Onus of Proof Principle
A venerable rule of logic which states that: the onus of proof is on him who asserts the positive, and that one must not attempt to prove a negative. Knowledge is not the default state; ignorance is. Therefore, to claim knowledge, one must demonstrate that the necessary cause — awareness — is present and operative. It is because man is not infallible and omniscient that he cannot ever validly assert arbitrary declarations.Because he's not infallible, he must adhere to the correct epistemological rules to claim that anything is true.
The onus of proof rule states the following: If a person asserts that a certain entity exists (such as God, gremlins, a disembodied soul), he is required to adduce Evidence supporting his claim. If he does so, one must either accept his conclusion or disqualify his evidence by showing that he has misinterpreted certain data. If they offer no evidence, their claim should be dismissed without further discussion. [1]
You cannot "prove a negative," meaning by the term: prove the nonexistence of an entity for which there is no evidence.
[...] A thing that exists is something; it is an entity in the world; as such, it has effects by which men can grasp and prove it—either directly, by perceptual means, or indirectly, by logical inference. A nonexistent is nothing; it is not a constituent of reality, and it has no effects. If gremlins, for instance, do not exist, then they are nothing and have no consequences.[2]
It's important to understand what is meant by a "positive" claim. It doesn't necessarily refer to something grammatically positive. For example, "the man is innocent" and "the man is guilty" are both grammatically affirmative. However, "the man is guilty" is the positive claim because it asserts the existence of a certain phenomenon (the crime). In contrast, "the man is innocent" is a negative claim because it denies the existence of that phenomenon. The onus of proof requires that if you claim something exists, you must provide evidence.
What does not require justification is non-consideration; that is the default state. One needs a reason to consider, not a reason not to consider. To know something, one must have used the means of gaining knowledge: evidence. That is all that the Burden of Proof Principle states.
All thought, argument, proof, refutation must start with that which exists. No inference can be drawn from a zero. If a person offers evidence for a positive, one can, if the claim is mistaken, identify his misinterpretations and in that sense refute him. But one cannot prove the corresponding negative by starting from a void.
[...] One can infer from any truth the falsehood of its contradictories. For example, from "X was in New York during the Dallas shooting of Y" one can infer the falsehood of "X shot Y." Thus one can disprove a claim or "prove a negative" ("X is not guilty")—but only by demonstrating that the claim contradicts established knowledge; i.e., only by relating the claim to a positive cognitive context, when this is available. What one cannot do is prove a negative apart from such a relationship; what one cannot do is establish the falsehood of an arbitrary claim qua arbitrary. One establishes the false by reference to the true, not by reference to nothing.[3]
The principle also extends to possibilities. To claim that something is possible, one must provide evidence supporting the possibility.[4] Arbitrary assertions, such as the existence of supernatural entities or the occurrence of events without evidence, cannot be considered without substantiation. This principle emphasizes that "proving a negative," in the sense of refuting an arbitrary claim, is impossible. In practical terms, the Onus of Proof Principle means that one does not need to provide reasons to disbelieve unsupported claims. The claimants must provide evidence for their assertions.
Objectivism's refutation of theism is not a case of "proving a negative" in the sense vetoed by the onus-of-proof principle. Ayn Rand does not start with a zero and seek to discover evidence of God's nonexistence. She starts with reality, i.e., with (philosophically) known fact, then denies a claim that clashes with it. Nor does she expect any such refutation to be accepted by apostles of the arbitrary. These individuals will merely reformulate the claim so as to protect it from evidence, then insist again: "Prove that it is not so." To this demand, there is only one valid response: "I refuse even to attempt such a task." An assertion outside the realm of cognition can impose no cognitive responsibility on a rational mind, neither of proof nor of disproof. The arbitrary is not open to either; it simply cannot be cognitively processed. The proper treatment of such an aberration is to refrain from sanctioning it by argument or discussion.[5]