This may by now be old news, but there is a recently started journal Annals of Mathematics and Philosophy. It aims to encourage dialogue between contemporary mathematics and philosophy. Issues are (it seems) to be freely available online. The first issue is out at the journal’s website here.
I confess I didn’t find this issue an encouraging start, being mostly low-level stuff that wouldn’t have got near publication in e.g. Philosophia Mathematica. Except that there is a substantial, characteristically lucid, and very interesting piece by Timothy Gowers, “What makes mathematicians believe unproved mathematical statements?” which I much enjoyed reading.