Dear Stephen,
On 25 Jan 2012, at 20:01, Stephen P. King wrote:
Dear Bruno,
I still think that we can synchronize our ideas!
Well, assuming there is no flaws in UDA, and in AUDA (which assumes
comp, but also the classical theory of knowledge, that is the axioms
of the modal logic S4 for describing knowledge(*)), then it is in the
interest of your theory to synchronize with the theory of the
universal machine by the universal machine.
;)
(*)
Kp -> p (if I know p, p is true)
Kp -> KKp (if I know p, I know that I know p) ; this one not not
necessary (and false in the "sensible matter").
K(p->q) -> (Kp->Kq) (If I know that p implies q, and if I know p, then
I know q).
On 1/25/2012 1:10 PM, Bruno Marchal wrote:
On 25 Jan 2012, at 18:04, Stephen P. King wrote:
Hi,
I am 99% in agreement with Craig here. The 1% difference is a
quibble over the math. We have to be careful that we don't
reproduce the same slide into sophistry that has happened in
physics.
I think I agree. I comment Craig below.
Onward!
Stephen
On 1/25/2012 7:41 AM, Craig Weinberg wrote:
On Jan 25, 2:05 am, meekerdb<meeke...@verizon.net> wrote:
It is not at all camouflaged; Lawrence Krause just wrote a book
called "A Universe From
Nothing". That the universe came from nothing is suggested by
calculations of the total
energy of the universe. Theories of the origin of the universe
have been developed by
Alexander Vilenkin, Stephen Hawking and James Hartle. Of course
the other view is that
there cannot have been Nothing and Something is the default.
"The most reasonable belief is that we came from nothing, by
nothing, and for nothing."
--- Quentin Smith
I think that we are all familiar with the universe from nothing
theories, but the problem is with how nothing is defined. The
possibility of creating a universe, or creating anything is not
'nothing', so that any theory of nothingness already fails if the
definition of nothing relies on concepts of symmetry and negation,
dynamic flux over time, and the potential for physical forces,
not to
mention living organisms and awareness. An honestly recognized
'nothing' must be in all ways sterile and lacking the potential for
existence of any sort, otherwise it's not nothing.
I agree too. That is why it is clearer to put *all* our assumptions
on the table. Physical theories of the origin, making it appearing
from physical nothingness, makes sense only in, usually
mathematical, theories of nothingness. It amounts to the fact that
the quantum vacuum is unstable, or even more simply, a quantum
universal dovetailer. This assumes de facto a particular case of
comp, the believes in the existence of at least one (Turing)
universal system.
As you might know, choosing this particular one is treachery, in
the mind body problem, given that if that is the one, it has to be
explained in term of a special sum on *all* computational histories
independently of the base (the universal system) chosen at the start.
The idea of theories of Nothing is that "Everything is
indistinguishable from Nothing".
That does not make much sense to me. Words like "everything",
"nothing", "existence" are theory independent.
"nothing" by itself has no meaning.
This is very different from distinctions between Something and
Nothing. I cannot emphasize enough how important the role of belief,
as it Bp&p,
as is Bp. (Bp & p is knowledge, obtained by applying Theaetetus'
definition (true belief) when "believability" of the ideal rational
correct machine, is believing in the modus ponens rule and in a
correct description on its own functioning at the right level (even if
only serendipitously). This behaves, like Gödel's provability, to the
logic of self-reference G and G*.
has and how "belief" automatically induces an entity that is capable
of having the belief.
Beliefs are defined by those entities, which you can see as (relative)
theorem provers. Let me fix one universal system (like any enough rich
describing an initial segment of (N,+,*)) then I can effectively
associate digital entities (machine, pieces of computation, machine's
discourse) with numbers. Like fixing 0 on a line can help me to relate
to points through numbers.
So relatively to a universal numbers, some numbers can develop
beliefs. All sort of beliefs. I limit myself to the study of ideally
rational machines. The amazing thing is that such machine get
mystical, and their discourses and silent are interesting.
We simply cannot divorce the action from the actor while we can
divorce the action from any *particular* actor.
Sure.
Your idea that we have to count *all* computational histories is
equally important, but note that a choice has to be made. This role,
in my thinking, is explained in terms of an infinite ensemble of
entities, each capable of making the choice. If we can cover all of
their necessary and sufficient properties by considering them as
Löbian, good, but I think that we need a tiny bit more structure to
involve bisimulations between multiple and separate Löbian entities
so that we can extract local notions of time and space.
My approach consists in asking them. I think UDA makes that
obligatory. And I don't know other way to allow the neat quanta/qualia
distinction, in the unavoidable octalism of the Löbian entities.
Any formalism describing the quantum vaccuum assumes much more that
the Robinson tiny arithmetical theory for the ontology needed in
comp. Nothing physical does not mean nothing conceptual. You have
still too assume the numbers, at the least. So it assumes more and
it copies nature (you can't, with comp, or you lost the big half of
everything).
I would like you to consider that the uniqueness of standard
models of arithmetic, such as that defined in the Tennenbaum
theorem, as a relative notion.
?
Each and every Löbian entity will always consider themselves as
recursive and countable
Actually Löbian entities are much more general than machines. Most
divine (no Turing emulable) self-referentially correct entity still
obey to G and G*. Comp implies that you need really go quite close to
God to lose Löbianity by adding knowledge. It is far simpler to lose
Löbianity by losing knowledge.
Now, you were more deeply wrong, with all my respect. No sound Löbian
entity, be it a machine or not, will ever consider themselves as
recursive or enumerable. It is a quite strong bet they might do
occasionally, but it entails, paradoxically enough perhaps, that, the
first person related to the machine, is not really (or not at all) a
machine.
and thus the "standard" of uniqueness. This refelcts the idea that
each of us as observers finds ourselves in the center of "the"
universe.
My view is that the default is neither nothing or something but
rather
Everything.
I think there coexist, and are explanativaely dual of each others.
In both case you need the assumptions needed to make precise what
can exist and what cannot exist.
This is a mistake because it tacitly assumes that a finite
theory can exactly model the totality of existence.
It cannot model the totality of the truth about reality, but it can
find the simplest realm where those truth can be explained to come from.
What I have proved is that if we assume comp, elementary arithmetic is
enough. The additive and multiplicative structure of the numbers
already enable the provable existence of infinite forum on what is
exactly happening.
If you have an eternal everything then the universe of
somethings and sometimes can be easily explained by there being
temporary bundling of everything into isolated wholes,
collections of
wholes, collections of collections, etc, each with their own
share of
small share of eternity.
OK.
Indeed!
This is what I am trying to say with Bruno about numbers starting
from
1 instead of 0. From 1 we can subtract 1 and get 0,
So we get 0 after all.
Right, but we recover 0 *after* the first act of distinguishing.
We cannot start with a notion of primitives that assume distinction
a priori.
You confuse the level. It is obvious that we assume some distinction
ability at the meta-level where we communicate the theory of the
beliefs.
- What is zero?
- An invention of the humand mind! (said the naturalist)
- What is the human mind?
- A neural net composed of 10 billions neural cells, and 200 billions
glial cells.
- What is 10 billions?
but from 0, no
logical concept of 1 need follow.
No logical concept, you are right (although this is not so easy to
proof). But you have the *arithmetical* (yes, *not* logical),
notion of a number's successor, noted s(x). We assume that all
numbers have successors. And we can even define 0 as the only one
which is not a successor, by assuming Ax(~(0= s(x))) (for all
number 0 is different from the successor of that number).
having the symbol 0, we can actually name all numbers: by 0, s(0),
s(s(0)), s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(0))))), ...
Yes, but only after making the initial distinction, an act which
requires an actor. This is a "chicken and the egg" problem.
Not at all. The question is only; do you agree with the RA and PA
axioms?
Then the beauty of RA and PA is that they can justify why, with less
than RA or PA, you will not get them. So if you assume less than RA,
you lost the existence of the universal machine, which is the main
heroin in the arithmetical drama.
There is no chicken and egg problem. I just make clear that I assume
elementary arithmetic. (As virtually all scientists and laymen).
0 is just 0. 0 minus 0 is still 0.
Yes. That's correct. And for all numbers x, you have also that x +
0 = x. Worst: for all number x, x*0 = 0.
That 0 is a famous number!
I invite you to take a look at the finitist system of
mathematics of Norman J. Wildberger.
Rational trigonometry looks like another choice of Turing universal
system. Certainly cute. Quite interesting, but might be a bit
distracting too. The comp mind-body problem involves them all. No
doubt that some universal systems are more important than others,
relatively to some question, but to keep the 1p and the 3p
distinction, and the quanta/qualia distinction, we have to extract
those relative importance from the "interview" of the universal
(Löbian) machine.
Bruno
http://iridia.ulb.ac.be/~marchal/
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