It's Gould's separate magisteria. Physical materialism rejects the separate magisteria, and I'm convinced that it is self-consistent in doing so. However, dualists do believe in the separate magisteria and you cannot try to interpret their beliefs in the context of monism -- it just comes out ridiculous.

It is not possible to interpret "separate magisteria" as different kinds of stuff, one "empirical" and one "non-empirical". What they are, rather, is different rules of thinking. For example, prayer can often help and never hurt in individual cases, but have no effect in the aggregate (e.g. when surveys are performed). There's no consistent model that has this attribute, but you can have a rule for thinking about this "separate magisterium" which says, "I'll say that it works and doesn't hurt in individual cases, but when someone tries to survey the aggregate, I won't expect positive experimental results, because it's not in the magisterium of things that get positive experimental results".

Mostly, "separate magisterium" is the classical Get-Out-Of-Jail-Free card. It can't be defined consistently. Mostly it means "Stop asking me those annoying questions!"

This division, needless to say, exists in the map, not in the territory.