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Sigh. What logical fallacy actually means is that something seems to prove something 100% but that is not the case
John wears a coat in the winter.
A person walks into Johns house in the winter wearing a coat.
That person must be John.
This is a logical fallacy because the criteria do not prove 100% the conclusion.
But obviously, it doesn't prove the person isn't john either.
Logical fallacies never, ever prove that something is not true.
Actually when something is guilty of a fallacy, the assumption that thing is not true is called the Fallacy fallacy, a name I find pretty awesome.
That's an undistributed middle, which is a real logical fallacy. Your syllogism is invalid. Most people don't know logic, and very rarely are such fallacies invoked.
The point you missed is that "logical fallacy" never disproves something.
Shitty internet poster response is to claim that slippery slope "disproves" something but all it actually show is that it's not 100% proven. Yeah slippery slope means it doesn't go there 100% of the time, but when it's 80% instead that's hardly disproving it.