Spirituality and moral values are not empirical phenomena. Nor are they adequately (or even correctly) described as axiomatic systems. They require a different, non-empirical, type of phenomena, to be "real". An alternate universe is a simple description of this non-empirical reality.
The best explanation I know of is by Terry Pratchett in Hogfather:
REALLY? AS IF IT WAS SOME KIND OF PINK PILL? NO. HUMANS NEED FANTASY TO BE HUMAN. TO BE THE PLACE WHERE THE FALLING ANGEL MEETS THE RISING APE.
"Tooth fairies? Hogfathers? Little—"
YES. AS PRACTICE. YOU HAVE TO START OUT LEARNING TO BELIEVE THE LITTLE LIES.
"So we can believe the big ones?"
YES. JUSTICE. MERCY. DUTY. THAT SORT OF THING.
"They're not the same at all!"
YOU THINK SO? THEN TAKE THE UNIVERSE AND GRIND IT DOWN TO THE FINEST POWDER AND SIEVE IT THROUGH THE FINEST SIEVE AND THEN SHOW ME ONE ATOM OF JUSTICE, ONE MOLECULE OF MERCY. AND YET - Death waved a hand - AND YET YOU ACT AS IF THERE IS SOME IDEAL ORDER IN THE WORLD, AS IF THERE IS SOME... SOME RIGHTNESS IN THE UNIVERSE BY WHICH IT MAY BE JUDGED.
"Yes, but people have got to believe that, or what's the point-"
MY POINT EXACTLY.”