If I may, http://en.wikipedia.org/wiki/Model_theory
The basic concept is that every model is composed of a set of elements, a set of n-ary relations between them, a set of constants and symbols, plus a set of axiomatic sentences to define it. It's been a few years since my mathematical logic MSc though.... -------------------------- - Did you ever hear of "The Seattle Seven"? - Mmm. - That was me... and six other guys. 2008/11/8 John Mikes <[EMAIL PROTECTED]> > Anna, > I wanted to write positively to your posts, procrastinated it though and > others took it up. > Now I want to reflect to one word, I use differently: > *---- MODEL ----* > There are several 'models', the mathematical (or simple physical) metaphor > of a different subject is one, not to mention the pretty women in > fashion-shows. > I use *model* in the sense of a reductionist cut from the totality aspect > for a topical view: the epitom of which is Occams razor. Observing > (studying) a topic within chosen boundaries - limitations of our selection > by our interest. > Of course Bruno's all encompassing arithmetic system can cover for this, > too, but I am not for restricting our discussions to the limitations of the > present human mind's potential (even if only in an allowance for what we > cannot comprehend or imagine). Beyond Brent's "yam-y" extension. > What we don't know or understand or even find possible is not impossible. > It is part of 'everything'. > > I chose to be vague and scientifically agnostic. > > Have fun in science > > John Mikes > > > ** > > > On Fri, Nov 7, 2008 at 7:41 PM, Brent Meeker <[EMAIL PROTECTED]>wrote: > >> >> A. Wolf wrote: >> >> So universes that consisted just of lists of (state_i)(state_i+1)... >> >> would exist, where a state might or might not have an implicate time >> value. >> >> >> > >> > Of course, but would something that arbitrary be capable of supporting >> > the kind of self-referential behavior necessary for sapience? >> > >> > Anna >> > >> "Capable of supporting" implies some physical laws that connect an >> environment and sapient beings. In an arbitrary list universe, the >> occurrence of sapience might be just another arbitrary entry in the list >> (like Boltzman brains). And what about the rules of inference? Do we >> consider universes with different rules of inference? Are universes >> considered contradictory, and hence non-existent, if you can prove X and >> not-X for some X, or only if you can prove Y for all Y? >> >> You see, that's what I like about Bruno's scheme, he assumes a definite >> mathematical structure (arithmetic) and proposes that everything comes >> out of it. I think there is still problem avoiding wonderland, but in >> Tegmark's broader approach the problem is much bigger and all the work >> has to be done by some anthropic principle (which in it's full >> generality might be called "the Popeye" principle - "I yam what I >> yam."). Once you start with all non-contradictory mathematics, you >> might as well let in the contradictory ones too. The Popeye principle >> can eliminate them as well. >> >> Brent >> >> >> --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---
