The actions for all classical (and consequently quantum) BF theories o
n n-manifolds is proven to be given by anti-commutators of hermitian,
nilpotent, scalar fermionic charges with Grassmann-odd functionals. In
order to show this, the space of fields in the theory must be enlarge
d to include ''mass terms'' for new, non-dynamical, Grassmann-odd fiel
ds. The implications of this result on observables are examined.