I disagree that Democracy, at least married with traditional Capitalism is best. You need to have proper safety measures baked in throughout the pie, especially education that encourages strong critical thinking then decentralize it strongly, both means of production and government. Big Bureaucracy always leads to crap like "The Trial' in Communism OR Capitalism.

OK then - what's a better alternative?

I hope that there is something better than democracy - not just due to bureaucracy, but also due to it being much easier to manipulate people to go for stupid (short-term) ideas than it is to convince people to back logical ideas for the long term.

Agree one needs critical thinking in education - unfortunately this has been distorted from critical thinking to SJW politics infusion, and even worse these days it appears to be at the expense of actually learning something useful (which required before learning critical thinking - learning the basics such as reading/writing, math, etc.).

Somehow I doubt that there is ever a system that is perfect. Why? Because all of these systems rely on people, and people tend to suck. The more powerful the person, the more crap they've had to do to get there, which generally increases the likelihood that they're assholes. All power structures inevitably suffer from this - even structures that were originally designed to encourage excellence (e.g. where people are supposedly rewarded based on skills and merit that's relevant).

The best thing about democracy is the fact that there's an explicit option to change the Government on a regular basis, where everyone's vote counts. Sure votes get manipulated by various media, but again that comes down to "people" and how easily manipulated they are.

In a dictatorship (for example), one would have to overthrow the existing system, which would generally involve a coup or an uprising of some sort - which generally wouldn't happen unless things were really bad (and if the incumbent possesses Stalin-like ruthlessness, the chance may never come due to any hint of dissent being squashed immediately).

Oh and there definitely is such a thing as "too many safeguards". We've got tons here - an Obudsman for almost every industry, strict consumer laws, safety laws etc. Unfortunately this causes vast amounts of red tape, while simultaneously encouraging stupidity. Example: Just because some idiot started a bushfire with fireworks, they're effectively illegal most places (except the capital, strangely enough). And while all those "anti-corruption" watchdogs or whatever give many people a nice fuzzy feeling of Government transparency, they're all staffed by moronic public servants - who are generally mates with the other idiotic public servants who they're supposed to be "watching".

Absolutely impossible by traditional understanding, considering that religion is organized system of faith and worship. It's by it's very essence political.

Oh, but they do, merely do the fact that scientists are still people, and as such still political beings. That doesn't mean that scientist's personal political beliefs and interests can't help in development of science; but that often those political interests makes them attack theories which are against those interests, or simply discredit those those theories to further their own careers.

P. S. I'll have to decline invitation merely do the fact that I categorically decline every request if I haven't met someone IRL

on a tangent of the neutrality of science:

a couple of years ago some medical doctors did a test, they offered a new drug to a random selection of GP's. However, the test was of the doctors, not the drug, which did not exist. Basically, the split the selection of doctors in two, and wrote different letters. To the first group they said - "This new drug gives a 90% survival rate", the second - "This new drug has a 10% mortality rate". as the astute of you may notice, the numbers are the same. However, almost everyone in group 1 said they would recommend the drug, while less than half of group 2 said they would.... even neutral natural science is politicized just through the way a scientist presents it.

I think this isn't connected with political worldview of the doctors as much is with human psychology - negative things affects (focus mortality in description instead of high survival rate) people more strongly than positive things. Political interests I am referring are fame, wealth or particular agenda.

ahh, but the slant a scientist gives is based on his own bias, such as fame or wealth. If the doctor presenting this drug is invested in the pharmaceutical company, or a competitor, there is a choice here. Also in science, people believe in different theories, it has also been proven that scientists are more likely to promote those theories more aligned to their own world view, not those that opposes it. so they can give different slants there.