Suppose I tell you that “Screeds exist.”
Then you ask some questions and it turns out that what I mean by “screed” is something that is bleen, croom, and weeq.
Then you ask some more questions about the terms bleen, croom, and weeq. It turns out that those terms mean, “reptile,” “married,” and “bachelor,” respectively. So here’s the disproof:
1. Suppose that X is a screed. Then it would follow that:
2. X is bachelor, and
3. X is a reptile.
4. Bachelors are unmarried, adult human males. So,
5. X is human (by 4) and X is not human (by 3)
6. X is unmarried (by 4) and X is not married (by 3—reptiles can’t be married.)
7. Contradictions are impossible. Nothing can both have a property and not have it.
8. Nothing contradictory can exist.
9. Therefore, screeds cannot exist.
We just proved a negative. What’s the problem, exactly? Why is it that the urban myth that “you can’t prove a negative” persists, and persists, and persists?
For centuries, nonbelievers have been giving deductive proofs for the impossibility of God that demonstrate that there is no God using a strategy like this. But rather than actually consider any of those attempted disproofs, the widespread practice is to simply declare “Everyone knows that you can’t prove a negative.” That’s complete nonsense. We can and do prove negatives of all sorts—ask any mathematician. How do you think they conclude that some piece of mathematical reasoning is flawed. If I present you with a complicated logical formula like this one: ~(~a --> ~b) --> ((~a --> b) --> a)) do you think you can simply declare that it is true because “You can’t prove a negative”? It turns out that this formula is contradictory so we can prove that it must be false.
So if the concept of God is logically contradictory, which many people have argued, then we can prove the negative. For a recent collection of articles purporting to do just that, see Martin and Monnier’s anthology, The Impossibility of God.