On 6/1/2016 2:01 AM, Telmo Menezes wrote:
On Wed, Jun 1, 2016 at 9:53 AM, Pierz <[email protected]
<mailto:[email protected]>> wrote:
On Wednesday, June 1, 2016 at 4:44:33 AM UTC+10, Brent wrote:
On 5/31/2016 10:08 AM, Bruno Marchal wrote:
>
> On 31 May 2016, at 00:36, Pierz wrote:
>
>> Clark v Marchal! I love this match-up. I predict it will go
47000
>> rounds without a knockout!
>
>
> I am interested in the problem why some machine get stuck at
step 3 of
> the UDA :)
>
> The translation into arithmetic of the reasoning does
provide light on
> this, if not an answer to that question. An ideally
arithmetically
> correct machines cannot believe in computationalism, she
will not
> identify her soul with her body or relative Gödel number,
that is she
> will not identify herself with any third person description
of what
> she really feel to be herself. The soul of the machine is not a
> machine from the soul's machine point of view.
>
> That is well sum up by simple theorem in G and G*. The
machine's body
> can be identified with its provability predicate []p. When
PA talk
> about her provability abilities, she derives them from a
specific
> thrid person description of its beliefs and how to generate
them.
> Now, accepting the classical analysis of knowledge, and
defining it in
> the Theaetetus' manner, by []p & p (p sigma_1 arithmetical
> propositions) and "[]" representing Gödel's arithmetical
beweisbar),
> we get that
>
> 1) G* proves []p <-> ([]p & p)
>
> 2) G can't prove in general that []p <-> ([]p & p)
>
> and indeed, the logic of []p & p will be quite different
from the
> logic of []p, due to incompleteness.
>
> I define the (proper) theology of the machine by G* minus G.
The local
> identity of the soul ([]p & p) and the body-brain-program
([]p) is
> true, but not provable, not even taken as an axiom. It is
necessarily
> a non justifiable belief, an hope or a fear.
>
> The other very nice thing, also, is that "[]p & p" does
indeed not
> admit any third person description available in its/her/his
language.
> Then it also defines an arithmetical interpretation of
intuitionistic
> logic (with the solipsist identity of truth and the personal
mental
> constructions), and when p is restricted in the sigma_1
(complete)
> domain (= UD*), we get a quantum logic, which was expected
for the UDA
> reson, but still surprising as it marries antisymmetry
(related to the
> logic of []p & p (S4Grz)) with symmetry (related to []p & p
when p is
> sigma_1).
>
> Judson Webb said that Gödel's theorem was a lucky chance for
the
> Mechanist theory of mind, but here we see that (Everett) QM,
even
> formally, is even a bigger chance for Mechanism.
>
> Now this remark, that machines cannot believe in Mechanism
(and its
> consequences), might apply better to someone like Craig
Weinberg, (if
> you remember the conversations here) and less to John Clark,
who
> "accept (and even practice) Mechanism, but still get stuck
for unknown
> reason (at step 3). We need another theory, which I think might
> involve notion of susceptibility and more emotional human
stuff. Now,
> if you can make (logical) sense of his refutation of step 3,
you would
> help!
>
> Note: I have introduced a new term: the surrational. It is,
like G*
> minus G, the part of the truth *on* a machine that a sound
machine
> cannot believe/prove/justify.
In that formulation you take believe, prove, and justify to
have the
same extension. But that's not a good model of anyone I
know. In
general believe many things they cannot prove from some set of
axioms -
and even if they could, their "proof" is contingent on the
axioms.
Brent
I tend to agree. Indeed the notion of "belief" is a very complex
one, psychologically. For example, a person might believe (or more
properly, believe they believe) in a doomsday prophecy, and yet as
the moment arrives uneventfully, find themselves quite
unsurprised. In other words, they were wrong about what they
thought they believed. Or a person might believe their husband to
be a good person, but upon his being charged with murder, discover
that they "knew all along, deep down". And so on. Sometimes I
think what we "believe" is merely what we assert to ourselves to
be true, and this assertion is in real life often not based upon
rational evidence, let alone anything as rigorous or abstract as
an "axiom". I'm not sure where that leaves a theory of humans as
arithmetical machines, but the level at which human beliefs about
the self and the world are formed and justified seems a long long
way from the level at which the "beliefs" of logicians are formed.
It seems to me that "belief" might have at least two distinct
meanings. You are alluding to belief in the sense of ideological
belief or political belief, for example. Bruno appears to be alluding
to the sense of belief as in "I believe there is a computer in front
of me right now". The latter is a perceptual "short-circuit" if you
want. I have no doubt or choice over the matter. To make it more clear:
How is the perceptual "short circuit" the same as proof from axioms?
Brent
I might have some doubt that the computer exists under some
sophisticated intellectual construct, but if my life is threatened I
am going to trust my senses 100%. I will not doubt for a second that
the guy coming in my direction with a baseball bat exists. I think
this is belief in Bruno's sense of recovering physics from machine dreams.
I agree with you that people fool themselves about what they really
believe, but this applies to the first sense of the word I alluded to.
Sometimes you can apply the "skin in the game" test. Someone believes
the world is going to end in 3 months? Why don't they max out their
credit card?
> It helps to see that between the irrational (false) and the
rational
> (justifiable), there are lands of true but non provable, and
of false
> but non refutable, associated to each machie is merely nes
(defined by its
> believability predicate (its own beweisbar). The proper theology of a
> machine is the study of (its) surrational land. I limit
myself to
> correct or sound machine, so that the surrational just
extends the
> rational (justifiable), like G is included in G*.
>
> I recall that "forever undecided" by Raymond Smullyan is an
excellent
> introduction at the logic G. The relation with mathematical
logic and
> computability theory comes from the theorems of Gödel, Löb,
> Grzegorczyk, Solovay, Boolos, Goldblatt, Visser. I think all
the
> pieces of the computationalist mind-body puzzle fits,
including about
> what we can't explain and what we cannot talk about.
>
> Bruno
>
>
>>
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>
>
>
>
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