"Prior probability" doesn't rely on Bayes's Theorem, but the notion of a Bayesian prior does - it's a deeper concept and to understand it requires things like understanding the prior probability of sequences or prior probability functions. It's definitely not a concept you could acquire without Bayes's Theorem.
Seems pretty odd for this to rely on Bayes Rule. Is that just a temporary thing?
So then should the title of the page be "Bayesian prior"?
"Prior probability" doesn't rely on Bayes's Theorem, but the notion of a Bayesian prior does - it's a deeper concept and to understand it requires things like understanding the prior probability of sequences or prior probability functions. It's definitely not a concept you could acquire without Bayes's Theorem.