On 10 Jan 2013, at 19:30, meekerdb wrote:
On 1/10/2013 7:23 AM, Bruno Marchal wrote:
On 09 Jan 2013, at 19:37, John Clark wrote:
On Wed, Jan 9, 2013 at 7:18 AM, Roger Clough <rclo...@verizon.net>
wrote:
> I sense God's presence.
That's nice, but how do you know (and more important how do we
know) if you are sensing a omnipotent being who created the
universe or if you are sensing a bad potato that you ate yesterday?
Or the devil imitating God to fail you. Yes.
I've never had a mystical experience, but if I did I'd have the
courtesy to keep my mouth shut about it if the evidence for its
validity was available only to myself. Even if I had discovered a
new fact about the nature of reality there would be no way to
communicate the truth about it to others. And even if you are
certain about it you can't be certain that you should be certain
about it, because you can be 100% sure about something and still
be dead wrong, in fact it's very common, just look at Muslim
suicide bombers.
OK. Again this is a theorem in the comp theory. The wise remains
mute (on the spiritual matter). But the machine can express some
part in the conditional way, like she cannot prove "non provable
(my-consistency), but she can prove "if I am consistent then non
provable (my-consistency).
But it's only that *she* cannot prove her consistency. Her
consistency may be provable by someone other machine - it's not
'unprovable' in an absolute sense.
Not really. The other machine will give a trivial proof, by assuming
the consistency of the machine at the start, or it will assume
something equivalent or stronger, but perhaps not trivially related to
the consistency of the machine we talk about.
Nobody can prove the consistency of arithmetic, from less than
something equivalent to that consistency. Proof of consistency are
equivalent to transfinite induction on a constructive ordinal. To
prove the consistency of an induction made on ordinals, you need an
induction on higher ordinal. Another machine can prove a consistency,
but that proof can only be convincing if we believe in the consistency
of the other machine.
Bruno
Brent
Likewise, a part of the "spiritual truth" can be proved in the form
"if comp then ...".
Bruno
http://iridia.ulb.ac.be/~marchal/
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