phd - Is it necessary to have a background in philosophy in order to get a position in logic in philosophy departments?

What the title asks.

Apparently there are some professors in departments of philosophy working on logic or semantics (e.g. William Starr or Nino Cocchiarella [retired]). Does one need to know the "real philosophy" to get such kinds of positions in departments of philosophy? Or does one only need to know logic/semantics (and not, say, treatises of Plato)? And does one have to have a PhD in philosophy, or does a PhD in math or linguistic suffice?