2014-02-12 20:37 GMT+01:00 Bruno Marchal <[email protected]>:
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 <[email protected]
> 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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