Unitarity of longitudinal weak vector boson scattering implies an
upper bound on the scale of electroweak symmetry breaking,
Lambda_{EWSB} = sqrt{8 pi} v ~ 1 TeV. Appelquist and
Chanowitz have derived an analogous upper bound on the scale of
fermion mass generation, proportional to v^2/m_f, by considering the
scattering of same-helicity fermions into pairs of longitudinal weak
vector bosons in a theory without a standard Higgs boson. We show
that there is no upper bound, beyond that on the scale of electroweak
symmetry breaking, in such a theory. This result is obtained by
considering the same process, but with a large number of longitudinal
weak vector bosons in the final state. We further argue that there is
no scale of (Dirac) fermion mass generation in the standard model. In
contrast, there is an upper bound on the scale of Majorana-neutrino
mass generation, given by Lambda_{Maj} = 4 pi v^2/m_nu.