what is thought?

[ayeshahaqqiqa]

Has anyone been able to explain what thought is? I know there have been studies that show when people are thinking, certain parts of the brain show activity, but this only describes what is going on in the brain, not what thought is.

And how is it that thoughts can be creative-thinking up something that has never been thought up before, or reinterpreting data in a new and unique way?

How does your answers to these questions relate to your religious/spiritual convictions?

[Donald Ian Rankin]

1. Nobody knows.

By far the biggest asked but answered question is "how does the mind work?"

People have only just begun to try to answer it, and so far none of the answers have got much beyond "we don't know, but here are some interesting ideas to play with". I've heard good things of Roger Penrose's "The Emperor's new mind", but I'm ashamed to say I've never read it.

I'm inclined to think that the mind is more closely linked to the brain than one might think - the ways the mind is effected when different bits of the brain are damaged is intriguing, vide e.g. "The man who mistook his wife for a hat", by Oliver Sacks - which implies to me that the process is much more deterministic that one might think, and it's not clear to me what the term "free will" actually means.

In terms of my religious convictions, this makes me pay less credence to those people who try and argue for the existance of an omnibenevolent supreme being by claiming that all evil is the result of human free will - I suspect (although I'm not sure) that an omniscient being could predict the actions of a human as accurately as they could predict anything else. I acknowledge that it's not a watertight argument, because of quantum uncertainty, but I think it's a strong one, especially if like me you're at heart a die-hard Laplacian determinist who believes that in the end it will all turn out to come down to hidden variables, and Bell's inequality be damned...

[aneerkoinos]

2. Time

We will not understand mind before we drop our illusion about time (which is product of mind-matter interaction, brain). What Einstein and Gödel said and understood about time is extremely relevant also to the study of conscience.

Buddhist science of mind, armed with introspective empirical method (meditation), has been the most advanced, and theoretical physics and western consciousness study is only now beginning to catch up with Buddhism (in the fringes of Academia).

One of the fringe scientist working with unified theory alternative to string-theories, whose theory also includes consciousness, is Matti Pitkänen: http://www.physics.helsinki.fi/~matpitka/

"The quite recent experiments of Radin, and Radin and Bierman give support for the quantum jumps between quantum histories concept in the sense that they give evidence for the change of the past in quantum jump. What is observed is that the physiological reactions before seing a picture are different for calm and emotional pictures! Standard physics would predict no difference in physiological reactions before the stimulus whereas TGD inspired theory suggests that the change of the past induced by a highly emotional moment of consciousness is more dramatic than that induced by a calm moment of conciousness. For details see the chapter 'Matter, Mind, Quantum' of 'TGD inspired theory of consciousness with applications to biosystems'."
http://www.physics.helsinki.fi/~matpitka/tgdc.html

[Az]

3. Here is a question to help ponder this

Do you suppose there would be a mind if there were no senses? Take as an example the classic brain in a vat. Instead of being fed false signals though what if it were kept isolated? Would a mind arise from this structure?

A mind seems to arise from the interaction between the stored experiences derived from our senses. How our sense of existance arises from this is unknown at this time. But perhaps consideration of this factor may lend some insite.

[aneerkoinos]

5. Terminological difficulties

It seems that by 'mind' you mean here 'human consciouss experience'.

What you attempt to discuss is closely related to the so called 'hard problem of consciense', ie. qualia. Sense of existance or self conscience by a system constantly measuring itself is not that hard problem.

Sorry, but the materialistic approach of mind being epiphenomenon of classical physics just don't cut it, but defies most basic logic: ex nihilo nihil.

[Az]

6. The nature of problems

is that we seek their answers. We do not simply presume that we have the one and only answer already. I don't know the answer. I further don't know that the answer is not a materialistic one.

[aneerkoinos]

9. I know ...

We do have enough hints to know from which direction to look from and from where not. If mind was epiphenomenon of (ie reduced to) classical physics, which we understand pretty well, with high probability we would have allready explained it.

What we know with high certainty is that psychological time is an emergent phenomenon, just following Einstein who showed that I don't live in the same time as you, even though that is a very dear illusion that both me and you share. So dear that very few of those studying consciousness can really think and imagine outside the box of psychological time, from which follows the obvious fallacy of trying to explain a phenomenon (mind) without really questioning a basic premise (psychological time) of the approach that is the result of the phenomenon in question.

So the answers we seek will most likely be very complicated and extremely weird when compared to our everyday experience, and truly understanding the answers, what ever they turn out to be, requires that we drop lots of very basic illusions related to basic experience of living in 4D-timespace. In the material world.

The evidence is strongly pointing the way to the direction that mind (or "protomind" which in interaction with biomatter gives rise to consciouss experience) is just as fundamental and irreducible aspect (or even more so) of being as matter, but immaterial, timeless aspect, that can be truly be called transcendental because it is not limited by the 4D-timespace. Yet it is not without form, which is describable, at least to some extent, by (very advanced) mathematics.

We seek answers. But in my search within the context of science, physics and math, the conclusion I have come to is that to really understand the answer to the question about mind in the scientific context, even if it was shown to me, would probably require that I have even more deep understanding and intuition about physics and mathematics than Gödel and Einstein. Sadly, when e.g. trying to read Matti Pitkänen's theory (see my post above for links), which for what I know might very well be the "answer", I don't get further than admitting that I really really really really don't even understand the p-adic numbers, on which the theory is based.

There was a sign above the entrance to the grove of Akademeia saying: "Let no-one enter who does not know mathematics". I'm starting to understand why ... :)

[Az]

13. Time and Complexity

I am quite aware of many studies that show that the brain's recognition of external stimuli is a linear and measurable chronological process. I would be interested in what studies you believe suggest that our minds do not result from linear measures of time. I will admit to being skeptical of such notions but will examine whatever information you may have.

As to us being able to explain something simply because it is the result of classical physics we cannot currently predict the weather beyond a few days. Its a matter of complexity. Or rather chaos. Even though we may be able to explain the basic physics on a very localised basis in complex structures we lose the ability to understand the outcomes. Simply put the brain is an astoundingly complex structure. So much so that we cannot yet rule out a macro explanation for the existance of the mind.

[aneerkoinos]

15. Being and time

The experiments by Radin, and Radin and Bierman, which strongly suggest backward causation in time, were mentioned in my post above.

The vast bulk of evidence of an consciousness related anomaly from the field of "paranormal", acknowledged in meta-analysis as weak but persistent, is not explainable by classical physics (hence "anomaly"), but presents no problem for the quantum approaches to mind.

Predicting weather and understanding mind are not comparable, there's nothing like hard problem of qualia etc. to be solved in weather prediction (or generally chaotic systems, Brownian motion etc.), which is basically just matter of insufficient data and calculus power, the basically deterministic processes involved are understood pretty well, no hard problems involved.

Sure, nothing can be ruled out, but I can't see macro explanation leading anywhere but to the eliminative materialism of Churchlands & co ( http://en.wikipedia.org/wiki/Eliminative_materialism ). Naturally I reject the thought that I am (just) a Zombie, not based on thought but because I've empirically realized that in the silence between thoughts (when and where "I" might not exist) there's still awareness.

[H2O Man]

4. A Poem:

IS THIS REAL?

Let us see, is this real.
Let us see, is this real,
This life I am living?
You, Gods, who dwell everywhere,
Let us see, is this real,
This life I am living?

- Pawnee; song of creation of consciousness

[H2O Man]

12. At this point

I believe the Pawnee song is the most accurate answer to the OP question.

[madeline_con]

7. many within the one

Here's a little something you can think on after you get bored counting the ceiling tiles.

Ever had one of those dreams where you know you're dreaming?

Did you ever think about how there are at least two 'people' in your head, the dreamer and the watcher who knows the dreamer is dreaming?

Does that stuff fascinate you, or is it just me? :think:

[aneerkoinos]

10. Stereomind

You need two eyes for stereovision and two ears for stereo hearing. Makes perfect sense. ;)

Eros and Psyche, Spirit and Soul, Ying and Yan, Ka and Ba... I'm fascinated. BTW the dreamer and the watcher, how do you know which one is which? ;)

If you ever get bored counting the ceiling tiles, and are passionate about the problem of one and many, try reading Plato's Parmenides... :)

[madeline_con]

14. thanks

for the suggested read. :)

[ayeshahaqqiqa]

17. watchers

yep. To realize the watcher and then asking who is watching the watcher is a fascinating exercise.

[Stunster]

8. Tough question

...an adequate account of thought will have to repudiate recent "naturalist" dogmas and indulge in some fairly hard-core metaphysics. But while I think that some such approach is very much in the right direction, it is far from obvious at present how it should go in detail.<16> The clear upshot, if I am right, is that on the question of the nature of thought itself, perhaps the most fundamental philosophical issue of all, we may need to start over almost from the beginning.

From the concluding section of this thoughtful paper.

[toddaa]

11. Some interesting books on Cognitive Science

Steven Pinker - The Blank Slate
Daniel C. Dennett - Consciousness Explained
Roger Penrose - The Emperor's New Mind*
Douglas Hofstadter - Gödel, Escher, Back
Susan Blackmore - The Meme Machine

All good, but be careful with Penrose. He's the odd man out of the group. As a physicist, he's out of his jurisdiction when dealing with cognitive science. I'm currently slogging through his "The Road to Reality" monstrosity and the Platonism is a bit overwhelming but as a fellow doubter of String Theory, I got to give him props for never falling for the latest scientific fad.

As far as spiritual connections to cognitive science, I believe it's best to start with what we know before we start fiddling around with what we don't.

[aneerkoinos]

16. Gödel is God ...

I don't think anybody, least of all those coming from the King of sciences, theoretical physics, is out of his jurisdiction when dealing with cognitive science, which is by nature multi-discipline field. As long as they are not narrowminded tube-brains with no understanding and knowledge outside their narrow field. Sir Roger is certainly well versed in philosophy, mathematics etc., as were also Bohr, Schrödinger and other fathers of quantum theory who also made important excursions in the cognitive sciences.

I've not read Penrose, but have been following the some of the discussion. I must say I've come to agree with Platonism regardless of my strong handicap in math, and Penrose is not the first one to claim that Gödel's incompleteness theorem proves wrong the idea that mind is a mechanical machine. Lucas said so already in 1961: http://users.ox.ac.uk/~jrlucas/mmg.html

That was also the position of Gödel himself:
"Marvin Minsky has reported that Kurt Gödel told him personally that he believed that human beings had an intuitive, not just computational, way of arriving at truth and that therefore his theorem did not limit what can be known to be true by humans."
http://en.wikipedia.org/wiki/G%F6del%27s_incompleteness_theorem#Misconceptions_about_G.F6del.27s_theorems

It should be added, that in history of philosophy from Plato and Aristotle to Heidegger, it is only small minority that thinks that only way of arriving at truth, aletheia, is computational. Rather, IMHO, that view is just projection of certain scientific (materialistic) methodologies on truth theory.

[toddaa]

18. The Cartesian model and Darwin

The problem with people like Searle and Penrose, who dispute strong AI, is that they seem to have an underlying distrust of evolution. The Cartesian mind/matter duality has dominated philosophy primarily because philosophers are not prepared to deal with the ramifications of natural selection. History may be on your side, but you and Penrose may be all that is left of the Platonists. Darwin's algorithm killed off the Cartesian mind.

Penrose was valient in his attempt to overthrough strong AI. The problem with his argument is that underneath it all, he has absolutely no understanding of what AI is. He keeps think of it in purely mathematical terms. In short, he's talking something that he knows intimately and using it to attack something he doesn't know but is afraid of. Penrose is a nondogmatic thinker, which is refreshing in these days of String Theory run amok, but he loses me when he claims that he distrusts natural selection and QM because they don't fit into his neat and tidy Platonic world. The philosophy of mind definitely has some fundamental problems to overcome before cognitive science has a working theory, but none of them can be found in Penrose's book.

What's funny about the Gödel Incompleteness Theorem is that strong AI defenders rely on it as starting point for their hypothesis. Penrose seems to be the only detractor willing to use it as the basis of his argument. I wonder if Penrose ever bothered to read Hofstadter's blockbuster bestseller?

[aneerkoinos]

19. TNT

For me Gödel's Incompleteness Theorem appears just one version of the old discussion that all (or at least all bivalent and finite) logical systems/languages are inherently contradictory/incomplete, cf. Heracleitus, Plato, Nagarjuna, late Wittgenstein, Heidegger, Bohm, etc., including last but not least your very own Whitehead and Korzybski. The history of Western Philosophy boils down to Aristotelian Law of the Exluded Middle and the persistent criticism against that (in various forms by those mentioned above and others). Eastern philosophy, for example the Madhyamika School of Buddhism, has not that problem since it has not accepted the Law of the Excluded Middle and bivalent truth theory from the beginning (Buddha himself), and thus Buddhist philosophy, quite accurately and revealingly, is often called "The Middle Way".

So it's just not me and Penrose, but the whole dynamical process oriented new paradigm (Phenomenalism, Quantum Theory, Post-Modernism etc.), that are winning and leading away from Aristotelian logic and towards Eastern Philosophy.

Darwin and natural selection are not really relevant imputs to that discussion, due their very limited context. I have a feeling it come's up here only because it's the central battlefield in the boring to the extent of nauseating headbanging between theists and materialists, both of which IMO are wrong. I hope not to divert this discussion, but let's just point out the facts that both sides acknowledge, even the current theories are infested with holes and do not even attempt to explain the origin of life.

So the scope of natural selection is very narrow, it gives a very plausible theory of some (material) aspects of life and processes involved, but does no by any means exclude other explanatory factors, e.g. platonic versions of quantum theory. To claim otherwise merely shows that the claimant has adopted a strong belief in metaphysical materialism, in a sense being a half-Cartesian, holding to the other half of the strong dualistic existential credo and ignoring the other half while clinging to dualism itself (sticking to bivalent truth theory and keeping on looking for a strict separation border between observer and object (mind and matter? ;)), so far not finding it), which is quite contradictory position to begin with, to say the least... ;)

Enough of Descartes. What strikes me odd is your claim that Penrose distrusts QM. AFAIK Penrose and Hameroff have stayed with mainstream collapse of wave function -interpretations of QM (of which I am personally critical aand partial to Bohm's interpretation) in their Quantum Mind theory, which is the publicly best known from the multitude of quantum approaches to Mind-Body problem. Perhaps you could enlighten me on this issue?

What is common to most if not all quantum approaches is view that mind (or protoconsciousness/etc) has something to do with the wave aspect of the wave-particle dualism, which we consider paradoxical because of our tradition of bivalent logics. So this has nothing to do with Cartesian dualism, but (Whiteheadian) context dependent differences of mind-like (including the Platonic domain if one insists on that) and rock-like aspects of being/becoming. So actually, with many quantum approaches to Mind the stakes are actually much higher than just (naive) materialism, what are in jeopardy are not only bivalent Aristotelian logics and observer/object dualism, but the whole notion of sequential causality.

Thanks for bringing up Hofstadter, Wikipedia had nice article on the book. So if "self" is a Typographical Number Theory(?), all the evidence points the way that if I say that I'm a TNT I don't explode ;). Rather, if we follow the Buddhist line, the (illusion of) separate self holds together only by constantly measuring and explaining itself.

Perhaps there is some common ground where it comes to AI. I stick with Penrose and claim that will never happen with classical discreet digital computation. However, with quantum computation the AI-problem moves to whole new level where difference of opinion between camps of Penrose and Hofstadter, if there is one, must be much more refined, and thus way over my head. Same goes perhaps for p-adic calculus, Pitkänen says that in his theory all but one p-adic are computable - don't ask me what that means, but maybe someone get's something from that. But interestingly, Sarfatti, whose in the same (kook) camp with Pitkänen, says that his post-quantum theory is testable by AI, as it predicts that complex enough quantum computer will become consciouss...

[toddaa]

20. Don't mistake me for a materialist

I'm a Taoist, meaning that Plato and Aristotle are both wrong. ;) I also have doubts about strong AI myself, but nothing to offer in the way of objective proof, much like Penrose. He starts his argument from the basis that he "feels" there's more to the mind than a simple algorithmic process. I am definitely not in Penrose's league when it comes to physics or mathematics. I struggled through Calc I & II. However, if you are going to take on the likes of Hans Morevec and Daniel Dennett, you are going to have to come up with a better argument than you feel AI is wrong and then grab some stuff off your own bookshelf (which doesn't seem to include a book on neurology!) to prop up your feeling. That's largely what I got out of the Emperor's New Mind. It's a very good book, but it's not very convincing. As for QM, he's uncomfortable with the messier parts of the quantum mechanics, which he hopes quantum gravity will resolve (I'm slogging through Road to Reality, so I'm probably missing something), and is merciless in his criticism of the MWI. He's still holding out for twisters to tie it all together and who knows? After 20 years of mickey mousing around with 10, 11, and 26 dimensional space, maybe we'll finally get back to something testable.

You're right that there is a middle ground between Penrose and Moravec. Hofstadter is a strong AI proponent, but he's more down to earth than Moravec, so let's use Penrose and Moravec as the extremes.

As for Darwin, what? Both sides infested with holes? I wanted to recommend Blackmore's book again, considering your interest in Buddhism, but if you remain unconvinced by the simplistic beauty of natural selection, then never mind.

[aneerkoinos]

21. Whoa

Don't mistake me for that well read, I can't keep up with all the new names. And what is MWI?

I'm not unconvinced by natural selection, I just don't think it's the whole truth, and there are very probably also other explanatory factors involved e.g. in sudden evolutionary jumps.

[toddaa]

23. Whoa back at you

Your post was the first time I had come across mention of Hameroff. I read Emperor's New Mind back when it came out and then promptly lost interest in Penrose's idea after that. MWI refers to Many Worlds Interpretation of Quantum Mechanics. Despite my doubt for Penrose's ideas on consciousness, I'm enjoying Road to Reality quite a bit. Most of the math goes way over my head, but it's nice to read a book by someone who overestimates the common man's intelligence for a change. In the intro, he claims that anyone who can do fractions can understand the book, but I doubt that the average math phobe is going to be able to make the leap from the Pythagoras Theorum to tensor calculus and Reimann surfaces in 300 pages, especially when Penrose has a tendency to go backwards in introducing new concepts.

I do recommend Blackmore's book, as she's a Zen practitioner. Memetics isn't so much science, as a really good metaphor, but she makes a pretty strong case for it.

[aneerkoinos]

22. Tao of Platonism

Perhaps there is even more common ground. You might like this page:
http://www.maths.ex.ac.uk/~mwatkins/isoc/NTli.htm



From this wonderfull site which I found when googeling for "p-adic quantum theory" (challenged by your fervent opposition to Platonism and claim that it's just me and Penrose left, so thanks!):
http://www.maths.ex.ac.uk/~mwatkins/isoc/index.htm

[toddaa]

24. Very cool

Not sure how it ties in with Platonism, but it's interesting. Don't take my ribbing too seriously. Plato and Confucious are very similar in their seriousness, which means they are both quite amusing to this Taoist.

[aneerkoinos]

25. Holy Grail

I find it usefull to be (occasionally) seriouss and take good ribbing seriously, because it pushes me to explore more serious stuff and find such treasures as number theory of primes and Reiman hypothesis and it's forever escaping proof, the Holy Grail of Science.

There was extremely interesting insight that the Reiman's hypothesis is not provable within the context of (linear) time, and Plato´s search for Ideal Forms were about eternal, timeless truths, by their very nature out of the reach for us timed shadows watching cave-dwellers. So the tie between Li of Tao and Platonic search for Holy Grail of the number theory (cf. Eros and Psyche) seems quite evident, even though not easily expressable in realistic language.

For Holy Grail and time see:
http://www.maths.ex.ac.uk/~mwatkins/zeta/NTandtime.htm

Edit to add this absolutely fascinating story:
http://www.maths.ex.ac.uk/~mwatkins/isoc/twins.htm

[toddaa]

26. The Tao is eternal

As is the Unity of heaven and earth, but after that creation rises and falls and is constantly changing. That is the fundamental difference between Taoism and Platonism. Plato emphasized the unchanging truth of the ideal. Taoism teaches that the only absolute is constant change. In Taoism, time is not linear or eternal, it is circular. I wish I could find a parallel in mathematics that is as close to Taoism as Platonism, but I don't think there is one. However, proving the Riemann Hypothesis may not necessarily convince this Taoist that there are timeless truths, but it will reaffirm my belief in the All is One. Something that Plato would certainly go along with.

There are parallels between Plato's Allegory of the Cave and Chuang Tzu's Autumn Floods, but they reach very different conclusions. Plato said that there is an ideal that we must strive for, Chuang Tzu said that our knowledge will always be limited and striving is pointless. So which one of us is right, the Platonist or the Taoist? Well, in true Taoist tradition I'd say we both are. As a Platonist, you seek the "holy grail" of number theory striving for the ideal. As a Taoist, I suspect that when your quest finishes it will only reveal another mystery to be treasured.

One final thought, in Taoism the principle action is doing nothing, or wu wei. Many misinterpret this as not doing, but notice that doing is active. It's a difficult principle to comprehend, but I've come to understand it as meaning that we must not force the Tao to conform to our will, but to align our will with the Tao. Wu wei is an intuitive process, letting goals reveal themselves to us, rather than desire outcomes that cannot happen. If there is a proof to the Reimann Hypothesis, the mathematician finds it will in all likelihood stumble upon it by chance. Something that no computer we have today can do.

[Jim__]

27. A few questions

From the paper by Lucas:

Gödel's theorem must apply to cybernetical machines, because it is of the essence of being a machine, that it should be a concrete instantiation of a formal system. It follows that given any machine which is consistent and capable of doing simple arithmetic, there is a formula which it is incapable of producing as being true---i.e., the formula is unprovable-in-the-system-but which we can see to be true. It follows that no machine can be a complete or adequate model of the mind, that minds are essentially different from machines.

I agree completely, up to this point:

It follows that given any machine which is consistent and capable of doing simple arithmetic, there is a formula which it is incapable of producing as being true---i.e., the formula is unprovable-in-the-system...

Does Godel's theorem tell us how, given any machine, we can find the formula that is undecideable? And, has anyone demonstrated that in all these cases the human mind can see that the formula is true? If not, then I don't see how (i)t follows that no machine can be a complete or adequate model of the mind, that minds are essentially different from machines.

Also, has anyone demonstrated that the mind is consistent? If not, is it not possible that the mind may be a mechanical machine that contains certain inconsistent elements?

And, on the quote from Minsky:

"Marvin Minsky has reported that Kurt Gödel told him personally that he believed that human beings had an intuitive, not just computational, way of arriving at truth and that therefore his theorem did not limit what can be known to be true by humans."

Even if it is true that human beings have an intuitive way of arriving at the truth, how do humans distinguish between their unprovable, but correct intuitions; and their unprovable but incorrect intuitions? In other words, even if we have an intuitive faculty for arriving at the truth, how do we know when we have arrived at the truth if we have no way of verifying it?

[aneerkoinos]

28. A Most (in)Consistent Post

>>Does Godel's theorem tell us how, given any machine, we can find the formula that is undecideable? And, has anyone demonstrated that in all these cases the human mind can see that the formula is true? If not, then I don't see how (i)t follows that no machine can be a complete or adequate model of the mind, that minds are essentially different from machines.<<

Let's be carefull with words. "Undecideable" does not equal "unprovable" (ie within a context of strong enough arithmetic). For Gödel and Gödelians the unescapable "unprovables" are most definately "decideables", they are "intuitively" true (or not).

>>Also, has anyone demonstrated that the mind is consistent? If not, is it not possible that the mind may be a mechanical machine that contains certain inconsistent elements?<<

What do you mean by "consistent"? I would say the question about consistency arises only in context of strong enough arithmetic/logical system. But what about consistency when dealing e.g. with irreal numbers, what does consistency mean then?

No, I don't think anyone has demonstrated that the mind is "consistent", more to the opposite... ;)

Mind certainly has its mechanical, deterministic aspects, but IMO only the most fervent believers in metaphysical materialism are mindless enough to claim that mechanical determinism is all that there is to mind. It is not a real well based scientific argument, but it can be a credo of the belief system of scientism, sometimes disguised as a scientific argument.

>>Even if it is true that human beings have an intuitive way of arriving at the truth, how do humans distinguish between their unprovable, but correct intuitions; and their unprovable but incorrect intuitions? In other words, even if we have an intuitive faculty for arriving at the truth, how do we know when we have arrived at the truth if we have no way of verifying it?<<

Empirically is the method most often used (notice in this Gödelian context "unprovable" refers only to formal proof inside a logical system). Riemann's hypothesis may be even a genuine unprovable, but the empirical evidence (millions and millions of calculations confirming it every time) gives it strong support.

Practically, since this is the Religion Forum, an intuitive truth can be verifyid e.g. by simply asking your Heart in a mindfull (/meditative/grounded) state, to minimize the risk of getting fooled by your hopes and fears (ego). Of course this requires a minimum of empirical intuitive practice of getting to Know Thyself. Generally, heuristics is about compassionate creative imagination, not about formal proof. Einstein didn't pull his insights from a formal analysis, in his mindfull imagination he rode a beam of light ...

[Jim__]

29. Looking to Godel's proof

Let's be carefull with words. "Undecideable" does not equal "unprovable" (ie within a context of strong enough arithmetic). For Gödel and Gödelians the unescapable "unprovables" are most definately "decideables", they are "intuitively" true (or not).

According to Godel:

From the remark that {R(q); q} asserts its own unprovability, it follows at once that {R(q); q} is correct, since {R(q); q} is certainly unprovable (because undecidable -(Godel's words, my bolding - Jim)). So the proposition which is undecidable in the system PM yet turns out to be decided by metamathematical considerations.

We can formally prove {R(q), q} in the metasystem. The inability to prove the proposition is not a short-fall of formal systems, it is a limitation of PM, a form of limitation that can be extended to all formal systems to which the theorem applies.

Further, to state that: For Gödel and Gödelians the unescapable "unprovables" are most definately "decideables", they are "intuitively" true (or not) is to beg the question. In the case of {R(q), q}, we don't need intuition. It is formally provable in a metasystem.

[aneerkoinos]

30. I stand corrected

but my point remains, "turns out to be decided by metamathematical considerations". (a link would be nice, BTW).

Further, proof in a metasystem is not "formal proof" as I understand the words, because then you need a meta-metasystem etc., the whole thing is recursive and incomplete.

I quote again from Wikipedia:
"Marvin Minsky has reported that Kurt Gödel told him personally that he believed that human beings had an intuitive, not just computational, way of arriving at truth and that therefore his theorem did not limit what can be known to be true by humans."

[Jim__]

31. Godel's paper includes a formal proof of the assertion

My quote from Godel was taken from his 1930 paper - (here) - just below {176}.

Further, proof in a metasystem is not "formal proof" as I understand the words, because then you need a meta-metasystem etc., the whole thing is recursive and incomplete.

Godel's paper is a formal proof of his assertion. The meat of his argument is in his proof of proposition VI:

Proposition VI: To every w-consistent recursive class c of formulae there correspond recursive class-signs r, such that neither v Gen r nor Neg (v Gen r) belongs to Flg(c) (where v is the free variable of r).

I quote again from Wikipedia:
"Marvin Minsky has reported that Kurt Gödel told him personally that he believed that human beings had an intuitive, not just computational, way of arriving at truth and that therefore his theorem did not limit what can be known to be true by humans."

I am not questioning whether or not Godel said this. I am questioning whether or not his Theorem constitutes proof of this assertion. I assume did not believe it did; otherwise he would have stated that his theorem proved his assertion.

[aneerkoinos]

32. Where's the beef?

Thinkers think which means not sticking to their thoughts. I think Gödel was a thinker, not a theorem.

If you prefere to get argumentative over math and logic, you win, since I got no formal training in these subject and don't understand the lingo. Woe me :(

And yep, intuitive/recursive/metameta/what ever "seeing" of truth is pretty much beyond and outside "formal proof", the thingie that to my understanding is possible only inside a logical (consistent) system.

Argument by appealing to authority (such as a recognicnized genious) is certainly not a strong argument, as it is well known that geniouses are also fallible. But neither is it an empty argument, because what we are dealing here with are the modes of thinking/sensing. And the (empirical) evidence of "savant idiots" mysteriously "sensing" (beyond the competence of any existing computer) large primes is and should be of profound importance in the search of Chalice of Mind.

[Jim__]

33. "The beef" is precisely what I was asking about in my post #27

If you prefere to get argumentative over math and logic, you win, since I got no formal training in these subject and don't understand the lingo.

Actually, I was interested in the statement in your post #16:

...Penrose is not the first one to claim that Gödel's incompleteness theorem proves wrong the idea that mind is a mechanical machine.

Saying, of course that Godel's Incompleteness Theorem proves something about the mind is to appeal to math and logic. I read the article you cited and found it unconvincing, which is why I asked about the proof. The questions that I asked in post #27 were actually seeking information, not an argument. I wondered if this line of reasoning was something that was worth pursuing. Since Lucas' argument appears flawed to me, and you can't offer any support for it; it seems it's not.

I believe it was Mark Twain who said something to the effect of: "It's not what we don't know that gets us in trouble. It's what we know that just ain't so."

[aneerkoinos]

34. OK

I see your point and where we got bogged done in semantics between undecideable and unprovable.

Of course my lack of ability to give support to Penrose (or Lucas), especially since I've not read Penrose, should not be taken as anything but proof of my lacking skills and knowledge. ;)

What I think is that these guys give sufficient proof of mind not being a mechanical machine, if we take "mechanical" to imply digitally/rationally computable. Quantum computation (and math based on irrational numbers such as p-adics) are qualitatively very different species, so it seems to me we should hold our judgmenent in that area.

[aneerkoinos]

35. Origin of numbers

"A set is a collection of things. An empty set is a collection of nothing at all. An empty set can be thought of as nothing with the potential to become something (that is to be become a set with at least one member).

Von Neumann proposed that all numbers could be bootstrapped out of the empty set by the operations of the mind.

The mind observes the empty set. The mind's act of observation causes the appearance another set - the set of empty sets. The set of empty sets is not empty, because it contains one non-thing - the empty set. The mind has thus generated the number 1 by producing the set containing the empty set.

Now the mind perceives the empty set and the set containing the empty set, so there are two non-things. The mind has generated the number 2 out of emptiness. And so it goes on all the way up.

So, the three levels of dependent relationship postulated by Kadampa Buddhist philosophy are apparent even at the very deepest level of mathematics."
http://home.btclick.com/scimah/emptyset.htm


"Consider also that the universe began as a quantum event which remained in a superposed state of all possibilities until acted upon by the mind of an observer (Copenhagen interpretation of quantum mechanics).

Now an observer existing in the absence of any objects or forms will have no knowledge of any material things. She will, however, have knowledge of mathematics, as mathematics arises from mind comtemplating emptiness, and needs no material objects or things to count.

A mind whose prior experience had been the contemplation of emptiness, might upon observing a superposed quantum system, have a predilection for collapsing the superposition around a primordial mathematical framework.

The mind of the sentient being who first collapsed the superposition is not different in fundamental nature to the minds of the physicists who observe the results - Tat Tvam Asi."
http://home.btclick.com/scimah/unreasonableeffectiveness.htm

[goodboy]

36. here:

www.whatthebleep.com