On 11 Jan 2014, at 18:42, John Mikes wrote:

## Advertising

Reply to Bruno; Wed, Jan 8, 2014 Bruno M wrote:Note also that Popper's principle has been refuted in the MachineLearning theory (by John Case & Al.). Allowing an inductiveinference machine to bet on some non refutable principle enlargesthe class of computable functions that they can infer in the limitof the presentations of their <input, output>.Don't mind too much. Popper criterion remains interesting, just not100% correct....Computationalism can justify that, in the matter of machine'spsychology, every general assertions have to be taken with someamount of grains of salt.------------------------------------Let me try to explain the three notions: 'machine', 'comp','universal'.Computability theory is a branch of mathematical logic, and thenotion of computable functions arise from studies in the foundationsof mathematics. Gödel, in his 1931 negative solution to a problemasked by Hilbert, already defined a large class of computablefunctions, needed in his translation of the syntax of arithmetic interm 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 theuniversal machine, or of the universal interpreter, missed by Gödel,but not by Emile Post, Turing, Kleene, etc. Gödel will take sometime to accept Church thesis. Eventually he will understand betterthan other, as he will be aware of what he called a *miracle*.I don't believe in miracles: they mostly turn into process-resultsby 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 programminglanguage.All definitions of computable leads to that same class, and they allcontains 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 withassignable mechanism. Not as 'organizations' that may containunidentified (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 ofuniversal machine (interpreter or compiler of programming language)until the (analog) quantum field implementing it into your laptop orGSM."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 replaceshis 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) finitemachine (computer) can completely replace my unrestricted mindworkincluding 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 bornwell before computers appears and develop. By machine I mean"digital machine", and the universal machines are the one which canimitate, by coded instruction, all digital machines.So far we are in close agreement.Those machines are enumerable. There is an enumeration of all ofthem: m_0, m_1, m_2, m_3, m_4, ...So, you can fix one universal language, like a base, and identifyeach machine with a number. Each programming language, or computersboolean net, correspond to some m_i, and are universal m_i, as theycan 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" andprocesses 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. Compmight be false, but at least it makes it possible to formulate theproblems 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. Andguess who put so much mess in Platonia? The mathematicians.The arithmetical reality is full of life and dreams. Even withoutassuming comp. "Strong AI" is enough here.Fee free to ask any question(s).I did (some). One more: Intrelligence (as in AI) is not restrictedto digital handling

? AI is based on digital machines.

and so is 'thinking' (putare - as in com - putare, the precursor ofcomputing).

`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.