When I rant about it, I claim his theorem says "any system that reference parts of itself is either incomplete or inconsistent," and that the universe is such a system, as we're a part of it, and refer to parts of it.
So therefore, the universe is either full of magic (in a system with inconsistency, anything can happen), or mystery (there are true things that we can never prove).
My belief is that the quest to find a unified physics that describes everything is provably impossible due to Godel's theorem.
And on the rare occasions when I look for evidence of God, the fact that one of the things we can know for sure - is that we can't know everything - provides about as much comfort as I need.
My belief is that the quest to find a unified physics that describes everything is provably impossible due to Godel's theorem.
How would that happen? Physics is an empirical science, all we have to do is to look at what actually happens and write it down. Even if we fail to find good mathematical expression to describe what we see, we can always just create charts and tables describing what happens. There is nothing that prevents us from fully describing physics.
Unifying physics then just means finding one mathematical model that is able to describe all the aspects we discovered in different limits. I can not see how Gödel's incompleteness theorem would have any bearing on this. We just have to find a set of equations that reproduce our observations given the experimental setup. This does not involve any proofs, it's just the question whether a set of equations accurately describes the universe.
I can really only think of one way in which describing the universe with mathematics must fail and that is if there is no mathematical description of the universe. Otherwise we could always guess a set of equations and then verify that it works in all experiments we ever performed. You can of course never be sure that you did not simply miss one experiment that causes your theory to fail, but that is in the nature of physics. This also seems pretty unlikely, I fail to imagine anything that could escape all attempts of mathematical describing it in principle.
> My belief is that the quest to find a unified physics that describes everything is provably impossible due to Godel's theorem.
To be precise: it tells us that it's not generally possible to build a complete consistent model, but it may still be possible in specific cases, like our universe. My hunch is that such a model does exist, that we will find it, and further, that it will actually be rather elegant. We'll never be able to prove we've found it though, because we only have partial information— if we were running on a virtual machine, is the host system running Linux or BSD?
This sort of application is wildly out of bounds of the true scope of the theory.
The relationship between physics (unified or otherwise) can't be resolved with reference to Godel's theorems.
Well, you're actually making metaphysical claims more than mathematical or physical ones. One of two assumptions, depending on how literally the sentiment that the universe is a formal system is intended, is being elided here:
1. That the universe _is_ a formal system, rather than being describable in the language of some formal system. It's not evident what the universe being a formal system even means, or how it squares with basic intuition regarding e.g. the fact that physical systems have state.
2. That, dropping the physical system <=> formal system equivalence and given some real system R consisting of some fundamental entities whose behaviors can be described in full in the language of some formal system S, (borrowing a useful construct from Lucas' anti-mechanism argument, even though I don't buy that argument) no machine can be constructed in R which computes theorems of some formal system S' in which all true statements of S are provable, meaning that no state of the system R can be said to contain a description of S', and that S' is therefore not describable by any arrangement of the entities in R (assuming some reasonable predicate over states of R that is true for a state when some arrangement of a subset of the entities in that state describes S'). Intuitively, this doesn't seem to hold up: by analogy, I can describe a universal Turing machine with a computer equipped with only finite memory. You could then attempt to go down the road of claiming that, even if a description of S' is possible in R, that a mind within R would not be capable of formulating that description, but then you're heaping on an even larger tangle of assumptions, unknowns, and things you have to define if you're going to argue the case rigorously.
The point being that confidence about _any_ hypothesis about the nature of reality made on the basis of Gödel's incompleteness theorems is not epistemologically warranted.
So therefore, the universe is either full of magic (in a system with inconsistency, anything can happen), or mystery (there are true things that we can never prove).
My belief is that the quest to find a unified physics that describes everything is provably impossible due to Godel's theorem.
And on the rare occasions when I look for evidence of God, the fact that one of the things we can know for sure - is that we can't know everything - provides about as much comfort as I need.