Let's go over the circularity issue in more detail. It starts with Swebs' statement that "[The big bang as a uniform expansion in spacetime] wouldn't work out because it wouldn't match what our telescopes are observing." Here we have a claim that the 'uniform expansion in spacetime' hypothesis (UEIS for short), which we all agree is wrong, has already been ruled out by astronomical observation.
Next, Swebs offers a specific argument for that claim, in the form of a diagram which shows that, in a uniformly expanding universe, each point appears to be that from which the expansion is ocurrring. One problem with that argument, which we both apparently agree on, is that this would be true for UEIS (for one thing, the image can be taken as a diagram of a demonstration using marbles on a table, which would literally be a UEIS.)
There is a second problem with it, however: none of our telescopes have observed the universe from the perspective of a distant galaxy, so we cannot say that our telescopes have shown that everywhere seems to be at the center of the expansion. We can deduce what it looks like from distant galaxies, if and only if we make some assumptions about the dynamics of the universe (there may be other observations from Earth that have already ruled out UEIS empirically, in which case the rest of this comment is moot. You have claimed that there are, but so far, you have have not presented any details.)
There are two possibilities: either it looks the same as from Earth (putting aside details local to the specific point of observation) or there is some difference. In the former case, which would hold if the expansion we observe is a uniform expansion of spacetime (UEOS), and which therefore is what we all, and cosmology in general, assumes to be so, I do not think these observations would rule out the possibility of UEIS. Therefore, for observations made in a distant galaxy to empirically settle the UEIS/UEOS issue, they must differ from those from Earth, in a way that is diagnostic of, and therefore causally dependent on, what form the expansion takes. Furthermore, because the local and remote results would differ in this case, UEOS would be ruled out.
So, when we try to deduce what can be observed from a distant galaxy, we must either assume that it is the same as from Earth (subject to local corrections), which will fail to resolve the issue, or we must deduce that there is some difference - but what difference? As shown in the previous paragraph, the relevant differences must be causally dependent on what form the expansion takes, so you have to make assumptions about the latter in order to deduce the former. There's the circularity, and it is general - i.e. not dependent on what specific measurements are being considered.
> You have claimed that there are, but so far, you have have not presented any details.
You can measure stars and watch the distances accelerate, or look at how the redshift of a star changes over time instead of staying static. These might take a while to do, but this is about what we can measure, not what we already have.
> As shown in the previous paragraph, the relevant differences must be causally dependent on what form the expansion takes, so you have to make assumptions about the latter in order to deduce the former.
This is that part where I see a breakdown in your logic. It's very possible that we can make measurements on Earth that would tell us exactly how our telescopes would differ from a distant galaxy. In that case, there would be no circularity.
Note that the proposition "We can only get this data by going to another galaxy and using telescopes there." is not part of this scenario.
> This is about what we can measure, not what we already have.
That is not so, this discussion started with a claim that we already have observational proof that distinguishes between the two scenarios. I have already suggested that the Hubble constant could, in principle, be measured without cosmological assumptions, but we do not, AFAIK, have good enough data, and you have not offered anything to alter that opinion.
>... look at how the redshift of a star changes over time instead of staying static.
Up until now, you have been very vague about what sort of measurements you have had in mind. This is getting closer, but under which scenario does the redshift stay static?
> This is that part where I see a breakdown in your logic...
All you are doing here is disagreeing with the conclusion; you have not offered any refutation of the argument that leads to it. The reason for me saying "the relevant differences must be causally dependent on what form the expansion takes" is that if they were not, then they would not be the sort of differences that could be used to choose between the alternatives. And if they were so dependent, then the mapping from what we observe from here to what would be observed there also has that dependency.
> It's very possible that we can make measurements on Earth that would tell us exactly how our telescopes would differ from a distant galaxy.
There is something very confused here, but I cannot figure out what it is. I can say that my point does not have anything to do with "how our telescopes would differ from a distant galaxy."
> Note that the proposition "We can only get this data by going to another galaxy and using telescopes there." is not part of this scenario.
Actually, Swebs' original claim was pretty much that, as it could accurately be paraphrased as "we have seen, with our telescopes, that, when observed from a different galaxy, the expansion also seems to have originated there." You seem to have put yourself into the position of defending a claim that you do not actually believe in.
Note that there are some conditionals here that you have to be careful of. What I said was that there are certain claims that, if they were made, would result in a circular argument. I did not say that Swebs had made those claims, as he had not done so; I wrote it in an attempt to forestall a trip down a dead end (so much for that!)
There's definitely some deep miscommunication going on. I'm just going to try to clarify a couple parts...
> All you are doing here is disagreeing with the conclusion; you have not offered any refutation of the argument that leads to it. The reason for me saying "the relevant differences must be causally dependent on what form the expansion takes" is that if they were not, then they would not be the sort of differences that could be used to choose between the alternatives. And if they were so dependent, then the mapping from what we observe from here to what would be observed there also has that dependency.
It's circular if we assume the form of the expansion. If the real form influences our measurements, and we use that to figure out what telescopes would show, which lets us calculate the real form, then nothing is circular.
> Actually, Swebs' original claim was pretty much that, as it could accurately be paraphrased as "we have seen, with our telescopes, that, when observed from a different galaxy, the expansion also seems to have originated there." You seem to have put yourself into the position of defending a claim that you do not actually believe in.
No, those are very different statements. "We can tell from here what telescopes would show" could be part of a valid argument. "We need to go there to know" is not necessary.
> There is something very confused here, but I cannot figure out what it is. I can say that my point does not have anything to do with "how our telescopes would differ from a distant galaxy."
I'm talking about the "none of our telescopes have observed the universe from the perspective of a distant galaxy" stuff.
Okay, look, this is clearly not working. If you want to format your argument as a numbered chain of logical statements, I can probably give you a response you'll understand. Otherwise I'm giving up. Big blobs of paragraphs are not conducive to debating whether there "must" be certain assumptions.
> I do not see how differing telescopes have anything to do with the issue.
How our telescope's observations would differ if they were placed in a different galaxy.
> it would have to be done without any tacit assumption about whether UEIS or UEOS applies
Yes! Now we're getting somewhere.
When you say "the argument is circular" that depends on all possible arguments using assumptions about UEIS/UEOS. I'm saying that you can make arguments that don't make assumptions about UEIS/UEOS. It's possible to make a circular or non-circular argument.
> In what way is that not exactly the sort of circularity that we just agreed about above, given that the real form is the issue to be decided?
Because I'm talking about measurements! You know, the same thing telescopes do. They measure. If you make measurements instead of assuming, then you don't have a circular argument.
> Mainly because you haven't said what measurements you think will substitute for Swebs' "the expansion appears to originate from wherever we are."
I don't have any in mind. I'm not saying there are any. I'm just saying that if the argument exists, it can be expressed in a non-circular form.
> point out the first statement in there that you disagree with
"We can deduce what it looks like from distant galaxies, if and only if we make some assumptions about the dynamics of the universe"
If "some assumptions about the dynamics" is supposed to include UEIS/UEOS assumptions, then this is where I disagree. We do not necessarily have to make those assumptions to make those deductions. You have not given any proof that all possible ways to deduce what it looks like will require those assumptions. We may be able to remove all of those assumptions with the right local measurements. Then we would have a non-circular argument.