When you’re trying to prove something, nine times out of ten you aren’t using only deduction, which is taking general rules and applying them to a specific case. Most of the time, you can’t just take rules you already know and apply them- you have to find some evidence. That evidence could be a news article, an action you see another person take, or some fact you think you remember from a book somewhere. You can use those pieces of evidence to prove that a politician is bad, a person is violent, or any number of other things. In all of those cases, the evidence you use is an example of the thing you are trying to prove. Like, of course it is. If you want to find evidence for the idea that pie tastes good, you have to go out and find some yummy pie. How else could you find out if pie tastes good? Well, according to this paradox, if you taste some disgusting brussel sprouts, you have already gathered some evidence for the idea that pie tastes good.
Let’s say, for example, that Dave wants to prove that all ravens are black. Dave could go on a walk, find a raven, and check if it is black or not. That would be gathering evidence. But let’s say that Dave is very lazy, and he wants to find evidence without leaving the couch. Well, after giving it a good think, he realizes that he can. Here’s how.
As I said before, Dave wants to prove that the statement ‘all ravens are black’ is true. As it turns out, that statement leads directly to the statement ‘everything that is not black is not a raven’. This make sense if you stare at it for a bit. If every single raven is black, then an object that is some other color, like red, cannot be a raven. By saying ‘everything that is not black is not a raven’, all Dave has done is restate ‘all ravens are black’ in a weird way. So, if Dave gathers evidence for the idea that ‘everything that is not black is not a raven’, he has also gathered evidence for the idea that ‘all ravens are black’.
Laying on the couch, Dave prepares to go do some ornithology. Sitting up a tiny bit, he opens his eyes. The first thing he sees is a red book. This is an object that is not black, and, with sharp wit and pure genius, he realizes that a book is not a raven. Satisfied, he lies back down.
Dave has found a case where something that is not black is not a raven. This is obviously evidence for the statement ‘everything that is not black is not a raven’, which means that it is also evidence for the idea that ‘all ravens are black’.
Now, the reasoning in this paradox is rock-solid. Once you’ve gone through it, you’d have a very hard time trying to argue with it. And yet, if you tried to prove that the Harry Potter books are good using the evidence that Fifty Shades of Grey is bad, I doubt your friend would be convinced. It’s an interesting example of something that works logically, but doesn’t match up with our natural assumptions about how things work.