The argument from ignorance is a frequent guest in most debates on religion. The fallacy here is fairly straight forward, and is based on the foundation principle that a non-falsifiable claim must be regarded as false. The fallacy committed in this case, is to assert that a claim is true, because it has not, or cannot be proven false.
Those of you who have read your Karl Popper know that this a fundamental error in reasoning, and here is why. If we adopt a principle where all claims that cannot be falsified or have not yet been falsified, that has great implications. See the following conversation:
Person 1: So, you were out of town last week, your wife banged half the Harlem Globetrotters and the starting lineup of the Pacers.
Person 2: That isn’t true, you can’t prove that it’s true.
Person 1: Well, you can’t prove that it’s not, so until you can, your wife fucked half the globetrotters and Pacers.
That’s is a bit of a glib example, but it teaches us the lesson that until something has been proven true, proven false, or as long as it remains impossible to prove it false, a claim must be regarded as false.
In the case of a criminal trial, the charges have to be believed until prove false: This would translate into “guilty until proven innocent”
Person 1: An allmighty being just told me that you have been living your life in the wrong way. It said that those who have should share with those who have not. So give me half your shit.
Person 2: I can’t prove that you’re full of shit, so here is my ATM card and PIN.
It also puts the burden of proof onto the person saying “No, there is no evidence for that” rather than on the person saying “This is true”.