Le 22-juin-05, à 21:23, [EMAIL PROTECTED] a écrit :
<x-tad-bigger>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...</x-tad-bigger>
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
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: 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!)