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 <jamikes.domain.name.hidden>
> 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 <meekerdb.domain.name.hidden>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
>> >>
>>
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Received on Sat Nov 08 2008 - 11:30:49 PST