May 29, 2017

Pythagoras, Plato, Moderatus of Gades, Plotinus, Augustine, Descartes, and Leibniz

Nice poem.

"Investigating consciousness via science
And mathematics can never be satisfying
Because of the subjective nature
Of the object of observation."

It depends on the assumption of your fundamental theory. 

With the mechanist assumption, you are not only right, but what you say becomes a theorem in the fundamental theory. With mechanism, even arithmetic entails the existence of the many subjective views, and of many possible observations, and their parts partially irreducible to anything 3p describable.

Mechanism saves the soul (of the machine) from all reduction to anything purely 3p describable. It provides a powerful vaccine against reductionisme (indeed against already the reductionist conception of what are capable the digital-machines/numbers).

Bruno
May 28, 2017

Thanks Bruno for appreciation and positive assessment. You have raised enough anticipation in this forum about your theory which, let's hope, will be unveiled by you someday so that it can be understood by non-specialists like me without being tortured by mathematical symbols or equations.

I have, however, added the final four lines to the above poem as follows:

It's agreed that we are far away
From any semblance of a solution
This should mean as a very sobering attitude
In the face of human finitude.

All the best,

Tusar

...

"Roger Penrose argues compellingly that the brain is not a classical computer."

Hameroff does that. penrose argues, non compellingly (I think), that the brain is not a computer at all, not even, unlike Hameroff, a quantum computer.

"Anyway, physics is not the good science to tackle the mind body problem, unless, like Penrose, you assume that mechanism is false. But that seems speculative to me."

Consciousness is no mystery. It is a non-algorithmic locally retrocausal post-quantum emergent phenomenon from direct action-reaction between quantum mind waves and the matter they move.

Do you agree that consciousness is "true", and non justifiable, yet undoubtable? can you explain why qualia verifies this in your theory?

Bruno
May 9, 2017
...

"Roger Penrose argues compellingly that the brain is not a classical computer."

His explanation using Gödel is invalid, as many logicians have shown. Judson Webb wrote a book on a similar error made by Lucas. In the long version of my work, I show how some machine can already defeat the Gödelian argument.  I can explain more, or give references. 

Consciousness is not algorithmic, OK. That is provable using mechanism. The conscious machine knows that their consciousness is not algorithmic. Not only Gödel's theorem does not refute Mechanism, but it implies that the machine have a very rich intricate theology, close to the negative theology of the neoplatonists.

Bruno Marchal
May 28, 2017
...

Priyedarshi,

"On 24 May 2017, at 19:41, priyedarshi jetli wrote: Srinavasa,
What you say seems plausible. Knowing one's limitations is the key. In the history of philosophy we see this emphasized by Socrates, Plato and Kant among others. However, most of the discussion in this forum is about going beyond the limit of human knowledge and big claims are made about the existence of God and consciousness and their causal role. This is what Kant would call dielectic illusion, that is claims to knowledge of something that is beyond the abilities of humans to know. To justify such knowledge the only recourse is to appeal to some sort of divine interference."

Important remark. 

"And it always amuses me how we know that God made humans superior so that only they can know this, yet every life form is necessary for the survival of the planet."

Or maybe God has not made the humans superior. Maybe all machine already "knows" that in some sense. May be God has only made the "universal machine" somehow superior ...

It is here that Gödel's theorem provides a formidable clue. For each machine there is an arithmetical proposition (Dt, no need to even know what it means just now) which is true, but beyond the machine's ability to prove. Penrose and Lucas used it to claim that we are superior to machine. 

But Penrose and Lucas did not see that the machine can prove its own incompleteness theorem. Peano Arithmetic can prove that If Dt is true, then Peano Arithmetic cannot prove Dt, and the machine can even postulate Dt to explain its inability to prove Dt.

Dt is ~[]f. It is the machine's self-consistency. A machine can prove that if she is self-consistent then she will never been able to prove its self-consistency.

Then, the machine can *bet* that the reason of why she cannot prove its self-consistency is the fact that she is self-consistent. This requires from the machine something akin to a reference to Truth, which plays the role of God (in this context). Note that tarski has proved that the machine cannot really define Truth.

"There is something similar with (human) consciousness. If X is conscious, X can eventually understand that X is unable to prove his consciousness to another."

In any case I see a paradox that even you might have to face. If you are going to claim that there is a God and this God is the final cause of everything or that there is a universal consciousness and it is supervenient over the physical, then how do we acquire knowledge of this since it is beyond the capacity of humans to know this as we hear repeatedly. 

"We can, by reason only, understand that there are truth which extends properly reason. Theology acquires a reasonable base. Something is beyond us. The question becomes if that something is a physical universe (impersonal god), or a personal god behind, or Consciousness, or the chinese Tao, or perhaps no more than the arithmetical truth.  A case for Arithmetical Truth playing the role of "God" can be made when we assume Mechanism. Please note that 99,9% of the Arithmetical Truth is well beyond the computable."

Scientific theology can become the scientific study of what extends properly science, and incompleteness illustrates that this has sense. 
Not all of theology can so reduced, though, but that very fact can also be proved (assuming mechanism), and can still let some places to many different religions, albeit consistent with arithmetic, and mechanism.

Bruno
May 25, 2017
...

Priyedarshi,

"Thanks for a detailed response. I like your turning on the head of Penrose's conclusion from incompleteness."

Thank you.

Emil Post anticipated all this in 1922. He found "Church's thesis", the proof of incompleteness from it (still rather unknown, one day I can give it here, because it is not that difficult, compared to Gödel's proof without it), but he found also the argument against Mechanism (like Lucas and Penrose), and then the main error in that argument, and then he found immateriality (my work) but added that he changes his mind on this after discussing with Turing, who was a Naturalist (and I think was wrong).

"Turing in his famous paper long time ago also encounter the incompleteness problem and simply said that computers in the future will be able to prove incompleteness. Though it will take me to understand you technically, you are essentially saying that."

I am not sure Turing talk about incompleteness in the Gödel sense. I would be astonished that Turing did not see this. The idea that the machines or theories, rich enough, can prove the incompleteness appears already at the end of Gödel 1931 paper, without proof, but that will be accepted quickly, even if not really understood (Gödel will miss Church's thesis, and Mechanism). That will be proved in 1939 by Hilbert and Bernays (and perfectionned by Löb in 1955).

"Now, if this is true, Turing's somewhat sarcastic remark is vindicated."

OK. But by adding the mechanist hypothesis. Turing, unlike Gödel, was rather in favor of mechanism, despite his naturalism. He did not see the incompatibilty between Mechanism and (metaphysical) Naturalism (assuming my own argument is correct).

He said, so what if one smart human (God) is smarter than all machines, but any machine is smarter than the average human. After all it took many millennia for Godel's incompleteness to emerge.  

Someday, I will give a "simple" proof of incompleteness, which is still rather unknown, although Post saw it in 1922 (ten years before Gödel!). Incompleteness can be proved in one diagonalization from Church thesis. Kleene also saw this.

"I also think, as I mentioned to you earlier that the halting problem cannot be realized in humans due to mortality"

Assuming the human mortality.

"whereas it can be realized in machines as they can build other machines to carry on the problem."

Is this not what we do with our kids? Or even with the machines?

Is the distinction between natural and artificial ... artificial?

"I do not know if this is related to what you are saying."

Of course we can go beyond our limitations to know. I was being a bit cryptic about the definitive jump to the conclusion of the existence of a God or cosmic consciousness that is often made here.

I use the word "God" in the general sense of whatever is the reason of our existence. Then the question becomes: is God a physical universe, or a universal person, or the arithmetical reality, or ...

I have a high respect for all sacred texts, but avoid any literal interpretations. I use them for inspirational personal insight only. I have my favorite one, like "the question of King Milinda", but I do think "Alice in Wonderland" is very deep too.

We can't prove the existence of God, but we can't prove the existence of any reality, in the admittedly string sense of "proof" the logician are accustomed with.

"Coming back to machines, it is interesting that Descartes thought of non human animals as machines without a mind."

I think that the idea that animals have a mind is recent, at least in occident. I take as a human mind progress to recognize a mind, paerhaps a soul, to animals. In the east, people have been more open, perhaps thanks to the re-incarnation theory.

"Surely they have brains and they seem to operate on principles such as induction which humans also operate on."

Indeed.

"A lot of work is done today on their cognitive abilities. In the end, if I understand you correctly, it is not a matter of 'superiority' but of completeness. Perhaps human have more completeness than other non human animals because they can build formal systems and prove completeness."

I am not sure. Animal might be more complete than us. Completeness is a sort of defect. A complete theory cannot be Turing complete. OK, I see the problem.

A complete-with-respect-proving-or-knowing theory cannot be complete-with-respect-to-computability. Turing (computability) completeness entails Gödel (provability) incompleteness. 

So provability incompleteness is a sort of quality, as it makes possible Turing (computability) completeness. It is a pedagogical problem: completeness is udes in different sense by logicians, which are sometimes opposite. We will have opportunities to come back on this.

"Yet, it is not easy for humans to prove incompleteness, which is a further stage of completeness."

In some sense; yes.

"But machines can prove incompleteness and the human proof given by Godel is also really a machine proof. So, it is the machine in us, like the machine in non human animals that is the computational mind that can prove incompleteness. What you are saying, if I am not wrong, is that without mechanism, incompleteness would not emerge and without being able to formalize the Godel sentence and then prove it we would really have an incomplete view  of the universe."

OK.

"In any case there can be a turning on the head of Descartes as well because he thoughts machines to be inferior to humans and thereby non human animals who were machines to be inferior to humans. Whereas as it turns out that humans are superior to non human animals because they are superior machines than non human animals and the machines built by humans is even more superior to the machine in humans and the machine of the universe of course is the most superior."

You can see it that way.

"I like that because as a student of philosophy I have always felt that Descartes is overrated as the founder of Modern philosophy. In terms of methodology Galileo was more of a founder of Modern philosophy and he was also closer to mechanism."

I like Galileo, but I have a deep respect for Descartes. We need to read him by taking into account he was harassed by the religious authorities, and so said things just to appease him. I don't really believe he took seriously his dualism. It is debatable of course. 

"That the universe is a machine and that our brains/minds are also machines is a match, as Leibniz would perhaps say, that is not surprising at all. It is not at all a matter of which came first or a final cause but of a simultaneity in which the perfection  (completeness including incompleteness) emerges."

Maybe, except I don't think that the physical universe, nor God, can be a machine. I will explain later.

"Sorry, I went into a stream of consciousness but it was spurned by your insights."

Thank you for your comment. I would like to add many precisions, but unfortunately I have to go, and the next days are overscheduled. Let us go slowly, at ease. I reassured you that I got the mails normally now. Don't worry if I don't answer quickly, because I will be superbusy those last days of May, and then I will have the June exams, etc. 

Kindest regards,

Bruno
May 26, 2017
...

Bruno,

I also have great respect for Descartes, especially as a mathematician. I am more worried about the press he gets as the founder of Modern philosophy that I am precarious about. In one way he was a continuation of medieval philosophy and his method of doubt can also be traced back as far as Augustine. Leibniz was a greater philosopher and a more comprehensive mind. 

I guess I tend to be a naturalist as well, but I am beginning to see your perspective of on what criterion do we distinguish the natural from the artificial. I believe Turing was interested in biology and chemistry, perhaps this is why he was a naturalist.

Priyedarshi
May 26, 2017
...

Bruno,

You may be right about Plato in terms of the perfection of the Forms. However, methodologically, Plato would welcome incompleteness as he practiced that throughout his dialogues with his second best hypothesis. Now, applying this to Plato's Forms, we could say that the hypothesis that Forms are perfect is the second best hypothesis. Hence, we can save Plato by Plato's methodology.

Priyedarshi
May 26, 2017
...

Priyedarshi,

I agree. I am pretty sure he would have love it. I think it would also have deepened his influence from Pythagoras.

Now, applying this to Plato's Forms, we could say that the hypothesis that Forms are perfect is the second best hypothesis. Hence, we can save Plato by Plato's methodology.

For me Plato's methodology is science in its purest form.

***

Let me answer the two mails in one,

"I also have great respect for Descartes, especially as a mathematician. I am more worried about the press he gets as the founder of Modern philosophy that I am precarious about."

I think he deserves this, because during his life he has not well been treated. Then, the honors, the name, ... it is not so important. 

I appreciate very much Descartes' methodology, also. 

Too bad, he missed the importance of logic, though. He was probably deter by the (already) common misuse of logic.

"In one way he was a continuation of medieval philosophy and his method of doubt can also be traced back as far as Augustine."

Even back to Plotinus, and perhaps Moderatus of Gades. In fact, all honest/correct machine's doubt. Some catholic pope said that the doubt is the devil. But in fact I have reason, and intuition, that it is certainty which is the devil, at least when made public.

"Leibniz was a greater philosopher and a more comprehensive mind."

I have tried to read it, but he is complex. Eventually, there are two or three Leibniz, somehow. Like there are two Wittgenstein (the young (Tractatus) and the old one who wrote a text on uncertainty which is quite interesting. Like Descartes, Wittgenstein get disciples or followers which exaggerates his ideas, and did not listen to his self-critic. His public success has not help him. 

"I guess I tend to be a naturalist as well, but I am beginning to see your perspective of on what criterion do we distinguish the natural from the artificial. I believe Turing was interested in biology and chemistry, perhaps this is why he was a naturalist."

I'm afraid I constitute a counter-example :)

I really started from biology. I looked at amoebas for years. The problem for me was the following: given that an amoeba divides itself every day, does she lives one day, or is she immortal?

The mechanist solution: I really took it from the book of Watson:  "Molecular Biology of the Gene", which has been my bible for a long time, as well as the paper of Jacob and Monod on Gene Regulations. But then, I found a little book on Gödel's proof, and realized that it provides a much larger frame for the "mechanist explanation of the self-duplication" than the chemistry of carbon. I will take time to understand that elementary arithmetic was enough, though. It is that little book which will decide me to study mathematics, instead of biology. But of course, only a theologian can be interested in the question of the immortality, or not, of the amoebas. The problem was that theology (non confessional) was not available at the university. But the greek are right, I think, mathematics is a not to bad approximation.

Bruno
Show quoted text

...

Bruno,

I agree with enthusiasm on your assessment of Plato. I think Aristotle would also have welcomed the mechanism you are talking about. As for the comparison of Leibniz to Wittgenstein I don't quite agree. Wittgenstein has become a cult figure. This is not the case with Leibniz. Later Wittgenstein is often difficult to understand because he is obscure as Russell also admitted. Leibniz however is difficult because he is complex but read carefully he is clear. Further, he was ahead of his times. He was almost always responding to someone or the other. More like journal articles. He had to be provoked to write. I think there not one or two or three Leibnizes. He is often topical, taking on various issues, but always one by one. He was not a system builder nor was he after a world view. But the history of modern philosophy is often looking for a world view as in Hegel. 

I don't know if you have read Kneale and Kneale's Development of Logic. They actually criticize Leibniz for being too fragmented and not completing anything. I think they are being really unfair. His incompleteness is his virtue. Further, expecting him to complete the algebraisation of logic, which he began, is like expecting the Nineteenth Century to arrive at the end of the 17th century or beginning of 18th century. What lies in between Leibniz and Boole is the emergence of symbolical algebra without which Boole could not have arrived at his destination. Couterat, in his book on Leibniz, claims that Leibniz had everything and even more than Boole had, but he did not have the development of algebra that was to come later of course. It is claimed that Boole was not aware of Leibniz's work. I don't think that is possible. After algebraising logic in 1847, in his later  work Laws of Thoiught Boole opens with a quotation in Greek from Aristotle. Is it possible that he read Aristotle in Greek but not Leibniz in Latin?

Priyedarshi
May 27, 2017
...

Incompleteness in knowledge and existence
http://loveofallwisdom.com/#article/3983
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Cross-posted at Love of All Wisdom. A friend read the previous post on ibn Sīnā and Śāntideva and asked (on Google+) what exactly I meant by “incompleteness”. It was a great question and made me realize there was a bit Continue reading →

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