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? 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. 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.
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. I see this as a basic
duality between abstract algebras and concrete structures, taking
neither 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. 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. 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!
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?
We can recast this problem in terms of explaining the appearance of
change in a universe that is static.
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'... 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.
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? 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. Does your UD
do this? BTW, this thought-experiement does not have the 'free lunch'
problem because it involves a physical/thermodynamic component..
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 and this cannot be abstracted away in some limit of
computational sequences. The same goes for the copy/clone scheme that is
used to explain 1p indeterminancy.
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.
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? This dualism vanishes in the limit of existence itself, but at
the level of existence itself we have a neutral monism; difference
itself vanishes there. There is not such thing as number or anything
else at that level!
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!
Onward!
Stephen
Bruno
http://iridia.ulb.ac.be/~marchal/ <http://iridia.ulb.ac.be/%7Emarchal/>
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