Why not?
Who said such existences were "unfalsifiable"?
That's why I said a sufficeintly defined thing, and a sufficiently defined space. Given your example, one could simply use a camera to prove that there was no alien at the door using "mind control" to prevent others from seeing it. Mind control doesn't work on cameras.
Perhaps you mean the god that you imagine as the counterpart to your argument. I doubt you mean to say "every god that has ever been claimed to exist", considering that some cultures have claimed that cows or trees are gods.
No, you dont' have to make any such additional claims. One can easily find evidence that certain gods do not exist - for instance, the "all good, omnipotent, omniscient god" has evidence against it in the form of the argument from evil. Just because something is claimed to be supernatural doesn't mean one cannot find sufficient evidence to become convinced that such a thing doesn't exist; after all, don't christians turn into agnostics or atheists every day, leaving their faith, because it has been sufficiently proven to them that that particular god doesn't exist?
If there is no way to disprove a particular god, how does anyone ever lose their faith and become non-believers?
No, but I do see the problem with yours.




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