Abstract : It is pointed out that the ground state of $n$ neutrons and $n$ protons in a single-$j$ shell,
interacting through an isoscalar ($T=0$) pairing force, is not paired, $J=0$, but rather spin-aligned, $J=n$.
This observation is explained in the context of a model of isoscalar $P$ ($J=1$) pairs,which is mapped onto a system of $p$ bosons, leading to an approximate analytic solutionof the isoscalar-pairing limit in $jj$ coupling.
