Le 16-avr.-05, à 01:21, Jonathan Colvin a écrit :
> At first glance that would seem to be the case. But isn't there a
> problem?
> If we consider worlds to be the propositions of formal systems (as in
> Tegmark), then by Godel there should be unprovable propositions (ie.
> worlds
> that are never instantiated). This seems in direct contradiction to the
> actual existence of everything conveivable, does it not?
Are you sure Tegmark identify worlds with propositions of FS? Anyway,
what logicians (and modal logicians in particular) are used to do is to
identify
worlds with maximal consistent sets of propositions (or sentences).
Then you
can extract from Godel that any FS can be instantiated in alternative
worlds.
For example if you take a typical FS like Peano Arithmetic, the
proposition that
PA is consistent is undecidable. This means that there is at least two
maximal consistent sets of propositions extending the set of theorems
of PA:
one with the proposition that PA is consistent and one with the
proposition
that PA is inconsistent. In that sense the non provable propositions are
instantiated in worlds. In general worlds are not effective
(computable) objects:
we cannot mechanically (even allowing infinite resources) generate a
world.
What we need to do is to put a measure on those maximal consistent
extensions.
(maximal = can no more be extended without making the world
inconsistent (containing
a contradictory proposition).
bruno
http://iridia.ulb.ac.be/~marchal/
Received on Sat Apr 16 2005 - 10:31:41 PDT