On 20 Mar 2015, at 18:28, Telmo Menezes wrote:
On Mon, Mar 16, 2015 at 7:04 PM, Bruno Marchal <[email protected]>
wrote:
On 16 Mar 2015, at 08:21, Telmo Menezes wrote:
On Sun, Mar 15, 2015 at 4:27 PM, Bruno Marchal <[email protected]>
wrote:
On 13 Mar 2015, at 17:57, Telmo Menezes wrote:
On Fri, Mar 13, 2015 at 4:42 PM, Bruno Marchal <[email protected]>
wrote:
On 13 Mar 2015, at 08:19, Telmo Menezes wrote:
On Fri, Mar 13, 2015 at 1:25 AM, meekerdb <[email protected]>
wrote:
On 3/12/2015 1:21 PM, Telmo Menezes wrote:
Not me. I'm the opposite, I was always confused by the idea that
rocks are not conscious.
If you ever have an operation, I suggest you check to see that
your anesthesiologist is not confused.
There's maybe a difference between being a conscious entity and
being conscious of something.
Does not consciousness entails the consciousness of at least one
thing?
Even before speculating about an entity (the future "little ego")
consciousness seems reflexive to me, before verbalizing.
It is the fixed point of the doubt. If we try to doubt everything,
we find the indubitable but non justifiable knowledge of one thing.
My intuitive impression (from some attempts at meditating, for
example) is that consciousness can exist in a completely self-
referential state. But I am not certain of this at all. I think
this is inline with what you say above, and with "cogito ergo sum".
That might be. Thomas Slezak, and myself, like to interpret
Descartes in arithmetic, so that a doubt of p, is defined by <>~p,
and thus ~[]p, and the fixed point is the famous Gödel sentence g,
which is such that PA proves (rationally believes) g <> ~[]g, which
should be then, as far as PA trust herself and her correctness,
true and non believable/justifiable.
But to get the knowledge itself, which results from that, you need
the knower variant= [1]p = []p & p. That one has [1]p -> p, and
just can't doubt everything: he is the one living the fixed point
of the doubt.
What does [1]p mean? Is it a reference to first person?
[1]p is defined by []p & p. It is the modal connector you get when
you apply Theaetetus idea to Gödel beweisbar predicate, which
describes the 3p-self of the machine, its "body" representation,
with possible higher level features, like I have legs, or I am in
Helsinki".
Ah, ok!
The logic of [1] is the one axiomatized by the logic S4Grz, and
S4Grz1 (when p is limited to the sigma_1 proposition, which
translate the UD in arithmetic.
We know (or strongly believe) that PA is correct, and Gödel-Löbian,
so we know that for all p, []p <-> [1]p. And indeed: G* proves []p <-
> ([]p & p), that is []p <-> []p & p. But PA does not know that, nor
can she believe that. G does not prove, for all p, that []p <-> ([]p
& p). There is no knowledge ([1]), nor belief ([]p) that I am that
machine []p. Only God knows your substitution level, where []p & []p
& p equate.
I think that meditation tries to diminish the dominance of the []p,
and meditation favor the "p", in the []p & p part of the knower.
I still don't fully grasp the []p & p thing. My naive
interpretation would be that meditation favours []p, given that it
sometimes generates a feeling of identification with the totality
of things.
You are right. Meditation leads you on the totality, that is the
truth. We can say "p is true" in arithmetic, so we say "p" instead,
which means "p is true", when asserted as p by the machine.
Ok.
On the contrary, []p is "beweisbar p", it represents a description
of the machinery in the language understandable by the machinery. It
is representational. It is, or might be the same truth of the same
p, but seen through to window of some 3-self/body/code/number/finite-
thing.
Ok. I was still a bit stuck with the "it is necessary that"
interpretation of []. If I switch to "it is provable that" it starts
to make more sense. I know you insisted on this several times, but
it's not exactly something easy to grasp.
p is associated with the truth, which might be more than what we,
earthly finite creature, can rationally believe ([]p).
Ok, this makes sense with mediation and other experiences.
It is the p in []p & p, which makes "machine's knowledge" not
definable in term of number and machine. S4Grz formalizable at a
level, what the machine cannot formalize about herself (but can bet
on, ...).
Thanks to incompleteness, the Theaetetus' definition makes sense,
and distinguish the knower from the rational believer for the machine.
Don't hesitate to ask precision. I am very literal here: the knower
is defined by the true believer. It is a modest definition of
knowledge, and it is not similar with "I know for sure that", which
needs some amount of consistency (like <>t, or <><>t, or <><><> t,
etc.).
What's the difference between <>t and <><>t and so on?
In the Kripke semantics, <>p means that you can, by starting form the
world you are in, access to another world where t is true. It means
that you are not in a cul-de-sac world. It means that you are "alive",
you can access some world. But <>t -> <>[]f. So you despite being
alive, you might be dead in that next world. That next world might be
a cul-de-sac world, where <>t is false, and thus []f is true. Now, if
you are in a world where <><>t is true, then you can access a world in
which <>t is true, so that you are still alive.
<>t = I can access some world (t is true in all worlds), but that
world might be a cul-de-sac world.
<><>t = I can access some world where <>t is true, so from there I can
access some other world.
Put differently:
<>t I am alive (but can die at the next instant)
<><>t, I am alive and I can access to an instant where I am still alive.
[0]p = []p, and obeys to G, and fully described by G* (at the
propositional level).
[1]p = []p & p, and obeys to S4Grz,
[2]p = []p & <>t obeys and define the logic Z
[3]p = []p & <>t & p
I definitely don't understand [2]p and [3]p.
[]p & <>t is a weakening of []p & p. Instead of asking p being
true, we ask only for p being consistent
(([]p & <>t) -> ([]p & <>p)).
If you can prove for all p that []p -> p (like with [1]), then you can
prove for all p []p -> <>t or []p & <>p.
So the logic of provability-and-consistency is weaker than the logic
of provability-and-truth.
Provability and consistency avoids the probability one for the false,
which would exist if we take []p as provability. The passage []p
=====> []p & <>p, approximate the main things for a probability one.
It models what the guy in Helsinki can be sure if, like drinking a cup
of coffee (in the protocol where he get a cup in both W and M). It
abstract (locally) from the cul-de-sac world. It use the bet on <>t
implicit in the yes-doctor.
Mathematically, you interpret the "p" by arithmetical proposition,
[]p by beweisbar("p"), an arithmetical predicate "provable(x)", with
x the proposition represented in the things the machine understand
(here the numbers, that is, the "Gödel numbers" of the sentence
expressing the proposition.
The book by Smullyan "Forever Undecided" introduces the logic G.
It's on my "to read" list :)
It is a good one.
"How to mock a mocking bird" is also very nice.
Note that G* is representable in G. I don't insist because people
tend to do repetitively the Searle, error, and believes that the G
understand and believe in what G* says about him/her (G; not G*),
but one day I should explain the representation theorem of G* in G,
because it mirrors someway the machines mind before a self-
multiplication, trying to justify the jump, without success, except
by betting (still) on finite parts of itself.
Bit this type of modest knowledge is not yet enough for the knowing-
for-sure, which is needed for a treatment of consciousness. It might
be <>t v t. Consciousness would be really obvious, from the 1p view
of the machine. I am not sure.
Thanks for the explanation and patience and sorry for the delay! I
wanted to take some time to read this.
No need to apologize ;)
Bruno
Telmo.
Bruno
It leads to the problem that consciousness becomes a feature of the
arithmetical truth, only restricted by the little ego, owner of the
body and representations. We might need that God (Truth) is a
knower itself, and thus a sort of person, because only God would be
conscious.
The word "God" still makes me cringe, but this is mostly because of
organized religion. I plan on reading Plotinus soon and see if I
change my mind. But I think I understand and agree with what you're
saying, otherwise.
I think.
You might say it is not a consciousness *of* something. I might
have missed a nuance.
I will clarify what I meant in a reply to Brent, to keep the
discussion linear.
Oops, sorry for bringing some non linearity, but that's because the
black hole in my basement is active again ...
The nice thing is that I just need to read your post to Brent to
get the clarification, and see if it matches the universal
machine's explanation.
Bruno
Bruno
Telmo.
Bruno
Telmo.
Brent
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