[extropy-chat] Indifference (was Coin Flip Paradox)

[gts]

A couple of things, Stu:

1) We're getting ahead of ourselves here; you posted at least two or three  
messages in the last two or three days to which I have not yet fully  
responded. As a result I think you are operating under the false  
assumption, among other things, that I am here trying to defend  
frequentism against Bayesianism. I am not. However I was defending  
frequentism against what I perceived as your false criticisms, e.g., your  
strange idea that contrary to theory, frequencies "orbit chaotically". The  
frequency theory deserves a fair hearing. So does the propensity theory,  
for that matter, which we've still barely touched on.

2) As I mentioned yesterday in private email, I worry that people here are  
getting annoyed with these debates about probability theory, mainly  
because Eugen has rung the warning bell not just once but twice now. I  
don't agree with that style of list management. As far as I can tell we  
are not flaming each other or doing anything else inappropriate and so we  
should be free to continue without questions and interruptions by the list  
managers. However I suspect nobody really cares what I think about list  
management. It might be time to drop the subject or take it elsewhere. I'm  
disappointed about this, but again this isn't about me. A similar thread  
exists on Ben's AGI list, on which this subject is welcome in so much as  
it relates to programming AI, so perhaps that would be the place to take  
it. Are you a subscriber there? In the meantime I've got you on the CC.

That being said, I appreciate your contributions and your post deserves an  
answer...

> That concludes my sloppy logical proof of the
> Principle of Indifference using frequentist rationale.

Because of 2) above I am reluctant to go into detail here as to the reason  
any such argument must fail, except to remind you that the frequency  
theory is an objectivist, non-epistemic account of probability in which  
the epistemic principle of indifference is irrelevant and nonsensical.  
That is, under frequentism the principle it is not even untrue, much less  
true.

A proper proof would be by formal logic, (an epistemic endeavor), which I  
maintain is impossible.

You simply cannot prove that total ignorance about the true state of  
nature gives one any real justification for assigning equal (or unequal)  
probabilities to each of the possible states of nature.

This is so because ignorance does not imply knowledge.

So when we invoke the principle of indifference, we do so without any  
formal justification.

> If this doesn't convince you, you will just have to go through life not  
> believeing
> in the Principle of Indifference.  :)

In that case I would go through life in good company, including the  
company of subjective Bayesians who know better than to imagine logical  
truth where none exists.

-gts