Not sure where you're saying Gödel's incompleteness theorems come in, but I agree that DAO is a game of Nomic.
Now... the ability to hard-fork is kind of in the rules as well. So it's a Nomic with a complicated endgame. Some guy just won the Nomic, but now he's finding that not only do you want to win, you want to win subtly, or else a majority can vote to undo your win.
But anyone who still thinks DAO is an investment vehicle is missing the fact that it's a high-stakes game, and cleverer people than them are going to win it.
"Not sure where you're saying Gödel's incompleteness theorems come in, but I agree that DAO is a game of Nomic."
I know what he means - he's suggesting that you can't ever get a bulletproof or watertight set of rules or guidelines for a system because ... blah blah ... Gödel's incompleteness theorem.
This is a very tempting idea and I myself have given it a lot of thought over the years.
The problem is, Gödel's incompleteness theorem applies to a system that contains the complexity of the set of all real numbers. But there are plenty of systems that do not have that much complexity and there are plenty of rulesets we could create and implement that would also not have anywhere near that amount of complexity.
So the analogy sort of falls apart there. It's still worth thinking about, though - the more complex your system of rules/laws/regulations/etc. becomes, the closer you are to a system that is mathematically guaranteed not to be airtight.
Good luck explaining that to lawmakers.
EDIT: YES, CORRECT, SORRY - I did mean to say the set of natural numbers, not the set of real numbers. Mea culpa.
Godel's theorem applies to systems that model the natural numbers (specifically, Robinson arithmetic), not real numbers. The first-order theory of the real numbers is decidable. (The second-order theory is not, since you can define the natural numbers in that, and then Godel's theorem applies.)
Your general point, of course, that Godel's theorem means a specific thing, and people should stop abusing it as if it means "everything has loopholes!", remains correct.
> The problem is, Gödel's incompleteness theorem applies to a system that contains the complexity of the set of all real numbers
As others have corrected that this should be naturals, I'll just also note that you can derive incompleteness just from addition and multiplication over naturals. So while you're correct that plenty of systems don't need full multiplication, you run into limitations quickly. Then you need proper theorem proving to recover the missing verification power.
Uh, I'm at least 70% confident that Gödel's incompleteness theorem applies to sufficiently strong systems of integer arithmetic, and extensions to those, and doesn't need real numbers.
That being said, saying it can't be bulletproof or watertight is too vague.
There is both a first and a second Gödel's incompleteness theorem.
The first shows that a system T which can do arithmetic has some statements that it can express, and which are 'true' , but which cannot be proven to be true by T.
The second shows that a system T which can do arithmetic cannot show that it is self consistent, unless it is not self consistent.
Neither of these seem to be a problem for smart contracts.
It is possible for a system to be self consistent. The smart contract or the system that the smart contract uses does not need to prove itself to be self consistent, so the second theorem is not a problem.
If there is some mathematical statement that can be expressed by the system that the smart contracts use, which the system cannot prove whether it is true or false, this is also not a problem. Which, Ethereum doesn't even have a proof checking thing built into it yet, so I don't see how this would be applicable.
I think that you are probably over-applying Gödel's incompleteness theorems.
Also, I don't think its so much complexity in the "wow these laws are complicated" sense, so much as "strength" in the "how many things can be talked about / shown to be true" sense.
You /might/ be able to do some weird program/proof analogy there, but I really don't think that applying it to law (by a law/program analogy) would really show all that much.
I would think that the law can be understood as being sort of like a function (these inputs result in these outputs), and a function can be both be complicated and total. The law doesn't really do much with formal proofs, as it is now anyway.
Keep in mind that there is also a Gödel's COMPLETENESS theorem.
Now... the ability to hard-fork is kind of in the rules as well. So it's a Nomic with a complicated endgame. Some guy just won the Nomic, but now he's finding that not only do you want to win, you want to win subtly, or else a majority can vote to undo your win.
But anyone who still thinks DAO is an investment vehicle is missing the fact that it's a high-stakes game, and cleverer people than them are going to win it.