Extraordinary claims require extraordinary evidence
This is a principle of epistemology popularized by Carl Sagan. It states that when considering the validity of a claim, we require more rigorous proof if the claim is especially unusual or implausible.
For example, claiming that "It rained every day in Seattle last week" is not an extraordinary claim, and we might reasonably take the claimant's word as sufficient evidence. However, "It rained every day in the Sahara Desert last week" describes an extremely unusual event. Anyone making such a claim should reasonably expect to be asked for some sort of additional supporting evidence, such as news reports or moisture readings.
The need for extraordinary evidence depends not only on the unusual nature of the claim, but also on the consequences for accepting the claim as true. For example, if somebody claims "I am carrying $5,000 in cash" then you might find this a surprising statement, but it may not be directly relevant to how you behave. On the other hand, if the same person tells you "Please give me the keys to your old car, and then I'll give you this $5,000 in cash from my pocket," you may suddenly become very interested in seeing evidence that this money really exists.
- Direct observation of a supernatural entity would be a highly unusual event.
- Proponents often claim that the supernatural entities violate known laws of science (as in the case of miracles or psychic powers). Therefore, these entities are difficult to square with the way that the universe is understood to work.
- Supernatural claims are frequently attached to substantial demands for changes in behavior.
For example, when a psychic claims that she has used her powers to solve a crime, the cost of checking this claim can be substantial in terms of police manpower. When a priest says "You must give 10% of your income to the church throughout your life," obviously there should be substantial interest in finding out whether there are sound reasons to do such a thing. Even regularly attending church carries an opportunity cost in terms of what you might do with your time if you were not in church.