I’ve always wondered why some people in Bayesian statistics still use the archaic term ‘a-priori’ for prior probabilities. Does it carry a special meaning that ‘prior’ doesn’t capture? Is there some philosophical reference behind it?
Edwin Jaynes, in Chapter 4 of his Probability Theory book, offers an interesting remark:
“The term ‘a-priori’ was introduced by Immanuel Kant to denote a proposition whose truth can be known independently of experience; which is most emphatically what we do not mean here.”
While I can’t confirm Kant was the first to use the term — it likely predates him, going back to medieval scholastics — Kant certainly gave it a strong philosophical weight. If Jaynes’s claim is right, it clarifies a common source of confusion: equating prior probabilities with absolute, mind-independent truths.
As Jaynes stresses, this is a misunderstanding. Probability theory is a logical framework for reasoning under uncertainty — it reflects our knowledge, not objective reality. This ties into what he calls the mind-projection fallacy: projecting our subjective ignorance onto the external world.
So what does it even mean to assign a probability to something a-priori, if a-priori truths (in the Kantian sense) are always true? That’s the contradiction the phrase invites — and why perhaps it’s time to retire it.