Erasmus,

That's true, we do make assumptions, but not ones that negate the results.

For example, let us assume that all the stars are part of the celestial sphere that is only 3000 miles away (As you have claimed). We should then observe one of two things.

1) No parallax owing to the stars being stationary.

2) Parallax of exactly the same amount in each star, as the Earth moves somehow relative to all of them.

But that is not observed. Instead, parallax occurs in different amounts, depending on which star you are looking at. The only way that we can get the mathematics to work out for every star is to assume that the stars are light-years away from us, and the Earth moves a significant amount.

Also, we have other ways of calculating stellar distances. Some of which are:

Spectral comparison: Something tells me you won't believe in Star types, or comparing them to our sun. You don't even believe that the sun is a star. So I'll just say this: In general, Parallax occurs in the greatest amounts with the brighter stars, and to smaller amounts with the dimmer stars. Although not all stars shine at the same luminosity, that still means that the brighter stars are closer then the dim ones. We know that luminosity falls off with the inverse square of the distance. So we run through the math, and get distances of light-years.

Doppler shift: This is one of the most reliable distance calculators in cosmology. If you want to debate the science that gives it credibility, feel free to.