  A carefully motivated symmetric variant of the Poisson bracket in ordinary
(not Grassmann) phase space variables is shown to satisfy identities which are
in algebraic correspondence with the anticommutation postulates for quantized
Fermion systems. "Symplecticity" in terms of this symmetric Poisson bracket
implies generalized Hamilton's equations that can only be of Schroedinger type
(e.g., the Dirac equation but not the Klein-Gordon or Maxwell equations). This
restriction also excludes the old "four-Fermion" theory of beta decay.
