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Caledonian2 comments on Science Isn't Strict Enough - Less Wrong
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Knowing an estimated probability of a thing is not the same as knowing the reality of the thing. Whether the estimation is precise or not is irrelevant. The woman either has breast cancer, or she does not have breast cancer - there is no 'probability' about it.
Statistical analysis suggests that there is a 7.5% chance the woman has breast cancer. What does that mean? It means that whether she has breast cancer or not is unknown. You do not believe that she does not have breast cancer. You do not believe that she does have breast cancer. You do not have enough evidence to justify either conclusion.
It's always unknown. There is nothing that could possibly happen that will make you absolutely certain. If you want to be sane, you must learn to make decisions with incomplete information. If you want to do this in a sane manner, you must follow the laws of probability.
Fallacy of Gray. Just because probabilities can't exactly equal 0 or 1 doesn't mean you shouldn't say “I know she has cancer” if the probability is 99.999%. (And, answering to the grandparent, if I say “I believe that she does not have cancer” I just mean that the posterior probability of her not having cancer given everything I know is greater than 50%.)
That's my point. If you treat all shades of gray the same, the result is insanity. If you treat all shades of gray in any manner that doesn't follow the laws of probability, the result is insanity.
You can use "believe" that way, but you can't act like everything is true iff it has a higher than 50% chance. You wouldn't want to leave someone untreated on the basis that they only have a 49% chance of having cancer.
I said "believe" not "assume"...