On 30 May 2013, at 21:04, meekerdb wrote:
On 5/30/2013 2:24 AM, Bruno Marchal wrote:
On 29 May 2013, at 20:12, meekerdb wrote:
On 5/29/2013 12:38 AM, Bruno Marchal wrote:
I don't see the analogy. I don't think consciousness can be
negative, or even that it can be measured by one dimension. "All-
or-nothing" would be a function that is either 1 or 0.
The point is more that it is > 0, or 0.
If you can be conscious of red and green, then I'd say you are
more conscious than someone who is red/green colorblind (albeit
by a tiny amount).
That is about consciousness' content. Not on being or not
conscious.
In order to have beliefs about arithmetic requires that you be
conscious of numbers and have a language in which to express
axioms and propositions. I doubt that simpler animals have this
and so have different consciousness than humans.
Most plausibly. But this again is about the content, and the
character of consciousness, not the existence or not on some
consciousness.
You seem to regard consciousness as a kind of magic vessel which
exists even when it is empty. I think John Mikes is right when he
says it is a process. When a process isn't doing anything it
doesn't exist.
To be sure, I don't use this in the usual reasoning, but I have to
say that I am more and more open that there is something like that,
indeed.
But I agree that consciousness is related to a process, in part (if
not comp would be meaningless).
It just appears that such a process is very basic, that it is
emulated by (many) arithmetical relations, and that it is also
related to arithmetical truth (which is not emulable by any
machine, but machine are confronted to it).
Consciousness per se is not just a process: it is a first person
mental state relating some process with truth. What I say is that
such process can be kept very minimal.
I don't venture to say less consciousness because I think of it
as multi-dimensional and an animal may have some other aspect of
consciousness that we lack.
Sure. Bats have plausibly some richer qualia associated to sound
than humans. But what we discuss is that consciousness is either
present or not. Then it can take many different shapes, and even
intensity, up to the altered state of consciousness. Cotard
syndrom is also interesting. People having it believe that they
are dead, and some argue that they are not conscious, but in fact
what happen is that they lack the ability to put any meaning on
their consciousness.
"Put meaning on consciousness"? That makes no sense to me. They
are obviously conscious of some things. If they were unconscious
they couldn't respond.
There is a possibility that we can access a state where we are
conscious only of one thing, that we are conscious. It *is* part of
the unbelievable (G* minus G).
You mean unprovable? I get confused because it seems that you
sometimes use Bp to mean "proves p" and sometimes "believes p"
Hmm... you might read the Plotinus paper, or the second part of
sane04, or my old posts, or my recent post on Russell's FOAR.
I will tell you the whole thing.
1) I adopt Dennett' intentional stances. I will say that a machine
believes p if and only if the machine asserts p.
2) Being a bit tried listening to machine saying basically anything, I
limit myself to machine which believes in few things (but not so few),
that is, they believe in the classical tautologies, and some
arithmetical things like 0, successors, the addition and
multiplication laws.
(I think I so share those beliefs).
I assume that they are rational, so if they believe p and if they
believe p -> q, they can or will believe q.
In that case 'belief' can be shown to be defined in arithmetic by
Gödel's beweisbar Sigma_1 complete (Turing universal) predicate.
If the machine believes in enough induction axiom, she can proves
(believe) in its sigma_1 completeness, and she becomes Löbian, meaning
that its mathematics of self-reference is governed by the logic G,
which has the Löb formula as its main axiom: B(Bp->p)->Bp. (Solovay
1976 first theorem)
From this you can see immediately that the machine cannot believe
that she is correct, that Bp -> p is always believable. Indeed she can
show that this entails B(Bp -> p), by necessitation, and then Bp, by
Löb, and then p, and then she can proves all sentences (with p = f,
she is already inconsistent).
So Bp -> p is not always believable, despite being true for the kind
of machine I am considering, and thus, although Bp and Bp & p are
equivalent (we know the machine is correct), she cannot know that.
So, thanks to incompleteness, or Löb, we can define a new abstract
modality []p = Bp & p, and this modality behaves like knowledge, and
gives the explanation why the machine cannot define it. She can of
course bet on comp, and define it in an abstract theory, like we did,
but the definition will refer, or be interpreted, by something truly
not definable in any third person way. Incompleteness shows, at the
least, the consistency of the definition of Theatetus for knowledge,
when applied to machine's believability, whatever the axioms are as
long as they are consistent with arithmetic or computer science.
Incompleteness makes "provability" behaving not like a "knowability",
as most people thought, but like a "believability". It makes the
universal machine modest.
But it still seems absurd to me. It invites an infinite regress: I
am conscious of being conscious of being conscious of being...
Why?
Already Gödel's beweisbar is transitive: Bp -> BBp, and so if the
machine believes p, she can or will believe Bp, BBp, BBBp, BBBBp, etc.
The same occurs for the Theaetetical knowability described above, but
it does not occurs for observability, nor sensibility, with the
definitions provided.
There is no infinite regression, just an infinities of consequences,
something usual in arithmetic.
Bruno
Brent
It shows that consciousness seems independent of the ability to
interpret the consciousness content. Many pathological states of
consciousness exist, but none makes me feel like if consciousness
was not something (rich and variated) or nothing. You refer to
the content of consciousness, not consciousness itself.
But you seem to contend that there can be consciousness without
content - which I find absurd.
There is always a content, but it looks like we can limit it to one
thing: "being conscious". This is coherent with Descartes and
mechanism. Consciousness is the fixed point of the doubt, notably.
Bruno
http://iridia.ulb.ac.be/~marchal/
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