I'll prefix my point by saying I'm not one of those people who think all reasoning should (or can) be Bayesian, but here, I think it applies at least as an anal

I'll prefix my point by saying I'm not one of those people who think all reasoning should (or can) be Bayesian, but here, I think it applies at least as an analogy. In what you call "real world reasoning", you never have the amount of logical rigor that you get when going from mathematical axiom to theorem. Instead, there are always varying degrees of knowledge, certainty and understanding. In such a setting, it's very easy to imagine a new, non-contradicatory fact pushing a conclusion from 80% certainty down to 40% certainty.