On 01 Jun 2016, at 11:01, Telmo Menezes wrote:
On Wed, Jun 1, 2016 at 9:53 AM, Pierz <[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:
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?
You are right. To derive physics from numbers, we need to limit
ourselves to correct beliefs. If not, it would be like criticizing
Einstein thought experiments for the reason that Einstein did not make
clear it assumes the physicists involved to be rational. In fact what
i prove works for any recursively enumerable extension of anything
believing in elementary arithmetic (that is the usual axioms I have
often given, including the induction axioms, but any Turing complete
and Löbian theory would do). The beliefs are closed for the modus
ponens rule *in principle*).
In fact my definition of rational belief is very simple: a machine
beliefs p if she asserts p. Then I limit myself to rational believers
because it would be nonsense to interview a non rational machine to
derive rationally, following the UDA prescription, the correct physics
or the correct theology.
Note that correct beliefs does NOT mean knowledge (in the sense of the
machine). The machine is not aware, and never will, that her beliefs
are in general correct. Knowledge, contrarily is correct *by
definition*, as it is formally defined, at the necessary meta-level,
by correct-beliefs. This is a subtle but extremely important point
made possible only thanks to incompleteness. (For those who have the
book by Gerson on Antic Epistemology, that is the precise point where
Gerson critics of the Theatetus" definition of knowledge get wrong:
it is the difference between a belief which happen to be correct, and
a belief restricted (non constructively) to correct proposition).
The goal is to derive physics and theology, not human psychology.
Bruno
> 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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