Tom wrote:
> 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...
Bruno wrote:
> 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. ...
< end quotes
Bruno, I have to be honest and say that I'm just starting to get into this stuff out of a passing interesting and that I probably don't have time and priority to study the math that would be sufficient to make a significant contribution in my view. For instance, I just learned about Church's lamba calculus last night. So I probably went in over my head in citing Lowenheim-Skolem. But is not my statement correct with regard to Lowenheim-Skolem and cardinalities? If so, then perhaps the iffy part is the application to this topic (so perhaps I committed the 1004 fallacy here). Nevertheless, regarding the application, on the surface it just seems that to make any conclusions about whether there is a non-zero probability of something being true or happening, you need to know the cardinalities of the sets you are working with. I will be gone on a marriage retreat this weekend, so I'll be back on Monday.
Tom Caylor
Received on Fri Jun 24 2005 - 14:17:24 PDT