I don't remember where I read it, nor the exact wording, but there is a quote that is perfect for this. It went something like this, "Godel proved incompleteness. Anyone who thinks there is a theory of everything laughs in the face of Godel."
My point is that physics does not exist in a vacuum. It is built up from observational data found in nature and taken from experiments. If mathematics can't come to complete truth (Godel has proven this), then there is no hope for a theory of everything in something that uses mathematics as its language.
That's complete nonsense. There's nothing about Godel's theorem that says the physical rules of the universe can't be described. You're babbling religiously.
"A small number of scientists claim that Gödel's incompleteness theorem proves that any attempt to construct a TOE is bound to fail. Gödel's theorem states that any non-trivial mathematical theory that has a finite description is either inconsistent or incomplete."
That's from the Wiki, FWIW. I'm not big on using Wiki as a source.
"Babbling religiously" is right on the line in my opinion. It makes you sound like an arrogant jerk. If you have problems with the content of the comment, state your case in neutral terms.
Learn to live with other people's ambiguity and looseness in phrasing. Then perhaps they'll be more forgiving of yours. (Downmod)
You appear to misunderstand the meaning of the terms "inconsistent" and "incomplete" in the context of Gödel's theorem.
"Inconsistent": There is at least one statement within the system that can be proved both true and false.
"Incomplete": There is at least one statement within the system that is true, but cannot be proved to be true within the system.
Since Gödel's theorem applies to formal systems in mathematics, it does not say anything about the possibility or impossibility of constructing a "complete" (whatever that means) mathematical description of our reality.
What about it? All Godel's incompleteness theorem says is that there will be open questions about a universe describable by finitely many rules. The laws of physics don't need to provide answers to questions about whether computers in its universe will halt or whether planetary systems are stable.
What do you mean "the laws of physics don't need to provide answers to whether planetary systems are stable"? Since when are planetary systems outside of physics?
Your sentence "All Godel's incompleteness theorems says is that there will be open questions about a universe describable by finitely many rules" shows right there that there cannot be a theory of everything. How can you have a theory of everything yet still have open questions? That means that you have not answered everything.
It's my understanding that a theory of everything describes the rules by which the universe operates. It doesn't say anything about emergent properties of these rules.
For example, if everything in the universe obeyed Newtonian mechanics, I would say that Newtonian mechanics was a theory of everything. You would say that it isn't.
Technically, a "Theory of Everything" in physics is just a theory that relates the four known forces in the universe: gravity, electromagnatism, strong nuclear, and weak nuclear. The latter three (I believe) have already been unified. It's a "theory of everything" because it describes every force in the universe.
That of course does not imply that the theory of everything automatically gets you a complete description of the universe. Even in the context of a single force, it can be difficult/impossible to come up with a closed form solution for how many different objects interact subject to that force. For example, the behavior of gravity is really well understood but that doesn't mean that we can come up with straightforward, closed form solutions for the n-body problem of a bunch of stars interacting with each other's gravitational pulls in space.
One counterexample for you: Conway's game of life has finite number of rules but you can construct universal turing machine with it that will have formally undecidable behaviour.
Godel showed (and guys tell me if I mess this up) that formal self-consistent systems have both statements that are true that cannot be proven and false statements that cannot disproved. In other words, complete systems are incomplete.
This does not mean that complete systems cannot model reality to a high degree -- there's no reason why a ToE could pop out from some rotation or transmutation of mathematics. It just means there would be parts of it that would be incomplete -- the model itself could have a very high degree of fidelity.
When applied to higher math and physics, this is another way of saying "you don't know what you don't know" ie, the models can work perfectly across all observation space and still be true to Godel.
"Theory of Everything" is not a theory for everything, literally. It is just a catchphrase used by physicists to mean a theory that encompasses the "Standard Model" (which describes particle physics) with General Relativity and gravitation, thus describing the whole physical universe (which, in the physicists narrow mind, is everything). So Godel has nothing to do with this.
You can have a theory of everything that is incomplete. There are no problems with that. And that's what people is looking for... ToE doesn't mean "a complete theory of physics", in the logical meaning of complete.
My point is that physics does not exist in a vacuum. It is built up from observational data found in nature and taken from experiments. If mathematics can't come to complete truth (Godel has proven this), then there is no hope for a theory of everything in something that uses mathematics as its language.