In Why Falsifiability, Though Flawed, Is Alluring: Part I , William M. Briggs argues that “most theories scientists hold are not falsifiable” because “if the predictions derived from a theory are probabilistic then the theory can never be falsified. This is so even if the predictions have very, very small probabilities. If the prediction (given the theory) is that X will only happen with probability ε (for those less mathematically inclined, ε is as small as you like but always > 0);, and X happens, then the theory is not falsified. Period. Practically false is (as I like to say) logically equivalent to practically a virgin.“
I think he’s right – at least if “falsifiable” means “provable to be false”. But I don’t think most scientists really demand scientific theories to be falsifiable in that sense. And many don’t even try to use that word any more; they are more inclined to use a less binding word like “testable”.
A theory might then be considered adequately testable if it can be used to predict that in some repeatable experiment there are outcomes of very low probability. If, after identifying such an outcome, we see it actually occur, then we say that the theory fails the test (though it could in principle still be true) and we reject it (ie strongly doubt it) – at least until the relative frequency of failure events in repeated experiments falls to somewhere near their predicted probability.