The recent paper by Roger Anderton (http://www.wbabin.net/science/anderton24.pdf
) is a very funny piece. If you read it you come to a very simple conclusion:
Both statement are mathematically correct, as demonstrated by Anderton:
(a) assuming the invariance of the speed of light leads to the Lorentz transformation
(b) assuming the Galilean transformation holds, leads to the non-invariance of the speed of light (c2=c1+v)
The author concludes from this that (a) is mathematically wrong and (b) is mathematically true.
However, since both assertion were derived without mistake by Anderton, we can indeed be sure that they are mathematically correct.
So where is the logic of Anderton? Certainly far from the logic of nature, since it is an experimental fact
that the speed of light is invariant.