On 26 Jun 2017, at 19:23, John Clark wrote:
On Mon, Jun 26, 2017 at 1:57 AM, Russell Standish <li...@hpcoders.com.au
> wrote:
> I've started with a different set of metaphysical
assumptions, namely that we live in a Multiverse,
Do you assume the number of universes are denumerable?
> and that observer moments are drawn from a much more
general measure than classical probability theory allows.
Infinite sets can cause problems with probability even if you can
count the elements, and if you can't it certainly doesn't help.
On the infinite enumerable set, you might need to relinquish the
additivity axiom, or to use local relations (like with the prime
number theory).
But on the non enumerable sets, (Like R, C) probabilities and measure
have nice theories, like the theories of Riemann, Lebesgue, or the
Haar measure on the Lie groups.
If you stab the number line at random with an infinitely sharp
needle your chances of hitting a rational number, or even a
computable number, are zero even though there are a infinite number
of them.
That is why we define the measure space by forbidding the infinite
intersection of interval or open sets, which can lead to points. We
allow infinite unions. In the iterated duplication, or any Bernouilli
experience, the probabilities of "successes" are given by the binomial
coefficients, but with big numbers the continuous Gaussian e^(- x2),
conveniently renormalized, simplifies the life of the statistician.
From a logician perspective, and assuming computationalism, the
infinities are sort of oversimplifications made by the finite things/
minds trying to understand the finite things/minds. Anyway, with
Mechanism, it is easier to classified them as epistemological, and
that is why the ontology is given by Robinson Arithmetic, and the
phenomenology by what will concern the "observer" PA (Peano
Arithmetic) which is emulated by Robinson Arithmetic (and thus
emulated in all models, even those with a biggest prime!).
Bruno
John K Clark
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