God: Broadly Logically Necessary, Narrowly Logically Necessary, Neither or Both?

I just wanted to make a brief post discussing the nature of God’s necessity.  It seems that we can conceive of God’s necessary existence.  It seems that we can conceive of God’s non-existence.  Given that conceivability is taken as a guide to possibility, is this a stalemate?  Chalmers argues that it isn’t, that conceiving of God’s non-existence wins given that it doesn’t depend on a meta-modal notion like necessity.  But as Rasmussen argues here, Chalmers is mistaken.  There is a parity tie between these two positions and neither wins out.

Swinburne holds that God exists neither in a broad nor narrowly logical sense.  

Narrow necessity:  Implies a contradiction.  

Broadly logically necessary:  A posteriori identity claims.  Something that is green all over not being capable of being red all over also seems necessary though not to imply a contradiction.   

Leftow attacks Swinburne’s conception of God’s contingency here.  PBT, as well as some versions of the PSR, seem to urge us in the direction of thinking that God is at least broadly logically necessary.  PBT also seems to urge us towards thinking that God is narrowly logically necessary if it can be coherently maintained. 

Both Leftow and Rasmussen set out arguments to think that God exhibits both sorts of necessity.  Leftow from God’s relationship to modality and Rasmussen through trying to show that atheism entails a contradiction.