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When Science Can't Help

A good way I've found to explain this to lay people is that Science is a very high quality way of finding out what is almost certainly wrong. If Science says something is wrong and here is why, then it most probably is correct (relative to other methods of finding truth that is). Science is much worse at figuring out what is right because it's method of determining what is right is "Of all the possible hypotheses, we'll eliminate the wrong ones and choose the most probably of what exists". As a result, scientific knowledge is often over turned and revised as it should.

But what people outside of Science can't see is that almost never is a theory overturned for one which was previously considered wrong, it's usually the case that the new explanation is one that was never ruled out but considered less than probable. What this means is that, from outside of science, it's very hard to tell the difference between two very similar statements: "What you're saying is wrong because you don't have sufficient evidence to justify your claims" and "What you're saying is wrong because we've already discounted that hypothesis and here's why". Scientists can see that difference very clearly and behave in very different ways according to which argument you're making but to the outsider, what it looks like is arrogance and close-mindedness when Scientists reject an explanation without even bothering to give it the dignity of argument.

A more succinct way of putting this is that "Science can never prove than God does not exist but it has proved that your God does not exist"