"Actual social structures are way more complex than anything we could ever hope to model - ever. We can't make predictions about them - period."

Nonsense. Of course we can not make exact predictions (like the real thing), but we can get a pretty good idea of some things. We have good idea why capitalism works better than communism, for example. Honestly, I think you are just nitpicking. Of course we can not predict everything, but we can get estimate of SOME things, which is better than nothing, and certainly more useful than philosophy.

Even ethics are eventually just subject to Evolution - evolution decides on the ethics that prevail, not philosophers.

" It's not as if we, the intellectuals, are sitting on high and that everyone else listens to us and changes their behaviors accordingly."

That's why philosophy is useless and economics is not. If economics can show that some path of action is beneficial, people might well listen. Or at the very least, they might listen if you exploit that path yourself and get rich by it. Economics is not just a theoretical things, it is happening all around us.

"Can you give me a good, concrete, example of how you can use math to prove anything about society, without relying on assumptions about what is "good" or "right?"

I can recommend the book "Priniciples of Economics" by Gregory Mankiw, it is full of examples. I don't see why you would need assumptions about "good" or "right" at all? Also, check out many of the economics submissions on HN, there were some good ones. One interesting experiment was the one about freeloaders, and groups in which people could spend "money" to punish the freeloaders, vs groups in which they couldn't - one could eliminate the freeloaders problem, the other couldn't. That seems a very useful result, for example.

I am more an artificial life guy, one example that amused me was a simulation of agents eating a "sugar mountain", and a comparison of the "society" with and without tax (showing that agents ended up better off on average with taxes - the tax was evenly distributed among all agents). But that is a long way from practical application (I tried to find it, but Google let me down - it was from an artificial life professor in Amsterdam). Another thing is catastrophe simulation, where mass events are being simulated to discover dangerous areas during panic outbreaks for example in football stadions or pilgrimages to mekka. But these are just very specific examples - honestly, most economics textbooks are full of answers to the question you are asking.

"Do you even know economics? Have you taken any graduate courses in it?"

Uh - do you know economics? Sorry, but I think this is getting silly. You seem to put exaggerated emphasis on academic titles - I really thought people on HN were beyond that. To answer your question: no, I have not taken such courses, I have only read some books and articles. I don't claim to be an economist, either, but I think I have a sufficient idea of what it is all about. My own definition might deviate from the public opinion, for example I think evolution theory is also relevant for economics - and some parts of biology could as well be called economics.

""They can't prove their ideas all the way down to ZFC"

I don't think that is true in general."

Do you actually know?"

Have I personally verified every mathematical proof that has ever been published? No, as it is impossible and would not be very useful. Another silly question, I am sorry. I think you are just nitpicking. Of course mathematicians sometimes work with unproven concepts, but the concept of a proof is fairly established I should think. If a mathematician publishes something conceptual, they won't call it a proof (or at least it won't be accepted as such as long as the community has not verified it). Actually "proof theory" and "logic" was also my main subject in my maths degree - so at the very least, I am sure some mathematicians have a very precise idea of what a proof is, namely the ones doing "proof theory".

"For instance, the statement "God Exists" is not wrong, it's incoherent. Have you ever thought about it that way? What's god? What does it mean for an undefined entity to "exist?""

Now it is getting interesting, the failure to address such questions is exactly what disappoints me about philosophy. If you are saying post-modern philosophers are doing a better job with it, point me to a worthwhile book.

Although if you quote something like "like that we can't claim moral absolutes, they are culturally dependent, etc." I say why bother at all? Why not just do our economics calculations, ie "moral rule #1 would make one billion people unhappy and save one million lives, moral rule #2 would make 500 million people unhappy and save 500000 people's lives" and let society decide (I made it up, but for example moral rules about smoking could well have such statistics). Of course there is still an issue with physics, we don't know what it means that something exists, but why bother with metaphysics if "normal" physics already provides all the answers?

Edit: found the tax link: http://www.cs.vu.nl/%7Egusz/papers/Tax-and-evolution.ps