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I stumbled upon this very interesting article :

Whose aim is to provide new axioms for probability theory that allow for a trivial and rigorous proof of Cox's theorem.

However, I really don't understand the motivation for theses 5 axioms, and what part of my "common sense" they should correspond to.

Anyone could make the link between those and my intuition? Possibly using knowledge of existing probability theory, bayesian or frequentist concepts.

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    $\begingroup$ why would you need this in layman terms? $\endgroup$ – Aksakal May 1 '18 at 14:15
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    $\begingroup$ @Aksakal, your comment made me think that "layman term" was not the right way to say what I want. I edited. I just want to understand why those axioms are "reasonable" intuitively. $\endgroup$ – Julien__ May 1 '18 at 14:29
  • $\begingroup$ People have been arguing back and forth for centuries around these notions, I doubt an "intuitive" presentation can be found... $\endgroup$ – Xi'an May 1 '18 at 20:01

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