  Recent indications of neutrino oscillations raise the question of the
possibility of incorporating massive neutrinos in the formulation of the
Standard Model (SM) within noncommutative geometry (NCG). We find that the NCG
requirement of Poincare duality constrains the numbers of massless quarks and
neutrinos to be unequal unless new fermions are introduced. Possible scenarios
in which this constraint is satisfied are discussed.
