At 09:16 13/01/05 -0500, Danny Mayes wrote:

Could you explain this  last line?

Bruno Marchal wrote:

At 10:24 13/01/05 +1100, Stathis Papaioannou wrote:

As for the "failure of induction" if all possible worlds exist, I prefer to simply bypass the problem.



Mmm... I think you make the same mistake as David Lewis (In the plurality of worlds, but in
"counterfactuals" it partially fix the mistake ...).
You bypass the most interesting problem which actually makes refutable classes of mathematical "theologies".


I will try. I will also try to be short and you can consult
my URL for more explanations including posts to this list.
The starting point is the assumption that I (we, you) are turing emulable.
Now computations are mathematical objects, and with some amount
of arithmetical realism or platonism all computations exists in the
same sense that all constructive reals exists. But some thought
experiment show that if we are turing emulable then we cannot know
which computations support us. Both Stathis and David Lewis are aware
that with a many-worlds postulate, or even just with many
computations postulates, there is a "failure of induction"
problem. Indeed, a priori, if you make induction from all the computationnal
histories going through your states you get many "white rabbit stories" if not just
"white noise", unless you discover that computations and observer relative
to them are highly non trivial mathematical object so that the "induction"
problem could perhaps be solved technically (and indeed progress has
been made and sometimes I make attempt to convey a little bit of it).
Solving the induction problem means in this context that we are able to
justify why the average observer can predict some normal (reversible, linear)
computation at the bottom and below.
'The term "theology" could be justified because it reminds us that once you
accept the idea that your immediate most probable "future" consistent
extension is determined by a mean on all your 2^Aleph0 maximal
consistent extensions, and that you "survive" always on the most normal/near
comp history, then the "dying"notion seems to belong to the category
of wishful thinking (making us more ignorant). But "theology", in this context
can also just be defined by the study of what machines can correctly (or just
consistently) prove and infer about themselves and their most probable
computations, and here deep results in mathematical logic and in theoretical
computer science give huge lightning (but necessitate of course some
math work). (Now I am not sanguine about any words but I recall the term
"theology" had been used by Plato to mean the study of the Gods, and then
if you are willing to believe (with Alan Watts) that we are all Gods ...


And, (this I add to John Mike, if you permit Danny,) when I say we are
Gods, John, I don't see any reason to limit the understanding of "we" to
the humans. You know I talk on something far larger yet non trivial.

Bruno

http://iridia.ulb.ac.be/~marchal/



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