On 14 Feb 2014, at 23:27, meekerdb wrote:
On 2/14/2014 1:10 AM, Bruno Marchal wrote:
On 13 Feb 2014, at 19:34, meekerdb wrote:
On 2/13/2014 1:10 AM, Bruno Marchal wrote:
What's the definition of G*?
G* is a quite peculiar modal logic. It has as axioms all the
theorem of G, + the axiom:
[]A -> A
But is NOT close for the necessitation rule (can you see why that
is impossible). This entails that G* has no Kripke semantics. But
it has some semantics in term of infinite sequence of G-multiverse.
By Solovay second theorem, G* axiomatizes what is true on the
machine. Not just what is provable by the machine.
G* minus G is not empty (it contains <>t, <><>t, <><><>t, ... for
example), and it axiomatizes the true but non provable modal
(provability) sentences.
It seems that the notation is inadequate since it depends on the
accesibility relation: For example if the accessibility relation
is T (for teleportation) then <T>M and <T>W may be false in
Helsinki
Why.
Because teleportation isn't possible (so far as we know).
? Comp implies the possibility in principle of classical
teleportation, (UDA step 1). We don't need more.
I was merely using teleportation as an example to illustrate that
"possible" is a relative concept depending on the accessiblity
relation.
OK. But with comp we define the box through computer science, and
isolate the accessibility relation from the math of the boxes, as UDA
shows it is the only way to do, given that we "cannot look at nature"
in that approach (cf the treachery).
That is an original and subtle points that perhaps some people are
still missing.
What does "possible in principle" mean?
But this was in UDA. It means that if the brain is some machine, we
can survive by substituting an equivalent one, at some level. I assume
teleportation being practical, in step 1-6, but this assumption is
eliminated in steps 7 and 8.
Does it only mean "not self contradictory"?
No, it means that to make this absolutely impossible in theory, you
need non-comp type of assumption.
Does it mean consistent with our best understanding of physics?
No, it means consistent with our best understanding of cognition,
life, brains and the notion of computation.
Lawrence Krauss discusses the possibility in his book "The Physics
of Star Trek". He estimates that it would take more energy than
available in the Milky Way just to obtain the information to
teleport a human being.
Classically or quantum mechanically?
Of course putting that much mass/energy in the vicinity of the human
being would create a black hole. So what does "possible" really mean?
The possibility of classical teleportation It is a way to explain what
is meant by saying that the brain is a machine. Nothing else.
Then in AUDA, there come 8 notion of possibility, defined in
arithmetical terms, all based on the math of self-reference.
Like Jean-Paul Delahaye wrote, you can compare such thought experience
with Einstein or Maxwell thought experiences to justify relativity or
electro-magnetism, before doing the math. To move along with a photon
is also hard to do in practice.
Bruno
Brent
Which brings up another point that bothers me: We are using [] as
an operator "necessary", and <> as "possible" as just symbols with
a defined syntax, but in application we must say what they mean.
What is necessary and what is possible are dependent on context;
just as above you casually assume that teleportation is possible -
even though you well know it isn't - just because you can write
<T>. This is similar to my complaint about arithmetical realism;
it is a sort of logical realism.
I use "[] and "<>" usually when I explain modal logic, through many
examples of different modal systems.
In the translation of UDA in arithmetic, all modalities are defined
in term of the provability predicate, that is the Gödel's Beweisbar.
What is necessary or possible depends on the worlds, yes, that is
what Kripke is all about.
All I explain is based on the fact that teleportation is possible
*theoretically*. Yes.
That it is hard to do in practice is not relevant. You could stop
at step 0, because the artificial brain is also impossible in
practice today. But it is not relevant.
We assume comp. They are both true, as H T M and H T W, if
teleportation is the accessibility relation.
while using F (for flying) would make <F>M and <F>W true.
OK, but it is the same with T.
No it's not. I can fly to Moscow.
By definition of the protocol in step three. If not you should have
made such remark at step 0, and just say no to the doctor. You just
say non-comp (even in theory).
The practicality of teleportation is not relevant for the
theoretical proof.
Bruno
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