  We show that a primitive axial algebra of Jordan type $\eta = \tfrac{1}{2}$
is a Jordan algebra if and only if every $2$-generated subalgebra is
\emph{solid}, a notion introduced recently by Ilya Gorshkov, Sergey Shpectorov
and Alexei Staroletov.
  As a byproduct, we show that a subalgebra generated by axes $a,b$ is solid if
and only if the associator $[L_a,L_b]$ is a derivation. Moreover, we show that
$2$-generated subalgebras that are not solid contain precisely $3$ axes.
