  A meson exchange model of the $\pi\pi$ interaction which fits free $\pi\pi$
scattering data is used to calculate the interactions of pions in nuclear
matter as a function of nuclear density. Polarization of the nuclear medium by
the pions results in a marked increase in the s-wave $\pi\pi$ attraction at low
energy. The influence of this effect on the nucleon-nucleon interaction is a
corresponding increase with density of the $NN$ central potential due to the
exchange of two correlated pions, resulting in an $NN$ interaction which fails
to saturate. A possible mechanism for restoring the theoretical stability of
nuclear matter is explored and found to be effective.
