Liz, if Brent don't mind, my answer to Brent here contains a bit on
modal logic, directly related to the machine discourse (and this will
be justified later, as it is not obvious at all).
On 12 Feb 2014, at 18:28, meekerdb wrote:
On 2/12/2014 1:30 AM, Bruno Marchal wrote:
On 11 Feb 2014, at 14:55, meekerdb wrote:
On 2/11/2014 12:42 AM, LizR wrote:
On 11 February 2014 17:21, Russell Standish
<li...@hpcoders.com.au> wrote:
On Tue, Feb 11, 2014 at 04:57:50PM +1300, LizR wrote:
>
> You wouldn't need to say that if you could show what's wrong
with it! :-)
>
> (Sorry!)
>
> I think the chances are a TOE will have to go a looong way
before it's
> likely to make predictions rather than retrodictions. Didn't
string theory
> retrodict the graviton or something, and everyone said that was
a positive
> result? Well, Bruno's got qualia, apparently...
>
I don't see how he does. He does have the existence of
incommunicable
facts (the G*\G thing), but that's not the same as qualia ISTM.
I said "apparently" because I have no idea how he does it.
I think a simpler form of the argument is that it must be possible
to simulate consciousness because (we think) any physical process
can be simulated and consciousness necessarily accompanies the
physical processes of one's brain. This is the bet of "saying yes
to the doctor".
With comp, I don't think we can simulate matter, nor consciousness.
We can only simulate the relevant part of the brain so that
consciousness is preserved. The price to pay is that matter becomes
something emergent in the 1p views (1p plural) and cannot be
simulated or emulated.
But there's a catch. When we simulate an aircraft flying or a
weather system those have a reference in the 'real' world and
that's why they are simulations. But if we simulate a conscious
brain the consciousness will be 'real' consciousness. So
simulating conscious is in a sense impossible; we may be able to
produce it but we can't simulate it. Consciousness must be
consciousness of something, but it need not be anything physical;
It needs to be physical, at least in the FPI sense of physical.
So you're saying that we cannot simulate matter or consciousness.
But I think we can still produce consciousness by manipulating
matter - we can still build a conscious Mars rover.
With comp we can say that, but only as a matter of speaking. Mars
Rover is in Heaven, and the hard task of computer we send on Mars is
to distracted it enough so that it can manifest its consciousness to
us, notably by sending us interesting data on mars. The consciousness
of Mars Rover is a 1-view, and it is more "a product" of the infinity
of computations going through its state in the arithmetical reality)
than with a "single" machine. Thanks to Everett, and our own
entanglement with mars, we can indeed bet that little Mars Rover share
some history with us.
it could just be consciousness of arithmetical truths. This
explains why aspects of consciousness are ineffable. It's because
conscious processes can prove Goedel's theorem and so know that
some truths are unprovable. Bruno takes "qualia are ineffable"
and "some arithmetical truths are unprovable" and postulates
"ineffable=unprovable".
Not really.
I guess people progress, as this is the new common error in
fashion, but some logician did it too, and is a confusion between
hypostases. Qualia are related to non communicable, but only
*indirectly* through G*. It happens through Z1* and X1* (and S4Grz1),
Don't understand that.
Incompleteness does not just separate the provability/consistency
modal logic G into two parts: the provable statements, and the true
statements, it also makes the logic of the differents modalities:
p
[]p
[]p & p
[]p & <>t
[]p & <>t & p
obeying different modal logics, despite G* proves them all equivalent
extensionnally (they "proves" the same true arithmetical propositions,
but they see them differently.
Among them, three logics splits into provable and non provable parts:
[]p (gives G and G*, by Solovay theorem)
[]p & <>p (gives Z and Z*-
[]p & <>t & p (gives X and X*)
That remains true when we restrict p on the sigma_1 arithmetical
reality (the arithmetical UD, which is a UD, provably).
That changes G into a modal logic G1 (G + p->[]p) and all hypostases
get changed by this. I change their names by adding a 1. And qualia
and quanta appears in S4Grz1, Z1*, X1*.
which translates the UDA. the Gödel provability cannot be used for
the UD measure, due to the cul-de-sac worlds. That is why we need
[]p & p, or []p & Dt, or []p & Dt & p.
Brent, do you see this?
Are you OK that in a cul-de-sac world we have []A for all A?
I repeat two arguments.
I recall first Kripke semantics:
All the worlds obeys CPL. And there is some fixed binary relation R on
that set of worlds (called "accessibility").
Then,
[]p is true in a world alpha if p is true in all worlds beta such that
alpha R beta
Or equivalently, (and dually):
<>p is true in a world alpha if it exists a world beta with p true in
beta and alpha R beta.
(re-verify that this entails well
<>p = ~[]~p
[]p = ~<>~p
~[]p = <>~p (jump law 1)
~<>p = []~p (jump law 2)
OK?)
Now consider some multiverse with zeta being a cul-de-sac world, like
{alpha, beta, gamma, zeta} with
alpha R beta, beta R gamma, gamma R zeta.
And nothing else. In that multiverse zeta is a cul-de-sac world.
OK?
Proposition. For any proposition A, []A is true in zeta.
Proof.
Imagine that []A is not true in Zeta. Zeta obeys CPL, so if []A is not
true, []A is false. OK? And if []A is false, then
~[]A is true, by classical logic. OK?
But if ~[]A is true, then <>~A is true, by the jump law 1 above. OK?
Then by Kripke semantics above, if <>~A is true in Zeta, it means that
there is a world accessible from Zeta, and in which ~A is true.
But that is impossible, given that Zeta is a culd-de-sac world.
Conclusion: []A cannot be false in Zeta.
Summary: []A is true, for any A, in any cul-de-sac world, of any
Kripke multiverse. This is a direct consequence of the jump law: as
[]A can only be false if <>~A is true, and all proposition beginning
by a diamond "<>" are false in a cul-de-sac world.
In particular []f is true in the cul-de-sac worlds. And in fact []f is
false in any non cul-de-sac world. So []f characterizes the cul-de-sac
worlds in Kripke semantics. OK?
definition: I will say that a world is transitory iff it is not cul-
de-sac world.
Now, the G modal logic has curious Kripke multiverse. No worlds can
ever access to itself, but worse, all worlds access to some cul-de-sac
world. (cf the image "you die at each instant in comp or in the little
buddhist theory).
G proves <>t -> <>[]f. This says, in Kripke semantics, that if I am in
a transitory world, then I can access to a cul-de-sac world.
OK?
So let us come back in reality, and let us consider our common very
small multiverse {Helsinki, Washington, Moscou}, or {H, W, M} to be
shorter.
We are in the protocol of step 3. And suppose we are told that in M
and W, we will have a cup of coffee.
Then we would like to say that
"[](we-will have a cup-of-coffee)"
is true in Helsinki. Ou guardian angel G* told us that <>W and <>M is
true in Helsinki, so it looks like the probability one is well
captured by the modal box/ in all accessible world, I get a cup of
coffee.
But we can't listen to the guardian angel in that way, because <>W and
<>M, although true in H, are not provable by the little finite
creature, and we might be already in a cul-de-sac world, from the
machine's point of view. If we apply G, that is a possible case, and
so, to get a decent probability, we must assume explicitly some world
being accessible. That is the "act of faith" I often mentionned. This
is what we will do by defining probability 1, not by
[]p (in G)
but by []p & <>t
The probability of an "event" is one, if that event occurs in all
accessible worlds AND there is an accessible world.
G* proves []p <-> []p & <>t,
so in the "eye of God", nothing changes.
But G, which represents the machine ability, does not prove that
equivalence, and this entails that []p and []p & <>t will obeys
different logics.
OK?
This allows him to identify specifically what makes some computer
program conscious: it's the ability to do induction and
diagnoalization and prove Goedel's theorems.
OK. But it is not a computable identification. We cannot recognize,
neither from code, nor from computational activity, is an
entity is Löbian or not.
I think you mean "we cannot *prove*". We can recognize intelligent
behavior and infer Lobian.
No we can't never be sure. We can in some case recognize that a
program computes the function factorial, but given arbitrary programs
and arbitrary computations, we can't necessarily infer what is computed.
(But well, what you say can be true in some context; I can be OK).
We can just prove non constructively that such programs and
computations exists in a non computable distribution.
My problem with this is that I don't believe in arithmetical
realism in the sense required for this argument.
Then you have to find me two numbers a and b contradicting the
axioms of RA.
I think consciousness depends of consciousness *of* an external
world and thoughts just about Peano's arithmetic is not enough to
realize consciousness and the "ineffable=unprovable"
identification is gratuitous.
This lowers the level only, unless you add something non computable
in the local environment.
There are obvious physical and evolutionary reasons that qualia
would be ineffable. That's why I think step 8 is invalid because
it assumes dreams (of arithmetic?)
Once you accept comp, it is standard computer science to show that
*all* dreams are emulated in Arithmetic.
?? But the argument proposes emulating dreams by a physical (but
inert) computer - not Arithmetic.
It cannot be inert then. It might have inert part, fro some
computations, but that is in the course of the MGA reasoning.
You jump into another difficulties.
That arithmetic emulated all computations is part of standard computer
science.
In step 8, it is shown that IF comp is assumed, it makes no sense to
add anything more than arithmetic at the base level.
are possible independent of any external world - or looked at
another way, I think to make it work would require that the
'inert' computation simulate a whole world in which the
consciousness would then exist *relative* to that world.
I guess we will need to come back on step 8, soon or later. Not
sure what you mean by "inert computation"? re you alluding to the
"inert" device in Maudlin and MGA,
Yes.
OK. But I don't see the relation with the thread. You were assessing
Clark on step 3. You might have changed your mind and jump on step 8,
but I suggest we wait everyone grasp steps 1-7, before looking at the
more subtle step 8.
But no problem, we will come back at step 8.
Bruno
Brent
or to the static computations which exist in arithmetic. In that
case it is the usual argument against block-time or block-universe,
and this has been debunked repeatedly. Time and activity are
indexicals (indeed translated into *variants* of G*).
Bruno
Brent
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