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 ...

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/