On 11 Jan 2014, at 18:42, John Mikes wrote:
Reply to Bruno;
Wed, Jan 8, 2014 Bruno M wrote:
Note also that Popper's principle has been refuted in the Machine
Learning theory (by John Case & Al.). Allowing an inductive
inference machine to bet on some non refutable principle enlarges
the class of computable functions that they can infer in the limit
of the presentations of their <input, output>.
Don't mind too much. Popper criterion remains interesting, just not
100% correct.
...
Computationalism can justify that, in the matter of machine's
psychology, every general assertions have to be taken with some
amount of grains of salt.
------------------------------------
Let me try to explain the three notions: 'machine', 'comp',
'universal'.
Computability theory is a branch of mathematical logic, and the
notion of computable functions arise from studies in the foundations
of mathematics. Gödel, in his 1931 negative solution to a problem
asked by Hilbert, already defined a large class of computable
functions, needed in his translation of the syntax of arithmetic in
term of addition and multiplication.
JM: How do you get to SMALLER values by using ONLY addition &
multiplication of natural integers? Is your world a ONE_WAY -UP?
Actually I can define "s" from 0, addition and multiplication. So we
have s, the successor notion, that I take often as a primitive too.
Numbers are then given by 0, s(0), s(s(0)), ....
Then you can define x is the predecessor of y by y = s(x). You have y
= s(x) if and only if x is the predecessor of y.
---BTW: math-logic is the product of human (machine? see below) mind.
With comp, human are particular case of machine.
This has led to the discovery that I sum up as the discovery of the
universal machine, or of the universal interpreter, missed by Gödel,
but not by Emile Post, Turing, Kleene, etc. Gödel will take some
time to accept Church thesis. Eventually he will understand better
than other, as he will be aware of what he called a *miracle*.
I don't believe in miracles: they mostly turn into process-results
by further learning.
Miracle means only "extremely weird". The "Godel miracle" (the closure
of the set of partial computable function) is a mathematically proven
fact for all the very diverse notion of computability, and provides a
very deep conceptual argument for the consistency of the Church's
thesis.
Church defined computable basically by a mathematical programming
language.
All definitions of computable leads to that same class, and they all
contains universal programs/machines/numbers.
Programing goes by known elements.
All theories do that. If not it is untestable jargon avoiding the
questions, and the testability.
Also MACHINES (in my view) include only knowable parts with
assignable mechanism. Not as 'organizations' that may contain
unidentified (infinite?) aspects. But I accept your 'machine' as "us".
Not at all. Comp would be a human can be replaced by a human, which is
absurd, or tautological.
The notion of machine I am using is the mathematically precise one
given by the Church thesis.
Those are digital machines (programs) interpreted by layers of
universal machine (interpreter or compiler of programming language)
until the (analog) quantum field implementing it into your laptop or
GSM.
"My laptop" does not go 'analogue'(quantum computing). Only digital.
Restricted.
Quantum computation is still digital. A ruler is analog.
Comp is the opinion of the one who agrees that his surgeon replaces
his brain with a computer simulating it at some substitution level.
More exactly comp is the assumption that this opinion is correct,
for some (unknown) level.
Sorry, Bruno, my answer to the doctor is "NO": no (digital) finite
machine (computer) can completely replace my unrestricted mindwork
including not-understood infinites etc.
But I will be franc: I don't mind. My point is not that comp is true.
My point is that if COMP is true, then physics is a theorem in comp,
and that this makes comp testable. So let us test it. Up to now, comp
gives a Platonic theology including a precise physics looking already
like a quantum mechanics.
Comp is for computer science. Theoretical computer science is born
well before computers appears and develop. By machine I mean
"digital machine", and the universal machines are the one which can
imitate, by coded instruction, all digital machines.
So far we are in close agreement.
Those machines are enumerable. There is an enumeration of all of
them: m_0, m_1, m_2, m_3, m_4, ...
So, you can fix one universal language, like a base, and identify
each machine with a number. Each programming language, or computers
boolean net, correspond to some m_i, and are universal m_i, as they
can imitate all others machines (accepting Church thesis).
What exactly FROM the Church theses?
With Church theses, you can prove Gödel incompleteness in very few
lines, and the universal machines is truly universal with respect to
computability ability. You need it to define mathematically the notion
of universal machine, or to accept that computer are universal machine.
The 'enumeration' is beyond me: you did not tell about "numbers" and
processes outside the mathematical logic people experience.
That is not an argument. You can say that for all theories brought by
a human, about anything. let us work in the theory, until we have a
best one, or until our theory is refuted.
You talk like if I was defending a theory. I do not. As a scinetist,
we can only be agnostic, in all matter. We can just hope to be
refuted. We never know the truth *as such*.
We had some exchanges.
But I don't want you embarrassed by too much technicalities. Comp
might be false, but at least it makes it possible to formulate the
problems thanks to computer science and mathematical logic.
The discovery of the (Löbian) Universal Machines is the discovery
*of* the mathematicians in arithmetic, *by* the mathematicians. And
guess who put so much mess in Platonia? The mathematicians.
The arithmetical reality is full of life and dreams. Even without
assuming comp. "Strong AI" is enough here.
Fee free to ask any question(s).
I did (some). One more: Intrelligence (as in AI) is not restricted
to digital handling
?
AI is based on digital machines.
and so is 'thinking' (putare - as in com - putare, the precursor of
computing).
In the human history, but after Church thesis, we can recognize the
computation in the additive-multiplicative structure of the numbers.
That appears already in Gödel 1931, and such a result has go much
stronger version since then.
I find your math based nature a restricted image (my fault)
Yes, your fault, as you might have a reductionist conception of
numbers. After Gödel, we know that we know nothing about the numbers.
and seek a more wide view of alll the unknown we still have to learn
(if we are capable of).
But today we know that the arithmetical reality defeats *all* theories
on them. To assume unknown is equivalent to assuming we cannot
progress, and this can make people stopping the research, and acting
like if they knew. You get the inverse of agnosticism if you refuse
theories and attempt of explanations. We must not fear to be wrong, as
science progress only by daring being wrong and corrected.
Best,
Bruno
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/groups/opt_out.
