[extropy-chat] Indexical Uncertainty

[Robin Hanson]

At 04:26 AM 10/18/2006, Russell Wallace wrote:
>The main reason to be interested in and think about indexical uncertainty
>is not because people in our world often have large degrees of such
>uncertainty.   The reason to be interested is that it opens up a new family
>of counterfactuals to reason about.   Postulating and applying rationality
>constraints that relate the reasonable beliefs under different counterfactuals
>is a powerful way to constrain the beliefs we should find reasonable.
>
>But the one does not imply the other.

Which claim is "one" and which is "other"?

>That we can postulate a mind of sufficiently low (dreaming) or 
>distorted (insane) consciousness as to genuinely not know whether 
>it's Russell or Napoleon doesn't mean I (the entity currently 
>thinking these thoughts) could have been Napoleon, any more than the 
>number 3 could have been the number 7. If you doubt this, consider 
>the extreme case: a rock doesn't know whether it's me or a rock. 
>That doesn't mean I could have been a rock.

A possible world specifies answers to all relevant questions.   That 
is, it should be straightforward to figure out, if that world were 
the true one, what the answer to any specific relevant question 
is.   So the problem with postulating "3=7" in a world is that 
ordinary math has clearly been thrown out in that world.  Thus to 
make sense of this world we need to also specify some other way to 
answer relevant math questions.   This is awkward, but for some 
purposes can be useful.

Counterfactuals are untrue claims useful to an analysis.   So clearly 
the mere fact that a counterfactual claim is not true is not a 
sufficient basis to reject it from consideration in an analysis.  I 
see three obvious reasons to reject a counterfactual:
1) it is ambiguous which possible worlds are intended to be included 
or excluded by this claim,
2) the relevant possible worlds are themselves not clear, not giving 
us a straightforward way to answer relevant questions, or
3) the claim is not relevant to some purpose, so that ignoring it 
won't change the results.

We also have one strong reason for considering a 
counterfactual.  This is when we are analyzing the reasonable beliefs 
of an agent who is not entirely sure that the counterfactual is in 
fact false.  It is hard to get such analyses right without including 
the possible worlds that the agents themselves are considering.

I don't see that any of these reasons for rejection apply to the 
counterfactual claim that I (or you) are Napoleon.   And I can 
imagine situations containing agents who are not sure they are 
false.  So I don't yet see a basis for rejecting such counterfactuals.




Robin Hanson  rhanson at gmu.edu  http://hanson.gmu.edu
Associate Professor of Economics, George Mason University
MSN 1D3, Carow Hall, Fairfax VA 22030-4444
703-993-2326  FAX: 703-993-2323