On 29 Sep 2014, at 02:22, Russell Standish wrote:
On Sun, Sep 28, 2014 at 07:35:44PM +0200, Bruno Marchal wrote:
On 27 Sep 2014, at 15:43, Platonist Guitar Cowboy wrote:
On Sat, Sep 27, 2014 at 8:29 AM, Russell Standish
<li...@hpcoders.com.au> wrote:
On Sat, Sep 27, 2014 at 05:33:00AM +0200, Platonist Guitar Cowboy
wrote:
On Sat, Sep 27, 2014 at 3:39 AM, Russell Standish
<li...@hpcoders.com.au>
wrote:
So I don't see: robust universe => all integers exist
Nor do I. But then that is the exact inverse of what I stated: the
arithmetic reality assumption in COMP entails a robust reality
(one in
which the UD runs to completion).
If I remember the thesis correctly, than robust is a placeholder
for some grandmother notion of physical reality, with enough
consistency in historical/spatial/causal relations to allow the UD
to run. Once reversal step is reached, the notion is dropped and
isn't further needed.
I agree. Non-robustness was introduced at step seven by the
physicalist trying to save physicalism + computationalism.
To say that the arithmetical reality is robust can mislead people in
thinking that now the arithmetical reality is our physical universe.
But if robust means "the ontology has sufficient resources to run
the universal
dovetailer", then the arithmetic reality is robust.
In your thesis you talk about the "extravagant hypothesis", which has
to do with the UD running "concretely". Surely the point of that
discussion is once the reversal is obtained, whether the UD runs
"concretely" or "abstractly" has no bearing on the actual observed
physics, thus eviscerating the whole notion of concreteness. We can do
a Laplace - "je n'ai pas besoin de cet hypothese".
But this is quite different to the discussion of whether the ontology
is robust or not, which relates to driving a contradiction between
computational and physical supervenience.
Why would people be misled into thinking that AR is our physical
universe? Didn't you define physical as being what we observe, ie
phenomenology, and so by the reversal, this cannot be AR. For one
thing,
phenomenal physics has random oracles which the AR doesn't have - that
is the point of your FPI finding, surely.
So we agree. AR is just the assumption that 2+2=4 and any arithmetical
propositions are true or false, independently of me. It is the basic
truth we need for talking and reason on computation, digital machines,
and their stopping or non stopping. Physics assumes this too, usually,
but some argue that this is what should be derived from physical laws
(but this leads to some difficulties per se).
Just that given the context, it is always better, I think, to make
clear if we talk about the physical universe, which should be an
emergent notion, or the basic ontology, which as a realm, is
sufficient for comp, as the richer apparent ontology of consciousness
and matter emerges from the statistics on the sigma_1 sentences,
structured by the type of points of view (p, []p, []p & p, etc.).
But the point is that the physical universe is redefined by a
modality of self-reference by entities emulated in the arithmetical
reality. Numbers does not become physical beings. It is more the
sigma_1 trues which become physical (observable) in the mind of the
(average) universal numbers/machines.
I answer the second post here:
On Sun, Sep 28, 2014 at 06:46:24PM +0200, Bruno Marchal wrote:
Additionally, in a robust universe, the Church-Turing thesis tells
us
that physics we supervene on must be emergent from the properties of
universal systems (Bruno's reversal result). Thus the matter we
supervene
on cannot be "primitive". The primitive urstuff is something else
entirely - the arithmetic of integers, perhaps, as Bruno suggests -
but not matter as we know it.
I would say that there is no primitive urstuff at all, nor any
physical universe, robust or not.
I introduced the term "urstuff" as a way of referring to what is
ontologically real. "primitive urstuff" is a tautology, of course, as
urstuff is primitive by definition.
Urstuff could be matter, or it could be a platonic system like the
integers. Since we can never know what it is, we should Wittgensteinly
shut our traps about it, but since we don't seem to be able to do
that, we need a label to talk about it.
But stuff is so much connotated to matter. Matter seems even more
abstract than stuff. Some people makes the error that physics becomes
arithmetic, which is against comp, where physics is a modality of
observation (the FPI bet "one" obeys the quantum logic S4Grz1, or Z1*).
Again, this is just vocabulary, but to say that numbers are stuff
seems to me to easily lead to the error of confusing math and physics
(which some people do when using comp naively).
I think that insisting that number are not physical, not stuffy, not
material, we are closer to your "nothing" intuition, given this makes
clear that there is nothing physical, except in the internal self-
emerging semantic in arithmetic, on arithmetic.
It demonstrates an inconsistency between physical supervenience and
computational supervenience, notably that physical supervenience
entails that certain very simple computations, such as the replaying
of a recording, will be conscious.
This only works in a non-robust universe, however, a point that is
often overlooked in treatments of this.
It seems to me that the MGA makes the robust/non-robustness
irrelevant. It is enough that elementary arithmetic, or the
combinators, is a robust reality.
I agree. The whole non-robust universe move is a rejection of your AR
postulate. But it does seem reasonable to ask what might happen if not
all possible programs could exist, ie that the Turing model of
computation is constrained in some way. I guess essential if you
really want to tackle Aristotelianism in its home ground.
I mention the sub-universal more often called sub-creative) set of
computable function. That might be interesting indeed. But if we
assume the usual computationalist assumption, for theology and
physics, introuicing such a restriction would already be like doing
terachery. If such a restriction plays a role (as I am sure it does),
that has to be extracted from self-reference to exploit the G/G*
distinction, and get both qualia and quanta.
The ultrafinitist physicalism has still to endow his "existing
matter" with magical non-Turing emulable to make its reality doing
the selection it seems to me.
I agree it is non-Turing, but magical might be a bit too strong an
epithet. The argument, presumably, is that some computations require
too great a resource in order to be instantiated. (By analogy with
Norm Wildberger's main argument against infinity).
Comp does not allow infinity in its basic ontology. All of 0, 1, 2,
3, ... are finite. [0, 1, 2, 3, ...} is already in the mind of some
machines, like ZF. It shorten the proofs, and enlighten the picture
from inside. Comp, as Judson Webb analyse it, is a finitism.
is Norm Wildberger an utltrafinitist in math? He look like a
materialist, and ultrafinitist in physics, but normally that is what
the MGA shows it can't really work (unless adding the "magic "needed).
That magic is more than non Turing emulable, it is also not FPI
recoverable. I have no idea what that could be except as something
incomprehensible (primitive matter) introduced to make something else
(machine's mind) incomprehensible.
Bruno
Bruno
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