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Calculus had poor foundation and was thus logically incoherent from Newton/Leibniz' discovery to roughly the middle of 19th Century. None-the-less it was a powerful tool and most of the key theorems were discovered then.

The basic situation, I think, is a set of tools can be consistent in the way mathematicians use them but in the way the mathematicians explain them. And the tools can be very useful despite this.

So my guess is saying "it has poor foundations" isn't saying "I'm against it, it's worthless"



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