On 17 Sep 2011, at 19:07, Stephen P. King wrote:
On 9/16/2011 2:30 PM, Bruno Marchal wrote:
On 15 Sep 2011, at 23:06, Stephen P. King wrote:
On 9/15/2011 2:43 PM, Bruno Marchal wrote:
On 14 Sep 2011, at 06:13, Stephen P. King wrote:
On 9/13/2011 11:28 AM, Bruno Marchal wrote:
On 12 Sep 2011, at 22:16, Craig Weinberg wrote:
To say that complex things can result from very simple rules
is true
enough, but it's circular reasoning that distracts from the
relevant
questions: What are 'rules' and where do they come from?
You are the one assuming some physical reality. But mechanism
can explains where such physical rules come from. They are
consequences of addition and multiplication. More exactly,
their appearances for the average universal machine are
consequences of 0, +, and *.
Dear Bruno,
Could you give us a sketch of exactly how 'physical rules'
or the appearance thereof are the "consequences of 0, + and *"?
I think that there is more to the explanation than the fact that
0, + and * exist.... This is the part of your work that
I still do not understand.
Well, it is the second part. the one I call AUDA.
In a sketch.
1) define provable-by-machine-PA in the arithmetical language {0,
s, +, *, "E", "A", etc.}. Like in Gödel 1931. This gives Bp (for
beweisbar <some arithmetical proposition>. This will play the
role of the "scientific rational opinion of the machine".
2) Solovay: the truth about the logic of Bp is given by G*. The
provable part of it is given by G.
3) define the knowledge of the machine by Bp & p. (Theatetus) The
logic of Bp & p is given by S4Grz (a logic of a form of
intuitionist evolving antisymmetrical knowledge.
4) define observable by Bp & Dt (logic Z and Z*-
5) define feel-able by Bp & Dt & p (logic X and X*)
Note that the splitting proof/truth (G/G*) extends to Bp & Dt,
and to Bp & Dt & p; that is the observable and the feel-able.
Then (eneter the arithmetical UD): restrict the arithmetical
realization of the sentence letters p to the sigma_1 sentence.
You get the logic Z1* (quanta and qualia). the quanta appears in
the non communicable part, and are particular case of qualia, and
this assure our coherence: we share histories (this is what
Everett confirms the most: we are collectively multiplied by huge
factor, and symmetry and linearity appears at the arithmetical
quantum bottom.
If comp is correct, and if the Theatetus's idea is correct, Z1*
gives the probability one, and you can deduce the other
probabilities from there (von Neumann old criteria for a genuine
quantum logic).
I hope I was not too sketchy. Use this to dig on the second part
(the interview of the LUM, it is AUDA) of the sane04 paper.
Bruno
snip
Umm, OK. David Deutsch discusses ideas in his new book that
seem to strongly ague against this idea that an equation, even a
sigma_1 sentence that is very elaborate, alone can act as a proof.
I have never said that. A proof is a sequence, or a graph, or a
diagram, but always amenable to a sequence, of formula, starting
from other formula.
[SPK]
So how do you avoid infinite regress?
By sthe second recursion theorem of Kleene. Or, more simply, by
diagonalization. If Dx gives xx, then DD gives DD. This simple idea
explain how numbers can be self-referential relatively to universal
numbers.
You seem posit as primitive some form of number and then build a
structure upon it that serves as an explanatory model for
'everything', including the appearance of a physical world with
laws, all the while not explaining how it is that the primitives
have the properties that they have other than pointing to our
experience of mathematical entities.
I postulate only two things:
1) that I can survive with a digital brain in this mundane consensual
reality (the nature of which I am neutral about)
2) that elementary proposition on natural numbers are true
independently of me and you. All scientists do this.
This is circular! In my thinking we can embrace circularity to some
extent, via non-well founded sets/logics, but even there we cannot
violate basic principles of contradiction and identity.
Where do I violate principles of contradiction and identity?
I distinguish between the implementation of a representation of
a proof - given in terms of some configuration of matter - and the
relations and structure of the proof itself.
Nice. me too.
I see this as a basic duality between abstract algebras and concrete
structures, taking neither as primitive.
What do you take as primitive?
I am having to reevaluate my thinking of UDA and AUDA as I read
The Beginning of Infinity...
This means you have not understand them. It is just a question of
understanding. You might decide to reevaluate the truth of the
mechanist assumption, but I am not really interested in that
question. The reasoning shows that mechanism is incompatible with
phsyicalism/naturalism, and it need to be understood, not evaluate,
nor reevaluate, nor accepted. But understood or perhaps to be shown
containing a flaw, or a missing step, or something unclear.
[SPK]
I see a difference between understanding an idea and believing
that it is true.
The point is that there is no idea, and certainly no truth assertion
at all. But you cannot understand a proof and still doubt that the
conclusion does follow from the premises. Once you understand the
proof that there is no natural numbers x and y such that x^2 = 2* y^2,
you stop to pretend that such numbers exist, or you are irrational. It
is the same with mechanism: it shows that substance-matter is a
concept void of any explanative power in physics, and that the
physical laws are not primitive and evolve in a precise way in
arithmetic.
My problem boils down to being asked to believe that an abstract
version of a perpetual motion machine can exist without problems.
?
A Platonic turing machine, or equivalent in Post, Peano, Goedel,
etc. terms, is defined in ways that ignore all requirements of
physical reality.
I don't postulate a physical reality, but even if I did, it is a fact
that computer can exist without violating any law of physics. The
physical requirements are explained in a non physical theory.
They can perform computations (which I interpret as transformations
of information) without any reliance on the ability of a physical
system to implement them. I know that this is explicit in their
definition, but it is this definition that I have a problem with!
This is basic and well explained in elementary textbook in theoretical
computer science. It is no more mysterious than the truth of
elementary arithmetical propositions.
How are we to take literally an idea, used to explain and
predict physical and psychical phenomena, that violates the
simple principle that 'there is not such thing as a free lunch',
without some explanation - other than some musings about the ideas
of some famous Greek fellow?
If you doubt in the independence of the arithmetical truth, then
explain me the law of dependence, and explain me what are your
primitive elements in your theory.
We can recast this problem in terms of explaining the appearance of
change in a universe that is static.
This is something else. This is explained by the indexical approach to
time, and is as much a problem for a physicalist than an objective
idealist. It concerns any block-conception of reality. With mechanism
the explanation is that the "Bp & p" is a logic of subjective
duration. Consciousness select histories and glue them into conception
of realities.
UDA shows that mechanism is not compatible with physicalism. David
Deutsch is both mechanist and physicalist, so its theory/world-view
is inconsistent/non-sensical (like the current widespread mechanist
Aristotelianism).
I still suspect that you are neglecting the role that you are
playing with regard to your work. Without a person (or something
like an entity to whom meaningfulness can obtain) to interpret the
sigma_1 sentences, they are not different from a random
configuration of marks on a chalkboard or pixels on a computer
monitor.
You confuse a formula (a mathematical object in metamathematics)
and a representation of a formula.
Am I? How do you explain the relation between the two? Oh, I
forgot, you claim that the physical stuff is just a 'dream of the
numbers'...
I am not claiming that. I am claiming that it follows logically from
the mechanist assumption. I am not saying that the mechanist
assumption is true.
Forgive my cynical tone, but I have invested a lot of time reading
and thinking about your ideas as expressed in your posts and papers,
please consider that I am trying very hard not to argue against a
straw man version of your idea.
I am used to cynical tone. The problem is that it is never clear if
your idea are presented for doubting mechanism (my working assumption)
or doubting that there is no flaw in the reasoning.
The problem of Boltzmann Brains in infinite universes seems
related to this problem that I am seeing!
The UD can be considered as a strong and precise generalization of
that idea. That is the comp mind-body problem. A transformation of
the mind-body problem into a purely arithmetical body problem. The
solution already found shows that the picture of the
epistemological reality of the machine is a theology in the greek
sense of the term: a theory of everything explaining the origin of
God, souls, intellect, the observable realm and the feel-able
dynamics/interactions.
[SPK]
The problem with Boltzmann Brains is how is it that the
computational content of one is related to the content of another in
some sequential way?
On the contrary. The BB problems comes from the assumption of
mechanism, which indeed can glue infinities of BB in ways which could
lead to contradiction with the known physics. With comp this is made
into a precise mathematical problem (the measure on the sigma_1
proposition and their constructive proofs (computations).
Any given BB is only instanciated for a moment by chance... So we
need an infinite ensemble of BBs and an explanation that is not
regressive of how their computations are connected.
Comp explains that there is a statistical connexion which drives the
consciousness fluxes.
Does your UD do this?
The UD generates the computations on which the statistic bear, and
consciousness build the epistemological realities, including the
physical one.
BTW, this thought-experiement does not have the 'free lunch' problem
because it involves a physical/thermodynamic component..
But that is a problem, because it assumes comp, and comp forbids the
reference to a primitive universe.
You seem to rely to much on a hypothetical 3p to act as an
abstract version of a "perceiver of meaningfulness" without
admitting this reliance.
It is explicit in the act of saying "yes to the doctor", which is
part of the explicit assumption. The 'hypothetical 3p", arithmetic,
is taught in schools since Pythagorus (at least). The human
intuition about it is probably as old as music.
[SPK]
"Yes Doctor' explicitly requires the existence of a physical
entity to make the choice
A person makes the choice. It is not a physical entity. You confuse a
person with one of its local body.
and this cannot be abstracted away in some limit of computational
sequences.
Then UDA is wrong. Where?
The same goes for the copy/clone scheme that is used to explain 1p
indeterminancy.
Only for pedagogical purpose. This is explicitly eliminated at step 7
and 8.
If 3p is truly independent of any 1p,
It is, by arithmetical realism. If you believe that "17 is prime"
depends on humans, I will ask you to define "humans" and to show
explicitly the functional dependence.
[SPK]
This is why I have a problem with realism. It fails to provide
an explanation of how the 3p and 1p are correlated other than
pointing to the fact that we humans do in fact experience something
that is like having an experience of something.
It is the relation between Bp and Bp & p. It is trivial for the
ideally correct machines, which use of is enough to explain the origin
of the physical laws, in a way coherent with the immaterialist
consequences of mechanism.
then how are they related such that we can, as individual minds,
have a subjective experience of 3p aspects of existence?
The 3p physical aspects is the 1p plural person views of the 3p
arithmetic, when seen from inside. (Consequence of UDA).
[SPK]
I agree this this, but cannot you see that this inside/outside
relation is the very same relation that I am promoting as a form
of dualism?
I have already agree on this many times. You are the one throwing
doubt on that connection. Mechanism leads to phenomenological octalism
(the eight hypostases). Your dualism is well approximated by the
dualism between Bp and Bp & p.
It is made precise by taking into account the communicable and non
communicable parts explicitly.
This dualism vanishes in the limit of existence itself, but at the
level of existence itself we have a neutral monism;
Yes, and with mechanism, the neutral monist ontology is given by any
first-order logical specification of any universal system. they all
leads to the same number theology, including physics. Physics is made
100% theory and observer independent, despite it being a construction
of "program" consciousness.
difference itself vanishes there. There is not such thing as number
or anything else at that level!
So what are the elements of your neutral monism?
With AUDA we can say more. The 1p/3p relations come, in the
machines' perspectives, from ignoring that Bp is equivalent with Bp
& p, which true equivalence is known only by the "divine
intellect" (G*). This gives a theory of non syntactical knowledge,
obeying the admitted knowledge theory (S4) , equivalent with the
correct opinion of the correct machine, but not in a way such that
the machine can know this, except by betting on comp and its own
correctness, and this, at its own risk and peril.
[SPK]
Sure, but this is just the abstract half of the duality!
I don't see what is missing, and I realize I have no clue about what
is your primitive ontology.
Bruno
http://iridia.ulb.ac.be/~marchal/
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