On 01 Jul 2015, at 21:13, meekerdb wrote:
On 7/1/2015 7:25 AM, Bruno Marchal wrote:
On 30 Jun 2015, at 20:10, meekerdb wrote:
On 6/30/2015 10:56 AM, Bruno Marchal wrote:
That is what unitary evolution means. As I said:
>> This means that physics is completely computable -- Turing
emulable.
>> But that is what quantum mechanics in the Everettian
interpretation
>> tells us. Unitary evolution preserves (quantum) information,
and is
>> completely calculable.
OK. No problem with this. But my interest are in consciousness
and qualia, and the advantage of computer science is that it can
handles the computer's truth that the computer cannot
communicate, observe feel, see, etc.
The computer cannot prove some theorems. And it's commonly said
people can't communicate qualia, e.g. perceptions, feelings,
emotions (although we manage at some level). But that doesn't
make (unprovable theorems)= qualia.
Yes, you are right. But the qualia is not related to non-
provability, but to ~[]p with [] being an intensional variants of
provability.
?? What are "intensional variants of provability"
?
I gave them very often. let [0]p = []p = beweisbar(ng(p)) & p (ng =
Gödel number)
Then incompleteness justify the different logics for all the folloing
intensional variants:
p (p is true)
[0]p = []p
[1]p = [0]p & p
[2]p = [0]p & ~[0]f ([]p & <>t)
[3]p = [2]p & p
Three have their logic splitted in two by inheriting the G/G*
distinction. That gives the 8 hypostases.
and why should they satisfy the same incompleteness relations as
provability?
They do not. They obey other one. PA can prove <2>t for example, and
it is [2]t which becomes non provable. That is the whole point: all
the intensional variants have the samùe extension: they "prove" the
same arithmetical propositions, but the logic of that knowledge are
different. One is a logic of rational believability,(G), one of
knowledge (S4Grz), one of immediate (non transitive) prediction (Z),
one of immediate measurable knowledge (X).
UDA imposes that the logic of the observable emerges from qS4Grz1,
qZ1*, qX1*, and this is confirmed as we get the needed quantization
exactly there, on the three of them, which less room for more nuances.
Roughly: intensional means depending on the form of the code, and
extensional means depending on truth or input-output relation. The two
following programs are equivalent extensionnally, but different
intensionally:
Defun factorial n
if n = 0 output 1
else output n * factorial (n - 1)
End
Defun factorial n
count to 10^100
if n = 0 output 1
else output n * factorial (n - 1)
End
It is the same with the provability predicate. []p and []p & p proves
exactly the same arithmetical p (G* proves []p <-> []p & p). But they
obey quite different logics.
Bruno
Brent
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