Hi Bruno Marchal 

It would be interesting to see which logical statements apply
to the monadic=quantum domain, which is beyond space and time.
Part of Quantum Information theory. 

[Roger Clough], [rclo...@verizon.net]
12/18/2012 
"Forever is a long time, especially near the end." -Woody Allen

----- Receiving the following content ----- 
From: Bruno Marchal 
Receiver: everything-list 
Time: 2012-12-16, 10:14:38
Subject: Re: On the need for perspective and relations in modelling the mind




On 16 Dec 2012, at 14:49, Roger Clough wrote:


Hi Bruno Marchal 

Pardon my ignorance, but what is Dt ?


Consistency of 0 = 0, or simply self-consistency.  It is the modal Diamond in 
the modal logic of provability). It is the same as ~Bf (not provable false). D 
is the same as ~B ~   (like it exists is the same as ~Forall ~)


In most modal logic, we have the "Aristotelian square", with B = necessary, and 
D= ~B~= possible.


Bp     ~Bp
B~p   ~B~p


In the alethic (Leibnizian) mode:  Bp = necessary p (true in all worlds), ~B~p 
= possible = true in at least one world (= not false in any world). In most 
classical modal logic systems, we have that:


~Bp = D~p
~Dp = B~p


In particular ~Bf = D~f = Dt   (t = "0=0", and t = ~(0=0), or simply they are 
the constant propositional truth and falsity).


So the negation transforms B into D, and vice versa. 


You can test this on all intuitive modality Where B and D represents 
respectively:


B = obligatory and D = permitted   (deontic modal logic)
B = everywhere and D = somewhere (space logic)
B = all the time and D = sometime (logic of time)
B = probability and D = consistency (logic of provability)
B = necessary and D = possibly (Alethic logic)
B = for all x, and D = it exists a x (quantifier)


All such modalities will obeys different axioms, of course.


Bruno












[Roger Clough], [rclo...@verizon.net]
12/16/2012 
"Forever is a long time, especially near the end." -Woody Allen

----- Receiving the following content ----- 
From: Bruno Marchal 
Receiver: everything-list 
Time: 2012-12-16, 04:47:59
Subject: Re: On the need for perspective and relations in modelling the mind


On 06 Dec 2012, at 18:58, Richard Ruquist wrote:

> On Thu, Dec 6, 2012 at 12:44 PM, Bruno Marchal <marc...@ulb.ac.be> 
> wrote:
>>
>>
>>
>> The 1p is not left out. Eventually comp singles out eight person 
>> points of
>> view. If you think comp left out the person, you miss the meaning 
>> of the
>> comp hope, or the comp fear.
>>
>> Bruno
>>
>
> Why just 8? I would have expected every possible "person points pf 
> view"
> consistent with MWI. Richard

There is 8 main types of points of view given by:

p
Bp
Bp & p
Bp & Dt
Bp & Dt & p

See sane04 for more detail. Bp is the arithmetical formula beweisbar 
of G?l 1931, p is an arbitrary Sigma_1 sentences.

In fact it is 4 + 4*infinity, as you have also all B^n p + D^m t with 
n < m. This gives a graded set of quantum logics.

And they all have different "color" fro different machines, that is, 
the logic of those points of view are the same for all correct 
machines, but their explicit content can be completely different.

Bruno


http://iridia.ulb.ac.be/~marchal/



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