On 08 Sep 2015, at 18:40, Brent Meeker wrote:
On 9/8/2015 5:57 AM, Quentin Anciaux wrote:
2015-09-08 14:11 GMT+02:00 Bruce Kellett <[email protected]>:
On 8/09/2015 9:14 pm, Stathis Papaioannou wrote:
On 8 September 2015 at 20:48, Bruce Kellett <[email protected]
> wrote:
On 8/09/2015 8:40 pm, Stathis Papaioannou wrote:
On 8 September 2015 at 17:39, Bruce Kellett <[email protected]
> wrote:
On 8/09/2015 4:56 pm, Stathis Papaioannou wrote:
I will ask you the same question as I did Brent: do you conclude
from the fact that when you toss a coin it comes up either as
head or tails that the world does not split into two parallel
versions of you, one of which sees heads and the other tails?
I would conclude that a coin toss does not provide any evidence
for multiple worlds or a split. The only evidence we have from
this data is that the outcome of the toss is uncertain. There is
no evidence there for any split of anything.
It is not evidence FOR a split but is it evidence AGAINST a split?
It is evidence that the assumption of a split is not necessary in
order to understand everyday happenings. So, by the application of
Occam's Razor, no split happens.
So you agree that we would still observe the probabilities we do
if we lived in a deterministic world in whaich all possibilities
are realised?
No, because not all possibilities happen in this world. If all
possibilities were realized in this world, then there would be no
uncertainty, no probabilities. Possibility and actuality would be
the same thing. All the horses would win the Melbourne cup; and we
don't live in such a world.
Either MWI is true, and all possibilities happen or it is not... so
the questions is, do you think that MWI is false, because
probabilities seems to means something in this world... because
what I understand of what you're saying, is that if MWI is true
then probabilities should have no meaning, but as you say they have
meaning, then MWI is false... Is that what you're implying ?
Bruce can answer for himself, but my view is that probability is
just a mathematical theory, like calculus or linear algebra. If
there is something that satisfies its axioms (to sufficient
approximation) then we can apply and use probability theory. MWI in
it's meta-physical form doesn't seem to satisfy the axioms. It
doesn't have a borel set with a measure. "Everything happens" isn't
a borel set.
Gleason theorem provides the Borel set in the quantum case, and it
make the measure unique, and in my opinion, it justifies the Born rule.
I do think that the quantum theory has the shape of a solution of the
*all computations* FPI problems.
But then the logic of []p & <>t (& p) must determine, on the p
sigma_1(*), a quantization, and a quantum logic. And that is confirmed.
It is just an open problem if we get a semantic for the quantum logic
such that we can apply Gleason theorem to get the quantum probability
rule for computationalism.
But it is not "everything happens". It is: every true sigma_1
sentence is proved.
We have p -> []p for the sigma_1 sentences, and that is equivalent
with "being a universal machine". That is why we can limit the
arithmetical sentences to the sigma_1 sentences in the logic of self-
reference by adding the axiom "p -> []p", p atomic, to G and all
intensional variants.
It is computer science. Comp invites to translate our discussion in
arithmetic.
Bruno
(*) I recall that a sigma_1 sentence, or Sigma_1 sentence, is a
sentence of arithmetic being provably equivalent (by the machine) with
a sentence having the shape ExP(x, y, z, ... ) with P(x, y, z, ...)
decidable.
It should be obvious to you that if such a proposition is true, it is
provable that it is true, just by testing P(x, y, z, ...) for x = 0,
1, 2, 3, .... P is decidable so all testing halt. If the proposition
is true, you will eventually find such x. Well, being able to do that
is equivalent with being a universal (Turing) machine.
Brent
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