I repeat Parallax is purely a measure of the distance to a star. A star at that distance can be of any size.
Please follow along:
1. It is thought that our sun is an average star
OK, I'll follow on! Yes, the sun is a reasonably average star.
2. Closer bodies parallax more than distant bodies
Here we deviate a bit. Saying stars "parallax" seems an odd way to put it. Parallax is defined as the
the angle subtended at a star by the mean radius of the Earth's orbit around the Sun.
it is often quoted in
mas, which stands for milli-arcseconds.
So, parallax is simply a measurement made on a star.
3. If the sun were to parallax as much as stars like Alpha Centauri, it has been computed that it should have a diameter of 0.5 degrees
So, saying "If the sun were to parallax" is
quite meaningless! The sun
simply cannot parallax. Surely from the definition you can see that.
4. Since the Alpha Centauri stars are much smaller than 0.5 degrees, yet still exhibits the parallax it does, the Round Earth model comes into question.
Well no, that is not what was said. Read a bit earlier from Wallace, and I believe you will see he says that if the sun extended out to the orbit of Neptune it would show a disc of about 0.5° at the distance of α Centauri etc (I am not quoting exactly as I am doing it from memory)
Then you say "
the Round Earth model comes into question".
No, not at all! What is called into question was
not the Globe Earth, but Wallace's
"Nebula Theory".
You must realise that Cosmology was very much in its infancy when this was written!
But, in any case the Globe Theory does not depend on Cosmology in any way. I am certainly no cosmologist. I read a bit on some of it with interest, but I don't really have any "belief" in particular theories.
5. The fact that there are no stars, who parallax to the degree that they do, which have a diameter of 0.5 degrees, it can be concluded that either the Sun is unique in that all other stars are tiny in comparison or that the underlying model is incorrect.
Nothing of the sort! When Wallace says "there are no stars", he is saying that there are no stars with diameters out to Neptune's orbit! I did mean to check on some of Wallace's figures there, but haven't had the time yet. I'm afraid I don't keep things like the diameter of Neptune's orbit in my head.
Again "the underlying model" is Wallace's nebula theory, and might be of interest to a cosmologist, but is of no relevance to the Globe model.
Again, please take this to a Round Earth forum if you are seeking answers. We would not be able to tell you why the observations don't match your model.
I am not looking for answers that I have not found and please tell me
why observations Wallace may or may not have made about his "nebula theory" might affect the validity of the Globe Earth.