  Huw Price has proposed an argument that suggests a time-symmetric ontology
for quantum theory must necessarily be retrocausal, i.e. it must involve
influences that travel backwards in time. One of Price's assumptions is that
the quantum state is a state of reality. However, one of the reasons for
exploring retrocausality is that it offers the potential for evading the
consequences of no-go theorems, including recent proofs of the reality of the
quantum state. Here, we show that this assumption can be replaced by a
different assumption, called $\lambda$-mediation, that plausibly holds
independently of the status of the quantum state. We also reformulate the other
assumptions behind the argument to place them in a more general framework and
pin down the notion of time symmetry involved more precisely. We show that our
assumptions imply a timelike analogue of Bell's local causality criterion and,
in doing so, give a new interpretation of timelike violations of Bell
inequalities. Namely, they show the impossibility of a (non-retrocausal)
time-symmetric ontology.
