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I am a math student and I don´t understand one thing. If scientific hypotheses can be falsified, why not falsify the negation of a hypothesis, proving the original conjecture?

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    Does this answer your question? If we can falsify hypothesis, cant we verify them by falsifying their negation?
    – user64708
    Feb 17, 2023 at 12:46
  • Yes, it does. ...
    – Adam
    Feb 17, 2023 at 13:43
  • An ideal model of empirical reasoning is Bayesian inference. In Bayesian inference, observations may increase the probability of a hypothesis or decrease it. We might never be 100% certain that a hypothesis has been verified or falsified, but if observations push the probability arbitrarily close to 1 or 0, then we can say it has been approximately verified or falsified. Even "All ravens are black" cannot be perfectly falsified by sighting a white raven, because you can't be certain what you have seen is not a trick of the light, or a different bird that is just similar to a raven.
    – causative
    Feb 17, 2023 at 13:45
  • @Adam then I guess you should either close or delete it (I'm not sure which is the standard procedure, search Meta if in doubt) for avoiding duplicates. Next time remember to search before asking.
    – user64708
    Feb 17, 2023 at 13:48
  • It depends on the logical form of the hypothesis. Universal statements ∀xP(x) can be falsified (by counterexamples) but not verified (one cannot possibly test all instances), existence statements ∃xP(x) can be verified (by examples) but not falsified (that an instance has not been encountered does not prove that it cannot be in the future). It is just that universal statements are typically of more scientific interest. More complex statements with nested quantifiers, like ∀x∃yP(x,y), can be, strictly speaking, neither verified nor falsified.
    – Conifold
    Feb 17, 2023 at 18:35

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