On Tuesday, April 25, 2017 at 4:50:08 AM UTC+2, Russell Standish wrote:
>
> On Mon, Apr 24, 2017 at 07:12:38PM -0700, Brent Meeker wrote: 
> > 
> > 
> > On 4/24/2017 2:15 AM, Bruno Marchal wrote: 
> > >>This world is 'objective' in the sense that there is 
> > >>intersubjective agreement about it. 
> > > 
> > >That happens in multi-user video games, and all the multi-user 
> > >games are implemented by all universal numbers, with all players 
> > >in arithmetic. The only problem is the relative measure, but we 
> > >have already that the measure one obeys a quantum logic. 
> > 
> > How do we "have" that?  Can you derive, from computationalism, that 
> > the description of the world must be in terms of vectors in a 
> > complex Hilbert space? 
> > 
>
> I looked into that claim, so maybe I can offer a different 
> perspective. Quantum logics are the logic of events in a complex 
> Hilbert space that have probability 1, ie the logic of Hilbert 
> subspaces. For example, if x is the statement that the system is in 
> subspace X and y the statement that the system is in subspace Y, we 
> can speak of x∧y being the statement that the system is in the 
> subspace X∩Y, and x∨y being the statement that the system is in X⊕Y 
> (X∪Y is not a subspace). It turns out that these logics (apparentally 
> a family of them, all quite distinct from classical logic) satisfy the 
> same axioms as Z and X, modal logics describing two of Bruno's hypostases 
> (that of the believer and the observer IIRC). 
>

Maybe you didn't look enough and/or you don't remember correctly. X/X* = 
the believer, huh? 


You proceed from Plotinus’ defining matter in the more platonic style of 
being “holder of contingency and possibility”. Then we get the distinction 
between the matter “over there”, which seems to be intelligible and matter 
“here” which has a feelable property. Through incompleteness and the work 
of the usual giants of theoretical computer science and logic, possibility 
includes indeterminacy. And since G logic is closed for necessitation, 
while G and G* are closed for ◇ possibilization, another intensional 
variant is required with []p & ◇t to get to Plotinus, giving us the logic 
of Zod, aka logic Z which differs from S4Grz due to properties of ◇t ; i.e. 
unprovable and true consistency. But the split Z and Z* between the 
provable and true but unprovable remains street legal. That’s how I 
remember it for the intelligible, observable part.


The sensible, sexy, feelable part or hypostasis (if you’re a layer 
fetishist, lol) has a more pronounce soulful property, which is why any 
comp training should include playing and listening to a lot of sexy soul 
music, which will clarify it along with a healthy sex life and lots of 
dancing. []p & p & ◇t  is gotten in Bruno’s game through reapplying 
Theaetetus to get the pair X and X*; again the split between provable and 
true but unprovable. But this is stuff intuitively arguing linguistic 
informal trash trolls like me can see, without infinite material hypostases 
and transfinite generalization ordinal games say… and interpreting “feeler 
of sensible” as “believer”  for X/X* is another impressive, deep step 
forward, in similar spirit to comp being compatible with physical 
supervenience. Science making forward leaps on this list over the last year 
in similar style to politics of the world. PGC
 

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