Imagine you are dreaming.
Imagine that in this dream you meet a philosopher who tells you of another realm that exists outside of your dream.
Imagine that you scoff, and ask the philosopher where that realm could possibly be.
Imagine he says "that realm is outside your brain, but this realm is inside your brain, and thus the two can never meet. This smaller reality is within that larger reality, but that larger reality cannot be within this smaller reality."
You say "Nonsense. Such a realm must be a fantasy because it doesn't lie in this reality, and you can't point to the direction where it is located. If it's not part of reality then it cannot exist."
But the philosopher replies "Just wait until you awaken, my son. Then you shall see the reality of the waking world."
You are about to counter with yet another devastating bit of cold logic when you suddenly wake up.
"OMG!" you say to yourself. "The philosopher was right all along."
No matter how you try to argue the existence of a place that is other than physical reality, you can never present a convincing case that it exists. You have to wait until you awaken, after which you won't need proof. You will have experience.
I'm not saying this is true, and I'm not saying I believe it. I'm just saying that while neither proof nor evidence can exist in the situation I've outlined, there can be a coherent argument for the existence of a realm which is either discontinuous with "reality" or which is larger, in some sense, and which either contains "reality" as a subset, or causes "reality" without being a part of reality, much as a television set causes the latest episode of CSI to appear without being a part of CSI.