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I find it plenty useful to assume that some things are predictable, that some things aren't, that other things are predictably unpredictable and that some things are unknowable. Based on these classifications i try to draw conclusions from experiences that i've had.
I find the concept of proof in an abstract sense to be rather off-putting. You need a structure in which to hang the proof; a set of assumptions. Then if you want to prove these assumptions valid you need a larger set of assumptions on which to hang this super-proof. It goes on forever, so i think the general idea is that you only do it as much as you need to.
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