Karl Popper said a theory lives or dies by falsification — one disconfirming result and it's out. Reality is messier. Newton's mechanics was "falsified" by Einstein, and we still use it every single day. So in what sense did it die?
The honest answer is that science doesn't discard a theory the moment a crack appears; it discards it when something better arrives. Newton still works beautifully at human scales — it's just that Einstein's is more precise and predicts more. Thomas Kuhn pushed this further, arguing science doesn't march by steady falsification at all but lurches through revolutions, each old paradigm valid up to a point. Paul Feyerabend went all the way to "anything goes."
I don't buy the strong version. If it were really anything goes, we wouldn't have pruned our theories of gravity down to two — Newton's and Einstein's — that agree almost everywhere and differ only at the extremes. That's not chaos; that's progress, and the more predictive of the two wins. The trick is keeping straight two things that constantly get blurred. Science advances by falsifying whole theories. Engineering advances by falsifying individual designs: if a bridge stands, it stands, whatever the theory says, and if it falls, no theory will save it. Newton's mechanics failed as fundamental science but remains perfectly good engineering — and confusing those two is where most of the arguments about falsification actually come from.