Alastair Malcolm wrote:
>From: Marchal <marchal.domain.name.hidden>
>>
>> Read [] as necessary.
>>
>> COMP -> [](such a theory [potential Everett rival] comes from COMP)
>>
>
>Does COMP require (I) the objective world (3-world in your terms?) to be
>quantisable/digitisable, or (II) only to the extent that it is
>phenomenologically indistinguishable from a continuous world (in the
>1-world?)?
COMP does not require that the objective world is quantisable/digitisable.
Eventually it follows from comp that there are no 3-worlds. Only 1-worlds
or 1-plural worlds (shared histories).
And (about II) comp entails that 1-world(s) have continuous features
(spectra).
>If (II), then we could have a theory describing the world, which, when
>explicated, specifies a world which includes continua.
Which world ? I don't understand. With comp I don't need to include
any continuum, I got it for free.
Remember that with comp, ontologically I have only discrete numbers and
their "natural" relations.
Continuity *is* a first person notion. (This does not mean that the
notion of continuity has not objective (and mathematical) nature, because
with comp the 1-person does obeys psychological laws.
>Then your statement
>above, without additional assumptions, would be false (that is, we could
>have a theory whose corresponding world is subjectively indistinguishable
>from that corresponding to a COMP-derived theory (which might have to be
>complex and ad-hoc in order to support this indistinguishability), but which
>in its explicated form is not itself precisely derivable from COMP).
How could "the" theory derived from COMP be ad hoc?
If it is derived it cannot be ad hoc. No theorem can be ad hoc. You
don't choose theorem.
What do you mean exactly by the "explicated form" of a (world?)-theory?
>> (COMP + MWI) -> [](COMP -> MWI),
>
>For the LHS, do you mean (a) MWI is true in the sense of being *consistent*
>in our world (but not necessarily actually *applying* to our world) or (b)
>MWI is actualy applicable to our world?
I mean MWI is actualy applicable to our many-worlds (many-histories).
The expression "our world" could be misleading here. Thus I mean (a).
>If (a), I agree, but can't see what point you are trying to make.
The point is that COMP *is* the theory (the TOE, in a large sense of
"theory"). If comp -> MWI', and MWI'‚ MWI, then empirical confirmations
of MWI would weaken or refute comp, and empirical evidence for MWI'
would provide evidence for comp.
To make my point clearer, look at the following progress in TOES:
Copenhague:
-Very vague theory of mind (A point ribbed by Jacques
-Schroedinger Equation Mallah in his URL)
-Wave Packet Reduction
Everett:
-COMP
-Schroedinger Equation
Your servitor:
-COMP
Now, this is caricatural because
-neither Everett succeed in deriving
the Wave Packet Reduction from Schroedinger Equation, but at least he
initiates the Hartle Graham Gell-Man (etc.) decoherence approach which complete
in some sense that derivation,
-nor have I succeed in
deriving Schroedinger Equation from COMP. But
1) I give a proof that if COMP is true, then COMP is enough!
And Schroedinger Equation (if true) must be derivable (from comp with comp!).
2) I have the hope that I initiate the derivation with my UTM
interview. I do take the result that Z1* prove p -> <>[]p as something
promising in this respect.
"1)" is really the UDA.
"2)" is my chapter 5 (
http://iridia.ulb.ac.be/~marchal)
Bruno
>If (b),
>then to my mind the RHS does not follow without additional assumptions,
>since the applicability of MWI to this world does not logically entail its
>applicability to others, COMP or no COMP. (I assume the normal
>interpretation of [] as 'for all logically possible worlds ...')
>Alastair
Received on Thu Feb 17 2000 - 02:27:18 PST