Let's posit that we're taking local measurements and using them to determine UEIS/UEOS.
We know it's possible to do a whole bunch of abstract math and get an answer, without involving remote galaxies.
But maybe that's hard math to do.
What if it's easier to extrapolate our measurements to a remote galaxy?
So we calculate what telescopes would show in a remote galaxy as an intermediate step.
And from that we actually determine UEIS/UEOS.
That would be a non-circular argument, in which the deduced remote measurements are a necessary step.
It's not the only argument we could have made, but it's a useful and valid one.
Is that hypothetical argument detailed enough to satisfy you? It's something that should apply to just about any measurements. There's an unlimited number of ways to prove anything. There's no reason "deduced remote telescope measurements" can't be an intermediate step for all sorts of proofs that look at stars for data.
> Update: Let's look at it from the other direction: if your deduced remote measurements do not differ depending on whether you assume UEIS or UEOS, then how are they going to resolve the issue? This is what makes Swebs' argument an invalid one.
I know that my local measurements will differ based on UEIS/UEOS. But I don't know specifically how. Just looking at my local measurements by themselves, I have no idea which one they support. And in the process of deducing the remote measurements, I don't assume either one. I just plug in the numbers.
If you want a math analogy, then uhhh think of the local measurements as a composite number, and factoring it to deduce the remote measurements? And the question we ultimately want to answer can easily be solved with the prime factors.
It would be possible to calculate the answer without factoring, but much harder.
And factoring does not depend on assuming the answer. It's just factoring. It depends only on the composite number.
I think the best thing we can do at this point is to agree to disagree, especially as we are disagreeing over a hypothetical set of measurements and a calculation that neither of us can specify.
I would say yes to this except for your parenthetical there. Reading that, I think we're finally on the same page.
> unless it merely duplicates a set of measurements that could just as well have been made locally, in which case the excercise would have been pointless
Yes, it does duplicate the measurements that could have been made locally. But to whoever is writing the proof it's easier to use them in the 'remote galaxy' form. So it's not pointless. It's a critical part of that particular proof.
So with that noted down, I think everything is resolved?
This goes back to the part of Swebs' argument that says, in effect, "if we were to observe the expansion of the universe from a distant galaxy, it would look like it does from here" (specifically, that we are at the center in both cases.) My position is that I do not think one could make any successful argument of that form - i.e. which depends on comparing what one would measure at a remote location with what one observes here - without it being circular. My reason for thinking that is so is that I suspect that, if the argument is valid (Swebs' was not), you cannot deduce what those remote measurements are without begging the question.
Now we get to the critical part: my reason for thinking it would be begging the question is that, if the measurements are capable of resolving the UEIS/UEOS issue, then I think they must have a causal dependency on which way UEIS/UEOS goes, and thus, on account of that dependency, one could not deduce what would be measured remotely without first picking one or the other.
Update: Let's look at it from the other direction: if your deduced remote measurements do not differ depending on whether you assume UEIS or UEOS, then how are they going to resolve the issue? This is what makes Swebs' argument an invalid one.
Note that this does not rule out UEIS/UEOS being settled by local measurements, and in fact, early in this thread, I mentioned what I thought might be a possible candidate: directly determine the Hubble constant without reference to redshift, through measurements over time of objects whose distance can be measured by other means. Such methods would not depend on comparing local and deduced remote measurements, and would render moot the whole issue of whether we can deduce relevant remote measurements, as well as all arguments that rely on doing so.
So my position is that I do not think there are any arguments that are both valid and non-circular, that depend on comparing deduced remote measurements to local ones, that show we already have observations that resolve the issue, and I will stand by it until I am persuaded otherwise. One valid counter-example would be sufficient.