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.




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