[extropy-chat] Coin Flip Paradox

gts gts_2000 at yahoo.com
Wed Jan 31 18:30:42 UTC 2007

> That Bayes law cannot predict outcomes reliably in an
> informational vaccuum is not at all a weakness of the
> principle.

To be clear, I am not here arguing against Bayes' theorem.

I am arguing that the principle of indifference sometimes invoked by  
Objective/Logical Bayesians, (not to be confused with Subjective  
Bayesians), and by other logical theorists of probability (those who take  
after John Maynard Keynes) in the complete absence of information is not a  
principle of logic in the formal sense of that word.

Subjective Bayesians may use the same principle, but they are wise enough  
in my opinion to know better than to think the principle of indifference  
can be derived or supported by formal logic.

Think about it (and you too, Jef)...

On what logical grounds can proposition A imply or entail proposition B?

A: "No information is available about the true probabilities of the two  
possible outcomes X and Y."

B: "Outcomes X and Y are therefore equiprobable."

Does A imply B, logically? I think not! If you or Jef can show me  
otherwise then please do.

The principle of indifference looks to me like illogical hocus-pocus, pure  
nonsense left over from the naive theory of Laplace. It may still be  
useful as a heuristic device, but let's call a spade and spade here!

If the principle looks like a beautiful and elegant principle of logic to  
some people then, well, too bad for them. :)


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