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    It absolutely answers the question. Note that referring to rainwater he says "such waters are naturally the best. But..." I think we can safely infer that water which is less good (ie not the best) also should be boiled. Commented Jun 10 at 16:42
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    On how people might have discovered this without germ theory: Many harmful contaminants are easily perceptible by sight, taste, or smell, and it’s easy to discover (by accident or guesswork) that filtering and boiling can perceptibly improve these. (Anyone who’s been wild-camping can confirm this.) It’s a natural guess (under most theories of the mechanism, or just as trial and error) then that the boiling will also improve water that’s bad in less-obvious ways. Commented Jun 11 at 11:57
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    In general, foul taste is associated with harmful effects, because our senses of taste and smell evolved to help us distinguish good foods from bad. So it was natural for them to associate the improved taste of purified water with health benfits.
    – Barmar
    Commented Jun 11 at 14:29
  • Neither filtering nor boiling will remove the salt from seawater. That Aristotle guy would have been a lot smarter if he'd just googled that.
    – user121330
    Commented Jun 12 at 16:41
  • There's definitely a lot Aristotle got wrong. Logic will only take you so far if you've built your case on bad premises.
    – cmw
    Commented Jun 12 at 17:04