"Is my non-existent deity the same as your non-existent deity?"

I owe the amusing title to philosopher Phil Gasper, who asked regarding this, "I wonder if philosophers of language have any insight into this issue?"  One thing that's clear is that academic freedom at some religious institutions has little meaning, alas.

UPDATE:  Ask and ye shall receive!  Philosopher Ephraim Glick (St Andrews) writes:

I thought you or your readers might be amused to hear that there is in fact some relevant literature in philosophy of language. The locus classicus is Geach's "Intentional Identity", which notes that someone who doesn't believe in witches can still truly assert something of the form "Hob think a witch did X, and Nob thinks she did Y". Similarly, even if Hob and Nob aren't familar with each other, someone could truly assert something of the form "Hob and Nob think the same witch did such-and-such". An early response by Dennett discusses an example involving gods. Other authors who have discussed the problem include Burge, Salmon, Walter Edelberg, and myself.

Don't get your hopes up, though --- no one in this literature has said enough to resolve disagreements about whether Christians and Muslims worship the same god!