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As far as I am aware, Falsifiability is generally held to have overcome the problem of induction, and
acts as the criterion of demarcation between science and non-science, despite its critics.
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Popper invented it. But in the rest of your question you're barking up the wrong tree. Falsification has
to do with proving scientific hypotheses. In his youth, members of the Vienna Circle had
propagandised the notion that philosophy should accept nothing as true that cannot be positively
proved to be true. When Popper examined this issue he realised that this is impossible: science can
prove practically nothing to be true, it can only prove that something is false. So it is not a
methodology as such, but an idea or principle, to be applied to every scientific experiment: the
experiment, if it successfully proves some hypothesis or theory false, can be said to have achieved a
truth. Finally, the connection to induction is that truth is impossible of proof precisely because 1000 or
a million experiments can never be accepted as truth as long as the possibility exists of just one
contradictory result. Induction therefore is only what Bacon originally wanted it to be: a collection of
facts usable for a working hypothesis. It confers no guarantees.
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