Let's not and say we did.
Recall I'm a lawyer fighting a fairly lonely battle for sound science in the courtroom. So let me tell you; abandoning Popper and falsification (i.e. rejecting Daubert v. Merrell Dow) and going to a subjective "more likely than not belief" standard is nothing but a recipe for handing billions more over to the already super rich trial lawyers (several of whom are starting to report to prison, along with their experts, for the perjury, bribing of judges, etc that went on back in the bad old days).
Alas. The claim that "science can't prove anything for sure so let's allow "experts" to testify about what they believe and have the jurors sort it out" is starting to surface in cases I work on. In those cases, self-proclaimed experts charging $500/hr or more per hour to testify to their beliefs, which allegedly arise out of the penumbras of their expertise, and which correlate precisely with the position of the side that hired them, are already cashing in. The law will not appreciate the niceties of the argument here and it won't be long before we have PhDs testifying that MRI machines damage ESP powers ... again. (My personal favorite was an expert in New York who was allowed to testify that C6H6 made synthetically was toxic at the one molecule dose level but that C6H6 generated by the body was not because "natural" benzene had a "life resonance electron level" which kept its "electron cloud in a harmless state". He believed it and believed it strongly so he got to testify to it because he is an MD/PhD.)
So just say "Hell NO!" to "subjective degrees of belief", or anything similar, as the standard definition of science in tort cases .... and that's what it will be if "science" says that's what real science is. Unless you're a trial lawyer who files his cases in a poor rural area it will cost you beaucoup otherwise. I get the distinction but most won't and the scoundrels will have a field day.
New Scientist on changing the definition of science, ungated here:
I'm a good deal less of a lonely iconoclast than I seem. Maybe it's just the way I talk.
The points of departure between myself and mainstream let's-reformulate-Science-as-Bayesianism is that:
(1) I'm not in academia and can censor myself a lot less when it comes to saying "extreme" things that others might well already be thinking.
(2) I think that just teaching probability theory won't be nearly enough. We'll have to synthesize lessons from multiple sciences like cognitive biases and social psychology, forming a new coherent Art of Bayescraft, before we are actually going to do any better in the real world than modern science. Science tolerates errors, Bayescraft does not. Nobel laureate Robert Aumann, who first proved that Bayesians with the same priors cannot agree to disagree, is a believing Orthodox Jew. Probability theory alone won't do the trick, when it comes to really teaching scientists. This is my primary point of departure, and it is not something I've seen suggested elsewhere.
(3) I think it is possible to do better in the real world. In the extreme case, a Bayesian superintelligence could use enormously less sensory information than a human scientist to come to correct conclusions. First time you ever see an apple fall down, you observe the position goes as the square of time, invent calculus, generalize Newton's Laws... and see that Newton's Laws involve action at a distance, look for alternative explanations with increased locality, invent relativistic covariance around a hypothetical speed limit, and consider that General Relativity might be worth testing. Humans do not process evidence efficiently—our minds are so noisy that it requires orders of magnitude more extra evidence to set us back on track after we derail. Our collective, academia, is even slower.