Well I won't say anything that I didn't say right after the S3 finale...
I think Jack's comment about his dad was a big fat honkin' clue that dad is still alive, in some sense.
My theory (and it has yet to be definitely contradicted, not that
Lost ever does anything "definitively"

) is that Jack & the others in the Six left the Island and rejoined a different but very similar reality to the one they originally left...where small details like dead relatives might be different...the Island is a nexus between multiple realities. Homer Simpson might have considered a reality where his family ate their dinner with long prehensile reptile tongues to be "close enough" but Jack is pickier, which is why he and Kate and the other four have to go back to the Island - and rejoin the reality they originally came from.
Or he could be a ghost, clone, hallucination, long-lost evil twin, etc etc.