You’ve heard the saying ‘you can’t prove a positive’. Well, you can’t prove a negative either. This means that you cannot prove that something did not happen or that something is true.
We often hear the phrase ‘you can’t prove anything’, but this isn’t always true. For example, you can prove that someone has lied to you. Or you can prove that someone is telling the truth.
‘You can’t prove a negative’ is a logical fallacy. If you want to prove something, then you should try to disprove it instead. You can’t prove that something doesn’t exist. So why would you want to?
A proof by contradiction is a type of argument which attempts to show that if an assertion is false, then some other statement must be true. In logic, a proof by contradiction is sometimes called a reductio ad absurdum (Latin for “reduction to absurdity”).
A proof by contradiction shows that if a statement is false, then its negation must also be false.
The reason that you can’t prove a “negative” is because there’s no such thing as a “negative”. It may seem counterintuitive at first, but in reality there’s nothing inherently wrong with this idea.
If I say “I’m going to eat pizza”, then I am eating pizza. There is no “not eating pizza”. Therefore, there is no “negating eating pizza”.
This same reasoning applies to all abstract concepts that have no concrete representation.
A negative claim is exactly the opposite of an affirmative one. It asserts that something doesn’t exist or isn’t excluded.
A negative claim may be true or false. Proofs of impossibility and evidence of absence are typical ways to fulfill the burden of proving a negative claim.