Baron and Kenny outlined several steps to aid in determining if a mediational analysis is appropriate to test a particular hypothesis. The very first step was "Show that the initial [independent] variable is correlated with the outcome [dependent]". This is referred here as an "effect to be mediated" ($X\rightarrow Y$).
Since then, however, several authors have highlighted that an effect to be mediated is not necessary (e.g., "Reconsidering Baron and Kenny: Myths and Truths about Mediation Analysis"). At first I found this difficult to conceptualize, but now I understand the rationale. Perhaps it is best to consider it in the context of a mediational model in which the independent variable is positively associated with one mediator and negatively associated with another other, leading to a total effect of near 0 (e.g., $X$ causes $Z$, $Z$ causes $Y$, $X$ has a negative effect on $P$, $P$ has a negative effect on $Y$). Despite the lack of a total effect, mediation could be statistically significant for both mediators.
From a statistical viewpoint this makes sense to me, and indeed I have even explained it to a few others; however, I have trouble understanding this from a logical or even philosophical standpoint. Start by considering that mediational models are inherently causal. How can a mediational model be theoretically possible without "an effect to be mediated"? Cause is defined by one thing leading to change in another. If changes in $X$ are not associated with changes in $Y$, how could mediation conceivably be present? In other words, if changes in $X$ lead to concurrent changes in mediators that lead to no effect on the dependent variables, how could this possibly be considered causation? What might be needed is a special instance in which changes in $X$ lead only to changes in certain mediators and leads to a total effect, but this seems like a different topic.
Consider this example in a universe in which only four variables exist (i.e., all possible mediators are present):
Intelligence ($X$) causes perceived need to have a healthy lifestyle ($Z$, mediator 1), which leads to weight loss ($-1Y$)
Intelligence causes increased attraction to video games ($A$, mediator 2), which leads to weight gain ($+1Y$).
Increasing or decreasing intelligence does not change weight