The Girard-Reynolds polymorphic $\lambda$-calculus is generally regarded as a
calculus of parametric polymorphism in which all well-formed terms are
strongly normal- izing with respect to $\beta$-reductions. Girard demonstrated
that the additional of a simple "non-parametric" operation, $J$, to the
calculus allows the definition of a non-normalizing term. Since the type of
$J$ is not inhabited by any closed term, one might suspect that this may play
a role in defining a non-normalizing term using it. We demonstrate that this
is not the case by giving a simple variant, $J'$ , of $J$ whose type is
otherwise inhabited and which causes normalization to fail. It appears that
impredicativity is essential to the argument; predicative variants of the
polymorphic $\lambda$-calculus admit non-parametric operations without
sacrificing normalization.