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,
