Talk:Cox's theorem

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Geometry guy 22:55, 16 June 2007 (UTC)

I've added a section about the laws of probability that are derived from Cox's postulates, following Jaynes's exposition. I make a remark about finite and countable additivity that someone else may wish to review. Wile E. Heresiarch 17:39, 8 Jan 2004 (UTC)

As noted by Mike Hardy, lines with both TeX and plain text don't look so good. One possibility to fix that up would be to format the lists entirely as equations (using matrix since eqnarray isn't supported). I think I'd prefer that to trying to make it all work out in plain text. Just a matter of taste. FWIW, Wile E. Heresiarch 23:45, 8 Jan 2004 (UTC)

- I've fixed up the equations to use only plain text (not TeX). Wile E. Heresiarch 18:00, 9 Jan 2004 (UTC)

I may be missing something here, but "All strictly increasing associative binary operations on the real numbers are isomorphic to multiplication of numbers in the interval [0, 1]. This function therefore may be taken to be multiplication." seems strange. Shouldn't this be "decreasing" operations? Multiplication in the interval [0, 1] is not increasing (e.g. 0.5*0.5 = 0.25) and neither is P(A and B) ("both A and B are true" is never more plausible than "A is true"). 82.103.195.37 21:00, 15 June 2006 (UTC)

It's an increasing function of each variable separately, i.e., xy increases as x increases (with y fixed). Michael Hardy 01:08, 16 June 2006 (UTC)

... and Pr(A and B) increases as the event A increases, i.e., if

$A_1 \subseteq A_2 \,$