On 13 Apr 2017, at 16:23, David Nyman wrote:
On 13 April 2017 at 14:56, Bruno Marchal <[email protected]> wrote:
Hmm.... You seem to want to replace the Outer-God, by the Inner-God.
That is a risky move toward solipsim. S4Grz does not see the gap,
but it does not see the other minds either.
But that's just it. We cannot ever "see" the other minds, nor even
our own for that matter, however much we examine mechanism. But we
can believe in them, as we do in our own.
We can feel our mind, and cannot feel the mind of the other.
We can believe in our mind, without doubt. But we cannot believe in
other mind, without doubt. They might be p-zombie, instant-creature in
a dream, hallucination, or something else.
S4Grz (the 1p described by S4Grz, to be precise) is indeed
solipsistic, even close to Brouwer solipsism/intuitionism.
Perhaps the least confusing conception of this (following Hoyle's
heuristic, which as you know I'm fond of) is to conceive the soul as
indeed a soles ipse, though one with innumerable personifications,
each profoundly amnesic with respect to the others.
Yes. That fits S4Grz. In the "machine theology", it plays the role of
Plotinus "universal soul", which is below the divine intellect (here
G*) and God (here denoted cryptically without any name by p, put for a
generic true arithmetical proposition (you can "define" God here by
the set of true arithmetical sentences: Warning: it is a highly non
computable set).
But surely that must be true of any computational device capable of
compartmentalising one program's states from another's. Is this then
the Inner-God?
That is a slight generalization. The salvia plant is "OK" with this,
but it makes non universal machine conscious, and then even more
conscious than the universal machine. It is unclear how will the much
simpler machine consciousness differentiate?
The theology of too much simple machine can degenerate, a bit like
attempting to divide by zero. They will have "God's consciousness",
out of time and space, and unique, in a, needless to say, highly
dissociated state.
How frustrating, your fridge (assuming that kind of things exists)
knows as much as God, but it flies so high that it can't hear your pray.
Perhaps, in concrete or perceptual form. But surely the abstract
Outer-God is still evidenced in that maximally-compressed creative
widget you call the UD?
Only after the machine's "blasphem", when she identify herself with
god: p <-> []p.
This is going near a death experience, near inconsistency, near []f.
With computationalism, we limit p to the sigma_1 sentences. They are
arithmetical translation of halting computations. The creative widget
is equivalent with Robinson Arithmetic. But the computationalist
machine I define (in Robinson arithmetic) believes in the induction
rules, and so it can prove that it is universal. In fact it can prove,
like PA and ZF (where the "[]" denotes their own provability predicate):
p -> []p
(given that we limit ourself to p sigma_1). It is a theorem of G1
(axioms of G + (p -> []p))
Do we have []p -> p?
Well, that is trivially true, given that we study the correct machine,
by choice. We believe also that it is true for simple machine that we
trust, like PA, and ZF (for many).
But, and very importantly, no machine at all can prove that about
itself. Only their divine intellect do: G* proves []p -> p (for those
correct machine). Note that the theology is personnalized for each
machine (as many "’[]" than machine), but are isomorphic and followes
the G, G*, S4Grz laws for the correct machines.
So the blasphem is true (G * proves p <-> []p), but the consistent
machine will remain silent on this,
That is a blasphem too, if said by the machine about itself. We are
in the corona G* minus G.
A good sum up diagram of the 8 "hypostases" or "type of points of
view" (make sure your window is big enough: you should se,
coincidentally, a sort of diamond above a a sort of square):
Truth
G1 G1* (the provable part of the provability
logic, and G1* gives the whole bigger truth about the provability and
consistency logic
S4Grz1 (the 1-p, the first person, the
universal soul, the inner-god, the "creative germ", the "terrible
child", the solipsist)
--------------------------
Z1 Z1* (intelligible matter)
X1 X1* (sensible matter)
G1* proves the seemingly ultra-blasphemic collapsing of the whole
adventure (writing a <-> b <-> c <-> ... for (a <-> b) & (b <-> c)
& ...)
G1* proves p <-> []p <-> ([]p & p) <-> ([]p & <>t) <-
> ([]p & <>t & p).
But G proves none of those equivalence, making the machines view
obeying quite different logic (leading from the start to some tension/
schizophrenia).
Take it easy. I dig toward the intermediate talk you suggested me.
More on those modal logics later. There are theorems relating them
precisely to what machine can and cannot believe/prove, know, observe
and feel about themselves.
I have to go. Tomorrow, I will not have the time to even look at my
mail. But Sunday that should be possible. Good weekend!
Bruno
David
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