The EPL Theorem (all parts)
Links and an acknowledgment
Links to all 5 parts of this series.
Since I forgot to mention it earlier, let me acknowledge here that the EPL Theorem was inspired by Aubrey Clayton and Travis Waddington’s paper, “Bridging the intuition gap in Cox’s theorem: A Jaynesian argument for universality.” Their paper proposes alternative requirements that they argue are more intuitively reasonable than those of Cox’s Theorem, to arrive at the same result as Cox. Thinking about their proof, and how the number of requirements might be reduced, led me to the EPL Theorem.
One of the important ideas they use is invariance under consistent renaming of all propositional symbols occurring in either the query 𝐴 or premise 𝑋 of a plausibility expression (𝐴 | 𝑋). Their proof also yields the classical definition of probability—as the ratio of the number of positive cases to the number of possible cases—as a theorem for certain cases they call “𝑁-urns.” The most important innovation of my proof was to show how to reduce every allowable query-premise pair to a certain kind of N-urn.