I agree with Joe and others: this thread is much more valuable if it doesn't turn into yet another I love/hate religion. Let's stick to discussing logic.

There is an excellent example of good real world results from bad premises in geometry and its derivations. This is the 5th proposition of Euclid. For millennia, people took it as a premise and most of science, including all Newton's work, for example, and all technology assumed it. But many mathematicians were not happy with it: they accept it, but believed it must be provable. So at times and up to around 1840 they tried a process known as 'reductio ad absurdum' which involves assuming it is not true and showing that introduces inconsistencies. But eventually it was accepted that there are several other, equally valid, geometries, not just the Euclidian.

Now Steve and others may well say this is another example of science-related subject adapting as understanding increases, and I would not disagree. But the point is that we managed perfectly well for millennia on a false premise and got useful things out of it.