  We argue that the best way to determine horizontal symmetry is from neutrino
mixing, and proceed to show that the only finite group capable of yielding the
tri-bimaximal mixing for all Yukawa couplings is $S_4$, or any group containing
it. The method used is largely group theoretical, but it can be implemented by
dynamical schemes in which the Higgs expectation values introduced to break
$S_4$ spontaneously are uniquely determined up to an unknown scale for each.
