Nevertheless the saying is clearly false.
A saying only has a meaning if it can be verified or falsified. The only way to falsify the saying would be to find something which really fools everyone all the time. But as soon as you realise it is fooling us, there is someone who has realised that it was foolery. As there is no theoretical way of falsifying the saying, it must be void.
And what does "all the time" mean? If it means "during the full lives of a generation", then we actually do have an example of something that fooled all of the people all the time: the saying itself. People have believed it for well over the lifetime of several generations since Lincoln died.
A paradox is a statement that can be neither true nor false. Lincoln's saying is not even a paradox, because it is false. And as he probably did not say it, it is not even a saying.
Anyone who believes the opposite is fooled.
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