Appeal to Ignorance

The fallacy of appeal to ignorance comes in two forms: (1) Not knowing that a certain statement is true is taken to be a proof that it is false. (2) Not knowing that a statement is false is taken to be a proof that it is true. The fallacy occurs in cases where absence of evidence is not good enough evidence of absence. The fallacy uses an unjustified attempt to shift the burden of proof. The fallacy is also called "Argument from Ignorance."

Example:

Nobody has ever proved to me there's a God, so I know there is no God.

This kind of reasoning is generally fallacious. It would be proper reasoning only if the proof attempts were quite thorough, and it were the case that if God did exist, then there would be a discoverable proof of this.