Pentcho offers a valuable parable from the history of thermodynamics
which, in essence, is a nice illustration that one cannot use the
true statement, A => B, to reach any conclusion about the truth of
its converse, B => A.
That is precisely why I was so careful to say that the spectacular
agreement of the predictions of special relativity with every
experiment that has been
performed "give us such enormous confidence in" (rather than "prove")
the primary postulate.
There is a critically important aesthetic aspect of science at work
here. We NEVER "prove" ANYTHING about WHY the real world does what
it does in an experimental science like physics. Instead, we seek
"simple" models of reality that have "wide ranges of applicability"
and that make new, hopefully counterintuitive or previously
unsuspected predictions. Thus, the attractiveness of a premise is
in some direct proportion to 1) its simplicity, 2) the range of
physical phenomena it "explains", and 3) the degree to which its
validated predictions run counter to our previous intuitions.
Judged by these criteria, the primary premise of special relativity
looks like a very serious winner!