As Sean Carroll notes, it is technically true (Hume and the problem of induction strike again!) that an immaterial soul exists and is outside the provability bounds, or investigation, of current science.
But, as he also notes, it's also technically true that the moon, or some part of it at least, could in fact be made of green cheese!
And, he makes the burden heavy by whipping out Dirac's electron interaction equation and then asking soul believers to explain, in the terms of that equation, or if not, by adding scientifically measurable terms to that equation, how a soul could interact with the brain.
That said, one could be an epiphenomenalist. Perhaps Adam Frank, to whom Carroll is replying, is. But, while not logically impossible, nor inductively disprovable in a narrow sense, an epiphenomenalist soul that totally mirrors brain activity while never interacting with it is even more ludicrous than a soul that does. It's not too much to claim that it's impossible for such a critter to have evolved. And a deity that made that sort of soul would be even more ... risible? ... than one who made an immaterial, but interactionist, soul.
That said, it is true that science hasn't come close to investigating everything; it's also true that logically, you can't prove the nonexistence of anything — it's the equivalent of dividing by zero.
But, realistically? ....
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