According to the late Bertrand Russel, there is a scandal at the root of probability theory: it is the scandal of induction.
Simply stated, the problem is that what has been verified a finite number of times has no reason to be verified beyond these occasions!
Because we can only make a finite number of experiments, we can never really infer from experiment the validity of any statement. Exit the frequentist interpretation of proability theory, which sees the probability for any event as the limit of its frequence. And other interpretations of probability would also appear not to make sense.
Now this is slightly embarassing.
And not the least because our second most successful scientific theory, quantum theory (you can probably guess what the first is?), tells us that our universe is fundamentally probabilistic (Feynman seems to never have fully overcome a certain reluctance for this feature of the theory, a feature he once half-jokingly called an abomination). Well but it's ok, because nobody really understands QT.
Could two scandals cancel each other? Well, some prominent scientists such as David Deutsch think that the scandal of induction is problematic for all but one interpretation of QT, namely the many-world interpretation. That's an idea worth tracking, although the many world interpretation is obviously completely crazy (and thus unsurprisingly, favoured among physicists).
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