You’ve probably encountered atheists who say, “There is no God” and then insist that the burden of proof is on you, the believer, to prove it wrong since you’re the one claiming that God exists.
That’s not how it works.
Atheists frequently confuse “positive” (philosophy) with “affirmative” (grammar), which is why they think “There is no God” isn’t a positive statement. That’s how they try to push the burden of proof to the God-believer after they make their claim.
“There is no God” is a negative statement in the grammatical sense, but the opposite of this — grammatically — is not a positive statement, but rather an affirmative statement. An affirmative statement in grammar is a statement that asserts the truth of something. Its opposite is a negative statement, which asserts falsity. For instance, “George Washington was the first President of the United States” is an affirmative statement, while “Benjamin Franklin was not a President of the United States” is a negative one. They are, however, both positive statements in the philosophical sense.
A positive statement in philosophy is a statement that is (at least ostensibly) based in fact and is subject to empirical testing. Some examples of positive statements:
“The average donut contains 500 calories.”
“There is no eighth continent.”
“Dinosaurs once existed on Earth.”
“The Earth is flat.”
Note that the statement doesn’t have to be affirmative or even true to be a positive statement, it just has to be based in fact and subject to testing. For instance, “There is no eighth continent” is a positive statement, because it makes a factual claim that is subject to testing. If a person were to make such a claim, he would then be obligated to show evidence of its truth. Satellite images of the Earth’s surface clearly showing only seven continents would suffice. “The Earth is flat” is a positive statement — it’s ostensibly based on fact and it’s subject to testing — even though it’s demonstrably false.
Positive statements that assert the non-existence of something are notoriously difficult to prove, which is why people don’t often make them, at least not seriously. While few people would contest the statement, “There are no rainbow-farting unicorns,” it’s actually difficult to prove, since you would have to have knowledge of everything everywhere on Earth to do so. This is why savvier atheists don’t fall into the trap of stating that there is no God. They will instead say that God’s existence is doubtful, laughable, risible, etc., which they know are much more supportable statements than God doesn’t exist.
“There is no God” is a positive statement. Whoever makes such a claim therefore has the burden of proof. If anyone denies this, he doesn’t understand the difference between positive and affirmative statements — or he thinks you don’t know the difference. If you find yourself with an argumentative atheist making this statement, point out his error and give him the opportunity to either retract it or to supply the proof.