On 18 Sep 2013, at 22:11, Craig Weinberg wrote:
On Wednesday, September 18, 2013 8:26:35 AM UTC-4, Bruno Marchal
wrote:
<snip>
Beyond the ambiguities, comp put the physical universe in the gap,
when the gap is modeled by the logic "*" minus the logic not-"*".
Why just the physical universe though? Don't you think comp needs to
put itself in the gap too?
Here I model the gap by the difference between true and provable,
versus true and not provable.
It amazes me at first that physics seems to appear only in the gap,
but then it is coherent with the idea that is is a first person plural
emergence, and that is confirmed by Everett QM. If we look at the same
particles we do get entangled and share the foregoing history. That's
why Everett saves computationalism from solipsism.
I mean G* minus G, etc. In fact physics (should) appear in Z* minus
Z, X* minus X.
G* and G don't show up in a Google search. I've never really
understood what you mean by that, but you're welcome to explain if
you have time.
I have done this many times on this list, but I will explain it again
on FOAR soon, or later. But I can say to words. G is the modal logic
of Gödel's beweisbar (provability by PM, or PA, I mean Principia
Mathematica, pr Peano Arithmetic, or any Löbian machine).
In fact G correspond to the provability proposition that the machine
can prove about herself, and G* corresponds to the true, but not
provable by the machine, propositions.
For example, take the (self) consistency proposition ~B f (I don't
prove the false). This is a typically true proposition (trivially for
the correct machines) but not provable by the machine. So you have G*
proves ~B f, but G does not prove it.
On the contrary, the sentence ~Bf -> ~B(~B f), which is the modal
translation of the second incompleteness theorem, (which says if I am
consistent then I cannot prove that I am consistent) *is* a theorem of
G, meaning that Löbian machine can prove their own incompleteness.
Like I said, beyond ambiguities, what you say fits very often comp,
except when you argue *from* what you say, that comp has to be
false, of course.
Hehe, I can do what comp can't :)
Comp is not a person, and not-comp makes the life of my sun-in-law
miserable ... ;)
Bruno
http://iridia.ulb.ac.be/~marchal/
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