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. 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 machines (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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