Hi Russell, Hi Stephen,
I comment the two (now three!) posts in one mail.
On 14 Apr 2011, at 04:12, Stephen Paul King wrote:
-----Original Message-----
From: Russell Standish
Sent: Wednesday, April 13, 2011 8:07 PM
To: everything-list@googlegroups.com
Subject: Re: A possible flaw un UDA?
I confess I got lost too with your presentation. My gut feeling is
your
discomfort stems from an "almost magical" insertion of the subjective
(ie a knower) into the UDA. Another way of putting it is "what runs
the UD?".
However, the knower is introduced explicitly with the "yes, doctor"
assumption - that I survive with my "brain" substituted by a digital
device. What is this "I" if it isn't the knower? What possible meaning
can "survive" have, without there being a sense of "being"?
Yes. And for the UDA (UD Argument), the knower is sufficiently defined
by his/her personal memory, like the sequence of self-localization in
its duplication history written in his diary (WWWMWMMWMWMMWMWWMMMW...).
In AUDA, the definition is more subtle, and is due to Theaetetus (or
Plato), it is the believer in some truth (by definition), and is
handled by the Bp & p translation. Remember that, by the second
incompleteness theorem, Bf is not equivalent with Bf & f, from the
point of view of the machine. G* (the 'divine intellect') proves that
Bf is equivalent with Bf & f, but the machine itself cannot.
Externally, a UD just exists as a static program (just a number that
exists platonically). However, once you have a knower, you can run the
UD, albeit viewed from the inside. In my book I make this explicit
with the TIME postulate, but I don't see anything hugely controversial
about it. It is not referring to any external time, just that the
knower cannot experience all experiences at once.
Which makes sense in the "block arithmetical universe" with TIME given
by the UD-steps. The *execution* of the UD is also static in Platonia.
It is static not through one static number, but through infinite (and
bifurcating/branching) sequence of numbers.
Here, physicists accepting even just special relativity have no
problem with that. Subjective time (re)appears in the static discourse
made by the machine inside that block statical mindscape.
I suspect that Stephen, in the manner of Prigogine, wants some basic
fundamental time. I suspect him also to be under the charm of some
mathematical mermaids!
I answer Stephen below.
Have I put my finger on it, or is this just wide of the mark?
--
**
[SPK] Hi Russell,
Yes, that is part of the discomfort. Another is a feeling that
the UDA is the semantic equivalent of building a beautiful castle in
midair. One first erects is a brilliant scaffolding then inserts
the castle high up on top of the scaffolding. We then are invited to
think that the castle will stay in place after the scaffolding is
removed. Let me be clear, I find Bruno's idea to be work of pure
genius. I delight in it and I deeply admire Bruno and his tenacity.
I just was to remove these nagging doubts I have about it. I want to
be absolutely sure that it can stand up to ferocious and diligent
attacks before I will commit to it.
Remember: if COMP is true, we will never know it for sure. We will
never be sure about it, and we might even be at risk if we take it for
granted. And that might happen.
If you are using each day a (classical) teleporting device, you might
find hard to doubt comp, yet you can't still not be sure. You might
suffer an 'agnosologic" disease, like that poor first pionneer of
teleportation: after being reconstituted, he was blind, deaf,
paralysed, and when after years of effort he succeed to communicate
something it was "great, the experience was successful, I feel
healthy, with all my capacities, and I am willing to do it again!".
That is one of the reason I insist that COMP belongs to theology, you
need an act of faith, and you need to reiterate it all the time. I do
think plausible that nature has already bet on it, in some way, and
that we do those reiteration bets, all the time, instinctively, but
that is a theory, and to believe and to apply a theory to yourself,
you need an unavoidable act of faith.
Let us consider in detail an idea that emerged here in my post
and Bruno's response:
***
start cut/paste
From: Bruno Marchal
Sent: Wednesday, April 13, 2011 7:02 AM
To: everything-list@googlegroups.com
Subject: Re: A possible flaw un UDA?
Hi Stephen,
On 13 Apr 2011, at 02:35, Stephen Paul King wrote:
AR must be expressible as some belief in each 1p (modulo coherent
and soundness):
[BM] Why? It is true, but I don't see the relevance.
for AR to exist
[BM]What do you mean by "AR exists"? That is ambiguous. And what you
are saying begin to look like "archeology is needed for dinosaur to
exist". The very idea of AR is that 1+1=2 does not need a human for
being true. Of course, a human or some alien is needed to say that
"1+1=2" is believed.
then it is necessary that a 1p believe that AR exists and the
statement “AR exists” is true. If the belief that AR exists cannot
be expressed by a CUD then AR cannot be said to exist since it
would be impossible to express the statement “AR exists”.
Diagonalizations require some form of CU support or else they all
collapse into Nothing.
[BM] Why does diagonalization need a CU?
...
For AR to exist as distinct from Nothing then there must exist
a concrete structure, a CU,
[BM] I doubt this.
end cut/paste
***
Why does diagonalization need a concrete universe? So that it
can represent something other than itself to some thing other than
itself. Does not more than one 1p exist? If only one 1p can exist
then we have a perfect example of a solipsism, no? If the 1p are
purely relations between numbers “as seen from the inside” (an idea
that I find to be wonderful and useful and expressed in the myth of
the Net of Indra), does this not lead to a duality between the
numbers and the representations that the multiple 1p have of
themselves, a duality exactly like what we see in the representation
theorems that I have referenced previously?
What I am thinking is that the sum of the inside views of the 1p
is a CU that cannot be removed or reduced to just the existence of
the numbers themselves so long as the numbers are collection of
entities that have some differences between themselves. In other
words the numbers are not Nothing.
Exactly. That is why they are postulated in the theory. But they are
postulated in all theories. Even Hartree Field in "science without
numbers" postulates them implicitly. It is nothing more than the
axiom: 0 is a number, and if x is a number, then s(x) is a number, and
if s(x) =s(y) then x = y.
+ the usual recursive axioms of addition and multiplication.
And to understand this, we have to use the intuitive informal numbers
we live with since we are born.
They are “something to something else” and that ‘somethingness’ is
concrete and irreducible even if it is the “inside looking out”
aspect of the numbers. The fact that there is an ‘inside’ that is
different from an ‘outside’ demands the kind of duality that I am
proposing.
OK. And here the numbers, when they introspect themselves relatively
to some local universal numbers, get better than a duality, they get
an octo-lity. They get four dualities. I have already compared yours
to the duality between Bp and Bp &p.
We talk a lot about Gödel's brilliant idea of representing
propositions of a theory that includes arithmetic using arithmetic
statements so that we can consider the theory to be able to “make
statements about itself”. We go on and consider Turing and others
that showed how this can be done in wider settings. All well and
good. But do these “theories” or “abstract machines” actually have
the property that we are ascribing to them absent a “knower”, to use
your word and implied definition? What does it means to claim that
something has such and such properties when it is in principle
impossible to determine if indeed that claim is true? That sounds a
bit too much like the idea of blind faith that we chastise religious
fanatics for!
You need faith to build a plane, and you will need even more faith to
use it. The religious fanatics are dangerous only when they pretend to
know. In science, and in "real religion" it is exactly the same. We
might encounter some certainties, but they are private and
incommunicable, like already consciousness.
Sure, we can go thru a long litany of reasonings and tangential
evidence and analogies, but if we remove the very ability to
determine truth as we know it,
Careful Stephen. The power of the Theaetetus's idea, is that we know
the truth, by *definition*. The price is that we never know the truth-
for-sure, except for consciousness and other private incommunicable
effects.
how can we continue to claim that truth exists unsupported (in the
sense of supervenience) by any representation of it that is not the
entity itself? Please help me figure this out. Can truth exist if
all that exists is Nothing without an Everything that is its dual
(as per your and Hal Ruhl’s definition) and capable of manifesting
concreteness?
I would say that you can't have a notion of nothing, without some
notion of everything going with it. We don't start from nothing in
comp. UDA, as Russell mentioned, even start from accepting some
amount of consensual reality (we believe in brain and doctors). Then a
reasoning shows that numbers and addition+multiplication put already
all the mess we need (and don't need) in Platonia, and explains why
from inside, that Platonia has a border/shadow which acts like a
physical reality. But like in Plato, the physical reality emerges from
something else (number theoretical truth).
The failure of logicism is that we cannot get the numbers from less
than the numbers, so all theories postulates the numbers, (or
equivalent) either at the level of objects, or at the metalevel.
I think that “the knower cannot experience all experiences at
once” is telling us something very important about what a knower is,
something not obvious!
It is basic with Mechanism. A knower needs a brain, and a brain is a
local structure. Personal memories are disconnected. No telepathy, but
as much axons, mobile phones, radio waves, TV, computers and
interacting devices as you need.
--------------
Oops... I was about sending this message, but I see you send a new
one. I will answer it here too:
Did you see my response to Russell’s comment on this thread? I was
using his definition of Nothing that is defined in his book.
See above.
I have more questions that puzzle me from your responses. You
wrote: “ The reason I assumed explicitly AR was for reason of
clarity, but AR is redundant, given that you need it to make sense
of Church thesis. As it is written in sane04, and in the text you
quote AR is just the idea that classical logic can be applied to
arithmetic. “
What is the status of AR now in your thinking?
AR is arithmetical realism. It is the statement that propositions like
"24 is even" are true independently of me, you, the humans, the
aliens, etc. It is the idea that such truth are absolute, atemporal,
aspatial, and that they would be true, but perhaps unknown, in case
the life did not appear here or anywhere.
More precisely, AR is the statement that all arithmetical statement
obeys classical logic. You need it to make sense of statements of the
kind 'machine i on input j does stop, or does not stop'. You need this
to get an understanding of Church thesis and of the notion of partial
computable functions and the possibility (and necessity) of universal
digital machine. In fact, without AR, a word like "digital machines"
loses its meaning, or becomes vague, or restricted in appearance.
Everyone believes in it, when it is not made explicit. Making it
explicit attracts the Sunday philosophers, or the ultrafinitist (which
are either mute, or do believe in it for being able to say that they
don't believe in it).
AR is the part of math where all mathematicians agree, in practice. By
a subtle result of Gödel, arithmetical intuitionism is basically
equivalent with arithmetical classical realism. Intuitionism becomes
sensibly different only when handling the real numbers, and with comp,
we don't need them at the ontological level. At the epistemological
level, we need more and will always need more than the 'existing
mathematics', due to incompleteness. Arithmetic seen from inside is
*much* more big than arithmetic seen from outside. It is a form of
Skolem paradox.
“AR gives all you need to have a concrete (even if immaterial)
implementation of the UD. In a sense, it arguable that AR is more
concrete than anything suggested by physical experiments and
physical theories.”
Does not AR require a 1p, such that we cannot say that one can
exist without the other?
The word "requires" is ambiguous. Accepting comp, AR *implies* the
existence of 1p. AR implies that all numbers developing correct
discourses about themselves (and that exists by AR) will be befuddled
by the apparent discrepancy between what they know (Bp & p) and what
they believes/proves (Bp).
Comp implies that numbers have unavoidable difficulties in betting
that they are relative numbers. Numbers will instinctively say NO to
the doctor, but, once 120 years old, and still wanting to see their
grand-grand-grand-children, or just to see the next soccer cup, they
might change their mind. The social pressure will even push them to do
that, if only because the society likes tax payers.
Bruno
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to
everything-list+unsubscr...@googlegroups.com.
For more options, visit this group at
http://groups.google.com/group/everything-list?hl=en.
