On 21 Jan 2013, at 18:48, Craig Weinberg wrote:
On Monday, January 21, 2013 12:31:00 PM UTC-5, Bruno Marchal wrote:
Impossible, or comp is false. No machine can ever figure out that
there is anything without postulating it by faith. The fact that
such postulation is unconscious makes this counter-intuitive, but
with comp it is provable with mathematical logic.
Aha, now this is interesting. Here I can begin to see the sub-
arithmetic sense that you are working with. By 'figure out', do you
mean that a machine has a conscious experience of reasoning?
Not systematically. Only if she is universal, or perhaps she has to be
Löbian. I am still not sure on this.
Or is the reasoning as unconscious as the faith upon which said
reasoning must rely?
Hard to say. But most people (as this discussion actually illustrates)
are not aware that the idea of a primary universe is something that we
infer. It is not something that we live. It is unconscious theory. It
is obvious (by natiral selection) that it would be a waste of energy
and time to make this systematically conscious.
Where does provability by mathematical logic come in?
I model the belief of an ideally correct machine by its provability
predicate. This is a predicate that we can translate in the language
of the machine (in arithmetic for example), an,d which obeys the usual
axiom for rational belief:
[](p -> q) -> ([]p -> []q)
[]p -> [][]p (for the "rich" machines).
Rules: modus ponens and necessitation (p/[]p).
In such a machine case, the machines (and all its consistent
extensions) will obey the Löb axioms: []([]p -> p) -> []p, which is
the building block of the comp hypostases.
In that frame work, the inferences in the proposition <>t, and more
generally of propositions in G* minus G, plays the role of
consciousness. But the inference itself is not conscious.
Why doesn't everything use unconscious faith
Faith is always conscious. The inference itself might be or not
unconscious, so I guess what you mean. If I said "unconscious faith",
I meant "unconscious inference of something" and the "unconscious"
bears on "inference", not on the content of the faith.
or how does unconscious faith become conscious only to become
partially obscured once again and in need of proof to restore it to
consciousness?
No need of proof as there is none. That consciousness comes, and quit
is usual. You are quite conscious of driving when being a young
driver, then most of the driving become unconscious when older ...
until you get a problem with the car and are conscious again.
Consciousness is related to focusing attention, notably.
It seems like the forces which are shaping faith into these
different qualities of consciousness are actually the more relevant
agents.
With comp, forces are a product of consciousness.
What would be the reason for or method of bringing a machine's
unconscious faith into a conscious experiential mode?
The machine is conscious when she infer <>t and other G*\ G-
propositions (true but non provable/believable). This confers to her
an ability to evolve, to change her mind, to speed-up its
computability abilities, to focuse attention, to differentiate on
different consistent extensions, etc. Of course there a tuns of open
problems. the advantage here is that we get physical consequences so
we can test that theory of consciousness.
Bruno
http://iridia.ulb.ac.be/~marchal/
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