  Many authors noted that the principle of relativity together with space-time
homogeneity and isotropy restrict the form of the coordinate transformations
from one inertial frame to another to being Lorentz-like. The equations contain
a free parameter, $k$ (equal to $c^{-2}$ in special relativity), which value is
claimed to be merely an empirical matter, so that special relativity does not
need the postulate of constancy of the speed of light. I analyze this claim and
argue that the distinction between the cases $k = 0$ and $k \neq 0$ is on the
level of a postulate and that until we assume one or the other, we have an
incomplete structure that leaves many fundamental questions undecided,
including basic prerequisites of experimentation. I examine an analogous case
in which isotropy is the postulate dropped and use it to illustrate the
problem. Finally I analyze two attempts by Sfarti, and Behera and Mukhopadhyay
to derive the constancy of the speed of light from the principle of relativity.
I show that these attempts make hidden assumptions that are equivalent to the
second postulate.
