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argument to ignorance (argumentum ad ignorantiam)
The argument to ignorance is a logical fallacy of irrelevance occurring when one claims that something is true only because it hasn't been proved false, or that something is false only because it has not been proved true. A claim's truth or falsity depends on supporting or refuting evidence to the claim, not the lack of support for a contrary or contradictory claim. (Contrary claims can't both be true but both can be false, unlike contradictory claims. "Jones was in Chicago at the time of the robbery" and "Jones was in Miami at the time of the robbery" are contrary claims--assuming there is no equivocation with 'Jones' or 'robbery'. "Jones was in Chicago at the time of the robbery" and "Jones was not in Chicago at the time of the robbery" are contradictory. A claim is proved true if its contradictory is proved false, and vice-versa.)
The fact that it cannot be proved that the universe is not designed by an intelligent creator does not prove that it is. Nor does the fact that it cannot be proved that the universe is designed by an intelligent creator prove that it isn't.
The argument to ignorance seems to be more seductive when it can prey on wishful thinking. People who want to believe in immortality, for example, may be more prone to think that the lack of proof to the contrary of their desired belief is somehow relevant to supporting it.
Using this fallacy is a tactic sometimes used to discredit people who can't disprove your claim. For example, when CBS News anchor Dan Rather was challenged about the authenticity of documents that indicated that George W. Bush had not fulfilled his National Guard duty as an honorable man, Rather was accused of using forged documents to discredit the president. Rather couldn't prove the documents weren't forgeries, but that doesn't prove that they were.* To argue this way is to make an argument to ignorance. Likewise, not being able to prove a document is a forgery doesn't mean it isn't, but given the sophisticated methods of document examiners these days it would go a long way toward establishing the probability that the document is genuine.
Your belief is not provided with any support by the fact that others can't prove to a high degree of probability that what you saw was a spacecraft from an alien world, or what you heard was the voice of your long-dead mother, or that only psychic ability can explain what you've witnessed. Lack of proof that your interpretation of perceptions is incorrect doesn't affect the probability that they're correct.
* I don't mean to imply that none of Rather's critics offered evidence in support of the claim that the documents were forgeries. This example is for illustrative purposes only. (See Little Green Footballs.)