  In metric geometry, the question of whether a distance metric is given by the
length of curves can be decided via the existence of midpoints with respect to
the metric $d$. We adapt a similar characterization to the setting of
Lorentzian pre-length spaces. In particular, we show that a given space is
strictly intrinsic provided it has $\tau$-midpoints and merely intrinsic
provided it has approximate $\tau$-midpoints. Our approach is based on the null
distance of C. Sormani and C. Vega.
