Our measurements of the flatness of the universe don't depend on which parts of the universe we can see. They derive from measuring CMB and apply to the universe as a whole, not just the portion of the universe we can observe.

The CMB is the part of the universe we can observe. Extrapolation arbitrarily and without bound is logically incorrect.

Yes it is, but we can make statements from it about the entire universe such as the flatness. I've never heard anyone state that the flatness we measure applies only to the observable universe.

Then you have never heard anyone distinguish the attributes of a model that involves arbitrary extrapolation, from a statement about what is. This only means we tend to get lazy about making such important distinctions.

I'm sorry, but I still believe that our measurements of the flatness of the universe (despite being made on the observable universe) apply to the entire universe. This is at the very least backed up by Wikipedia (I know that's not the best source). I'd readily accept any sources you have to the contrary though!

Everyone is free to have their beliefs, but we should not confuse them with scientific evidence.

The cosmological principle can be empirically justified from our observations of the observable universe, for the most part we assume it applies beyond the observable universe (after all our observable universe is a mere accident of our position, so there is no obvious reason to assume outside of it is any different). However models such as eternal inflation drop this assumption on scales very much larger than the observable universe.

Right, so we must be clear when we say "the cosmological principle," which of these do you mean:

1) that the universe we can observe is the same everywhere at every age, 2) that the universe extrapolated arbitrarily and without bound is the same at every age, or 3) that what we will choose to regard as our simplest and best model will invoke an arbitrarily extrapolated cosmological principle, without making a claim that the universe itself is beholden to what we will regard as our best model. And when we say which of those we mean, we must keep track of what observations support which meaning.

@KenG none of those are what is commonly understood as the cosmological principle. In this context the CP is simply understood as spatial homogeneity and isotropy on the very largest scales.

The bottom line is, we must always notice the difference between making a convenient assumption in a model, and stating something that can cite observational support. If we lose that distinction, we forget the difference between science and faith.

Of course the cosmological principle is an attribute of a model, so it involves assumptions. Hence, i think it's pretty clear that the cosmological principle is the third of the three things I listed. Whenever we assume something in science, we must never claim we are asserting a constraint the universe must follow, we are simply asserting a modeling choice we have made for reasons we should be able to state clearly.

@zephyr See physics.stackexchange.com/a/2918/28199. "Sometimes, especially in pop-science writing, people imply that we know a lot more about the global properties of the Universe than we do. We often assume things like homogeneity to make our lives simpler, but in fact we have precisely no idea what things are like outside of our horizon volume."

I didn't mean to start such a metaphysical debate. I think ultimately KenG is correct in stating that we can make no claims about the entire universe and thus the only statement we can make with any certainty is on the observable universe. Saying the entire universe is flat is technical an unprovable statement. However, I have to agree with John Davis in his statement that it is reasonable to assume the larger universe is not any different from the observable one. Without evidence to the contrary, I think it's reasonable to suppose the entire universe is flat just as the observable universe is

But is science a list of things that is reasonable to assume, or a set of validated predictions? The ancient Greeks thought it was reasonable to assume that stars could not be so far away that we would not see them appear to move if Earth orbited the Sun. I don't see much point in making reasonable assumptions, science is about questioning and doubting and using that to motivate new observations. But I agree it is fine to make models that are as simple as possible, but that's not the same as assuming things to be true.

@zephyr Given that we agree that this is a philosophical discussion, rather than a factual issue with Ken's answer, I'm going to move this to chat.