I like to think of it in terms of classical vs. constructive logic—the former is concerned with truth and falsehood, the latter with provability. In mathematics

I like to think of it in terms of classical vs. constructive logic—the former is concerned with truth and falsehood, the latter with provability. In mathematics you can show that some hypothesis is true or false. In science you can only demonstrate that you have been unable to find an example of anything inconsistent with your hypothesis; that is, in the real world we don’t have the law of the excluded middle: ¬¬P is not the same as P. This also means that mathematics lets us talk about universal properties ∀x∈S.P(x) (“for all x in S, P is true of x”), but science really only gives you existential properties ∃x∈S.P(x) (“there is some x in S for which P is true of x”). The scientific method is based on the idea that enough statements of the form ¬K∃x∈S.¬P(x) (“it is not known that there is an x in S for which P is not true of x”) resulting from a large number of convincing experiments can serve as evidence of ¬∃x∈S.¬P(x) (“there is no x in S for which P is not true of x”) which gives us an approximation of ∀x∈S.P(x).