Dear Jose, dear Loet, dear Krassimir, dear Alex, dear Pedro, dear All,
I sum up answers to Loet, and many others in this answer to Jose, to
avoid too much posts, but also I am in a very busy period.
On 16 Oct 2017, at 01:34, Jose Javier Blanco Rivero wrote:
Dear Krassimir, dear all,
I have noticed that some descriptions of information make use of
anthropocentric metaphors and that might be misguiding (for
instance, subjective and objective information (Sung)). Agent is a
concept that retains some sort of action-theoretic background but at
the same time assumes the existence of nonhuman agents. Agency would
be then a causal relation wherein the agent "causes" some sort of
effects.
I don`t feel confortable with this concept. I prefer the the concept
of observer. But this one is problematic too, for the same reason:
it is supposed that a human is there watching, feeling, measuring,
etc.
I think we have to get rid of these humanistic assumptions in order
to gain insight into the issues we want to explore.
Definitely I don`t think I have the answer, but following D.
Hofstadter, H. von Foerster, N. Luhmann and others we could think of
a agent/observer as a self-referential loop. Most of information
processing devices consist of a design of some sort of feedback
loop. I don`t know if we could translate this idea to all the kinds
of systems we all deal with. But it would be worth finding out.
Hofstadter is a rare physicist who is not wrong on Gödel's theorem,
technically, and with respect to the digital mechanist thesis.
Logicians, including myself, have exploited this a lot in the
fundamental studies. See my paper "Amoeba, Planaria, and Dreaming
Machine". But see also the work of Myhill, John Case, Emil Post
refered in.
Note also the very good book by Judson Webb illustrating how the
discovery of "incompleteness" is a lucky event for mechanist philosophy.
In fact incompleteness saves machine from reductionist theories, as it
makes all theories of them essentially undecidable ("essentially"
means incomplete *and* incomplete-able).
In fact, I was about deciding to study biology when I discovered that
Gödel exploited the same kind of self-reference, in arithmetic (!)
that I discovered in the books of molecular biology.
Today, we got the ultimate theory of self-reference through two
fundamental theorems by Solovay:
1) The provable part of self-reference is axiomatized soundly and
completely by the modal logic G, and
2) the true (provable and non provable) part is axiomatized
soundly and completely by the modal logic G*. G is properly included
in G*, by incompleteness. For example, Gödel's second incompleteness
theorem, with "~" for "not", and [] for the modal box representing
Gödel's arithmetical provability predicate, and "f" representing the
sentence "0 = 1":
~[]f -> ~[](~[]f) (if I am consistent (~[]f) then I will
never prove that I am consistent),
is a theorem of G. But consistency itself is not, and is (only) a
theorem of G*.
The machine which is as powerful as Peano Arithmetical in arithmetic,
and all its sound effective (recursively enumerable) extensions obeys
to G and G*. Their beweisbar (provable) predicate is sigma_1 complete,
which is an arithmetical equivalent with Turing universal.
This offers eventually a complete "Neopythagorean or Neoplatonist
theology" to all arithmetically sound machine.
As Gödel said in his 1933 short notice: "provable" does not obey to a
logic of knowledge. It cannot prove its own soundness, in fact it
cannot prove all []p -> p. Indeed consistency ~[]f is equivalent with
[]f -> f.
That invites to take back the oldest theory of knowledge from
Theaetetus; to know is to believe and be true: to know p is (to
believe p , and it is the case that p). This works: the logic of
"beweisbar ('p') & p" to obey to a logic of knowledge. In fact we get
the 8 nuances:
p (true)
[]p (provable, rationally justifiable, third person self-reference)
split on G/G*
[]p & p (knowable, first person self-reference, not justifiable as
such, not nameable, "soul", and does not split on G/G*)
[]p & ~[]f (bet-table, predictible, observable, repeatable, quanta,
observer, split on G/G*)
[]p & ~[]f & p (sensible, feel-able, qualia, feeler, split on G/G*)
with p restricted on the semi-computable (sigma_1) predicate, this
provides arithmetical interpretations of intuitionist logic and
quantum (and mixed) logics, at the place some thought experiences show
where it should be.
G* proves, at that sigma_1 (partial computable, semi-decidable,
machine) level all the equivalence betwen the nuance above. It can be
shwon axiomatized by G + p -> []p.
G1* proves p <-> []p <-> ([]p & p) <-> ([]p & ~[]f) <-> ([]p & ~[]f &
p).
But G1 does not prove them, and indeed, they obey to those different
logics mentionned above. This means that there is one "simple" truth
(the sigma_/semicomputable reality), but viewed from the machine
"living" in arithmetic with respect to probable universal numbers.
An operative loop enables the differentiation of system and
environment. The system acquires the capacity to control its own
behavior.
Yes. The universal machine is not the omniscient machine Hilbert was
hoping for, but it is more like an ultimate alien which invites itself
in the debate. It is mainly a door to the unknown, and it is
responsible for the uncomputable mess in even that little
"platonia" (taught in primary school already, note).
At some point its internal states are so many that it biffucartes
and grow complex. Subsystems can differentiate by the same
mechanism. So, that`s my point: one have to look for self-
referential loops in order to find the observer/agent.
Self-reference, of different kinds is where theoretical computer
science excels the most. The main theorem is Kleene's second recursion
theorem, which provides extraordinary extensional and intensional sort
of self-reference.
Take any enumeration of the partial computable functions (from N to N,
say): phi_i, and take any particular transformation phi_t, you can
always find a program/number e such phi_e(x, y, z ...) = phi_t(e, x,
y, z ...). I exploited this for a constructive theory for self-
reproduction and embryogenesis.
Solovay's proof of the completeness of G and G* involves a program
which defines itself in term of its own limiting value (in some
computer science term).
An intelligent agent would be some kind of loop (strange loop,
maybe). It`s just a hypothesis anyway...
In arithmetic, I would use agent for the universal numbers. I am still
trying to understand their "theology", which might be close to
trivial, but have some doubt. The theology above would be for the
"intelligent agent", in Krassimir's terming. They are universal, but
also knows that they are universal.
It is the difference between Robinson Arithmetic: Classical
propositional logic with the (non logical) axioms
0 ≠ (x + 1)
((x + 1) = (y + 1)) -> x = y
x = 0 v Ey(x = y + 1)
x + 0 = x
x + (y + 1) = (x + y) + 1
x * 0 = 0
x * (y + 1) = (x * y) + x
and Peano arithmetic:
0 ≠ (x + 1)
((x + 1) = (y + 1)) -> x = y
x = 0 v Ey(x = y + 1)
x + 0 = x
x + (y + 1) = (x + y) + 1
x * 0 = 0
x * (y + 1) = (x * y) + x
with all formula (F(0) & Ax(F(x) -> F(s(x))) -> AxF(x)), with F(x)
being a formula in the arithmetical language (with "0, s, +, *),
Robinson arithmetic is Turing universal, but knows not much on
arithmetic, it cannot even justify 0 + x = x. It is not Gödelian-
Löbian, and as a subject, does not obey to the "theology" above.
I use "theology" in the sense of the analysis of Hirschberger on
Plato. "The God of Plato is Truth". Not the Truth that we assert but
the one we search, and the "correct" (with respect to mechanism)
intuition is that it has a transcendental, undefinable, aspect. With
Mechanism, we can limit oneself to the arithmetical truth (a quite non
computable reality), and the computationalist can identify it with the
far more restricted apparently sigma_1 arithmetical truth (but has to
keep this for him, and never presented this as true!). The non
emptiness of G* minus G gives the proper non justifiable theology.
Similarly, consciousnes can be explained by the existence of truth,
which are knowable by the machine/entity, undoubtable, but are not
rationally justifiable, nor even nameable or third person describable
by the entity.
Note that Vardanyan and others have shown the high non computability
of the first order modal logics of probability(*). The miracle is the
completeness at the propositional level. G and G* (and G1, and G1*)
are also decidable, and we can compare the logic of the observable "in
the head of the machine" with the logic of the observable inferred
from the observations. It fits well up to now thanks to quantum
mechanics and some quantum logics.
About information, what I find intriguing is that in a computation,
the only thing which cost energy is the erasure of information. Hao
Wang showed a long time ago that universal machine which never erase
information exist, and we can "build" reversible universal machinery.
Indeed, some quantum computation necessitate the exploitation of
unitarity, and without collapse, the full universal quantum
computation has to be reversible. That aspect is not fully apprehended
in the machine's logic of the observable ([]p & ~[]f, p sigma_1).
Consciousness seems to differentiate by getting information, like in
the self-duplication thought experience, and consciousness "fuse" by
either erasing information, or discarding it leading to dissociation
and self-multiplication.
I work on this since a long time, I can give references with more
details.
Of course, humans in real life have a non monotonical layer of belief,
so that they can change their mind and withdraw some "beliefs". The
theory here is very fundamental and mainly attept to formulate the
mind-body problem assuming the digital mechanist hypothesis in psycho/
theo/biology.
Algorithmic information theory is also a place where arithmetic and
information theories can met, with the notion of immune and simple
sets, due to Emil Post.
Best regards,
Bruno
(*) For those who knows Kleene's hierarchies, quantified G (qG) is
PI-1 complete (a divine (I mean a non-machine) being) and qG*is PI_1-
complete in the Truth oracle: The machine intelligible Noùs is above
God's ability to handle, at least in one step!
Best regards,
El oct 15, 2017 6:29 PM, "Krassimir Markov" <mar...@foibg.com>
escribió:
Dear FIS Colleagues,
After nice collaboration last weeks, a paper Called “Data versus
Information” is prepared in very beginning draft variant and
already is
sent to authors for refining.
Many thanks for fruitful work!
What we have till now is the understanding that the information is
some
more than data.
In other words:
d = r
i = r + e
where:
d => data;
i => information;
r => reflection;
e => something Else, internal for the Agent (subject,
interpreter,
etc.).
Simple question: What is “Agent”?
When an entity became an Agent? What is important to qualify the
entity as
Agent or as an Intelligent Agent? What kind of agent is the cell? At
the
end - does information exist for Agents or only for Intelligent
Agents?
Thesis: Information exists only for the Intelligent Agents.
Antithesis: Information exists at all levels of Agents.
Friendly greetings
Krassimir
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