On 6/29/2018 2:20 AM, Bruno Marchal wrote:
On 28 Jun 2018, at 20:00, Brent Meeker <[email protected]
<mailto:[email protected]>> wrote:
On 6/28/2018 8:46 AM, Bruno Marchal wrote:
Also, if another sort of a multiverse exists besides the quantum multiverse,
then in any physics experiment you're going to measure the totality of all the
effects of all multiverses in which you have exact copies. The effects of these
other multiverses e.g. as provided by inflation theory cannot necessarily be
dismissed as trivial (e.g. by saying that it leads to uncertainty of the
quantum state, the effects of which can be absorbed in a density matrix), as
counting states with the restriction that the same observer is present per my
argument in the previous posting, also leads to quantum-like laws.
Eventually, that can be related to the importance of not assuming any
infinities. With arithmetic, we elude the non standard models of arithmetic,
because the laws of addition and multiplication in such non standard model can
be proved to be non computable. But with any theories which assumes some
infinity, we can no more fight against the white rabbits. No Infinities is not
an option, as I thought sometimes ago, but is made obligatory. Judson Webb
insight was correct: Mechanism is a finitism.
How is that consistent with your idea of the UD producing infinitely
many threads of computation through the same state?
I do not see the inconsistency. I guess you confuse the object in the
model (the natural numbers, the finite pieces of computations, …) and
the model itself (N is infinite, but is not an existing object in
arithmetic, just a meta-decor when we take some meat-distance). The UD
is a finite being, and do only finite things, forever, but that
“forever” needs a richer phenomenology to be accounted for.
That sounds like double talk. The "forever" is just another way
introducing infinity while pretending that the infinity is not reached
because it is only potential in time. But there is no "time" in these
abstractions; if they exist at all, they exist complete.
Brent
The paradox resolve when we distinguish what we can prove and what is
true. All semantics of the rich theories are based on some axiom of
infinity, but no semantics of a theory can be part of the theory. That
is a consequence of results by Gödel and Tarski. We cannot define
“infinity” in arithmetic, and there is none. But of course, the model
are all infinite, but not part of the theory.
Bruno
Brent
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