On 21 Sep 2013, at 15:10, Telmo Menezes wrote:
On Fri, Sep 20, 2013 at 3:58 PM, Bruno Marchal <marc...@ulb.ac.be>
On 19 Sep 2013, at 16:51, Telmo Menezes wrote:
On Thu, Sep 19, 2013 at 4:31 PM, Bruno Marchal <marc...@ulb.ac.be>
On 18 Sep 2013, at 21:45, Telmo Menezes wrote:
On Wed, Sep 18, 2013 at 6:13 PM, Bruno Marchal <marc...@ulb.ac.be>
On 18 Sep 2013, at 11:43, Telmo Menezes wrote:
I know, I meant Dt vs. Dp. Was it a typo? Otherwise what's Dt as
OK, sorry. "t" is for the logical constant true. In arithmetic you
interpret it by "1=1". I use for the logical constant false.
As the modal logic G has a Kripke semantics (it is a so-called
logic), The intensional nuance Bp & Dp is equivalent with Bp & Dt.
just means that there is an accessible world, and by Bp, p will be
If there is one or more accessible worlds, why not say t? (I'm using
 for the necessity operator)
 p means that p is true in all accessible worlds. But this makes p
true, for all p, in the cul-de-sac worlds. We reason in classical
logic. "If alpha is accessible then p is true in alpha" is trivially
true, because for any alpha "alpha is accessible" is false, for a cul-
And incompleteness makes such cul-de-sac worlds unavoidable (from each
world), in that semantics. In fact  t is provable in all worlds, but
Dt is provable in none, meaning, in that semantics, that a cul-de-sac
world is always accessible.
If you interpret "accessing a culd-de-sac world" as dying, the machine
told us that she can die at each instant! (of course there are other
Is there any conceivable world where D~t?
But the Z logic can have DDf, like the original (non normal) first
modal logic of Lewis (the S1, S2, S3, less known than S4 (knowlegde)
and S5 (basically Leibniz many-worlds, used by Gödel in his formal
"proof of the existence of God")
If so, can't we say ~D~t and thus t?
Yes, t is a theorem, of G and most modal logic, but not of Z!
Isn't the only situation where ~Dt the one where this is no world?
~Dt, that is  f, inconsistency, is the type of the error, dream,
lie, and "near-death", or in-a-cul-de-sac.
We should *try* to avoid it, but we can't avoid it without loosing our
The consistent machines face the dilemma between security and lack of
freedom-universality. With <>p = ~ ~p, here are equivalent way to
<>t -> ~<>t
<>t -> <>  f
<>t ->  f
In G (and thus in arithmetic, with  = beweisbar, and f = "0 = 1",
and t = "1= 1".
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