How do you know the solution is any good? I'm not going to go all Socrates on you so I'll jump to my point: when discussing bayesian statistics, we're touching

How do you know the solution is any good? I'm not going to go all Socrates on you so I'll jump to my point: when discussing bayesian statistics, we're touching something very profound about epistemology that can't be swept under the rug in the name of pragmatism. We're dealing with the core philosophical underpinnings of what it means to "know" something.