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鰁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/
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com
.
For more options, visit this group at http://groups.google.com/group/everything-list?hl=en
.
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com
.
For more options, visit this group at http://groups.google.com/group/everything-list?hl=en
.
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to
everything-list+unsubscr...@googlegroups.com.
For more options, visit this group at
http://groups.google.com/group/everything-list?hl=en.
