On 22 Mar 2015, at 20:27, meekerdb wrote:
On 3/22/2015 8:53 AM, Bruno Marchal wrote:
You are right, it is mystical, but keep in mind that in the
universal machine theory, the mystical is not hard to circumscribe,
machines get them by the intensional variants of G* \ G.
With the precise definitions given, it is not speculative
philosophical: it is computer science, and rigorous definition. All
the definitions I gave are the standard one used in the field
crossed.
That's the standard trick of theologians. They take something
precisely defined in science or mathematics and give it a name, like
"intelligence" or "God", which carries many different connotations
which cannot be derived from the precise definitions, but the
theologian then pretends that the connotations are as firmly
grounded and precise as the definitions. I don't think you can show
that G*\G entails intelligence in it's dictionary meaning.
Right, you can't do that for intelligence. Indeed, as I explained, G
works for all protagorean virtue, which can be taught only by example
and personal experience.
It still gives a precise axiomatic and law. Then we candebate on the
name. Is it intelligence (in the sense of the mystics), or is it
wiseness (in the sense of the philosophers?), is it just being alive,
in the sense of the Kripke semantic of the theory?
But if it does not work for intelligence (today, the dictionnary are
late!), it already works for some dictionary of theology. Hirchberger
makes clear that the the God of Plato is Truth, the one we search, and
which Plato suspect to be transcendental, so that the human theology
extends (and include) the human science.
And that is exactly what G* is, at least partially, for the universal
machine looking inward, once she has enough induction abilities (and a
trivial amount of inductive inference ability of any sort).
qG* is not axiomatizable, so you need infinities of new axioms to
develop it, well, like the arithmetical realm itself.
If you assume only the induction of the sigma_0 (recursive) relation,
you can't derive the exponentiation formula
x E 0 = 1
x E s(y) = x * (x E y)
from addition and multiplication. But adding just that axiom of
exponentiation, makes the machine using only sigma_0 induction Löbian.
So PA is not the least Löbian machine. The so-called EXP-delta_0, the
löbian machine described above, is much weaker, it proves much less
arithmetical proposition. (delta_0 = sigma_0 = pi_0).
OK, I define rational belief inductively. A rational believer believes
in the PA's theorems and its possible beliefs are close for the modus
ponens rule. The logic G* axiomatize the truth about the logic of
consistency and provability (rational-believability) of the machine on
itself.
If you don't abstract from one millenium of theology, it makes perfect
sense to say that G* is the theology of the machine (or a subtheory of
an aspect of that theology). G* \ G, the theology*proper* is the true,
but unjustifiable by the machine, theology of the ideally correct
machine. It is still pure 3p, and verifiable and verified.
Then the theory justifies the existence of different logics for the
intensional variants: knowledge ([]p & p), observable ([]p & <>t), etc.
It is useful to say "theology", because the theory shows that if we
say that it is science, then we blasphem.
To admit it is theology consists in admitting that we need some act of
faith, so it is a type of religion. It is a belief in the possibility
of some reincarnation.
It really means that it is not a matter for a government to legiferate
on that, as the state must be separated from the religion. It entails
the right to say "no" to the doctor.
Computationalism will never be a matter of truth, only a matter of
right.
And the practical one is a bit vain, as once we grasp the
consequences, we grasp that we are already "there": artficial brains
prolongate the Samsara and the suffering, but this belongs to G* \ G,
and must be understood technically. So people are free, at their risks
and perils.
Bruno
Brent
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