conversation with a Bayesian

From: Wei Dai <weidai.domain.name.hidden>
Date: Tue, 20 Apr 2004 01:07:11 -0400

This is an imaginary conversation between me and a Bayesian. His answers
are in parenthesis. Do you find this line of argument convincing?

----
Consider all possible worlds consistent with your memories and current 
experiences. In other words, all possible worlds that contain at least one 
observer with memories and current experiences exactly identical to yours. 
Are there more than one such world?
(yes)
Is every one of these worlds isomorphic to some mathematical structure?
(How do you define "mathematical structure"?)
A set class.
(then yes)
What criteria would you use to decide which of these possible worlds is 
actual, given that they are all consistent with your memories and current 
experiences?
(more observations, experiments)
Ok, but after every new observation or experiment, there will still be 
more than one possible world that is consistent with the new emperical 
result, right?
(yes)
So then what?
(apply Bayes's rule)
Where does the prior come from?
(???)
Do you assign a non-zero prior to the class of all sets being the actual 
world?
(yes)
Pragmatically, how does that differ from assigning a prior of 1 for the 
class of all sets?
(What do you mean by "pragmatically"?)
I mean are there any circumstances in which you'd act differently if you 
assigned a prior of 1 instead?
(no)
So why not just assume that the actual world is the class of all sets?
(My principles of reasoning do not allow me to do so.)
If you go back and look at how those principles of reasoning were derived 
or justified, it was on the basis of simplicity and avoiding absurd 
actions ("absurd" being defined by intuition or common sense). The 
assumption that the actual world is the class of all sets is equally 
justified on the basis of avoiding absurd actions and is simpler than 
having a prior over possible worlds, so why not?
(...)

Received on Tue Apr 20 2004 - 01:13:22 PDT