Le 22-juin-05, à 21:23, daddycaylor.domain.name.hidden a écrit :
> Jesse, it seems to me that starting from a set of axioms, like the
> concept of a measure on observer-moments and "hope that somehow the
> appearance of a phyical universe can be recovered" is problematic in
> light of the upward and downward Lowenheim-Skolem theorems. Taking
> this into account, it seems that you can't conclude anything about the
> cardinality of the some aspect of the universe model's domain based on
> a set of axioms. I've brought up the problem of cardinalities before
> in the "copy method important?" thread. I think the cardinality would
> have to be an assumption...
>
Either you are saying something very interesting, in which case I would
be pleased if you could elaborate a little bit (or refer to a precise
link if you have already done so), or you are falling in the 1004
fallacy(*): using too precise notion in a less precise context.
(I'm refraining to use the Lowenheim-Skolem theorems which are very
nice and have certainly some relevance (in particular against too much
big TOE a-la Tegmark), but are not so simple, and people here are not
yet enough motivated in mathematical logic.
If you know french, or even if you don't know french (because the
figure are clear enough if you know Skolem paradox) you can take a look
at my "brussel's thesis" page deux-272, deux-273, deux-275 of
http://iridia.ulb.ac.be/~marchal/bxlthesis/Volume2CC/2%20%203.pdf
where I use the Skolem's theorem to illustrate the fact that a 3-person
countable structure can be 1-person uncountable.
It is a point which play some role in my explanation to George Levy
that with comp, although the 3-universe (the UD) is really 3-poor,
3-countable, 3-shallow, ... it is close to the full 1-plenitude. With
comp the 1-plenitude is so big that any machine giving it a name or
description would become inconsistent.
Bruno
(*) Bruno: there is about 1004 sheep in the prairie.
Sylvie: you cannot say "about 1004", it is meaningless to say
"about" and then 1004, you should have said "about 1000".
Bruno: not at all. I am sure there is 4 sheep, I can see them near
here. The "about" concerns the 1000 about which I'm much less sure.
From my poor memory of "Sylvie and Bruno" from Lewis Carroll. Of
course Sylvie is right against Bruno (it just happens Bruno is gifted
getting always the last answer. Hope I am not like him!)
;)
Bruno
http://iridia.ulb.ac.be/~marchal/
Received on Fri Jun 24 2005 - 10:49:49 PDT