Did Godel disprove the idea of artificial intelligence?

[jay gw]

Has artificial intelligence been discredited by Godel's incompleteness theorem?

Hao Wang A logical journey: From Godel to philosophy, 1997

Godel's Incompleteness Theorem states that in any consistent formal system which is adequate for arithmetic there is a true but unprovable sentence.

Second Theorem

If an axiomatic system can be proven to be consistent from within itself, then it is inconsistent. No consistent system can be used to prove its own consistency.

Therefore, in order to establish the consistency of a system S, one needs to utilize some other system T, but a proof in T is not completely convincing unless T's consistency has already been established without using S.

The theorem does not imply that every interesting axiom system is incomplete. The theorem only applies to systems that allow you to define the natural numbers as a set.

Minds, Machines and Gödel

Gödel's theorem seems to me to prove that Mechanism is false, that is, that minds cannot be explained as machines. So also has it seemed to many other people: almost every mathematical logician I have put the matter to has confessed to similar thoughts, but has felt reluctant to commit himself definitely until he could see the whole argument set out, with all objections fully stated and properly met.

The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics
by Roger Penrose

For decades, proponents of artificial intelligence have argued that computers will soon be doing everything that a human mind can do. Admittedly, computers now play chess at the grandmaster level, but do they understand the game as we do? Can a computer eventually do everything a human mind can do?

Roger Penrose--physicist, and Stephen Hawking - puts forward his view that there are some facets of human thinking that can never be emulated by a machine.

Penrose examines what physics and mathematics can tell us about how the mind works, what they can't, and what we need to know to understand the physical processes of consciousness. He is among a growing number of physicists who think Einstein wasn't being stubborn when he said his "little finger" told him that quantum mechanics is incomplete, and he concludes that laws even deeper than quantum mechanics are essential for the operation of a mind.

[drkitten]

Originally posted by jay gw
Has artificial intelligence been discredited by Godel's incompleteness theorem?


Simply put, no. Assuming for the sake of argument that humans are considered to be "intelligent," then we must accept that a hypothetical perfect artificial copy of the human cognitive system would also be "intelligent."

Godel's theorem simply states that a sufficiently powerful formal system must be either incomplete or inconsistent. Humans are known to be both incomplete and inconsistent. Therefore, insofar as as human reasoning would be modeled by a formal system, the formal system itself would be both incomplete and inconsistent, entirely compatible with Godel.

Actually, this question (and many, many more implications for AI than I have the room to address here) were done to death by Doug Hofstadter in Godel, Escher, Bach : An Eternal Golden Braid, to which I recommend you. But the Godelian argument is explicitly refuted (he attributes this argument to the philosopher Lucas) in detail.

[phildonnia]

On the contrary, I think Goedel's theorem suggested inherent limitations to human minds.

Machines can never be "truly intelligent" in the sense of being able to know all truth. If one takes the view that Mind is a product of Brain, then the same argument applies, and we must conclude that human minds can never be "truly intelligent" either.

[patnray]

I voted "No".

For an alternative view point try "Godel, Escher, Bach : An Eternal Golden Braid" by Douglas R Hofstadter, a delightfully witty book in which he argues that intelligence emerges from a complex multilevel system.

"My belief is that the explanations of 'emergent' phenomena in our brains -- . . . [including] finally consciousness and free will -- are based on a kind of Strange Loop, an interaction between levels in which the top level reaches back down towards the bottom level and influences it, while at the same time being determined by the bottom level. In other words, a self-reinforcing 'resonance' between different levels . . . ."

The book, itself, is a complex, multilevel synthesis of "top down" and "bottom up" approaches to underestanding intelligence...

Damn. new drkitten beat me to it...

[drkitten]

Originally posted by jay gw

The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics
by Roger Penrose

[...]
Penrose examines what physics and mathematics can tell us about how the mind works, what they can't, and what we need to know to understand the physical processes of consciousness. He is among a growing number of physicists who think Einstein wasn't being stubborn when he said his "little finger" told him that quantum mechanics is incomplete, and he concludes that laws even deeper than quantum mechanics are essential for the operation of a mind.

I'd feel much more confident about Penrose's explanation of either physics or psychology (or indeed, of computer science) if he actually knew anything about any of these disciplines. Unfortunately, Penrose is a mathematician (and an exceptionally good one), but not a polymath. The Emperor's New Mind, in particular, is not a particularly well-thought out book, and is fundamentally full of holes in how it presents stuff. Check out some of the excerpts from the reviews on amazon.com:


Right. Take a deep breath here. For it's a scary thing for a mere mortal (with a decidedly ordinary bachelor's degree in the humanities) to say something like this about the one of the cleverest men on the planet, but I can't see any way around it: In this book Roger Penrose completely, totally, misses the point. Insofar as it's considered an entry on the Consciousness/AI debate, The Emperor's New Mind - all 583 pages of it - is all but worthless.

Here's where I think he goes wrong. Firstly, his attempt to undermine the AI position is founded on purely mathematical reasoning. Pure mathematics is a closed logical system. Its truths aren't falsifiable, so by themselves have no explanatory force. Mathematical statements (such as "1+1=2") are necessarily true for all time and all universes so, ipso facto, they can't - by themselves - tell us anything about any particular universe. Yet that is just what Penrose asks them to do. He invokes Gödel's theorem of undecidability, perhaps to counter the argument I have just made, but it isn't convincing - being logically unable to prove all truths in a particular set (even though you know they are true) is very different from being able to falsify them. Without that power, you have no explanatory traction in the outside world. Penrose's entire attack on Strong AI is based on an unfalsifiable, and therefore non-content carrying, argument.

Ultimately, when Penrose says "quantum theory explains consciousness" he is really saying no more than "something magic happens!" or even "THEN A MIRACLE OCCURS".

Mr Penrose, I think you should be more explicit here in step two.



or this


His arguments are unclear, weak and largely dependent on philosphers like Lucas and Searle, while his idea of quantum effects is improbable and surely in the end irrelevant (cannot computers tap into quantum effects?) and his knowledge of computer science deeply, deeply suspect.
For example, I quote here from the final sections which actually have something to do with his ostensible reason for writing the book:
"Neverthless, one still might imagine some kind of natural selection process being effective for producing approximately valid algorithms. Personally, I find this very hard to believe, however."
The entire flourishing, commercially succesful field of evolutionary computing begs to differ here, Mr. Penrose. SUch bonehead errors compells me to point out that this mathematician has no clothes.


From a more formal context, here's the abstract of a recent paper on Penrose's work, by professional philosophers working on AI ( Selmer Bringsjord, Hong Xiao, published in JETAI 2000).


Having, as it is generally agreed, failed to destroy the computational conception of mind with the Godelian attack he articulated in his The Emperor's New Mind, Penrose has returned, armed with a more elaborate and more fastidious Godelian case.... The core argument... is enthymenmatic, and when formalized, a remarkable number of technical glitches come to light. Over and above these defects, the argument, at best, is an instance of either the fallacy of denying the antecedent, the fallacy of petitio principii, or the fallacy of equivocation. More recently, writing in response to his critics in the electronic journal Psyche, Penrose has offered a Godelian case designed to improve on the version presented in [Shadows of the Mind]. But this version is yet again another failure. In falling prey to the errors we unconver, Penrose's new Godelian case is unmasked as the same confused refrain J. R. Lucas initiated 35 years ago.


(I should note that the author of this article (Bringsjord) is himself an opponent of AI, so this isn't simply an instance of "preaching to the choir.")

Penrose, and more generally Godel via Lucas, has nothing useful to contribute to the AI discussion. Penrose in particular has this fundamental problem of an lack of understanding of the material under discussion --- when he's correct, he's not interesting. When he's interesting, he's unfortunately not correct. It's a bad combination that I urge you to eschew.

[MESchlum]

I just read the topic of the poll - after voting according to the topic of the discussion.

Bait and switch.

Annoying.

And what does quantum mechanics being incomplete (or not) have to do with abstract logic, exactly?

[Robin]

Silly question really. The human mind is a machine so one machine already thinks as a human mind does. No other machine will ever be able to think exactly as the human mind does (and why would we want to try?).

(I am assuming that 'machine' is used in its general sense rather than mathematical as in 'Turing machine').

But once we have properly understood the mechanisms involved I see no reason why the same principles should not be applied to other machines.

I totally fail to see what Godel's theorems have to do with the case. The human mind is not a system of logic.

[patnray]

Good point MESchlum. I voted "No" to the question "Did Godel disprove the idea of artificial intelligence?"

[Soapy Sam]

Define "Artificial intelligence."

Do we mean conscious awareness or simply complex response to stimuli?

Wire up a motion sensor to a servo operated machine gun. Hook in a pc and write the obvious "track and fire" software. Now put a burglar over the fence. Turing test anybody?

If it's smart enough to kill you, how much more intelligent does it have to get?


The first AI probably had the intelligence of a fundamentalist. We passed that stage a few years ago. We are probably up to bacterial levels now, at least. That's a billion years of organic evolution in about a century. Give things a chance. They'll be here soon enough.

[phildonnia]

Originally posted by Robin
I totally fail to see what Godel's theorems have to do with the case. The human mind is not a system of logic.

I think the idea is: human minds are based on physical brains, and physical brains are subject to the laws of physics, and the laws of physics can be modeled by logic.

Therefore, if the mind is capable of discerning truth, then so is the logical system that can ultimately model it.

[T'ai Chi]

As far as I am aware, the human brain does not work like + and * with the numbers {0,1,2,...}, so I too fail to see where Godel's theorem comes in.

[Jorghnassen]

I don't see how Godel's theorem comes in either (though pure math isn't my forte). I don't think it is required in a discussion on whether artificial intelligence is achievable or not.

[Jorghnassen]

Originally posted by phildonnia
I think the idea is: human minds are based on physical brains, and physical brains are subject to the laws of physics, and the laws of physics can be modeled by logic.


What a reductionist argument...

[Robin]

Originally posted by jzs
As far as I am aware, the human brain does not work like + and * with the numbers {0,1,2,...}, so I too fail to see where Godel's theorem comes in.

Philidonnia's reply is clearly not what Penrose had in mind and I have not read the book, but here is a quote from a review of the book by John McCarthy:

The Penrose argument against AI of most interest to mathematicians is that whatever system of axioms a computer is programmed to work in, e.g. Zermelo-Fraenkel set theory, a man can form a Gödel sentence for the system, true but not provable within the system.

If McCarthy has accurately represented Penrose then he appears to be assuming that a machine must work with a specific system of axioms. In which case the argument appears to be irrelevant on a number of levels.

[phildonnia]

Originally posted by Jorghnassen
What a reductionist argument...

Um, yeah. Ok, glad we got that observation out of the way.

Originally posted by jzs
As far as I am aware, the human brain does not work like + and * with the numbers {0,1,2,...}, so I too fail to see where Godel's theorem comes in.

As far as we can tell, the physical world does work like + and *. If mind can be entirely explained in terms of its physical substrate¹, then it must be possible for number theory to produce anything that mind can.

That is, mind cannot produce anything that number theory cannot. This is where Goedel's theorem comes in.

Originally posted by Robin
Philidonnia's reply is clearly not what Penrose had in mind...

Well that's good, since I would be arguing against Penrose.

¹ For frantic and desperate attempts to refute this idea, search this forum for posts by "Interesting Ian".

[drkitten]

Originally posted by phildonnia

As far as we can tell, the physical world does work like + and *.

As far as we can tell, the physical world is not described by a finite set of axioms. That's part of the legacy of quantum mechanics and the intellectual death of God-the-Watchmaker.

If the physical world is not axiomatizable, then a) it doesn't work like + and *, which are defined by their axioms, and b) is entirely outside the auspices of Godel's theorem, which is a theorem about formal axiomatic systems.

In fact, even Penrose recognizes the first paragraph above -- that the physical world is not axiomatizable. That's part of why he claims that artificial intelligence is not possible, because in his unbelievably naive view of computers, they are axiomatic systems, while realistic (quantum) effects are not. Ergo, the mind, being non-axiomatic, must be related somehow to quantum.

[phildonnia]

quote:
--------------------------------------------------------------------------------
The Penrose argument against AI of most interest to mathematicians is that whatever system of axioms a computer is programmed to work in, e.g. Zermelo-Fraenkel set theory, a man can form a Gödel sentence for the system, true but not provable within the system.
--------------------------------------------------------------------------------

This is the classic "Goedel" argument for the impossibility of AI. Two holes in this argument:

We cannot be really sure that a man always can form a Goedel sentence for a given axiomatic system. We've only really tried this on systems that are simple enough for our minds to understand. As you might guess, there is no way to formalize this process.

We cannot be sure that it is impossible for a machine to create a Goedel sentence for a human mind. This would require a computer capable of analyzing the entire underlying brain structure, which obviously is not now feasable.

[phildonnia]

Originally posted by new drkitten
As far as we can tell, the physical world is not described by a finite set of axioms. That's part of the legacy of quantum mechanics and the intellectual death of God-the-Watchmaker.
...Ergo, the mind, being non-axiomatic, must be related somehow to quantum.


I see your point that if the mind were "non-axiomatic", then quantum mechanics would be one possible explanation. However, there is no indication that the mind is "non-axiomatic", nor that quantum mechanics plays any role in the workings of the brain or mind.

[Jorghnassen]

Originally posted by phildonnia


That is, mind cannot produce anything that number theory cannot. This is where Goedel's theorem comes in.


How does number theory produce anything?

[Dr Adequate]

The Penrose argument against AI of most interest to mathematicians is that whatever system of axioms a computer is programmed to work in, e.g. Zermelo-Fraenkel set theory, a man can form a Gödel sentence for the system, true but not provable within the system.
And so, of course, could the computer. Only it would do it a million times faster, and would be much less likely to make a mistake.

The incomleteness of first-order axiomatisations of the arithmetic of the integers has nothing to do with the hardware or wetware trying to make use of such an incomplete axiomatisation. Consider the following equally valid --- or rather, equally invalid --- argument:

"The argument against human intelligence of most interest to mathematicians is that whatever system of axioms a human is asked to work in, e.g. Zermelo-Fraenkel set theory, a computer can form a Gödel sentence for the system, true but not provable within the system."

Convincing, huh?

[phildonnia]

Originally posted by Jorghnassen
How does number theory produce anything?

Following the rules of number theory produces "theorems". The question was whether these theorems represented "truth". Goedel's theorem showed that not all truths were represented by theorems (assuming that no falsehoods were represented).

The question is whether human minds are also subject to this limitation.

If minds can be modeled by number theory, then they are subject to this limitation. If not, then other systems that can be modeled by number theory (such as AI) are necessarily less able to recognize truth.

At our current level of understanding, it seems to be something of a point of faith one way or the other, and I suspect that some measure of anthropocentric pride may get involved.

[phildonnia]

Originally posted by Dr Adequate
"The argument against human intelligence of most interest to mathematicians is that whatever system of axioms a human is asked to work in, e.g. Zermelo-Fraenkel set theory, a computer can form a Gödel sentence for the system, true but not provable within the system."

Very nice.

I would like to add that:

Dr Adequate does not believe this sentence.

Since this sentence is obviously true to everyone else, and we have no trouble believing it, this demonstrates the inadequacy of Dr. Adequate with respect to the truth of his beliefs.

[Jorghnassen]

Originally posted by phildonnia
Following the rules of number theory produces "theorems". The question was whether these theorems represented "truth". Goedel's theorem showed that not all truths were represented by theorems (assuming that no falsehoods were represented).

The question is whether human minds are also subject to this limitation.

If minds can be modeled by number theory, then they are subject to this limitation. If not, then other systems that can be modeled by number theory (such as AI) are necessarily less able to recognize truth.

At our current level of understanding, it seems to be something of a point of faith one way or the other, and I suspect that some measure of anthropocentric pride may get involved.

I was under the impression that the human mind produced number theory and its theorems, axioms, corrolaries, etc. My point is that number theory doesn't exist outside of the human mind. I don't think number theory can model the mind (as it only deals with abstract notions), because it does not deal with the very physical aspect of the mind: the human brain.

My quarrel with AI, in the sense of a machine being able to think like a human does, is that it is not purely a software problem, and that trying to come up with AI from a purely axiomatic approach is bound to failure. A better approach (that is of course, already being worked on) would also consider reverse engineering the humain brain...

[drkitten]

Originally posted by phildonnia
I see your point that if the mind were "non-axiomatic", then quantum mechanics would be one possible explanation. However, there is no indication that the mind is "non-axiomatic", nor that quantum mechanics plays any role in the workings of the brain or mind.

.... which is part of why the Penrose argument is a load of tosh.

[jay gw]

I don't think number theory can model the mind (as it only deals with abstract notions), because it does not deal with the very physical aspect of the mind: the human brain.

Can the physical brain be mapped entirely? Can the map be expressed as numbers?

[Robin]

Originally posted by jay gw
Can the physical brain be mapped entirely? Can the map be expressed as numbers?

That is not really the point. To my knowledge the point of AI is to understand the processes by which the brain produces thought and to replicate this process using a machine.

To my knowledge there is no-one doubting that this can be done and that there will be one day computers that not only pass the Turing test but that will replace current call-centres and that we probably will not be able to tell the difference.

The debate that Penrose appears to be entering is whether a machine that appears in every respect to think, reason, use common sense, solve problems like a human can truly be said to be a 'mind'.

[Jorghnassen]

Originally posted by jay gw
Can the physical brain be mapped entirely? Can the map be expressed as numbers?

It takes more than a map to know how the brain works (besides, brain mapping has its own problems), and to build an artificial brain. Can an omelet be mapped? Can number theory make an artificial omelet (or rather, how does one use number theory to make an artificial omelet)? You see there is a huge difference between description (math can be used to describe reality, but in a limited way), and implementation.

/stealing and misusing material from a lecture on A.I. I once attended...

[AWPrime]

Why does the poll question differ from the title question?

[Interesting Ian]

Originally posted by new drkitten
[B]Simply put, no. Assuming for the sake of argument that humans are considered to be "intelligent," then we must accept that a hypothetical perfect artificial copy of the human cognitive system would also be "intelligent."



We must accept no such thing, I certainly don't accept it.



Godel's theorem simply states that a sufficiently powerful formal system must be either incomplete or inconsistent. Humans are known to be both incomplete and inconsistent. Therefore, insofar as as human reasoning would be modeled by a formal system, the formal system itself would be both incomplete and inconsistent, entirely compatible with Godel.


We human beings can recognise truths that do not appear to have been derived from an algorithmic process.

[Robin]

Originally posted by new drkitten
[B]Simply put, no. Assuming for the sake of argument that humans are considered to be "intelligent," then we must accept that a hypothetical perfect artificial copy of the human cognitive system would also be "intelligent."

Interesting Ian
We must accept no such thing, I certainly don't accept it.

But suppose you have a machine that takes a university exam paper and generates answers (say for Mathematics or English literature) and a human marks it, believing the paper to be the result of a human and gives the paper a high distinction.

How could you not describe that process as intelligent? You could certainly say that it was not conscious, or that that it was not a mind. But it would clearly be intelligent.

[Interesting Ian]

Originally posted by Robin
Silly question really. The human mind is a machine so one machine already thinks as a human mind does.

And I imagine that no justification will be given for this outrageous assertion. :rolleyes:

Wheel out your conscious robot, then I too will believe that we are merely machines. Yer going to have to do that since all philosophical arguments which attempt to establiush we are machines are somewhat lacking.

[Interesting Ian]

Originally posted by Robin
But suppose you have a machine that takes a university exam paper and generates answers (say for Mathematics or English literature) and a human marks it, believing the paper to be the result of a human and gives the paper a high distinction.

How could you not describe that process as intelligent? You could certainly say that it was not conscious, or that that it was not a mind. But it would clearly be intelligent.

OK, that's fine, I merely deny it is conscious.

[Robin]

Originally posted by Interesting Ian
And I imagine that no justification will be given for this outrageous assertion. :rolleyes:

Wheel out your conscious robot, then I too will believe that we are merely machines. Yer going to have to do that since all philosophical arguments which attempt to establiush we are machines are somewhat lacking.
Ah, finally the reaction I was trying to provoke! Unfortunately I don't have time to answer properly at the moment, I will do so in a couple of days.

It is interesting to note that the participants in the debate that Penrose is responding to (for example Searle, Dennet, McCarthy) all stipulate this as a premise.

[Robin]

Interesting Ian,

Just so I don't waste my time, if you don't agree that the human mind is a machine, do you agree that the human brain is a machine?

[Interesting Ian]

Originally posted by Robin
Interesting Ian,

Just so I don't waste my time, if you don't agree that the human mind is a machine, do you agree that the human brain is a machine?

Yes, although I think the processes within it can be influenced by the mind.

[phildonnia]

Man, that took a while. I've been laying Ian-bait all over this thread.

Originally posted by Interesting Ian
We human beings can recognise truths that do not appear to have been derived from an algorithmic process.

Such as?

Be prepared to discuss
1) how we know they are truths.
2) how we know they can not derived from an algorithmic process.

[Correa Neto]

Originally posted by Interesting Ian
OK, that's fine, I merely deny it is conscious.

Why?

Here there have been lots of discussions using hypothetical machines. Please allow me to propose one more.

Suppose at last a sci-fi robot or computer is created (wheeled out, using your sentence). Let it be Robin´s machine, C3P0, one of Asimov´s robots, whatever. This hipothetical machine can gather information on its environment and its own components, it can proccess these informations, learn (it even manage to successfully finish a course at an university), propose solutions to problems based on all the iformation it gathered, is aware of its own skills, of the data it has stored in its databanks and can perform tasks by itself, without being comanded do do so, it avoids being damaged, tries to repair itself and gather energy to continue its operations.

You are having a dialogue with it at an internet forum, at a chat, or at the telephone, without knowing its not a human being.

Would you be able to recognize it as artificial and therefore labell it as non counsient? If so, based on what aspects? What types of criteria do you propose to use in order to diferentiate a counsient entity from one that just behaves like as a counsient being?

Or you are assuming that it will not be really counsient because its a machine, a non-organic entity? Or because its not a human being?

[Interesting Ian]

Originally posted by Correa Neto
Why?

Here there have been lots of discussions using hypothetical machines. Please allow me to propose one more.

Suppose at last a sci-fi robot or computer is created (wheeled out, using your sentence). Let it be Robin´s machine, C3P0, one of Asimov´s robots, whatever. This hipothetical machine can gather information on its environment and its own components, it can proccess these informations, learn (it even manage to successfully finish a course at an university), propose solutions to problems based on all the iformation it gathered, is aware of its own skills, of the data it has stored in its databanks and can perform tasks by itself, without being comanded do do so, it avoids being damaged, tries to repair itself and gather energy to continue its operations.

You are having a dialogue with it at an internet forum, at a chat, or at the telephone, without knowing its not a human being.

Would you be able to recognize it as artificial and therefore labell it as non counsient? If so, based on what aspects? What types of criteria do you propose to use in order to diferentiate a counsient entity from one that just behaves like as a counsient being?

Or you are assuming that it will not be really counsient because its a machine, a non-organic entity? Or because its not a human being?

We would need to feel it is conscious. I propose that even an android that behaved exactly like a human being would not arouse such a feeling. This is because I suspect we know that other people are conscious partially through anomalous cognition.

[jay gw]

The debate that Penrose appears to be entering is whether a machine that appears in every respect to think, reason, use common sense, solve problems like a human can truly be said to be a 'mind'.

Plenty of humans can't do that - who said artificial intelligence has to have "common sense"? What is common sense?

solve problems like a human

How do I solve problems, exactly? Please explain.

Yes, it is necessary to map the brain before you can understand it. The map provides the blueprint. But then someone wanting to duplicate/build it from nothing would have to understand how all the parts interact. That is probably the thing that keeps AI researchers stumped.

The brain seems to be divided into components, then assembled into a whole. Very simplistic yes I know, but the verbal/art/math/conscience abilities are not randomly distributed. They're in the same location, grouped together.

One of the big problems that AI faces is that circuits made of metal and plastic cannot, physically can't, duplicate the circuits in the brain. I don't know how anyone will get around this.

At some point, it will be possible to build mechanical material that can simulate cells.

Maybe it's wrong, but it seems that if every circuit in the brain were recreated AND grouped as the brain is, and energy introduced, something very interesting would happen.

People discuss "consciousness" and "intuition" as if they're something metaphysical. I think they are natural outcomes from the circuits interacting with senses and the environment.

[Robin]

Originally posted by Interesting Ian
OK, that's fine, I merely deny it is conscious.

And in fact I probably agree with you. I think that it is a valuable distinction to make - we are debating what John Searle calls the "Strong AI" hypothesis, that an artificially intelligent machine is necessarily a mind.

[Interesting Ian]

Originally posted by phildonnia
Man, that took a while. I've been laying Ian-bait all over this thread.



Such as?

Be prepared to discuss
1) how we know they are truths.
2) how we know they can not derived from an algorithmic process.

I admit I know very little about this subject, but did not Goedel show that human beings can know things that cannot be known by computation?

Anyway, we can't specify how these truths are known - perhaps not surprising as these truths are simply intuited. That is to say they are simply seen to be true by an inner understanding.

[phildonnia]

Originally posted by Interesting Ian
We would need to feel it is conscious. I propose that even an android that behaved exactly like a human being would not arouse such a feeling.

I think we can all agree that if there's some extra-physical component to consciousness, then a physical system can't match up. That is, of course, a big "if", and I've certainly never seen any evidence for it.

We don't even need Goedel's theorem for that, except to point to the existence of "truth" outside of a physical system.

This is because I suspect we know that other people are conscious partially through anomalous cognition.

Thus, in your opinion, the Turing test will always fail, since we can always detect through "anomalous cognition" whether we're talking to a machine or not. I'll just mention an often observed phenomenon called the "Eliza Effect" where people are fooled by the most superficial imitations of human behavior into supposing the existence of intelligence. So if we have a consciousness-detector, it's really not used very well.

[Jeff Corey]

The Eliza program has evolved in some weird ways. Rather than just just parroting Rogerian non-directive therapy, variants have gone beyond that.
They have even done Bruce Sterling stuff with spiderbots impersonating people on websites.
I figger that's what Ian is.

[Robin]

Originally posted by Jeff Corey
The Eliza program has evolved in some weird ways. Rather than just just parroting Rogerian non-directive therapy, variants have gone beyond that.
They have even done Bruce Sperling stuff with spiderbots impersonating people on websites.
I figger that's what Ian is.

I have my suspicions in this respect about some JREF contributors, but not Interesting Ian.

[Robin]

Originally posted by Interesting Ian
I admit I know very little about this subject, but did not Goedel show that human beings can know things that cannot be known by computation?


No.

[Jeff Corey]

Originally posted by Robin
I have my suspicions in this respect about some JREF contributors, but not Interesting Ian.
Nor De-Bunk nor Pillory.
Show me the evidences for the schoolarship?

[Interesting Ian]

Originally posted by phildonnia


Thus, in your opinion, the Turing test will always fail, since we can always detect through "anomalous cognition" whether we're talking to a machine or not. I'll just mention an often observed phenomenon called the "Eliza Effect" where people are fooled by the most superficial imitations of human behavior into supposing the existence of intelligence. So if we have a consciousness-detector, it's really not used very well. [/B]

No, not the turing test. I said an android. For example you would need to gaze into someones eyes when they express emotions. Merely reading a paragraph of text is insufficient to establish whether consciousness is there!

[Interesting Ian]

Originally posted by Interesting Ian
I admit I know very little about this subject, but did not Goedel show that human beings can know things that cannot be known by computation?

Robin
No.

I refer you to this article here. (http://users.ox.ac.uk/~jrlucas/Godel/mmg.html)


Gödel's theorem seems to me to prove that Mechanism is false, that is, that minds cannot be explained as machines. So also has it seemed to many other people: almost every mathematical logician I have put the matter to has confessed to similar thoughts, but has felt reluctant to commit himself definitely until he could see the whole argument set out, with all objections fully stated and properly met.1 This I attempt to do.

Gödel's theorem states that in any consistent system which is strong enough to produce simple arithmetic there are formulae which cannot {44} be proved-in-the-system, but which we can see to be true.

[Robin]

Originally posted by Interesting Ian
I refer you to this article here. (http://users.ox.ac.uk/~jrlucas/Godel/mmg.html)

If you are quoting John Lucas then you should have said "...did not John Lucas show that human beings can know things that cannot be known by computation?"

Because Lucas referred to Godel in his article does not mean that the views reflect those of Godel.

[Interesting Ian]

Originally posted by Robin
If you are quoting John Lucas then you should have said "...did not John Lucas show that human beings can know things that cannot be known by computation?"

Because Lucas referred to Godel in his article does not mean that the views reflect those of Godel.

I wasn't quoting Lucas in my original statement. I was merely drawing upon my general knowledge.

[Robin]

Originally posted by Interesting Ian
I wasn't quoting Lucas in my original statement. I was merely drawing upon my general knowledge.
You should read the Lucas article in the context of the definition he is using:
In fact we should say briefly that any system which was not floored by the Gödel question was eo ipso not a Turing machine, i.e., not a machine within the meaning of the act.
So he is talking about Turing machines so even if he is right he is not precluding the idea that some physical device might be able to do all that a mind can.

(Anybody who is about to jump in with the "Church-Turing thesis" please note that they did not claim a Turing machine can do anything that any physical system can)

[Interesting Ian]

Originally posted by Robin
Originally posted by Interesting Ian
I wasn't quoting Lucas in my original statement. I was merely drawing upon my general knowledge.

Robin
You should read the Lucas article in the context of the definition he is using:

quote:In fact we should say briefly that any system which was not floored by the Gödel question was eo ipso not a Turing machine, i.e., not a machine within the meaning of the act.

Robin
So he is talking about Turing machines so even if he is right he is not precluding the idea that some physical device might be able to do all that a mind can.



But any machine will function according to physical laws. Cannot all physical laws be expressed algorthimically? After all, physical laws are characterized by their mathematical form. Thus there are no non-turing machines.

[Robin]

Originally posted by Interesting Ian
But any machine will function according to physical laws. Cannot all physical laws be expressed algorthimically? After all, physical laws are characterized by their mathematical form. Thus there are no non-turing machines.
No non-turing machines? Certainly Lucas appears to be suggesting the possibility of one in the second to last paragraph of the article you quoted.

Turing never suggested that there were no non-Turing machines. There are things that happen in real machines like randomness, parallelism that have no place in a Turing machine.

If all physical laws could be expressed algorithmically that would appear to negate the very premise of Lucas's article.

[Robin]

See for example the following entry in the Stanford Encyclopedia of Philosphy:

A myth seems to have arisen concerning Turing's paper of 1936, namely that he there gave a treatment of the limits of mechanism and established a fundamental result to the effect that the universal Turing machine can simulate the behaviour of any machine. The myth has passed into the philosophy of mind, generally to pernicious effect.

[Kopji]

I don't see Gödel's theorems addressing the possibility of artificial intelligence one way or another.

We could eventually create human-like artificial intelligence but not fully understand how or why it works.

[T'ai Chi]

Originally posted by phildonnia

As far as we can tell, the physical world does work like + and *.


What does that mean for the world to work like + and * ?

I'm sitting here with a copy of Godel's actual proof in front of me, and I can't manage to see how a theorem for systems of numbers and some operations, which concluded there exists propositions in it that are neither provable or disprovable, translates to the 'real world'.

It is an interesting analogy to be sure, but I just can't see how it relates to the real, as you say, physical, world.

[Kopji]

A practical real world application of Gödel might be computer virus detection (at least polymorphic ones). Since viruses break the normal rules, detecting them also requires, to some extent, getting outside the system 'rules'.

[hammegk]

A myth seems to have arisen concerning Turing's paper of 1936, namely that he there gave a treatment of the limits of mechanism and established a fundamental result to the effect that the universal Turing machine can simulate the behaviour of any machine.

Is homo sap a machine?

What other machine has been proposed that cannot be 'simulated' by a (theoretical) Turing machine, real-time considerations aside?

[Interesting Ian]

Originally posted by Robin
No non-turing machines? Certainly Lucas appears to be suggesting the possibility of one in the second to last paragraph of the article you quoted.

Turing never suggested that there were no non-Turing machines. There are things that happen in real machines like randomness, parallelism that have no place in a Turing machine.

If all physical laws could be expressed algorithmically that would appear to negate the very premise of Lucas's article.

Randomness? You mean intrinsic randomness as described by QM? I don't know what you mean by parallelism.

But sure, a non-turing machine, meaning something that operates by physical processes, some of which cannot be expressed algorithmically, would be immune to such criticisms. But something like randomness could be built into a computer couldn't it?

[drkitten]

Originally posted by Interesting Ian
I admit I know very little about this subject, but did not Goedel show that human beings can know things that cannot be known by computation?


Um, no. He didn't. Not in the slightest. I don't think the word "human" appears at all in any of his work on logic.

[drkitten]

Originally posted by Interesting Ian
But any machine will function according to physical laws. Cannot all physical laws be expressed algorthimically?

No. Again. Re-read your QM, and specifically the Bell Inequalities.

[Interesting Ian]

Originally posted by Kopji
I don't see Gödel's theorems addressing the possibility of artificial intelligence one way or another.

We could eventually create human-like artificial intelligence but not fully understand how or why it works.

If you're declaring it would be conscious, I say that we need to understand what consciousness is first before trying to create it.

[drkitten]

Originally posted by Interesting Ian
But something like randomness could be built into a computer couldn't it?

Into a computer, yes, but not into a Turing machine. You'd need an oracle for randomness, a device that is physically easy to build, but not part of the TM formalism.

And once you've attached such a device to a TM, the resulting assembly is no longer a TM.

[Interesting Ian]

Originally posted by new drkitten
Um, no. He didn't. Not in the slightest. I don't think the word
"human" appears at all in any of his work on logic.

It's supposed to be a direct implication of his proof. You need to justify your assertion "not in the slightest" (this is not to say you're wrong, I simply do not know enough about the subject).


No. Again. Re-read your QM, and specifically the Bell Inequalities.


Well, I would need to read it in the first place. Well look, if algorithms cannot describe QM despite the fact that QM is described by mathematics like all other physical laws, and presumably quantum processes occur in the brain, why do most materialists say that a brain is simply a computer??

[drkitten]

Originally posted by Interesting Ian
It's supposed to be a direct implication of his proof. You need to justify your assertion "not in the slightest" (this is not to say you're wrong, I simply do not know enough about the subject).


Well, his proof applies to axiomatic systems of logic.

Humans aren't axiomatic systems of logic.

Godel's theorem doesn't apply to ham sandwiches, or pieces of chalk, either, for approximately the same reason.




Well, I would need to read it in the first place. Well look, if algorithms cannot describe QM despite the fact that QM is described by mathematics like all other physical laws,

Algorithms and mathematics are not synonymous terms; lots of QM cannot be expressed in algorithmic terms because of the apparent randomness and interactivity involved. It's possible to build an interactive machine with a random oracle, but such a machine is neither axiomatic (unless you postulate the underlying hidden variables that Bell disproved) or nor a Turing machine, by the definition of TM.

[Interesting Ian]

Originally posted by new drkitten
Well, his proof applies to axiomatic systems of logic.

Humans aren't axiomatic systems of logic.

Godel's theorem doesn't apply to ham sandwiches, or pieces of chalk, either, for approximately the same reason.





Algorithms and mathematics are not synonymous terms; lots of QM cannot be expressed in algorithmic terms because of the apparent randomness and interactivity involved. It's possible to build an interactive machine with a random oracle, but such a machine is neither axiomatic (unless you postulate the underlying hidden variables that Bell disproved) or nor a Turing machine, by the definition of TM.

I think the idea might be that QM is irrelevant to the brain because the effects of QM would be too miniscule to have any impact on the functioning of the brain? Thus the brain can be described algorithmically, and hence is essentially a computer.

[drkitten]

Originally posted by Interesting Ian
I think the idea might be that QM is irrelevant to the brain because the effects of QM would be too miniscule to have any impact on the functioning of the brain? Thus the brain can be described algorithmically, and hence is essentially a computer.

Well, that might be the idea, but it's at best unproven (and directly contradicts the theories of Penrose in the opening post, as a start). Notice, however, if you make this argument, you are still faced with the problem that the computer, being interactive, is not an axiomatic system of logic, and Godel's theorem doesn't apply to it. As a general rule, if you want to know whether or not Godel's theorem applies to a given system, simply enumerate the (formal) axioms under which it operates. If you can't do that, then Godel is irrelevant.

There's a very interesting debate about whether or not intelligence can be obtained by a computer.

None of it happens anywhere the word "Godel."

In the context of the artificial intelligence debate, the only meaning that the word "Godel" has is that one of the debaters has essentially zero understanding of any of the fields of logic, psychology, or computer science. This applies to J.R. Lucas, it applies to Roger Penrose, and applies specifically to a number of participants in this thread that forum rules prevent me from naming directly.

[Interesting Ian]

Originally posted by new drkitten


Humans aren't axiomatic systems of logic.




What does this actually mean? Humans operate according to physical laws. These laws are precisely encapsulated by mathematics. So you're saying mathematics is not an axiomatic system of logic??

[AWPrime]

Originally posted by Robin
I have my suspicions in this respect about some JREF contributors

1inChrist?

- posted 24 hours
- posts contain no intelligence

[AWPrime]

Originally posted by AWPrime
Why does the poll question differ from the title question?

Poll question: Will machines ever be able to think as humans do?

Title question: Did Godel disprove the idea of artificial intelligence?


A NO to the title question doesn't mean a NO to the poll question. Is this a attempt to manipulate the poll?

[Bodhi Dharma Zen]

The brain IS NOT a computer.

We dont know what it is "AI"

Godel is complex to understand.

[Interesting Ian]

Originally posted by Bodhi Dharma Zen
The brain IS NOT a computer.


There seem to be quite a lot of people maintaining this. First of all, does anyone disagree?

Secondly, if the brain is not a computer, then this would imply computers cannot produce consciousness, yes?

But a brain can, and presumably therefore people think this is because of QM events in the brain? I presume that ones interaction with the environment does not produce consciousness per se since a computer could collect information from the environment?

I'm just wondering what's so special about QM events that they can magically produce consciousness?

[drkitten]

Originally posted by Interesting Ian
What does this actually mean? Humans operate according to physical laws. These laws are precisely encapsulated by mathematics. So you're saying mathematics is not an axiomatic system of logic??

Fallacy of equivocation.

Humans "operate according to" physical laws. This does not mean that they "are" physical laws.

Physical laws are "described by" mathematics. This does not mean that they "are" mathematics.

Mathematics "includes" axiomatic systems of logic. This does not mean that it "is" an axiomatic system of logic.

Godel's theorem applies to things that "are" axiomatic systems of logic.

[drkitten]

Originally posted by Interesting Ian
There seem to be quite a lot of people maintaining this. First of all, does anyone disagree?

Of course the brain isn't a computer. It's not silicon-based, has no transistors, does not require a battery or external electrical power, et cetera.

[QUOTE]
Secondly, if the brain is not a computer, then this would imply computers cannot produce consciousness, yes?


Why on earth would it imply this? Leopards are spotted. But a giraffe is not a leopard, and so this implies a giraffe cannot be spotted?


But a brain can, and presumably therefore people think this is because of QM events in the brain?


This has indeed been proposed, mostly by people (such as Penrose) with litle knowledge of either the brain or of quantum mechanics. There's very little reason to give intellectual weight to this "presumption," as there's no evidence to support it other than as an abstract and ill-founded supposition.

Other people think that a brain can produce consciousness for a wide variety of other reasons, for which you are handwaved generally to "the literature." It's fair to say that the number of people who actually believe that QM causes consciousness is an extreme minority, mostly spearheaded by Roger Penrose. It is neither a well-regarded nor widely-accepted theory, and the regard and acceptance decrease the higher up the food chain you get.




I presume that ones interaction with the environment does not produce consciousness per se

That has also indeed been proposed (demonstrably, since you just proposed it, but it's also been independently proposed by people such as Searle). It's been the subject of much debate and many scholars (Chalmers, the Churchlands, Hofstadter) reject it out of hand.

since a computer could collect information from the environment?


Irrelevant unless you assume that a computer cannot be conscious, which is at best both unproven and controversial.


I'm just wondering what's so special about QM events that they can magically produce consciousness?

You're not the only one. In context, QM is usually dragged up to support the ill-founded Godelian argument you posed above. But since the argument itself is clearly false, it doesn't matter what mechanism is proposed.

[Interesting Ian]

Originally posted by new drkitten
Fallacy of equivocation.

Humans "operate according to" physical laws. This does not mean that they "are" physical laws.

Physical laws are "described by" mathematics. This does not mean that they "are" mathematics.

Mathematics "includes" axiomatic systems of logic. This does not mean that it "is" an axiomatic system of logic.

Godel's theorem applies to things that "are" axiomatic systems of logic.

Let's get to the nitty gritty. I imagine you would also assert that an android, whose behaviour is indistinguishable from a human being's, would also not be an axiomatic system of logic?

I'll wait for your reply before proceeding.

[drkitten]

Originally posted by Interesting Ian
Let's get to the nitty gritty. I imagine you would also assert that an android, whose behaviour is indistinguishable from a human being's, would also not be an axiomatic system of logic?


Trivially, yes. For example, an android would have weight and occupy space -- an axiomatic system of logic, being an abstraction, does neither.

You're conflating fundamentally different levels of reality here.

[hammegk]

Originally posted by new drkitten
Into a computer, yes, but not into a Turing machine. You'd need an oracle for randomness, a device that is physically easy to build, but not part of the TM formalism.

And once you've attached such a device to a TM, the resulting assembly is no longer a TM.
Interesting contention. Why is the TM itself unable to correctly incorporate a random-generator algorithm, or a multitude of them?


You're not the only one. In context, QM is usually dragged up to support the ill-founded Godelian argument you posed above. But since the argument itself is clearly false, it doesn't matter what mechanism is proposed.
Clearly false?

Are you avering that calcium ions involved in brain function move so rapidly that qm effects are irrelevant? (An effect which of course could be digitally simulated.)

[Interesting Ian]

Originally posted by new drkitten
Originally posted by Interesting Ian
There seem to be quite a lot of people maintaining this. First of all, does anyone disagree?


Dr
Of course the brain isn't a computer. It's not silicon-based, has no transistors, does not require a battery or external electrical power, et cetera.



Let's try to be sensible about this. I mean that people are not maintaining that a brain is effectively a computer.


Secondly, if the brain is not a computer, then this would imply computers cannot produce consciousness, yes?

Dr
Why on earth would it imply this?



Because brains produce consciousness which a priori is an astonishing fact. So it would therefore be extremely surprising if some other physical processes, of quite a characteristically different nature, also produced consciousness. You seem to be leaning towards the view that all things are conscious, even rocks etc.


But a brain can, and presumably therefore people think this is because of QM events in the brain?


Dr
This has indeed been proposed, mostly by people (such as Penrose) with litle knowledge of either the brain or of quantum mechanics. There's very little reason to give intellectual weight to this "presumption," as there's no evidence to support it other than as an abstract and ill-founded supposition.



So hang on a sec. You're denying that the execution of algoritms produce consciousness, and you're denying that throwing QM events into the mix produces consciousness, so therefore what is it that does produce consciousness?? :eek:




Other people think that a brain can produce consciousness for a wide variety of other reasons, for which you are handwaved generally to "the literature." It's fair to say that the number of people who actually believe that QM causes consciousness is an extreme minority, mostly spearheaded by Roger Penrose. It is neither a well-regarded nor widely-accepted theory, and the regard and acceptance decrease the higher up the food chain you get.



I fail to see what else there could be apart from the execution of algorithms or QM events which produce consciousness. Please enlighten me.





II
I presume that ones interaction with the environment does not produce consciousness per se


Dr
That has also indeed been proposed (demonstrably, since you just proposed it, but it's also been independently proposed by people such as Searle). It's been the subject of much debate and many scholars (Chalmers, the Churchlands, Hofstadter) reject it out of hand.



Sorry? They reject what?





II
since a computer could collect information from the environment?


Dr
Irrelevant unless you assume that a computer cannot be conscious, which is at best both unproven and controversial.



Huh? You implied that was your position since a brain is not (effectively) a computer. Do you hold that absolutely all processes/things are conscious then? This would tend to be the consequence of your position.



II
I'm just wondering what's so special about QM events that they can magically produce consciousness?

Dr
You're not the only one. In context, QM is usually dragged up to support the ill-founded Godelian argument you posed above. But since the argument itself is clearly false, it doesn't matter what mechanism is proposed.


I think their position is that the pure execution of algorithms is not capable of generating some truths, but which we can clearly see are true. Therefore something else is required. What else could there be apart from QM? Nothing physical it would seem. I say a non-physical substantial self.

[drkitten]

Originally posted by Interesting Ian
I'll wait for your reply before proceeding.

I've decided to take pity on you and try to frame the question properly that I believe you want to ask. As I said, you are conflating fundamentally different levels of reality when you ask whether or not human beings are axiomatic systems of logic (or something like that), because human beings are concrete entities, not abstractions like logic. You can't even meaningfully ask whether or not the behavior of human beings is an axiomatic system of logic, because behavior, being a series of events, occurs at specific space/time locations.

The question that I think you want to ask is : "Can human behavior [or more specifically cognitive behavior] be modelled by an axiomatic system of logic?"

I think we will agree that this is a very deep question; in a nutshell, it's a major component of the Strong AI hypothesis. A definitive "no" answer would send many current AI researchers scurrying for other fields of practice and rather deplete the ranks of current graduate students. On the other hand, it would also specifically not exclude all the currently taken approaches to AI that are being studied; there are a number of approaches that are not axiomatic or logic based, and even if the above answer were a definitive "no," these other approaches might work.

Now, let's look at what Godel's theorem really says. For a sufficiently complex axiomatic system of logic (systematically complex basically means can do arithmetic correctly), then there is either an undecidable sentence (a sentence that can neither be proven true or proven false), or or a sentence that can be proven both true and false. Hence any such system is either "incomplete" or "inconsistent."

Let us take as a working assumption that the answer to the question above is "yes," that we can describe human cognitive behavior with an axiomatic system. In that case, we either have the case that

1) the system can't do arithmetic correctly
2) there are some statements that the system will never be able to validate as either true or false.
3) there are some statements that the system will believe to be both true and false.

If you make two further assumptions, first that the second case above holds, and second that human beings will be able to determine if the statement in question is true or false, then you have a "proof" that human cognitive behavior is capable of doing something that no axiomatic system can do. In other words, no axiomatic system can perfectly model human cognition. That's the Lucas/Penrose argument in a very quick summary.

It's also total tosh, specifically because of the two "further assumptions" detailed above. Let's look at the three cases further, but apply them to human beings above.

1) the system can't do arithmetic correctly
2) there are some statements that the system will never be able to validate as either true or false.
3) there are some statements that the system will believe to be both true and false.

Case 1 -- is there anyone here who claims to be able to do arithmetic "correctly"? As in, never makes a mistake, and can handle problems of unlimited size? I doubt it. Humans have rather serious cognitive limitations in terms of, for example, attention span, short-term memory, and reliability/reproducibility of cognitive tasks. If humans really could do arithmetic "correctly," everyone in the world would have gotten perfect scores on their standardized tests. I think it's fairly clear that an axiomatic system that perfectly models human cognitive behavior wouldn't necessarily do arithmetic "correctly."

Similarly, case 3 -- there's lots of work done, including Nobel-prize work, about the various long-standing cognitive biases that cause people to simultaneously believe contradictory things. Type "Linda is a feminist bank teller" into your web browser if you don't believe me. Humans simply aren't perfectly consistent reasoners, and so there's no reason to believe their models should be either.

So what we're really talking about if you want to make the Lucas/Penrose argument about AI go through is not a statement about human-like intelligence, but about God-like inhuman intelligence, the sort that has access to truths and abilities beyond the merely human. But in this case, if we already assume that such truths exist, then we've already assumed that case 2 above applies, not only to the formal system, but to human cognition itself. We've assumed that there are statements whose truth is inaccessible to humans. In this case, it should be no surprise that a detailed model of us finds that exact same truth inaccessible. Now, a different axiomatic system of logic may be able to establish the truth of the proposition, but only via a chain of logic so long and so convoluted that we will never understand or be able to follow the proof. In fact, we already have a candidate for such a statement in the four-color theorem, which has been "proved," but by a computer program of such complexity that no human could duplicate or even understand the proof in its entirety. This theorem may well be our equivalent of the Godel sentence, because the fundamental limitations on how we perform our thoughts limit our ability to understand that proof.

So, basically, Godel's theorem says nothing at all about whether or not there are truths inaccessible to humans, except in the very general statement that if you assume (without justification) that the theorem applies, then one of three cases holds --- and a good case, consistent with our current knowledge of psychology, can be made for any of the three cases. Alternatively, you can assume that Godel's theorem does not apply to human cognition, in which case all bets are off for both the humans and for the computers that model them. In no case does quantum mechanics amount to more than an intellectual detour, and usually an attempt to blind the readership with science that they don't understand.

In that regard, it's fairly good. Most people who understand mathematics well enough to know Godel know little psych or QM. Most physicists don't know psych. Et cetera. Unfortunately, the set of people who know all three fields do not include either Lucas, Penrose, or a number of unnamed participants on this thread.

[drkitten]

Originally posted by hammegk
Interesting contention. Why is the TM itself unable to correctly incorporate a random-generator algorithm, or a multitude of them?


For approximately the same reason you can't have three wheels on a unicycle. If you build a unicycle, and put two more wheels on it, it's no longer a unicycle.

The notion of a "random-generator algorithm" is inherently contradictory and does not exist. What laymen call "random number generators" are more properly called "pseudo-random number generators," as the number they generate aren't really random, but look random enough for most purposes if you don't examine them really closely. For people for whom the quality of random numbers really matters (e.g. cryptographers), there's a tremendous amount of research effort establishing and improving the statistical quality of algorithmically generated sequences, exactly because Turing machines, and by extension algorithms in general, cannot generate them.



Clearly false?

Are you avering that calcium ions involved in brain function move so rapidly that qm effects are irrelevant? (An effect which of course could be digitally simulated.)

No. I am averring that the argument that Godel's theorem prohibits axiomitization of human-like intelligence is clearly false. If you do not assume that human-like intelligence is non-axiomatizable, there is no reason to invoke quantum mechanics to explain why.

(I also note in passing that digital similation is insufficient, due to the butterfly effect.)

[drkitten]

Originally posted by Interesting Ian
Let's try to be sensible about this. I mean that people are not maintaining that a brain is effectively a computer.


Assuming that by "computer" you mean algorithmic computational device, then, um, you're flat-out wrong. Lots of people maintain this -- Dennett, McCarthy, the Churchlands, Minsky, Hofstadter, Fodor, Berwick, Pinker, Marcus, Plunkett, &c.

The question is not whether the position is popular, but whether
it is true.




Because brains produce consciousness which a priori is an astonishing fact. So it would therefore be extremely surprising if some other physical processes, of quite a characteristically different nature, also produced consciousness.


Ah, yes. We call this "argument from incredulity" and fail students for using it where I come from. Lots of surprising things happen. Is this one of them? Do you have any evidence that it isn't?

I'm not affirming, or denying, anything. I am specifically rejecting arguments that cannot be supported either rationally (through reasoned, non-fallacious argumentation) or empirically (through generally available and accepted "scientific" data).



I think their position is that the pure execution of algorithms is not capable of generating some truths, but which we can clearly see are true.


This is indeed their position. It is at best unproven, since they have given no explanation about how we can clearly see they are true. If they use that as an assumption, then they're clearly begging the question. (As such, it's not rationally supported.) It also contradicts widely available and accepted data -- for example, I can easily show you an algorithm that is capable of generating every truth (but also every falsehood). Therefore, the statement that "the pure execution of algorithms is not capable of generating some truths" is not empirically supported, either, and they're committing a simple error in logical reasoning. Finally, their assessment of human capabilities contradicts widely available psychological data.

In other words, bollocks to them.

[hammegk]

Originally posted by new drkitten
For approximately the same reason you can't have three wheels on a unicycle. If you build a unicycle, and put two more wheels on it, it's no longer a unicycle.
If you say so.


The notion of a "random-generator algorithm" is inherently contradictory and does not exist. .... there's a tremendous amount of research effort establishing and improving the statistical quality of algorithmically generated sequences, exactly because Turing machines, and by extension algorithms in general, cannot generate them.
So true, in (practical) fact. We could also debate what is or even could be actually "random" in any finite system.

Yet what is wrong with my position that any "random number" no matter how generated can be simulated by a Turing Machine?


If you do not assume that human-like intelligence is non-axiomatizable, there is no reason to invoke quantum mechanics to explain why.
Agreed, although I haven't invoked anything. My understanding is that qm effects do govern calcium ion propagation in the brain.

And if you do assume human intelligence is an axiom, hello Turing machine.


(I also note in passing that digital similation is insufficient, due to the butterfly effect.)
Not currently forwards computable, but amenable to simulation in any case.

[Interesting Ian]

Originally posted by new drkitten
Trivially, yes. For example, an android would have weight and occupy space -- an axiomatic system of logic, being an abstraction, does neither.

You're conflating fundamentally different levels of reality here.

Indeed, and I am doing so in a forlorn endeavour to ease communication. The android is conscious and is merely the execution of algorithms. This very strongly suggests that the brain is merely the execution of algorithms too.

Now let's have a straight answer from you instead of going off into an irrelevant tangency like you are prone to do.

Do you agree that the brain is merely a algorithmic machine or not?

[MESchlum]

One point I got out of reading GEB (and other things) is that the undecidable postulates in your system are not true or false in an absolute sense.

Example: geometry. Euclid's postulate about parallel lines is non provable using the others. Assume it's true, you get Euclidian geometry. Assume it's false, you get non-Euclidian geometry.

Both geometries work, in their specific contexts. The undecidable postulate can be true, or false, and you will get a different system in either case - but both systems are valid.

The assumption that it is possible to "know" whether an undecidable postulate is correct or not is false. One version can seem more obvious (Euclidian geometry), but this does not invalidate the other.

This makes me ignore claims stating that humans (or whatever) can go beyond "mere" algorithms because they "know" if an undecidable proposition is true or not. If you have a better argument, I'm happy to hear it - but this one, as stated, does not hold water (to me).

[Interesting Ian]

Originally posted by new drkitten


The question that I think you want to ask is : "Can human behavior [or more specifically cognitive behavior] be modelled by an axiomatic system of logic?"



Before even reading the rest of your post, I just want to address this. I wasn't trying to ask this question, because surely it obviously can be?? Even *I*, who believes that we are souls, thinks that our behaviour can be so modelled.

Why?

Because if enough knowledge were available regarding someone's psyche, and therefore we can in principle predict exactly how that person will react under appropriate circumstances, then surely this can be modelled using the appropriate algorithms?? In practice an appropriately programmed android's behaviour would be indistinguishable from a human being's (but maybe not absolutely indistinguishable).

No, I was trying to ask the question:

"Can consciousness be modelled by an axiomatic system of logic?" Or maybe, "is consciousness nothing but the execution of algorithms"?

Now to read the rest of your post. Thanks for taking the time to respond in detail :)

[69dodge]

Originally posted by new drkitten
for example, I can easily show you an algorithm that is capable of generating every truth (but also every falsehood).Yes, exactly.

People are getting their quantifiers mixed up. Goedel didn't show that some truth exists which no algorithm can produce. He showed that each algorithm has some truth, possibly specific to it, which it cannot produce. (Unless the algorithm also produces some falsehoods, that is. But then it's a "bad" algorithm, so we don't much care about it.) But another algorithm always exists which can produce that truth.

Of course, the other algorithm has its own limitations.

Which a third algorithm doesn't have.

And so on, ad infinitum.

So when a person "intuitively sees" the truth of a Goedel sentence, it is not the case that he knows something that no algorithm can produce; it is merely the case that he knows something that one particular algorithm can't produce. A Goedel sentence is only a Goedel sentence relative to a particular axiomatic system. It's not provable within that system, but other systems exist in which it is provable.

Unless people are infinitely smart, which clearly they aren't, Goedel's theorem provides no reason to suppose that there's more to their reasoning abilities than algorithms.

[Interesting Ian]

Originally posted by new drkitten
I've decided to take pity on you and try to frame the question properly that I believe you want to ask. As I said, you are conflating fundamentally different levels of reality when you ask whether or not human beings are axiomatic systems of logic (or something like that), because human beings are concrete entities, not abstractions like logic. You can't even meaningfully ask whether or not the behavior of human beings is an axiomatic system of logic, because behavior, being a series of events, occurs at specific space/time locations.

The question that I think you want to ask is : "Can human behavior [or more specifically cognitive behavior] be modelled by an axiomatic system of logic?"

I think we will agree that this is a very deep question;



Not at all; surely it can be?

[Dr Adequate]

Originally posted by Interesting Ian
I admit I know very little about this subject, but did not Goedel show that human beings can know things that cannot be known by computation?
No.

[Interesting Ian]

Originally posted by new drkitten

The question that I think you want to ask is : "Can human behavior [or more specifically cognitive behavior] be modelled by an axiomatic system of logic?"

I think we will agree that this is a very deep question; in a nutshell, it's a major component of the Strong AI hypothesis. A definitive "no" answer would send many current AI researchers scurrying for other fields of practice and rather deplete the ranks of current graduate students. On the other hand, it would also specifically not exclude all the currently taken approaches to AI that are being studied; there are a number of approaches that are not axiomatic or logic based, and even if the above answer were a definitive "no," these other approaches might work.

Now, let's look at what Godel's theorem really says. For a sufficiently complex axiomatic system of logic (systematically complex basically means can do arithmetic correctly), then there is either an undecidable sentence (a sentence that can neither be proven true or proven false), or or a sentence that can be proven both true and false. Hence any such system is either "incomplete" or "inconsistent."

Let us take as a working assumption that the answer to the question above is "yes," that we can describe human cognitive behavior with an axiomatic system. In that case, we either have the case that


1) the system can't do arithmetic correctly
2) there are some statements that the system will never be able to validate as either true or false.
3) there are some statements that the system will believe to be both true and false.

If you make two further assumptions, first that the second case above holds, and second that human beings will be able to determine if the statement in question is true or false, then you have a "proof" that human cognitive behavior is capable of doing something that no axiomatic system can do. In other words, no axiomatic system can perfectly model human cognition. That's the Lucas/Penrose argument in a very quick summary.

It's also total tosh, specifically because of the two "further assumptions" detailed above. Let's look at the three cases further, but apply them to human beings above.

1) the system can't do arithmetic correctly
2) there are some statements that the system will never be able to validate as either true or false.
3) there are some statements that the system will believe to be both true and false.

Case 1 -- is there anyone here who claims to be able to do arithmetic "correctly"? As in, never makes a mistake, and can handle problems of unlimited size? I doubt it. Humans have rather serious cognitive limitations in terms of, for example, attention span, short-term memory, and reliability/reproducibility of cognitive tasks. If humans really could do arithmetic "correctly," everyone in the world would have gotten perfect scores on their standardized tests. I think it's fairly clear that an axiomatic system that perfectly models human cognitive behavior wouldn't necessarily do arithmetic "correctly."



Well of course it wouldn't. But the point is that it couldn't whether or not it models human cognitive behaviour. Also the fact that in practise no-one can do arithmetic perfectly is not relevant. I think the argument might be (although I don't know, only having as much knowledge as a average man in the street regarding Goedel's theorem) that in principle there is no reason we couldn't. But in principle there is a reason why a computer couldn't. Therefore we are not algorithmic machines.

[Interesting Ian]

Originally posted by new drkitten


Similarly, case 3 -- there's lots of work done, including Nobel-prize work, about the various long-standing cognitive biases that cause people to simultaneously believe contradictory things. Type "Linda is a feminist bank teller" into your web browser if you don't believe me. Humans simply aren't perfectly consistent reasoners, and so there's no reason to believe their models should be either.



None of this matters. There is no logical reason why we are inconsistent; only psychological reasons . .or reasons of intellectual deficiency etc.

Although I know nothing about mathematics, or Goedel's theorem, from what little knowledge I do know, I'm pretty sure you're simply not getting the arguments employed to show that we are not simply algorithmic machines.

I agree though I can't really argue for it. I might look into this Goedel stuff some more

(PS how do you put those 2 dots above the "o"?)

[Interesting Ian]

Originally posted by new drkitten
Originally posted by hammegk
Interesting contention. Why is the TM itself unable to correctly incorporate a random-generator algorithm, or a multitude of them?


Dr
For approximately the same reason you can't have three wheels on a unicycle. If you build a unicycle, and put two more wheels on it, it's no longer a unicycle.

The notion of a "random-generator algorithm" is inherently contradictory and does not exist. What laymen call "random number generators" are more properly called "pseudo-random number generators," as the number they generate aren't really random, but look random enough for most purposes if you don't examine them really closely. For people for whom the quality of random numbers really matters (e.g. cryptographers), there's a tremendous amount of research effort establishing and improving the statistical quality of algorithmically generated sequences, exactly because Turing machines, and by extension algorithms in general, cannot generate them.


Not all "random" number generators are pseudo-random number generators. Indeed, pseudo-random number generators are not random at all, on the converse, they are determined!




No. I am averring that the argument that Godel's theorem prohibits axiomitization of human-like intelligence is clearly false. If you do not assume that human-like intelligence is non-axiomatizable, there is no reason to invoke quantum mechanics to explain why.

(I also note in passing that digital similation is insufficient, due to the butterfly effect.) [/B]

Why does everyone keep talking about intelligence rather than consciousness?? Of course computers can be "intelligent", but that's not interesting. I want to know if they could be conscious!

[Interesting Ian]

Originally posted by new drkitten
Originally posted by Interesting Ian
Let's try to be sensible about this. I mean that people are not maintaining that a brain is effectively a computer.


Dr
Assuming that by "computer" you mean algorithmic computational device, then, um, you're flat-out wrong. Lots of people maintain this -- Dennett, McCarthy, the Churchlands, Minsky, Hofstadter, Fodor, Berwick, Pinker, Marcus, Plunkett, &c.

The question is not whether the position is popular, but whether
it is true.


I meant people on this thread like yourself. But apparently I was getting the wrong impression in your case. And yup, I wasn't talking about quantum computers ;)





II
Because brains produce consciousness which a priori is an astonishing fact. So it would therefore be extremely surprising if some other physical processes, of quite a characteristically different nature, also produced consciousness.

Dr

Ah, yes. We call this "argument from incredulity" and fail students for using it where I come from.



I'm worried that they fail students for what they erroneously regard as an "argument from incredulity".
My argument is not. Materialism has just one problem, and it's a huge one. Namely how do brain processes produce consciousness? Now you want to compound that by saying that brain processes are not algorithmic but produce consciousness, but also algorithmic processes produce consciousness too. Now, if you're maintaining that not everything is conscious (eg an obvious algorthmic process such as a boulder rolling down a hill)), then basically you're making your metaphysic that much more complex than is apparently warranted. This is because you're saying some algorithmic processes produce consciousness, but others don't.

BTW, these students you fail? I guess they're not allowed to dispute their failure by show that it is in fact you who is in error?? :rolleyes: Typical of teachers/lecturers. Just justifies my often repeated contention that formal education is a waste of time. For a kick off, too many teachers/lecturers are intellectual deficient.




II
I think their position is that the pure execution of algorithms is not capable of generating some truths, but which we can clearly see are true.


Dr
This is indeed their position. It is at best unproven, since they have given no explanation about how we can clearly see they are true.



Yes, this is because an explanation is not possible. It's a sudden understanding. Maybe we're making temporary contact with the Platonic world of forms?



If they use that as an assumption, then they're clearly begging the question. (As such, it's not rationally supported.)



Well, are they not pointing to certain limitations as to the truths the execution of algorithms can reach? Are we like wise logically limited? Only psychologically limited it would seem, which is a completely different thing.


It also contradicts widely available and accepted data -- for example, I can easily show you an algorithm that is capable of generating every truth (but also every falsehood). Therefore, the statement that "the pure execution of algorithms is not capable of generating some truths" is not empirically supported, either, and they're committing a simple error in logical reasoning.


I'm sorry, but I do not understand this error.



Finally, their assessment of human capabilities contradicts widely available psychological data.

In other words, bollocks to them.



I haven't read their arguments, so I do not know what they are. But I'm guessing they're saying that there is no logical reason why we cannot get to know all truths, although they would certainly acknowledge the psychological reasons.

[69dodge]

Originally posted by MESchlum
The assumption that it is possible to "know" whether an undecidable postulate is correct or not is false.How did Goedel show that the sentence he constructed was undecidable, in the first place? He did it by constructing a sentence that said, basically, "I'm not provable". Such a sentence can't be provable, if the system is to be consistent. (If it were provable and yet it says, "I'm not provable", that would mean it's false. But only in an inconsistent system could a false sentence be provable.)

Well, if says it's not provable, and in fact it's not provable, that means it's true, right?

[drkitten]

Originally posted by hammegk

So true, in (practical) fact. We could also debate what is or even could be actually "random" in any finite system.

Yet what is wrong with my position that any "random number" no matter how generated can be simulated by a Turing Machine?


The same thing that is wrong with a position that any number of wheels can be attached to a unicycle.

Basically, what's wrong is the meanings of the words you are using.

[Interesting Ian]

Originally posted by 69dodge
Yes, exactly.

People are getting their quantifiers mixed up. Goedel didn't show that some truth exists which no algorithm can produce. He showed that each algorithm has some truth, possibly specific to it, which it cannot produce. (Unless the algorithm also produces some falsehoods, that is. But then it's a "bad" algorithm, so we don't much care about it.) But another algorithm always exists which can produce that truth.

Of course, the other algorithm has its own limitations.

Which a third algorithm doesn't have.

And so on, ad infinitum.

So when a person "intuitively sees" the truth of a Goedel sentence, it is not the case that he knows something that no algorithm can produce; it is merely the case that he knows something that one particular algorithm can't produce. A Goedel sentence is only a Goedel sentence relative to a particular axiomatic system. It's not provable within that system, but other systems exist in which it is provable.

Unless people are infinitely smart, which clearly they aren't, Goedel's theorem provides no reason to suppose that there's more to their reasoning abilities than algorithms.

They don't need to be infinitely smart. They just need to be not logically limited unlike any algorithm is.

[drkitten]

Originally posted by Interesting Ian
I think the argument might be (although I don't know, only having as much knowledge as a average man in the street regarding Goedel's theorem) that in principle there is no reason we couldn't.


Well, no. In principle, human beings are limited by their psychological abilities as much as their physical ones, which is why concepts like "short term memory" and "digit span" exist.

Talking about "in principle there is no reason why we couldn't have an infinite digit span is exactly as realistic as a statement that "in principle, there's no reason we couldn't jump 300m in the air without aid." You're talking about an utterly unrealistic idealization of the human capacity here.


But in principle there is a reason why a computer couldn't. Therefore we are not algorithmic machines.

The fundamental reason that axiomatic systems cannot do everything is because they're finite. The fundamental reason that humans cannot do anything is because they're finite, too. Not only is there a reason, in principle, but in extremely broad terms it's the same darn reason.

[drkitten]

Originally posted by Interesting Ian

Although I know nothing about mathematics, or Goedel's theorem, from what little knowledge I do know, I'm pretty sure you're simply not getting the arguments employed to show that we are not simply algorithmic machines.

Should this go down as another classic Ian quote? "Although I know nothing about the subject, I'm pretty sure you're not getting it."

You're right. If you assume, first of all, that human capacity is not limited by their physical or psychological makeup, and second of all, that human beings are capable of performing acts that are logically impossible, then there's no reason to conclude that they are in any way limited in the same way that systems limited by logic, physics, or psychology would be. If men were gods, they would have different capacities.

I just consider that an unrealistic starting assumption. In what way do you consider a human with an infinitely long lifespan, an infinitely long attention span, and total recall of every detail s/he has ever experienced to be a legitimate standard of human capacity? But even if we assume that such a creation existed, there's still nothing in evidence that such a creature would be able to unerringly sort truth from falsehood, or would be able to determine every truth in the universe. In fact, Tarski's work suggests quite the opposite.

[MESchlum]

Originally posted by 69dodge
How did Goedel show that the sentence he constructed was undecidable, in the first place? He did it by constructing a sentence that said, basically, "I'm not provable". Such a sentence can't be provable, if the system is to be consistent. (If it were provable and yet it says, "I'm not provable", that would mean it's false. But only in an inconsistent system could a false sentence be provable.)

Well, if says it's not provable, and in fact it's not provable, that means it's true, right?

Well...

If:

*a statement that is not false is true
* the system is consistent

Then you've just proven (within the system) that the statement is true. So it must be false, since it's been proven. Of course, if a statement that is not false can also be not true, you have no problem (besides, perhaps, consistency?)

By my interpretation of the setup (which, I will grant, is a bit rusty), we can build a new system, containing the statement, and use that.

"I'm not provable in system X"

Is not provable in X, and can be assumed to be true (in system Y which contains X and "the sentence is provable in Y") or not (system Z). You can then build up a sentence that says "I'm not provable in Y", or course.

[Interesting Ian]

Originally posted by new drkitten
Originally posted by Interesting Ian
I think the argument might be (although I don't know, only having as much knowledge as a average man in the street regarding Goedel's theorem) that in principle there is no reason we couldn't.


Dr
Well, no. In principle, human beings are limited by their psychological abilities as much as their physical ones, which is why concepts like "short term memory" and "digit span" exist.

Talking about "in principle there is no reason why we couldn't have an infinite digit span is exactly as realistic as a statement that "in principle, there's no reason we couldn't jump 300m in the air without aid." You're talking about an utterly unrealistic idealization of the human capacity here.



Yes. But it doesn't matter. It still doesn't alter the case that we are not logically limited. Any algorithm (but not of course an infinte number of them) is logically limited. You need to argue that we are likewise logically limited, not merely psychologically limited or even nomologically limited.



II
But in principle there is a reason why a computer couldn't. Therefore we are not algorithmic machines.


Dr
The fundamental reason that axiomatic systems cannot do everything is because they're finite. The fundamental reason that humans cannot do anything is because they're finite, too. Not only is there a reason, in principle, but in extremely broad terms it's the same darn reason.

No, this is an error. Although the reason might be because of finite capacities in both instances, that doesn't entail that that which limits in both cases is identical.

You gat a fail Dr Kitten!

Love to be in one of your classes and say that! :D

[drkitten]

Originally posted by Interesting Ian
Yes. But it doesn't matter. It still doesn't alter the case that we are not logically limited. Any algorithm (but not of course an infinte number of them) is logically limited. You need to argue that we are likewise logically limited, not merely psychologically limited or even nomologically limited.


I will be happy to do so when you provide working definitions of the distinctions between logical limitations, psychological limitations, and nomological limitations. Because from where I sit, a psychological limitation such as short term memory can be proven to be isomorphic and equivalent to a logical limitation.

(Actually, that particular isomorphism is rather fundamental to a lot of the field called "theory of computation" and appears in a lot of contexts. For example, any finite approximation to the set of all palindromes is finitely computable (and can be captured by a regular expression), but the set itself is not. The fundamental difference here can be expressed as a "psychological" limitation on the capacity of the processing unit, or alternatively as a formal, logical limitation on the sets themselves. So you see, the difference that you attempt to draw is one that most practitioners in the field would disbelieve. Not merely ignore, but actively claim to be nonexistent.)

[Bodhi Dharma Zen]

Originally posted by new drkitten
Fallacy of equivocation.

Humans "operate according to" physical laws. This does not mean that they "are" physical laws.

Physical laws are "described by" mathematics. This does not mean that they "are" mathematics.

Mathematics "includes" axiomatic systems of logic. This does not mean that it "is" an axiomatic system of logic.

Godel's theorem applies to things that "are" axiomatic systems of logic.

Well exposed. A great percentage of the discussions on this forum would be absurd if we all knew how to argue.

[Interesting Ian]

Originally posted by Bodhi Dharma Zen
Originally posted by new drkitten
Fallacy of equivocation.

Humans "operate according to" physical laws. This does not mean that they "are" physical laws.

Physical laws are "described by" mathematics. This does not mean that they "are" mathematics.

Mathematics "includes" axiomatic systems of logic. This does not mean that it "is" an axiomatic system of logic.

Godel's theorem applies to things that "are" axiomatic systems of logic.


Bodhi Dharma Zen
Well exposed. A great percentage of the discussions on this forum would be absurd if we all knew how to argue.

I don't think it is well exposed at all. He is being deliberately pedantic in order to ignore the essence of my points. In other words it was a complete irrelevancy.

[Interesting Ian]

Originally posted by new drkitten
I will be happy to do so when you provide working definitions of the distinctions between logical limitations, psychological limitations, and nomological limitations. Because from where I sit, a psychological limitation such as short term memory can be proven to be isomorphic and equivalent to a logical limitation.



Really, what can I say to a person who cannot understand, on one hand, the distinction between a psychological limitation/nomological limitation, and on the other hand a logical limitation?

A logical limitation means that you cannot achieve the logically impossible -- it is inherently inconsistent. For example, it is logically impossible for an object to be both simultaneously a sphere and a cube. A psychological/nomological limitation simply means that, as a matter of fact, we cannot do something -- although if circumstances have been different we could have. For example, in another logically possible universe, we could have been like gods and have stupendous powers. There is no logical inconsistency in this. However, for any algorithm, even with the element of randomness introduced within it, it will always be logically impossible, in any logically possible universe , for it to prove some thing that happens to be true. But it seems that we are not likewise logically limited.

[hammegk]

Originally posted by new drkitten
The same thing that is wrong with a position that any number of wheels can be attached to a unicycle.
Strange sentence, huh?


Basically, what's wrong is the meanings of the words you are using.
Basically, what's wrong is the meanings of the words you are using.


Basically, what's wrong is the meanings of the words you are using.


Basically, what's wrong is the meanings of the words you are using.


BTW, what is "consciousness"? Do you contend Strong AI is "conscious"?

[MESchlum]

Originally posted by Interesting Ian
Really, what can I say to a person who cannot understand, on one hand, the distinction between a psychological limitation/nomological limitation, and on the other hand a logical limitation?

A logical limitation means that you cannot achieve the logically impossible -- it is inherently inconsistent. For example, it is logically impossible for an object to be both simultaneously a sphere and a cube.

[Raise hand] Me! Me! Me!

Consider a diameter on a sphere. It's a circle, right? Now look at four points placed at regular intervals on the diameter. The diameter is therefore (relative to the sphere) a quadrilateral with all sides equal. What's more, the angle at each point is the same, so it's a square.

Hence, with the proper geometry (non-Euclidian, by the way, see other posts) you can have a square that is simultaneously a circle.

Go up a dimension or two, and I'm not sure if it still works, but it should...

A psychological/nomological limitation simply means that, as a matter of fact, we cannot do something -- although if circumstances have been different we could have. For example, in another logically possible universe, we could have been like gods and have stupendous powers. There is no logical inconsistency in this.

Okay. So a "logical impossibility" is something that contradicts the basic axioms used (1+1=3 if you have stated earlier that 1+1=2), while the other kind is something else?

Listing all the axioms and seeing how they interact will get you into a lot of trouble, but if that's what you want...

By the way, if my logically stupendous power is to be immovable and yours is to move anything you like, what happens?

However, for any algorithm, even with the element of randomness introduced within it, it will always be logically impossible, in any logically possible universe , for it to prove some thing that happens to be true. But it seems that we are not likewise logically limited.

I'm confused.

There are statements that, within a given system cannot be proved. You can use a larger system, that contains the old one, and postulates the statement is true. Or you can postulate it's false (Euclidian vs. non-Euclidian geometry, both are valid).

So this "we" you mention is limiting itself to a single answer to every issue where two are feasible, and valuable? Give me a computer that includes the curvature of space (and so can deal with Euclidian and non-Euclidian geometry) instead.

Now if you're arguing about understanding a system, and its limitations, I'll grant that we've got a head start over computers. We can often "see", for simple systems, where the inconsistencies lie (parallel postulate, division by zero, etc.).

Though a modern computer armed with geometry (minus the parallel postulate) would not intuit the postulate, it should (via Godel's technique) be able to find statements that are non provable. Then, by assuming one such statement is true, it would derive a new geometry A. And by assuming it's false, it would derive a new geometry B.

[Interesting Ian]

Here is a appropriate quote from that article I referenced earlier which answers some of the objections that people have raised.


This is the answer to one objection put forward by Turing.3 He argues that the limitation to the powers of a machine do not amount to anything much. Although each individual machine is incapable of getting the right answer to some questions, after all each individual human being is fallible also: and in any case "our superiority can only be felt on such an occasion in relation to the one machine over which we have scored our petty triumph. There would be no question of triumphing simultaneously over all machines." But this is not the point. We are not discussing whether machines or minds are superior, but whether they are the same. In some respect machines are undoubtedly superior to human minds; and the question on which they are stumped is admittedly, a rather niggling, even (118) trivial, question. But it is enough, enough to show that the machine is not the same as a mind. True, the machine can do many things that a human mind cannot do: but if there is of necessity something that the machine cannot do, though the mind can, then, however trivial the matter is, we cannot equate the two, and cannot hope ever to have a mechanical model that will adequately represent the mind. Nor does it signify that it is only an individual machine we have triumphed over: for the triumph is not over only an individual machine, but over any individual that anybody cares to specify---in Latin {50} quivis or quilibet, not quidam---and a mechanical model of a mind must be an individual machine. Although it is true that any particular "triumph" of a mind over a machine could be "trumped" by another machine able to produce the answer the first machine could not produce, so that "there is no question of triumphing simultaneously over all machines", yet this is irrelevant. What is at issue is not the unequal contest between one mind and all machines, but whether there could be any, single, machine that could do all a mind can do. For the mechanist thesis to hold water, it must be possible, in principle, to produce a model, a single model, which can do everything the mind can do. It is like a game.4 The mechanist has first turn. He produces a---any, but only a definite one---mechanical model of the mind. I point to something that it cannot do, but the mind can. The mechanist is free to modify his example, but each time he does so, I am entitled to look for defects in the revised model. If the mechanist can devise a model that I cannot find fault with, his [262] thesis is established: if he cannot, then it is not proven: and since---as it turns out-he necessarily cannot, it is refuted. To succeed, he must be able to produce some definite mechanical model of the mind---anyone he likes, but one he can specify, and will stick to. But since he cannot, in principle cannot, produce any mechanical model that is adequate, even though the point of failure is a minor one, he is bound to fail, and mechanism must be false.

http://users.ox.ac.uk/~jrlucas/Godel/mmg.html

[69dodge]

Originally posted by Interesting Ian
It still doesn't alter the case that we are not logically limited. Any algorithm (but not of course an infinte number of them) is logically limited. You need to argue that we are likewise logically limited, not merely psychologically limited or even nomologically limited.Are you saying that you know we are not logically limited, or are you just suggesting it as a possibility?

I can't describe to you exactly how my reasoning ability is limited. If I knew enough to describe a supposed limitation precisely, I'd know enough not to be limited in that way!

If my reasoning does follow an algorithm, and is therefore limited in some way, there will be some logical truths which I cannot demonstrate. The precise nature of my reasoning's limitations will be among those. So the fact that I can't logically show how my reasoning is limited should hardly be considered evidence that it isn't limited.A psychological/nomological limitation simply means that, as a matter of fact, we cannot do something -- although if circumstances have been different we could have. For example, in another logically possible universe, we could have been like gods and have stupendous powers. There is no logical inconsistency in this. However, for any algorithm, even with the element of randomness introduced within it, it will always be logically impossible, in any logically possible universe , for it to prove some thing that happens to be true. But it seems that we are not likewise logically limited.You are treating people and algorithms very differently here. I do not see why that is justified. You are allowing people to have different abilities in the other hypothetical universe, but are restricting the algorithm to be the same. If, in the other universe, the algorithm were allowed to be different than in this universe, it would also be able to prove things in that universe that it can't in this one.

Of course, conventionally we'd just call it an entirely different algorithm, rather than a changed version of the same algorithm. But a superman is an entirely different person than a regular person, too; isn't he?

[Interesting Ian]

Originally posted by 69dodge
Are you saying that you know we are not logically limited, or are you just suggesting it as a possibility?



No, I don't know this, although I suspect this. But we know that an algorithm is.



You are treating people and algorithms very differently here. I do not see why that is justified. You are allowing people to have different abilities in the other hypothetical universe, but are restricting the algorithm to be the same. If, in the other universe, the algorithm were allowed to be different than in this universe, it would also be able to prove things in that universe that it can't in this one.

Of course, conventionally we'd just call it an entirely different algorithm, rather than a changed version of the same algorithm. But a superman is an entirely different person than a regular person, too; isn't he? [/B]

Yes, we can have any conceivable algorithm you would care to choose. So you can prove anything you wish by choosing the appropriate algorithm. But there will always be truths which any particular algorithm cannot logically prove (and the algorithm could be unlimitedly complex, albeit not infinitely complex).

But is that the case with human beings? In a logically possible Universe where someone has unlimited intellect (but not infinite) would there be anything which he could not prove? Because he has an unlimited intellect there would only be logical limitations. Are there such logical limitations? I don't know, but I was originally arguing against Dr Kitten with his assertion that because human beings are psychologically limited, this destroys Lucas's/Penrose's argument. I don't think that particular point does refutes their argument, although I have admitted I know very little about mathematics, or Turing, or Goedel's theorem! :)

[TillEulenspiegel]

Well one cannot prove a negative Hypothesis.
Systemic limitations may be pointed out but all that may remain is our logical view of the way we BELIEVE things work.

That engenders a kind of "well it doesn't function outlook " rather then the appropriate , "were not sure, let's try different avenues " mindset.

Remember Logic is a human cognitive construct and as such remains plyable under real world constraints.

[Correa Neto]

Originally posted by Interesting Ian
We would need to feel it is conscious. I propose that even an android that behaved exactly like a human being would not arouse such a feeling. This is because I suspect we know that other people are conscious partially through anomalous cognition.

It does not seems a very efective criteria.

What exactly would this anomalous cognition be? Interpretation of subtle body language signs? Since at a later post you said you would need to "look in to the eyes" to reach a conclusion, I will consider you are referring to body language.

Now, what if the person has no eyes? What if the person has some disfunction that does not allows her to correctly use body language? You would not be able to perceive the subject as a counsient being! That´s why, to avoid this sort of bias, I proposed that all contact would be by voice (of course, assume it would not be a "robotic voice") or text.

The same flaw would potentially happen if the subject is say, an intelligent octopus-like alien.

I think that to be labelled self-counsient, the android must have reached by itself, using logic, its senses and the data it has stored, the conclusion of its own existence and what are its own limits, components, etc. So, if it managed to do so, it would be self-counsient. Its the android that must think it is self-counscient...

I think that this would be all that´s needed.

Of course, programming it to say "I think, ergo I exist" would not qualify.

But, of course, its not just a question if this is theoretically reachable. Its also a question of tehcnical feasibillity.

[Interesting Ian]

Originally posted by Correa Neto
[B]It does not seems a very efective criteria.

What exactly would this anomalous cognition be? Interpretation of subtle body language signs? Since at a later post you said you would need to "look in to the eyes" to reach a conclusion, I will consider you are referring to body language.



No, I was referring to anomalous cognition. This mean psi.

[69dodge]

Originally posted by MESchlum
Then you've just proven (within the system) that the statement is true.No, not within the system.

Within the system, statements don't mean anything; they're just strings of symbols that are manipulated according to certain rules. If a bit of reasoning assumes that the statement "I'm not provable" actually means that the statement isn't provable, then that bit of reasoning is outside the system."I'm not provable in system X"

Is not provable in X, and can be assumed to be true (in system Y which contains X and "the sentence is provable in Y") or not (system Z).System Z might be consistent (i.e., if a statement is provable, its negation isn't), but if we want to be able to say that only true statements are provable, we have to interpret the statement "I'm not provable in system X" as not having its usual meaning. Because Z can prove its negation; but using the usual meaning, its negation is false.

(But if we can play so freely with its meaning now, why were we so sure it meant what it said when we originally showed that it wasn't provable in X? Hmm . . . I must think about this some more.)

[Interesting Ian]

Here (http://users.ox.ac.uk/~jrlucas/Godel/satan.html) is the essence of the argument.



The argument is a dialectical one. It is not a direct proof that the mind is something more than a machine, but a schema of disproof for any particular version of mechanism that may be put forward. If the mechanist maintains any specific thesis, I show that [146] a contradiction ensues. But only if. It depends on the mechanist making the first move and putting forward his claim for inspection. I do not think Benacerraf has quite taken the point. He criticizes me both for "failing to notice" that my ability to show that the Gödel sentence of a formal system is true "depends very much on how he is given that system"2 and for putting the argument in the form of a challenge in which I challenge the mechanist to produce a definite specification of the Turing machine that he claims I am.3 Benacerraf thinks that the argument by challenge reduces the argument to a mere contest of wits between me and the mechanist. But we are not trying to see who can construct the smartest machine, we are attempting to decide the mechanist's claim that I am a machine: and however clever the mechanist is, even if he were not a mere man but Satan himself, I, or at least an idealised and immortal I, could out-Gödel it, and see to be true something it could not. Benacerraf protests that "It is conceivable that another machine could do that as well." Of course. But that other machine was not the machine that the mechanist was claiming that I was. It is the machine which I am alleged to be that is relevant: and since I can do something that it cannot, I cannot be it.


So it seems that he is saying that you cannot come up with an algorithm that describes me, because I could see something is true which the execution of the algorithm could not derive. The fact that some algorithm could, is besides the point. With this other algorithm there will also be something I can see to be true but which this other algorithm could not derive.

The materialist who thinks we are simply Turing machines (maybe with some randomness etc added) must hold that this is not true i.e for an appropriate algorithm that he can dream up, I could not out-Goedel it for some (any) true assertion. The fact that some other algorithm could not be out-Goedel'd for this specific truth is neither here nor there.

Yeah, think I'm beginning to understand this :)

[Interesting Ian]

Originally posted by Interesting Ian
Here (http://users.ox.ac.uk/~jrlucas/Godel/satan.html) is the essence of the argument.



So it seems that he is saying that you cannot come up with an algorithm that describes me, because I could see something is true which the execution of the algorithm could not derive. The fact that some algorithm could, is besides the point. With this other algorithm there will also be something I can see to be true but which this other algorithm could not derive.

The materialist who thinks we are simply Turing machines (maybe with some randomness etc added) must hold that this is not true i.e for an appropriate algorithm that he can dream up, I could not out-Goedel it for some (any) true assertion. The fact that some other algorithm could not be out-Goedel'd for this specific truth is neither here nor there.

Yeah, think I'm beginning to understand this :)

So say you create an android which is supposed to exactly model me. But it transpires that I can see the truth of some assertion that the android can't. Well ok, that certainly doesn't refute that we are machines, let's modify the android so it too can see the truth of this assertion. But then it transpires that there is another assertion that I can see is true, but the android can't. So we modify the android yet again so that it can understand all that it could before, plus this new assertion.

Now for me to be simply a machine (executing algorithms) this process at some point must come to an end. If it never comes to an end, then the hypothesis that we are mere machines executing algorithms is refuted.

Everyone agree?

[Interesting Ian]

Originally posted by Interesting Ian
So say you create an android which is supposed to exactly model me. But it transpires that I can see the truth of some assertion that the android can't. Well ok, that certainly doesn't refute that we are machines, let's modify the android so it too can see the truth of this assertion. But then it transpires that there is another assertion that I can see is true, but the android can't. So we modify the android yet again so that it can understand all that it could before, plus this new assertion.

Now for me to be simply a machine (executing algorithms) this process at some point must come to an end. If it never comes to an end, then the hypothesis that we are mere machines executing algorithms is refuted.

Everyone agree?

And of course I can be as intelligent as it takes to see the truth of some assertion i.e as intelligent as any mind (not necessarily human) could in principle be.

[TillEulenspiegel]

Cripes Ian your quoting yourself, bad form sir.

As far as your example of the dis-accommodation of difference between likes., EX. a pair of identical twins ( biological machines) raised in the same environment subject to the same experiences will and do react differently to the same stimulus. They do have a propensity for remarkable similarity in outlooks and reactions, but ultimately there is difference.
Point being that there is no solid expectation for an artificial construct ( which is a model after all) to react identically to it's blueprint. Adaptive behavior is after all the hallmark of a successfull organism. .so rather then judge success of our experiment by how well your " shadow" intellect agrees with Your course of actions, see how well the mimic preforms..

P.S Trvth is a mutable quantity , Ian

[69dodge]

Originally posted by Interesting Ian
Here (http://users.ox.ac.uk/~jrlucas/Godel/satan.html) is the essence of the argument.<blockquote>But we are not trying to see who can construct the smartest machine, we are attempting to decide the mechanist's claim that I am a machine: and however clever the mechanist is, even if he were not a mere man but Satan himself, I, or at least an idealised and immortal I, could out-Gödel it, and see to be true something it could not.</blockquote>No, no, no. You can't insist that the mechanist propose a specific Turing machine as the one which supposedly simulates you, and yet you have the freedom to use an "idealized and immortal" version of yourself in order to outwit it. The mechanist claimed only that his Turing machine can simulate the actual you, so it's the actual you who needs to outwit it. If you can't, the mechanist's claim may well be true.

If people are in fact essentially Turing machines, there is no such thing as a single "idealized and immortal" version of you. There are merely various different versions of you with various different reasoning capacities. Given any specific Turing machine, some version of you can outwit it. But given any specific version of you, there's some Turing machine that it can't outwit.

[Interesting Ian]

Originally posted by TillEulenspiegel
Cripes Ian your quoting yourself, bad form sir.

As far as your example of the dis-accommodation of difference between likes., EX. a pair of identical twins ( biological machines) raised in the same environment subject to the same experiences will and do react differently to the same stimulus. They do have a propensity for remarkable similarity in outlooks and reactions, but ultimately there is difference.
Point being that there is no solid expectation for an artificial construct ( which is a model after all) to react identically to it's blueprint. Adaptive behavior is after all the hallmark of a successfull organism. .so rather then judge success of our experiment by how well your " shadow" intellect agrees with Your course of actions, see how well the mimic preforms..

P.S Trvth is a mutable quantity , Ian

What?? We're not talking about reacting, but rather seeing the truth of some assertion.

[Interesting Ian]

Originally posted by 69dodge
Originally posted by Interesting Ian
Here is the essence of the argument.

Lucas
But we are not trying to see who can construct the smartest machine, we are attempting to decide the mechanist's claim that I am a machine: and however clever the mechanist is, even if he were not a mere man but Satan himself, I, or at least an idealised and immortal I, could out-Gödel it, and see to be true something it could not.



As a matter of interest, this was the same thing I was getting at before when I mentioned we could be gods or supermen, and this was before I read Lucas.



69dodge

No, no, no. You can't insist that the mechanist propose a specific Turing machine as the one which supposedly simulates you, and yet you have the freedom to use an "idealized and immortal" version of yourself in order to outwit it.



To be clear, the ""idealized and immortal" version of yourself" is fixed, and the mechanist wheels out his robot which is supposed to model it. And if that robot is lacking, he can wheel another robot out, and if that robot too is lacking, then he can wheel yet another robot out. And he can do this as often as he like, but he cannot do it forever without refuting the notion that we are merely algorithmic machines..



The mechanist claimed only that his Turing machine can simulate the actual you, so it's the actual you who needs to outwit it. If you can't, the mechanist's claim may well be true.



It doesn't need to be the actual me. The fact that I live 70 years is surely not a relevant consideration. It can't be the case that if I live for a million years rather than merely 70, that I would somehow cease to be essentially an algorithmic machine! :eek: And the idealized self? That's just getting at the idea that if I can potentially understand something, then any specific algorithm you care to choose should be able to model this potential self. It seems to me that Lucas is simply saying the same thing as I was saying before in this thread (before I read him). We're interested in the logical limitations of the mind, not psychological or nomological limitations. Indeed I have nothing to add to what I said in previous posts on this issue :)



If people are in fact essentially Turing machines, there is no such thing as a single "idealized and immortal" version of you.



Of course there is. If I am a turing machine, how does that prevent me from being effectively immortal? And idealized simply means that I equate to a more complex algorithm. But no matter how complex an algorithm a person might be . .ummm . .obviously it can in principle be modelled!


There are merely various different versions of you with various different reasoning capacities. Given any specific Turing machine, some version of you can outwit it. But given any specific version of you, there's some Turing machine that it can't outwit.

Oh well {shrugs} I cannot say if that is true given my ignorance of mathematics and Goedel's theorem. My understanding was that should I be sufficiently intelligent and knowledgeable, I will be able to see the truth of some assertion that any particular Turing machine will not be able to. Moreover, whatever Turing machine you wheel out, should I be sufficiently intelligent and knowledgeable, then there will be some truth I can see (but not the same truth as for other Turing machines), but which the specific Turing machine concerned will not be able to.

Now, if the above paragraph is true, then the notion that we are Turing machines, or even Turing machines with randomness thrown in, is refuted. If it is not true, then this whole thread is a waste of time.

But my understanding of Lucas is that this paragraph is true. Which means that since yesterday, I have discovered yet another proof against materialism! :D

[69dodge]

Originally posted by Interesting Ian
The fact that I live 70 years is surely not a relevant consideration. It can't be the case that if I live for a million years rather than merely 70, that I would somehow cease to be essentially an algorithmic machine!That's true. The immortality is not the important point; the idealization is.And the idealized self? That's just getting at the idea that if I can potentially understand something, then any specific algorithm you care to choose should be able to model this potential self.I don't see why it's fair to compare an actual algorithm with a potential you. You could potentially understand it, but only if you were smarter than you actually are. And the computer could potentially prove it, but only if it were running a more complex algorithm than it actually is.We're interested in the logical limitations of the mind, not psychological or nomological limitations.Well, of course, anyone can be interested in whatever they want. But some people, I think, are interested in whether an actual person can be simulated by a Turing machine, not whether infinitely many different potential persons can all be simulated by a (single) Turing machine.And idealized simply means that I equate to a more complex algorithm.But there is no most complex algorithm. There are only ever increasingly complex algorithms. So none of them can really be called ideal.My understanding was that should I be sufficiently intelligent and knowledgeable, I will be able to see the truth of some assertion that any particular Turing machine will not be able to. Moreover, whatever Turing machine you wheel out, should I be sufficiently intelligent and knowledgeable, then there will be some truth I can see (but not the same truth as for other Turing machines), but which the specific Turing machine concerned will not be able to.Not if your level of intelligence and knowledge is fixed before I decide which Turing machine to wheel out.

In my opinion, at least.

But I don't see what basis there is for making assumptions about what a smarter version of yourself might be able to do, if in reality you're not smart enough actually to do it. Maybe it's only slightly beyond your present capabilities, or maybe it's quite impossible. How could you tell the difference?

[TillEulenspiegel]

Originally posted by Interesting Ian
What?? We're not talking about reacting, but rather seeing the truth of some assertion.

Exactly why I said that Trvth is a mutable concept. There is no "THE" truth. Something You hold true at 20 may at 30 not be . Two similar people looking at the same idea may have vastly separated ideas of what is true. You may conceder it akin to moral relativism but the reality is that the judgment of the correctness of an idea or situation IS a reaction to stimuli based of learned values.

[Interesting Ian]

69dodge, let's consider this argument in a nutshell.

Let's consider the greatest, intelligent, knowledgeable mind they could conceivably possibly be. Now, in order for that mind to be a Turing machine, anyone or anything can dream up a sufficiently complex algorithm to see if they can model it. If they cannot, then they can come up with another algorithm to see if they can model it, if they still cannot, then they try yet again. They keep doing this until they succeed. I will accept that the eventual success will entail that we are all Turing machines. If they never succeed even after an unlimited number of tries (albeit not an infinite number of tries) i.e one can try as many algorithms as it takes and for them to be as complex as it takes, then the notion that minds are Turing machines is refuted.

But why cannot normal minds like my own, or yours, not be Turing machines even if this greatest conceivable mind is not?

The answer to this is that it would be very strange for some minds to be Turing machines but not others. Whatever minds might be, you would not expect my mind to be a Turing machine for example, but your mind not to be! Likewise you would not expect my mind to be a Turing machine, but the greatest possible mind not to be a Turing machine!

[Interesting Ian]

Originally posted by TillEulenspiegel
Exactly why I said that Trvth is a mutable concept. There is no "THE" truth. Something You hold true at 20 may at 30 not be . Two similar people looking at the same idea may have vastly separated ideas of what is true. You may conceder it akin to moral relativism but the reality is that the judgment of the correctness of an idea or situation IS a reaction to stimuli based of learned values.

I cannot debate with someone who says there is no such thing as the truth. Clearly there sometimes is, even if only in logic and mathematics! And I would say there is the truth in everything; even in ethics (not that this is relevant -- so long as there are THE Truth in mathematics).

[69dodge]

Originally posted by Interesting Ian
Let's consider the greatest, intelligent, knowledgeable mind they could conceivably possibly be. Now, in order for that mind to be a Turing machine, anyone or anything can dream up a sufficiently complex algorithm to see if they can model it. If they cannot, then they can come up with another algorithm to see if they can model it, if they still cannot, then they try yet again. They keep doing this until they succeed. I will accept that the eventual success will entail that we are all Turing machines. If they never succeed even after an unlimited number of tries (albeit not an infinite number of tries) i.e one can try as many algorithms as it takes and for them to be as complex as it takes, then the notion that minds are Turing machines is refuted.
Ok. Although there's no reason to try more than once, really. If any Turing machine works, just try that one first.

Either way, why shouldn't some Turing machine work?

And I don't think there's any such thing as "the greatest possible mind" to begin with. Kind of like there's no such thing as "the largest possible integer".

[Kopji]

If you're declaring it would be conscious, I say that we need to understand what consciousness is first before trying to create it. - I Ian

Many great discoveries came about 'by accident' long before we understood the underlying science. I agree that it would be advisable to understand consciousness before creating artificial (human) life (I'm a big fan of 'B' scifi movies), and it may even be an ethical mandate, but understanding something is not a developmental constraint. :)

Gödel's theorem probably has a philosophical component within it that says we cannot create artificial intelligence like 'computers' of today: finite pathways create limitations on data, even if we do not perceive the limitations.

The Incompleteness theorem says nothing about something like growing or developing artificial life, only that human-like artificial life would not be like a computer as we know it.

I suspect that insisting on comparing the brain of an artificial life form to a computer is a straw man. There is a real sense that living things are a manifestation of their environment: We evolved here, and belong here and are an integral part of here. We cannot exist apart from the ecology of our universe and neither could human-like artificial life.

[TillEulenspiegel]

Originally posted by Interesting Ian
I cannot debate with someone who says there is no such thing as the truth. Clearly there sometimes is, even if only in logic and mathematics! And I would say there is the truth in everything; even in ethics (not that this is relevant -- so long as there are THE Truth in mathematics).

Logic and mathematics are both attempts toward an accommodation where we as humans can quantify and qualify the universe around us. Mathematics comes closer to a rule set that is fairly concrete but even there we can distort and manipulate the language to say pretty much what we want it to. Ex. .99999...=1 or using imaginary numbers (Sqrt -1) to balance equations.

That on a primary school level is nonsense both logically and mathematically , but it is ultimately true when we progress in our understanding of the language. You can torture logic to say anything..logic and "truth" do not have to have any common ground.
So if You know any great immutable truths , please tell me what they are as the only one I know is " And this too shall pass".



edit to add:
To think of "intelligence as "AN" algorithm is not the correct approach in modeling or mimicking Human behavior or processes. The more correct understanding would be..MPP Massively Parallel Processing, where there are several distinct processes occurring at the same time, all considered and weighted by an overall rule set then a course of action or judgment is arrived upon.

[Interesting Ian]

Originally posted by TillEulenspiegel
Logic and mathematics are both attempts toward an accommodation where we as humans can quantify and qualify the universe around us. Mathematics comes closer to a rule set that is fairly concrete but even there we can distort and manipulate the language to say pretty much what we want it to. Ex. .99999...=1 or using imaginary numbers (Sqrt -1) to balance equations.

That on a primary school level is nonsense both logically and mathematically , but it is ultimately true when we progress in our understanding of the language. You can torture logic to say anything..logic and "truth" do not have to have any common ground.
So if You know any great immutable truths , please tell me what they are as the only one I know is " And this too shall pass".



We all need to apprehend the timeless perfection of all existence. Then we will all know the truth.

[Interesting Ian]

Originally posted by 69dodge
Originally posted by Interesting Ian
Let's consider the greatest, intelligent, knowledgeable mind they could conceivably possibly be. Now, in order for that mind to be a Turing machine, anyone or anything can dream up a sufficiently complex algorithm to see if they can model it. If they cannot, then they can come up with another algorithm to see if they can model it, if they still cannot, then they try yet again. They keep doing this until they succeed. I will accept that the eventual success will entail that we are all Turing machines. If they never succeed even after an unlimited number of tries (albeit not an infinite number of tries) i.e one can try as many algorithms as it takes and for them to be as complex as it takes, then the notion that minds are Turing machines is refuted.

69dodge
Ok. Although there's no reason to try more than once, really. If any Turing machine works, just try that one first.

Either way, why shouldn't some Turing machine work?

And I don't think there's any such thing as "the greatest possible mind" to begin with. Kind of like there's no such thing as "the largest possible integer".

I agree with you that there is no such thing as "the greatest possible mind". Let's just say that a mind needs to be great enough that it apprehends all mathematical truths. Now of course the AI enthusiasts will maintain, indeed must maintain, that no matter how great a mind is there will always be some mathematical truth that it is unable to see/derive. This must be so if any mind is nothing more than the execution of some algorithm. But then of course we come full circle.

It seems that we can recognise some truths that are not arrived at by an algorithmic process. We can see something is true even though a computer cannot i.e. Goedelian sentences. Or consider how mathematicians sometimes discover new mathematical truths. They often declare that it is a moment of insight. They suddenly know , beyond doubt, its truth -- only afterwards do they produce the proof of that which they already know.

[Interesting Ian]

Originally posted by TillEulenspiegel


edit to add:
To think of "intelligence as "AN" algorithm is not the correct approach in modeling or mimicking Human behavior or processes. The more correct understanding would be..MPP Massively Parallel Processing, where there are several distinct processes occurring at the same time, all considered and weighted by an overall rule set then a course of action or judgment is arrived upon. [/B]

You mean the execution of more than one algorithm at once? That obviously does nothing to defeat the argument. 2 algorithms are no more capable of producing a miracle than one algorithm.

[Interesting Ian]

Originally posted by TillEulenspiegel
Logic and mathematics are both attempts toward an accommodation where we as humans can quantify and qualify the universe around us. Mathematics comes closer to a rule set that is fairly concrete but even there we can distort and manipulate the language to say pretty much what we want it to. Ex. .99999...=1 or using imaginary numbers (Sqrt -1) to balance equations.



I do not understand how that is distorting or manipulating language.



That on a primary school level is nonsense both logically and mathematically , but it is ultimately true when we progress in our understanding of the language. You can torture logic to say anything..logic and "truth" do not have to have any common ground.



I don't think so. Logic is logic. You can't distort it to say anything else apart from that which is deductively derived.


So if You know any great immutable truths , please tell me what they are as the only one I know is " And this too shall pass".


Certainly.

I am conscious.
1 + 1 = 2.
0.9999 . . . = 1

[TillEulenspiegel]

Originally posted by Interesting Ian


I don't think so. Logic is logic. You can't distort it to say anything else apart from that which is deductively derived.

Ian , any real study of logic includes concederation of "Logical Fallacies". Inductive, deductive, categorical syllogisms, argument by analogy , so on Ad Nausium.
There are many and some that call into question as to the efficacy of applying logic at all to the question at hand. I.E. counterfactuals, an attempt to accommodate the non-logical outcome of quantum mechanics with real life observation.

Certainly.

I am conscious.
1 + 1 = 2.
0.9999 . . . = 1 [/B]

Any of which can be disproved I.E : "I am conscious". How do I know that? You may have passed out from drinking too much by the time I read your post or maybe you while typing on Your reply on Your wireless laptop got hit by a car and are actually dead when I read this. Maybe "You" are an intelligent bot. Any of which negates your declaration that You are conscious, heck how about solipsism? You only exist in my mind ? Silly I agree but as viable a concept as Your declaration of self awareness on a ephemeral medium such as the net. No Ian , logic is plastic as much as math.
On a thread I started "prove 1=2"
-1/1 = 1/(-1)

Take the square root of both sides:
sqrt(-1)/sqrt(1) = sqrt(1)/sqrt(-1)

i/1 = 1/i

Divide by 2: i/2 = 1/(2i)
Add 3/(2i): i/2 + 3/(2i) = 1/(2i)+ 3/(2i)
Multiply by i:
i^2/2 + 3/2 = 1/2 + 3/2
-1/2 + 3/2 = 1/2 + 3/2
1 = 2
There are other more creative examples.
http://www.randi.org/vbulletin/showthread.php?s=&threadid=48997&highlight=prove

I'm not quite sure what motivates You to engage in these bottomless debates , since most of the concepts expressed at the beginning of the threads are fairly straight forward and do not require the reductionism and tangential arguments that are finally realized by the Nth post and finally, not reaching accommodation, left to rot on the vine.. Perhaps you enjoy typing
more then most?

You may believe what You want, that does not however make it true.

[hammegk]

Originally posted by TillEulenspiegel

You may believe what You want, that does not however make it true.
Gee, that sounds True, doesn't it.

[TillEulenspiegel]

smarty pants...........

[hammegk]

Is that comment Experiential or anecdotal? Someone mentioned that such examples are not empirical proof.

[TillEulenspiegel]

He he , in answer to your question -Yes.
I see your humor organ is larger then I estimated, but I'm not sure of the standing of cross forum poaching .

[hammegk]

Hmm. Do you believe you can prove the words are not of my devising? :D

[Interesting Ian]

Originally posted by Interesting Ian


I don't think so. Logic is logic. You can't distort it to say anything else apart from that which is deductively derived.


TillEulenspiegel
Ian , any real study of logic includes concederation of "Logical Fallacies". Inductive, deductive, categorical syllogisms, argument by analogy , so on Ad Nausium.



Yes indeed this is so if you conflate informal and formal logic. I understood we were simply referring to formal logic. Now could you be so good as to state what your point is?



There are many and some that call into question as to the efficacy of applying logic at all to the question at hand. I.E. counterfactuals, an attempt to accommodate the non-logical outcome of quantum mechanics with real life observation.



There is no "non-logical" outcome of quantum mechanics; it's all in your fevered imagination.



Certainly.

I am conscious.
1 + 1 = 2.
0.9999 . . . = 1 [/B]


TillEulenspiegel
Any of which can be disproved



I think not.



I.E : "I am conscious". How do I know that? You may have passed out from drinking too much by the time I read your post or maybe you while typing on Your reply on Your wireless laptop got hit by a car and are actually dead when I read this. Maybe "You" are an intelligent bot. Any of which negates your declaration that You are conscious,



It does not. I know, absolutely, 100%, that I am conscious.




heck how about solipsism? You only exist in my mind ? Silly I agree but as viable a concept as Your declaration of self awareness on a ephemeral medium such as the net. No Ian , logic is plastic as much as math.



I think not.



On a thread I started "prove 1=2"
-1/1 = 1/(-1)

Take the square root of both sides:
sqrt(-1)/sqrt(1) = sqrt(1)/sqrt(-1)

i/1 = 1/i

Divide by 2: i/2 = 1/(2i)
Add 3/(2i): i/2 + 3/(2i) = 1/(2i)+ 3/(2i)
Multiply by i:
i^2/2 + 3/2 = 1/2 + 3/2
-1/2 + 3/2 = 1/2 + 3/2
1 = 2
There are other more creative examples.
http://www.randi.org/vbulletin/show...highlight=prove



I really have no interest in these games. I'm willing to bet that this reasoning is fallacious at some point. Now, I do not have any knowledge of mathematics, so I cannot point out the error, but this is supremely unimportant. The point is that it is fallacious. Now, do you have a point to make?



I'm not quite sure what motivates You to engage in these bottomless debates , since most of the concepts expressed at the beginning of the threads are fairly straight forward and do not require the reductionism and tangential arguments that are finally realized by the Nth post and finally, not reaching accommodation, left to rot on the vine.. Perhaps you enjoy typing
more then most?



It is a "bottomless" debate because either I, or my opponents, or both sides, do not fully understand the intricacies of the argument. If you think that this whole debate is a waste of time, then so be it; but there again, nobody is asking you. If we adopt your attitude nobody would ever discuss anything contentious. Personally I feel this is undesirable.

[TillEulenspiegel]

OK bud . You win. I quit.

[Interesting Ian]

Originally posted by TillEulenspiegel
OK bud . You win. I quit.

I'm not trying to win anything. I'm trying to find out the truth about the world.

[69dodge]

Originally posted by Kopji
Gödel's theorem probably has a philosophical component within it that says we cannot create artificial intelligence like 'computers' of today:I don't agree.finite pathways create limitations on data, even if we do not perceive the limitations.Computers are limited but so are we.

[69dodge]

Originally posted by Interesting Ian
I agree with you that there is no such thing as "the greatest possible mind". Let's just say that a mind needs to be great enough that it apprehends all mathematical truths. Now of course the AI enthusiasts will maintain, indeed must maintain, that no matter how great a mind is there will always be some mathematical truth that it is unable to see/derive. This must be so if any mind is nothing more than the execution of some algorithm. But then of course we come full circle.Yes.It seems that we can recognise some truths that are not arrived at by an algorithmic process. We can see something is true even though a computer cannot i.e. Goedelian sentences.No. We can recognize some truth that was not arrived at by a particular algorithmic process; we can see something is true even though a particular computer cannot. We may have arrived at that truth by a different algorithmic process---namely, one running in our brains---even though we don't know exactly which algorithmic process that is.Or consider how mathematicians sometimes discover new mathematical truths. They often declare that it is a moment of insight. They suddenly know, beyond doubt, its truth -- only afterwards do they produce the proof of that which they already know.I don't know. That doesn't sound right to me. Sometimes I'll be pretty sure of something even though I haven't proved it yet, although I wouldn't say I know it. So then I try to prove it. If I can, I say to myself, "See? I was right! I knew it all along." And if I end up disproving it, I say, "See? In the back of my mind, I knew something was wrong. That's why I felt the need to check it." :D

But, anyway, this doesn't prove anything one way or the other. No one says that people are aware of the algorithm that's running in their heads, just that some algorithm is in fact running. So, the mathematician's lack of awareness of how he arrived at his insight doesn't mean that it wasn't arrived at algorithmically; it just means that he doesn't know what algorithm his brain used.You mean the execution of more than one algorithm at once? That obviously does nothing to defeat the argument. 2 algorithms are no more capable of producing a miracle than one algorithm.Correct. A single Turing machine can simulate multiple other Turing machines running in parallel. Actual parallelism buys you nothing but speed.

[Correa Neto]

Originally posted by Interesting Ian
No, I was referring to anomalous cognition. This mean psi.

Still, I say it would be a potentially ineffective criteria.

Lets suppose psi is true (and leave the discussion if it really is or not for another time/thread).

Wouldn´t you consider the possibility that a human being would not be able to, using psi, recognize self-counsience in a mind that is radically different from those from his/hers species?

So, I think that the artificial having by itself managed to reach a conclusion such as "I think that I exist and I am composed by the following parts, stored data, have the following skills, etc..." would be the best criteria.

As for the "They suddenly know, beyond doubt, its truth -- only afterwards do they produce the proof of that which they already know." argument, on 69dodge´s line, what actually happens (not only with mathematicians, but also with professionals from all branches) is that after this brief moment of inspiration, comes a lot of work, that in most cases, shows that the wonderfull inspiration moment pointed to the wrong path. So, that´s not a valid criteria neither a truth.

[Interesting Ian]

69dodge,

You deny then that for any algorithm we dream up, a person (or at least an idealised and immortal version of that person) will always be able to understand something which the algorithm cannot derive?

[Interesting Ian]

Originally posted by Correa Neto
Still, I say it would be a potentially ineffective criteria.

Lets suppose psi is true (and leave the discussion if it really is or not for another time/thread).

Wouldn´t you consider the possibility that a human being would not be able to, using psi, recognize self-counsience in a mind that is radically different from those from his/hers species?

So, I think that the artificial having by itself managed to reach a conclusion such as "I think that I exist and I am composed by the following parts, stored data, have the following skills, etc..." would be the best criteria.

As for the "They suddenly know, beyond doubt, its truth -- only afterwards do they produce the proof of that which they already know." argument, on 69dodge´s line, what actually happens (not only with mathematicians, but also with professionals from all branches) is that after this brief moment of inspiration, comes a lot of work, that in most cases, shows that the wonderfull inspiration moment pointed to the wrong path. So, that´s not a valid criteria neither a truth.

Correa,

It is my hypothesis that if you gaze into a android's eyes, it will seem that there is nothing inside there, there would seem to be a strange sort of emptiness. Now obviously I do not know this.

As for mathematicians suddenly seeing something is true, I've read that there is an inner conviction, that they know, that the proof is simply proving that which they already know. Now I don't know if this actually does occur, I'm only going by what I've read. But I must admit it seems very plausible to me. I don't suppose it's fruitful to pursue this anyway.

[Correa Neto]

Originally posted by Interesting Ian
Correa,

It is my hypothesis that if you gaze into a android's eyes, it will seem that there is nothing inside there, there would seem to be a strange sort of emptiness. Now obviously I do not know this.

Then you are not sure you would be able, using this method, to recognize a self-counscient being that is not a Homo Sapiens, regardless it being an android or an alien octopus.

Now, do you agree that a being that reached by itself a conclusion similar to "I think therefore I am" can be labelled self-counsious?

Originally posted by Interesting Ian
As for mathematicians suddenly seeing something is true, I've read that there is an inner conviction, that they know, that the proof is simply proving that which they already know. Now I don't know if this actually does occur, I'm only going by what I've read. But I must admit it seems very plausible to me. I don't suppose it's fruitful to pursue this anyway.

Please allow me to disagree. As raised, the argument applies only to the "1% inspiration plus 99% transpiration", leaving aside the times when the inspiration was later proved wrong - after more transpiration. My personal experience (OK, its anedoctal evidence) is that in most cases the intuition later proves to be a dead end. We all have countless "inner convictions" through our lives, and many if not most of them are later shown to be wrong. Sticking to the cases where the intution proved right is to introduce a bias to your analysis.

It was raised as an argument that this "intution" is an attribute of human mind that could not be recreated. However, its not an attribute of human mind, since the whole reasoning regarding its existence is flawed. So it does not matter if it can be replicated or not. And it also can not be used as theoreticall or technicall evidence that a human-like mid will never be artificially created. So, in this sense, I have to agree that its it's not fruitful to pursue this anyway.

[MESchlum]

Originally posted by Interesting Ian
I agree with you that there is no such thing as "the greatest possible mind". Let's just say that a mind needs to be great enough that it apprehends all mathematical truths.

You write this, and you are aware of Godel? How odd. Godel showed that if you take a system (as you are), and the system is complex enough ("all mathematics" is more complex than arithmetic) and is consistent (I'd hope that truths are), you will have statements that cannot be proven.

Statements that are neither truths (correct) nor untruths (false) so to say.

So your not-quite greatest mind is still beyond the realms of feasibility.

And what is more, some of the meta-statements ("I'm not provable" and variations) will lead to different mathematics depending on whether they are set as being true or not. And according to the postulates, you can get staments that contradict each other, and are true. See my post on square circles (you can get cupic spheres by using 8 points on the sphere, by the way) for an example.

So the domain of mathematical truths is a) infinite (not just the way integers are - where you can always find another, but more so: for any set of truths (even infinite) you can always find a larger set) and b) extremely context dependent (see squares and circles). Which makes any mind capable of apprehending all of them (if feasible, which seems unlikely) something I would not view as human.


Originally posted by Interesting Ian
As for mathematicians suddenly seeing something is true, I've read that there is an inner conviction, that they know, that the proof is simply proving that which they already know. Now I don't know if this actually does occur, I'm only going by what I've read. But I must admit it seems very plausible to me. I don't suppose it's fruitful to pursue this anyway.

Aaargh (horrible beast of ;) ). Socratic claptrap. Sorry, I don't mean to disparge Socrates (much), but his "proof" that everyone knows everything, demonstrated via one of the earliest instances of directed cold reading I know of, is not a good foundation.

Do not pursue. Please. Or explain why the romans did not use 0 and advanced number theory, since they should "already know" about them, and had plenty of people with leisure time to ponder math. If you don't like the romans (Latin is a pain), ask similar questions of any early mathematicians, even the great ones. They were great mathematicians. Why didn't they know everything?

Please, no.

[Interesting Ian]

Originally posted by Correa Neto
[B]Then you are not sure you would be able, using this method, to recognize a self-counscient being that is not a Homo Sapiens, regardless it being an android or an alien octopus.

Now, do you agree that a being that reached by itself a conclusion similar to "I think therefore I am" can be labelled self-counsious?



I don't understand this. Is this being conscious or not?



Please allow me to disagree. As raised, the argument applies only to the "1% inspiration plus 99% transpiration", leaving aside the times when the inspiration was later proved wrong - after more transpiration. My personal experience (OK, its anedoctal evidence) is that in most cases the intuition later proves to be a dead end. We all have countless "inner convictions" through our lives, and many if not most of them are later shown to be wrong. Sticking to the cases where the intution proved right is to introduce a bias to your analysis.



I think this experience is supposed to be akin to a mystical experience where you simply understand what reality is. In the case of maths maybe your mind makes contact with the world of platonic forms. Now I am somewhat sceptical about your claim that those who do have such an insight, are more often wrong than right. I suspect we're not talking about the same thing. You seem to be talking about some vague intuition.



It was raised as an argument that this "intution" is an attribute of human mind that could not be recreated. However, its not an attribute of human mind, since the whole reasoning regarding its existence is flawed.



What reasoning? People simply say it exists.



So it does not matter if it can be replicated or not. And it also can not be used as theoreticall or technicall evidence that a human-like mid will never be artificially created. So, in this sense, I have to agree that its it's not fruitful to pursue this anyway.

Well the existence of this ability would entail we are not a mere machine; at least not an algorithmic one.

[Interesting Ian]

Originally posted by Interesting Ian
I agree with you that there is no such thing as "the greatest possible mind". Let's just say that a mind needs to be great enough that it apprehends all mathematical truths.


MESchlum
You write this, and you are aware of Godel? How odd. Godel showed that if you take a system (as you are), and the system is complex enough ("all mathematics" is more complex than arithmetic) and is consistent (I'd hope that truths are), you will have statements that cannot be proven.

Statements that are neither truths (correct) nor untruths (false) so to say.

So your not-quite greatest mind is still beyond the realms of feasibility.



Huh?? You're simply presupposing that people are mere algorithmic machines here! :eek: But we know they're not because we can always understand some Godelian sentance which cannot be derived from any given specific algorithm, no matter how complex. This is apart from the sheer absurdity that an execution of an algorithm can somehow mysteriously generate consciousness. It's just rule following. Let's consider a chess computer. Place a rook into an empty file unless certain conditions pertain blah blah blah. There is not the remotest hint or suggestion that any consciousness, and hence mind is involved. Do you seriously suggest that a chess computer is conscious? If not then neither would an android be conscious or have a mind. It would only appear to have consciousness.



And what is more, some of the meta-statements ("I'm not provable" and variations) will lead to different mathematics depending on whether they are set as being true or not. And according to the postulates, you can get staments that contradict each other, and are true. See my post on square circles (you can get cupic spheres by using 8 points on the sphere, by the way) for an example.



There is no such existent as a square circle. An object cannot simultaneously being a circle/sphere and square/cube. This is by virtue of what these terms mean.

[Interesting Ian]

Originally posted by MESchlum
[B]You write this, and you are aware of Godel? How odd. Godel showed that if you take a system (as you are),


I am not a system, I am a self.

[Robin]

Originally posted by hammegk
Is homo sap a machine?

What other machine has been proposed that cannot be 'simulated' by a (theoretical) Turing machine, real-time considerations aside?

It is an interesting question but irrelevant since 'simulated' does not mean 'is'. The relevant point is that even if you have an algorithm that provides a very high resolution simulation of some physical process it does not follow that any statement about the algorithm also applies to the physical process.

Also if a physical system can be described using mathematics it does not follow that any statement about the metamathematics also applies to the physical system (as Lucas appears to be suggesting).

[Robin]

Originally posted by AWPrime
1inChrist?

- posted 24 hours
- posts contain no intelligence

1inC was one of the posters I was considering. The other possibility with 1inChrist is that he was a committee which could achieve the same effect.

[Robin]

Interesting Ian
Randomness? You mean intrinsic randomness as described by QM?
No I just mean randomness, whatever shop you bought it from. To be more precise, there may be some difference between randomness produced by some sub-atomic event or randomness produced by shaking a bunch of numbered marbles round in a barrel. But as an effect you could not tell the difference.
I don't know what you mean by parallelism.
Nothing very profound, just independent, unsynchronised, simultaneous processes.

But sure, a non-turing machine, meaning something that operates by physical processes, some of which cannot be expressed algorithmically, would be immune to such criticisms. But something like randomness could be built into a computer couldn't it?
Yes, and you can have parallelism. I believe that Stephen Wolfram even contends that you can implement true randomness in an algorithm which, if true, would knock out my first point.
Still I think that there is plenty wrong with Lucas's argument even leaving aside the TM question.

[Correa Neto]

Originally posted by Interesting Ian
I don't understand this. Is this being conscious or not?

If you consider as self-counsient an entity that, by logical reasoning, reaches by itself (its not a programmed result), the conclusion of its own existence, than it is.

The way I see it, the sole (OK, I´ll be prudent and write main) requisite to labell a being as self-counsient is that it´s aware of its existence, (at least parts of) what compose it, its memories, its limits, and its begining (better keep the issue regarding the end of a sentient being aside in this thread).

Originally posted by Interesting Ian
I think this experience is supposed to be akin to a mystical experience where you simply understand what reality is. In the case of maths maybe your mind makes contact with the world of platonic forms. Now I am somewhat sceptical about your claim that those who do have such an insight, are more often wrong than right. I suspect we're not talking about the same thing. You seem to be talking about some vague intuition.

You should be. It´s a healthy attitude when it comes to anedoctal evidence. I´ll try to make it a bit more clear. Quite often, when one deals with problems (as varied as the validity of a theorem, the behavior of a species, if there is or not ore in a certain place, the feasibility of a certain project, a theological issue, etc.), a possible solution "pops up" in our minds. That´s the inspiration, the revelation of the truth, and I don´t see why the mathematicians´ experiences (and the mechanisms behind it)should be radically different from that from the other people.

Now, after this revelation, that indeed sometimes can be compared to mystical revelations, comes the times to test it. And, basing on my personal experience (this involves my own "eureka moments" and those of many people I know, from a number of academic and industry occupations, as well as what I read about it - sorry, I can´t remember any sources right now), most of times the revelation turns out on a dead end. Then it´s time to start again with the whole proccess and search for a new possible solution.

And here´s why I do like your analogy with mystical experiences, since they can be very different from each other, specially when one looks at diferent cuktures (sure, there may be points in common, like the feeling of being one wih the universe).

Originally posted by Interesting Ian
What reasoning? People simply say it exists.

I don´t object their existence. I disagree on their efficiency when it comes to reveal the truth.

Originally posted by Interesting Ian
Well the existence of this ability would entail we are not a mere machine; at least not an algorithmic one.

Perhaps, but my point is regarding the eficiency of the mechanism. I suspect the hits may be quite close to what expected from random cases. I really would like to see a statistical study on this.

Originally posted by Interesting Ian
I am not a system, I am a self.

But the self may be the product of a system composed by body, brain and environment...

[Interesting Ian]

Originally posted by Robin

Still I think that there is plenty wrong with Lucas's argument even leaving aside the TM question. [/B]

But no-one's actually pointed out what's wrong with his argument yet :con2:

Looks ok from my, admittedly, superficial appraisal.

[Robin]

Originally posted by Interesting Ian
But no-one's actually pointed out what's wrong with his argument yet :con2:

Looks ok from my, admittedly, superficial appraisal.
I am tapping away at it this very moment.

But I did put an initial objection:

I totally fail to see what Godel's theorems have to do with the case. The human mind is not a system of logic.

And jzs put it fairly succinctly:

As far as I am aware, the human brain does not work like + and * with the numbers {0,1,2,...}, so I too fail to see where Godel's theorem comes in.

[MESchlum]

Originally posted by Interesting Ian
Huh?? You're simply presupposing that people are mere algorithmic machines here! :eek:


No. I'm asserting that absolute knowledge of all "truths" in mathematics is beyond the realms of feasibility.


But we know they're not because we can always understand some Godelian sentance which cannot be derived from any given specific algorithm, no matter how complex.


No. There is no magical "Godel Sentence" that NO algorithm can derive. For a SPECIFIC algorithm, it is possible to CREATE a sentence that the algorithm will not derive. Change the algorithm, the sentence changes.

And since there is a method (Godel) for constructing these sentences, we could program an algorithm to write some, then derive the mathematics that follow. And I'm fairly sure that we (as human beings) would find it extremely difficult to understand the sentences, and their implications, after a few degrees of iteration.


This is apart from the sheer absurdity that an execution of an algorithm can somehow mysteriously generate consciousness. It's just rule following. Let's consider a chess computer. Place a rook into an empty file unless certain conditions pertain blah blah blah. There is not the remotest hint or suggestion that any consciousness, and hence mind is involved. Do you seriously suggest that a chess computer is conscious? If not then neither would an android be conscious or have a mind. It would only appear to have consciousness.

How does this relate to what I was saying? I stated that (due to Godel among others) a "being that knows all mathematical truths" is not possible.

The impossibility is, I will grant, my opinion. Even if such a thing exists, I am quite certain that it would not be anything close to human (probably a lot more like a machine, with infinite memory, and the dogged persistance to run down each and every implication of each and every outcome).


There is no such existent as a square circle. An object cannot simultaneously being a circle/sphere and square/cube. This is by virtue of what these terms mean.



Square: 4 sides, each of equal length, the angle at each corner is the same. Yes?

Circle: set of points on a plane such that all points are the same distance from a given center. Yes?

Great diameter of a sphere with center C.

Circle? Yes.

Square? Consider 4 equidistant points on the diamter. The arcs linking them are the same length (first constraint for a square). The angle at the corners are the same (second constraint for a square) (since the angle is tangentially zero, or the curvature of the sphere if you're picky). Yes.


If you rephrase your statement to "there is no circle that is also a square in Euclidian geometry", I'll let it pass (technically, it's more complex than that, but mentionning Euclidian geometry at least shows you know where the obvious problems are).

And that just goes to show how "obvious" things don't work as soon as you get slightly complex. In my geometry, a square is a circle. It's a mathematical truth (outlined above). Or, if I change geometries, it isn't. Another truth.

I can create (using an algorithm) any number of totally warped geometries where everything you think you know about space is patently false. That's another truth.

And so back to my earlier point - thanks for putting them together! Any thing that can "know" "all" "mathematical truths" is going to be so far from human (and from possibility) that it isn't worth using as a reference.

[Robin]

The OP, as all will agree, is a mess. There is the 'bait-and-switch' poll question. The messy bit of cut and paste. Lucas is quoted but unattributed. Stephen Hawking is incorrectly credited as sharing Penrose's view on artificial intelligence.

In hindsight the whole thing should have been ignored. But credit to Interesting Ian to provide a reference to John Lucas' original article (here is is again http://users.ox.ac.uk/~jrlucas/Godel/mmg.html) which forms the basis of the argument.

Now Lucas is a good deal smarter than me so it seems presumptious to take issue, but I will anyway.

I should probably also quote Godel's paper (http://home.ddc.net/ygg/etext/godel/godel3.htm) and I think that Proposition XI is the one that all the fuss is about.

The short form of my objection is that Godel is just not applicable. Naturally there have been thousands of philosophical speculations using poor old Godel but we should probably not dismiss out of hand the view of such a respected figure as Lucas.

OK, here is my first objection to Lucas that he has not met:
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.
As John McCarthy points out there is no reason why a machine should instantiate just one formal system. It might use any number of formal systems. I would add that it might not use any formal system of axioms at all.
We now construct a Gödelian formula in this formal system. This formula cannot be proved-in-the- system. Therefore the machine cannot produce the corresponding formula as being true. But we can see that the Gödelian formula is true: any rational being could follow Gödel's argument, and convince himself that the Gödelian formula, although unprovable-in-the-system, was nonetheless----in fact, for that very reason---true
For the moment let's leave aside Lucas' rather hopeful "... any rational being could follow Godel's argument ..." and ask how do we know that it is true? Not intuition certainly, intuition can be wrong (Aristotle intuited that the natural state of a body was at rest) so you can't by definition know anything through intuition.

Clearly what Lucas has in mind is that we know it through some logically valid process. If we can do this, why can't a machine follow Godel using the same logical process? It is not necessary that a computer has all possible logical processes pre-programmed in, there is no reason presented here why a machine should not be able to understand and even construct any logical system that a human can.

One result of Lucas' argument is that he seems to be suggest - indirectly - that a computer program is of the type of system that Godel has under consideration. Despite similarities they are not the same. A computer program is just a set of instructions and is not subject to Godel's result - ie provable and non-provable have no meaning within an algorithm.

Basically Lucas' argument is a slightly more sophisticated version of the old science fiction cliche that if you give a paradox to a computer then smoke will start to pour out of it. Lemme Caution may be able to destroy the evil computer in Alphaville by feeding it poetry but a real AI system might well appreciate the thought.

[Interesting Ian]

I wish people would use the quote function!


Originally posted by Interesting Ian
Huh?? You're simply presupposing that people are mere algorithmic machines here!

MESchlum
No. I'm asserting that absolute knowledge of all "truths" in mathematics is beyond the realms of feasibility.



You might assert that, but you cannot prove it. Goedel's proof only applies to algorithms, it does not preclude a mind just seeing some mathematical truth. I am not interested in your unsubstantiated assertions.



II
But we know they're not because we can always understand some Godelian sentance which cannot be derived from any given specific algorithm, no matter how complex.

MESchlum
No.



then you need to read up on Goedel's proof.



There is no magical "Godel Sentence" that NO algorithm can derive.



Indeed, although I do not recall anybody denying this; certainly it has absolutely nothing whatsoever to do with my paragraph that you are responding to.


For a SPECIFIC algorithm, it is possible to CREATE a sentence that the algorithm will not derive. Change the algorithm, the sentence changes.


We all know this, why don't you address the argument that the execution of an algorithm cannot simulate a mind??



This is apart from the sheer absurdity that an execution of an algorithm can somehow mysteriously generate consciousness. It's just rule following. Let's consider a chess computer. Place a rook into an empty file unless certain conditions pertain blah blah blah. There is not the remotest hint or suggestion that any consciousness, and hence mind is involved. Do you seriously suggest that a chess computer is conscious? If not then neither would an android be conscious or have a mind. It would only appear to have consciousness.

MESchlum
How does this relate to what I was saying?


you insinuated that consciousness is no more than the execution of algorithms.



I stated that (due to Godel among others) a "being that knows all mathematical truths" is not possible.


And I'm still waiting for you to substantiate this statement.



II
There is no such existent as a square circle. An object cannot simultaneously being a circle/sphere and square/cube. This is by virtue of what these terms mean.


MESchlum
Square: 4 sides, each of equal length, the angle at each corner is the same. Yes?

Circle: set of points on a plane such that all points are the same distance from a given center. Yes?

Great diameter of a sphere with center C.

Circle? Yes.

Square? Consider 4 equidistant points on the diamter.



A square does not have a diameter.


The arcs linking them are the same length (first constraint for a square). The angle at the corners are the same (second constraint for a square) (since the angle is tangentially zero, or the curvature of the sphere if you're picky). Yes.


If you rephrase your statement to "there is no circle that is also a square in Euclidian geometry", I'll let it pass (technically, it's more complex than that, but mentionning Euclidian geometry at least shows you know where the obvious problems are).

And that just goes to show how "obvious" things don't work as soon as you get slightly complex. In my geometry, a square is a circle. It's a mathematical truth (outlined above). Or, if I change geometries, it isn't. Another truth.



Nothing that you have said implies in the remotest that a square and a circle can be and one the same thing. It is logically impossible by virtue of what we mean by circle and square i.e a certain characteristic visual appearance. I believe I understand what you mean though; we just need to draw a square on some sphere to see what you're getting at. But as I said, it's not relevant. To understand this forget your mathematical definitions of squares and circles, and think in terms of qualia.



I can create (using an algorithm) any number of totally warped geometries where everything you think you know about space is patently false. That's another truth.



It certainly is not another truth as I don't think anything about space; I have no (or little) physical knowledge of space. Sure, we can check if we live in Euclidean space by drawing a huge triangle in space to see if the angles are less or greater than 180 degrees. But this has nothing to do with a circle or square drawn on paper.


And so back to my earlier point - thanks for putting them together! Any thing that can "know" "all" "mathematical truths" is going to be so far from human (and from possibility) that it isn't worth using as a reference.


The fact that it is a human mind or not a human mind is not relevant. It is implausible to say that one mind is simply an execution of of an algorithm, but that another mind is of quite a differing nature. I've already said this earlier on in the thread.

[Interesting Ian]

Originally posted by Robin
But I did put an initial objection:

quote:I totally fail to see what Godel's theorems have to do with the case. The human mind is not a system of logic.



Huh?? but here you are denying that the human mind is simply the execution of algorithms! If the human mind amounts to no more than the execution of algorithms, then it proceeds via logic. So how come you are saying the human mind is not a system of logic?


And jzs put it fairly succinctly:

quote:As far as I am aware, the human brain does not work like + and * with the numbers {0,1,2,...}, so I too fail to see where Godel's theorem comes in.



I think we need to ask those people who maintain that consciousness is just the execution of algorithms.

[Interesting Ian]

Originally posted by Robin


Clearly what Lucas has in mind is that we know it through some logically valid process.

I've read 2 of his articles. He explicitly states he does not mean this. After all, if it were a process, then an algorithm could simulate it. Which indeed you proceed to point out. Do you really think that Lucas is so dim as to not understand this?

I agree about the poll question. I voted incorrectly.

[69dodge]

Originally posted by MESchlum
I stated that (due to Godel among others) a "being that knows all mathematical truths" is not possible.

The impossibility is, I will grant, my opinion. Even if such a thing exists, I am quite certain that it would not be anything close to human (probably a lot more like a machine, with infinite memory, and the dogged persistance to run down each and every implication of each and every outcome).A Turing machine has infinite memory.

And an equal amount of persistence. :D

But that's still not good enough.

Now if it were infinitely fast, too, then we'd be getting somewhere. But that is a much less realistic assumption than infinite memory. Because it would actually have to use its infinite speed. On the other hand, for a standard finite-speed machine, any computation that terminates uses a finite amount of memory; the only reason the machine needs an infinite amount is to be absolutely sure that it won't run out of memory in the middle, because it doesn't know beforehand how much it will need.

I wouldn't say that a "being that knows all mathematical truths" is impossible, exactly. But even if it were standing in front of us, spouting mathematical truths, we'd have no way to check that they really were truths, unless they were among the truths that we could have proved for ourselves to begin with. So what good is the being, after all? We have no way to verify that it is what it claims to be.

[Robin]

Interesting Ian
Huh?? but here you are denying that the human mind is simply the execution of algorithms! If the human mind amounts to no more than the execution of algorithms, then it proceeds via logic. So how come you are saying the human mind is not a system of logic?
Maybe because that is the position I have maintained in this forum for a number of months now.
Of course there are several definitions for algorithm, but at least in the TM sense and algorithm is:

1. a finite number of exact instructions (each instruction being expressed by means of a finite number of symbols);
2. if carried out without error, it will produce the desired result in a finite number of steps;
By which definition it would be ludicrous to describe any mind as an algorithm. Neither is the mind a system of logic (which is something different from an algorithm).

Clearly the human mind is capable of devising and running algorithms and similarly of devising and using systems of logic. It may even be possible to model the human mind using an algorithm. But it is not an algorithm.

Not every physical deterministic system is an algorithm. If a system is not an algorithmic then you might still be able to understand it. But if anybody is trying to find the instruction set for the mind they are barking up the wrong tree.

In terms of consciousness I do not reject that an artificial machine can be conscious - I don't know one way or the other. But I reject the idea that it is conscious just because it appears to be conscious.

The crude argument is that if I have a computer simulation of a washing machine, no matter how well it simulates the physics involved it will never get my washing clean. A computer model of a mind is no more a mind than the computer simulation of a washing machine is a washing machine.

I've read 2 of his articles. He explicitly states he does not mean this. After all, if it were a process, then an algorithm could simulate it. Which indeed you proceed to point out. Do you really think that Lucas is so dim as to not understand this?

Well then how do we know it? If he can't state this then how does he know that we know? And precisely what is it that we can know that we can't logically prove? Can you at least point me to the other article?

Godel's propositions, after all, have logically valid proofs. I don't think that Lucas is dim but he has left a great deal unsaid. Smart people are capable of saying stupid things. Kepler, for example, spent part of his life with rigorous science and part with nonsense (to give him credit he abandoned his weird theories when the evidence mounted against them).

[69dodge]

Originally posted by Robin
(Anybody who is about to jump in with the "Church-Turing thesis" please note that they did not claim a Turing machine can do anything that any physical system can)Do you mean, like washing clothes? Or do you mean, even information-processing-wise (i.e., tasks for which a simulation is as good as the real thing)?

[69dodge]

Originally posted by Jorghnassen
It takes more than a map to know how the brain works (besides, brain mapping has its own problems), and to build an artificial brain. Can an omelet be mapped? Can number theory make an artificial omelet (or rather, how does one use number theory to make an artificial omelet)? You see there is a huge difference between description (math can be used to describe reality, but in a limited way), and implementation.

/stealing and misusing material from a lecture on A.I. I once attended... It depends what you're trying to implement. There is not a huge difference between a computer program and a description of a computer program. A precise description of a computer program is a perfectly good computer program itself, albeit in a different programming language.

Of course, a physical computer is needed to run programs. But we already have physical computers.

If you already have a kitchen and the right ingredients, all you need to make an omelet is the recipe.

[69dodge]

Originally posted by Robin
Not every physical deterministic system is an algorithm.Is any?

I do not think I understand what you mean by "algorithm". Or, possibly, what you mean by "is".Godel's propositions, after all, have logically valid proofs.Apparently. And yet, if a computer applied the very same proof to the axiomatic system underlying its own operation, it would end up "proving" something that's false!

And if it were firmly convinced (so to speak) that the proof was logically valid---as we are convinced when we carry out the proof---it would thereby convince itself that it wasn't either a Turing machine, although of course it is one.

So how do we know we aren't one too?

Tricky business, this whole Goedel thing ... :D

[Jorghnassen]

Originally posted by 69dodge

Of course, a physical computer is needed to run programs. But we already have physical computers.

If you already have a kitchen and the right ingredients, all you need to make an omelet is the recipe.

My point was that, to make an A.I. that is equivalent to a human brain (essentially rewording the poll question), the "right ingredients" might have to be exactly the same "ingredients" as the ones for a real human brain. Computers as we know today (or more advanced versions of the same kind of building blocks) will not be able to think as humans do. You can't make an omelet out of Cadbury eggs, even with the right recipe...

[Robin]

69dodge
Do you mean, like washing clothes? Or do you mean, even information-processing-wise (i.e., tasks for which a simulation is as good as the real thing)?
You are jumping back and forth a bit with my posts here but the it has not even been proved that the TM is capable of any information-processing task.
Godel's propositions, after all, have logically valid proofs.
--------------------------------------------------------------------------------

Apparently. And yet, if a computer applied the very same proof to the axiomatic system underlying its own operation, it would end up "proving" something that's false!

But there is no axiomatic system underlying its own operation. A computer programming language (or instruction set) is not an axiomatic system of the type considered by Godel. This is one major flaw with Lucas' argument.
And if it were firmly convinced (so to speak) that the proof was logically valid---as we are convinced when we carry out the proof---it would thereby convince itself that it wasn't either a Turing machine, although of course it is one.
Firstly, the computer would not necessarily operate by the principles of a Turing Machine and secondly even if it does, Godel's theorem does not apply to a Turing Machine.

So my main point still stands - Lucas is saying that there is at least one thing that we can know, but which a given machine can not know. How exactly does he say that we know this thing, if not through a valid logical process?

[TillEulenspiegel]

My point was that, to make an A.I. that is equivalent to a human brain (essentially rewording the poll question), the "right ingredients" might have to be exactly the same "ingredients" as the ones for a real human brain.

/agree Jorghnassen

Much like a quantum state machine . To be a complete model of the universe the machine would have to be a carbon copy of the universe it is modeling down to the last photon. We can mimic certain behaviors but to be %100 accurate means to be all inclusive. So topically the answer is no we cannot have AI that "thinks" like a human. Even identical twins don't have identical thoughts and reactions all of the time,and their biological machines not mimics.

That does not mean however that a good computer model on a fast machine could not pass the Turing test. In fact certain "Expert Systems" do as well as any human but with the understanding that they are generally confined to a single discipline I.E. Deep Blue, Medical Programs for diagnosis, etc.

[Peskanov]

TillEulenspiegel,

So topically the answer is no we cannot have AI that "thinks" like a human. Even identical twins don't have identical thoughts and reactions all of the time,and their biological machines not mimics.


And what do you mean with that? That one of the twins does not think like a human???
You are self-contradicting. Precisely, that's the reason you should consider seriously the posibility of machines thinking. No brain is equal to any other, and for start you don't know how much difference in a brain will stop resulting in human intelligence. How about substituting all neurones with electrical equivalents, for example?

[Peskanov]

BTW, there is an interesting page that makes a good argument against Penrose position, and gives a much more credible analysis about the consequences of Godel's theorem.

http://psyche.cs.monash.edu.au/v2/psyche-2-04-mccullough.html

Here there is the conclusion of the author:

8.1 Penrose's arguments that our reasoning can't be formalized is in some sense correct. There is no way to formalize our own reasoning and be absolutely certain that the resulting theory is sound and consistent. However, this turns out not to be a limitation on what computers or formal systems can accomplish relative to humans. Instead, it is an intrinsic limitation in our abilities to reason about our own reasoning process. To the extent that we understand our own reasoning, we can't be certain that it is sound, and to the extent that we know we are sound, we don't understand our reasoning well enough to formalize it. This limitation is not due to lack of intelligence on our part, but is inherent in any reasoning system that is capable of reasoning about itself.

[TillEulenspiegel]

Originally posted by Peskanov
TillEulenspiegel,


And what do you mean with that? That one of the twins does not think like a human???
You are self-contradicting. Precisely, that's the reason you should consider seriously the possibility of machines thinking. No brain is equal to any other, and for start you don't know how much difference in a brain will stop resulting in human intelligence. How about substituting all neurones with electrical equivalents, for example?

Perhaps I wasn't clear.

The Acme, the idealized form of a thinking human is a thinking human.When we look for example of a standardized "sameness" it would be ( IMO ) a set of identical twins who had the same biological attributes, upbringing, environment etc.

The fact that they still show divergence is an example of the problems of modeling "human" thinking. A demonstration of the fuzziness or gray areas of the hidden processes that make a human intelligence what it is, a sort of "la deux ex machina" .
If it's not possible to standardize behavioral and thought processes in the closest example we can have ( now )of the mechanism of thinking, How can we think that we could manufacture a successful counterfeit?

As I stated "Expert Programs do some things better then humans, but they do one thing only while You can argue with Your spouse on your cell phone,(Reasoning and speech skills, learned manipulation of a technical gadget) while driving, ( motor activity ) ,around a curve ( trig on the fly) and eating a doughnut ( -8- (l) um mm doughnut. It is definitely not a simplistic , linear process that some people here try to equate it with I.E.an "algorithm". We can't even quntify the basics or define the concepts, how could we possibly construct an effective model?


Good read here: http://www.abc.net.au/science/bigquestions/s460741.htm

[Peskanov]

The fact that they still show divergence is an example of the problems of modeling "human" thinking. A demonstration of the fuzziness or gray areas of the hidden processes that make a human intelligence what it is, a sort of "la deux ex machina" .
If it's not possible to standardize behavioral and thought processes in the closest example we can have ( now )of the mechanism of thinking, How can we think that we could manufacture a successful counterfeit?

How does a twin reckon his brother is intelligent? Interaction, plus physical reckoning (he looks also as a human) makes reasonable to think so.
The turing test only adresses the first step, interaction. If the machines talks with you like a human, you have half of the picture.
How can you complete the picture and know the machine thinks like you? Only if you can identify it's physical processes with yours. If the computer is modelled as a human brain (e.g. neural nets disposed in a human brain-like configuration).
If the machine was designed as a human brain, and behaves like one, my intuition would tell me the machine is intelligent.


As I stated "Expert Programs do some things better then humans, but they do one thing only while You can...

But that's a missconception of yours. The quantity of tasks (experts systems or not) a computer can carry simultaneously is infinite. We can enter into practical details if you want, but you must know that theorically the number of decissions a computer can make at the same time has no limit.
Usual expert systems are strictly interactive (they only "think" when requested) and one-user-only. Others are multiuser, they share their time between several questions done by remote users. But those are implementation details, they are not designed to develop the kind of intelligence humans have. Other AI systems are more complex and show the attributes of decission and volition.

A good analogy for this question could be wheater modelling. Modern wheater modelling systems simulate the whole atmosphere, a highly interactive system which happens "all at the same time". Every portion of air exchanges properties with the neighbour portions.
For practical purposes, parallel computing is used. Hundreds of computers share the problem, taking a piece of it and solving them locally.
However, the same computation can be solved by just one computer, much more slowly.

The deal is that any task solved by many computers or Turing machines, can also be solved by just one more slowly. And that's the reason philosophers don't have to deal with problems like the one you present, because just answering the general question is enough.

[Robin]

Me:
Godel's theorem does not apply to a Turing Machine
I must amend this. I was using the fact that there is no concept of 'provable' within an algorithm. Moreover there is no concept of true and false other than values defined by the programmer.

But Penrose has recast Godel's theorem using the concept of 'halting'. So while the Lucas argument merely assumes that a TM is such a system, Penrose explains why it might be.

It does not effect the main objections to Lucas' argument as put here.

[Jorghnassen]

Originally posted by Peskanov
How does a twin reckon his brother is intelligent? Interaction, plus physical reckoning (he looks also as a human) makes reasonable to think so.
The turing test only adresses the first step, interaction. If the machines talks with you like a human, you have half of the picture.
How can you complete the picture and know the machine thinks like you? Only if you can identify it's physical processes with yours. If the computer is modelled as a human brain (e.g. neural nets disposed in a human brain-like configuration).
If the machine was designed as a human brain, and behaves like one, my intuition would tell me the machine is intelligent.


But that's a missconception of yours. The quantity of tasks (experts systems or not) a computer can carry simultaneously is infinite. We can enter into practical details if you want, but you must know that theorically the number of decissions a computer can make at the same time has no limit.
Usual expert systems are strictly interactive (they only "think" when requested) and one-user-only. Others are multiuser, they share their time between several questions done by remote users. But those are implementation details, they are not designed to develop the kind of intelligence humans have. Other AI systems are more complex and show the attributes of decission and volition.

A good analogy for this question could be wheater modelling. Modern wheater modelling systems simulate the whole atmosphere, a highly interactive system which happens "all at the same time". Every portion of air exchanges properties with the neighbour portions.
For practical purposes, parallel computing is used. Hundreds of computers share the problem, taking a piece of it and solving them locally.
However, the same computation can be solved by just one computer, much more slowly.

The deal is that any task solved by many computers or Turing machines, can also be solved by just one more slowly. And that's the reason philosophers don't have to deal with problems like the one you present, because just answering the general question is enough.

A few things. All computers are finite machines and can only deal with finitely many tasks at one point in time. Second, massive parallelism is no indication of intelligence, neither is crunching numbers. It's not too hard to devise algorithms that involve doing some straight-forward decision making (like playing chess). Some very easy pattern recognition in the presence of interference suddenly isn't so trivial, even when using very "smart" algorithms. And that's not even going into less defined areas such as "creativity" and "imagination".

Now if one could make a machine, that didn't know anything at first and just had sensor devices to see, hear, touch, smell and taste, and some motor devices to move, and some sound emitting device, and that machine then learned to interact with one lifeform, be it cockroaches, squirrels, parrots or humans, now that would be truly artificial intelligence. Until then, it's just a fancy abacus.

[Peskanov]

A few things. All computers are finite machines and can only deal with finitely many tasks at one point in time.

Wrong; read again, I said a "theorical computer". A physical computer is only limited by the quantity of matter and energy avalaible in the universe to build it. There is no theorical limit to the quantity of nodes a parallel computer can have. In practical terms, every year the size and power of supercomputers grows more and more, only limited by budgets.
Mind that the current model of brain, used by neuroscientist, is a giant parallel computer where the neurons are the computational units.
Recently, supercomputers reached 100 Teraflops, which compares well with some estimations of the computational power of the brain.

Second, massive parallelism is no indication of intelligence, neither is crunching numbers.

Nobody said so. I only argue that it's necesary to replicate what brains do in similar timings.
Aside from speed, huge memory capacity is a necesity. You can calculate your way with 1 bit a time if needed, but the data must be there, and in case of human intelligence is a big quantity of data.

It's not too hard to devise algorithms that involve doing some straight-forward decision making (like playing chess). Some very easy pattern recognition in the presence of interference suddenly isn't so trivial, even when using very "smart" algorithms. And that's not even going into less defined areas such as "creativity" and "imagination".

So? Nobody here is offering reasons against the possible systematization of those propierties of the brain,( aside from intuitive arguments). Ian says that the default position should be "impossible", but his reasons seem weak to me. Neuroscientist says the most sensible position now, with all the information about the brain available, should be "possible"; and near all of them think "sure, it's just another proccess of the brain, like visual recognition".

Now if one could make a machine, that didn't know anything at first and just had sensor devices to see, hear, touch, smell and taste, and some motor devices to move, and some sound emitting device, and that machine then learned to interact with one lifeform, be it cockroaches, squirrels, parrots or humans, now that would be truly artificial intelligence. Until then, it's just a fancy abacus.

I don't get it. This kind of thing has been done several times, with bees, fishes, and even big mamals like cows. Most animals have a very low capability of interaction and it's easy to fool them, that does not prove anything...

[Peskanov]

TillEulenspiegel, about your link:
http://www.abc.net.au/science/bigquestions/s460741.htm
After reading the article, I can only say it's a nice example of this disaster area called "theory of the mind". They totally fail to tell why the human intelligence is not / can not be the fruit of a deterministic system (aka machine). Take a look at the game:

Now, how can thoughts do that? How can the desire ‘I would like to raise my arm’ be turned into the physical activity of the arm moving? Well, we can trace back a sort of chain of command, can’t we? We know that there are nerve impulses in my arm that cause the muscles to contract, and these nerve impulses have travelled down my nerve fibres from my brain, so the signals originate in electrical activity in my brain. But what is it that just triggers all that, that chain of command? What starts those electric currents off in the first place? How is it that a thought can be translated into electrons moving down nerves, and so on?

Incredibly fuzzy question. Why should a "though be translated" into electrons if you already ignore the nature of though? How do you know is not already composed by electrons?

Thoughts can’t move electrons or arms or whatever, because there are no thoughts – at least, there are no thoughts that are things with physical efficacy; there are only electrons and other matter frolicking about in accordance with physical laws.

Same here. I find it funny, because in fact most idealist and dualist, which defend a non-material nature of the mind (as this article) will argue that thoughts can, in fact, move electrons or arms.

Phillip: Let’s get back to the question that you raised earlier. What role does consciousness play? What is its advantage?

Paul: This is the mystery if we try to define it away, for then why do we possess it (or imagine we possess it) at all? In other words, if a cleverly programmed automaton, or a zombie, that had evolved to perform a lot of complicated functions, can get by in the world without being conscious of its own existence, what is the purpose of us having this consciousness or this self-consciousness, this self-awareness? It does seem to be a mystery if it doesn’t fulfil any useful role in nature. So I think we have to take consciousness seriously, in spite of the fact that many scientists would like to do away with it.

Here they take the stance that consciousness is awareness of our functions, but not the function themselves which could be produced by a machine.
But then:

Let us accept that consciousness is real. Can you deduce some practical evolutionary purpose for our degree of it?

Paul: It’s easy to use consciousness-type language to see an advantage. For example, it is clearly advantageous to be able to predict the future to a limited extent – to plan

Nice one; after all consciousness can perform functions: e.g. guessing the future.
This function can be, and is, performed by machines. So?. Next:

You know, it’s a very curious thing about the self, that it is a paradoxical mixture of something which is unchanged with time and something that changes with time. If you ask, ‘Are you the same person you were at the age of ten?’ well, in one sense you are; there’s a continuity of memory, certain personality traits remain unchanged, and so on. On the other hand, you are clearly not exactly the same person. Not only has your body changed but your mind has changed as well. So there is something that we like to call the ‘self’ which is preserved intact through time, and yet something in there is changing, too. So I don’t think we are ever going to understand what we mean by the self without understanding the psychology of temporality and the puzzle of the sensation of the flux of time

This property is shared by all complex systems, from wheater to economic markets to computer programs, and noboy has problems identifying those as entities. No mistery here. Next:

Paul: I’ve made it very clear that I think that consciousness is something associated with complexity, and therefore that I wouldn’t expect to find a rock to be conscious, or for that matter a star or a planet. Consciousness seems to be something that emerges over time as complexity advances.

Then, where is the problem in accepting that the brain is a machine, and another complex machine could be conscious?

Conclusion: where is the argument against a thinking machine, or machines with self-awareness? I am unable to find it.
And, sadly, this is the common trend in those discussions. An argument from ignorance. "I don't know, so what you say is impossible".

[Jorghnassen]

Look, I'm not saying it's impossible, I'm saying a two things:
-first our understanding of the brain is still too rudimentary to reverse-engineer it completely;
-computers, as we know them today (now, I'm not talking speed and memory size, which can increase a whole lot and it's still not going to make a difference, I'm talking more basic architecture, building blocks), are likely not going to be good enough to emulate a brain.

Now you are going to say that my second position is purely hypothetical and I have no proof that computers are insufficient, but the other position is just as hypothetical, and has no evidence for it other than wishful thinking. Call me skeptical, but until someone comes up with the software for sufficient human brain emulation, I'm going to stick to the position that thinking machines are just as possible as cold fusion.

[Interesting Ian]

Originally posted by Jorghnassen
I'm going to stick to the position that thinking machines are just as possible as cold fusion. [/B]

I have no problem with either intelligent or thinking machines, so long as people are not suggesting that they would be conscious. How can the execution of an algorithm lead to consciousness?

[Peskanov]

Jorghnassen, I am not trying to create an argument from authority, but I have the feeling you are uninformed about neuroscience.

first our understanding of the brain is still too rudimentary to reverse-engineer it completely

That's true and I think undisputed.

computers, as we know them today (now, I'm not talking speed and memory size, which can increase a whole lot and it's still not going to make a difference, I'm talking more basic architecture, building blocks), are likely not going to be good enough to emulate a brain.

The problem here is that you are denying the validity of current neuroscience; I mean that you are being over-skeptical.
Neuroscience has a basic model for brains (a functional, mathematical model of the neuron as the base of it). This model is known to be incomplete as some of the "slow" properties of the neuron have an unkown behaviour. For example, the way in which neurones (slowly) wire within themselves. This proccess seems computationally inexpensive, but it's a necessary property of the brain.
Scientist can use the current model to imitate most of the expensive, complex processes known in the brain, like reckoning of sounds for example. However our artificial neurons still lack the plasticity of the real ones.

Now, you claim that modern computers are not ready to emulate a brain. And neuroscience claims the reverse, and they have the numbers. They can't produce a working brain because they lack the general map of the brain and details like this neuronal rewiring, however the computational cost IS reasonably estimated, and it is within the reach of current hardware!

In this forum we have discussed several time about the advances in artificial neural nets. Take a look at one of the most powerful examples of neuroscience, the computerised emulation of a well-known section the brain:
http://www.newscientist.com/article.ns?id=dn3488

[Peskanov]

Ian,
I also don't have a problem with non-interactive dualism, where consciousness sit there "feeling" passively while the machine works it's way through the world. However I don't see any logical reason to support that idea.
And I certainly have a problem with the other two popular philosophical options, clasic dualism and idealism, because both require consciousness modifying the brain processes to include their concept of free will.
The concept of the brain being manipulated to a grade in which it can choose to pick a cookie, for example, seems huge to me.
Maybe that seems a simple decision, however my view as a programmer is that the quantity of elements present is enormous. This kind of sophisticated soul/body interaction seems extremely impausible sitting from the neuroscientist chair.

[hammegk]

Peskanov, nice to hear from you ....

Originally posted by Peskanov
This kind of sophisticated soul/body interaction seems extremely impausible sitting from the neuroscientist chair.
The naturalist Master Control Program, or the idealist 'conciousness' would seldom be needed if the body (for the idealist perceived-as-body) is processing normally.

[Jorghnassen]

Originally posted by Peskanov

In this forum we have discussed several time about the advances in artificial neural nets. Take a look at one of the most powerful examples of neuroscience, the computerised emulation of a well-known section the brain:
http://www.newscientist.com/article.ns?id=dn3488

Nice example. From your article (emphasis mine):


No one understands how the hippocampus encodes information. So the team simply copied its behaviour.

...

They are about to test it on slices of rat brain kept alive in cerebrospinal fluid, they will tell a neural engineering conference in Capri, Italy, next week.
...

If it works, the team will test the prosthesis in live rats within six months, and then in monkeys trained to carry out memory tasks.


So any update on that? Did it work on slices of rat brains? Have they tested it on live rats yet? This article is almost 2 years old, I'm sure that at least the slices of rat brains interface results should be out by now.

Either way, memory storage is still far from emergence of conciousness, which might just be a real tough nut to crack (like how the brain encodes information), just like abiogenesis (has that problem been solved yet?).

[MESchlum]

/initiate math derail. Again. Wheee!

I'm trying to organise things, hopefully my summaries of viewpoints are roughly correct.


Topic: ideal humans knowing all mathematical truths.

My stance: knowing all mathematical truths is not possible (I repent: it just calls for a few orders of infinite ressources), and anything that does is not human.

Ian's stance: it is possible to know all mathematical truths.

Originally posted by Interesting Ian

You might assert that, but you cannot prove it. Goedel's proof only applies to algorithms, it does not preclude a mind just seeing some mathematical truth. I am not interested in your unsubstantiated assertions.


then you need to read up on Goedel's proof.

<snip>

And I'm still waiting for you to substantiate this statement.

<snip>

The fact that it is a human mind or not a human mind is not relevant. It is implausible to say that one mind is simply an execution of of an algorithm, but that another mind is of quite a differing nature. I've already said this earlier on in the thread.



(reminder: I am stating "that (due to Godel among others) a "being that knows all mathematical truths" is not possible.")

My thanks to 69dodge, who seems to enjoy making sure of my facts (incidentally, the proof that "I am not provable in X" is true does not seem acheivable in X, for what it's worth in confusion). I know enjoy having them set aright, with convincing arguments to boot.

So... impossible is, perhaps, a bit too strong. (I did claim it was my opinion). Inhuman (which is the issue here - reminder: Ian wants an idealised human to do this) is a lot closer. What exactly is human about a being with infinite processing speed and infinite memory? And even if it were human, there is no way to prove that it's always right (i.e. providing "truths") without doing all the checking yourself. So it's useless as a reference.

Summary: if it were possible (you just need a few infinities here and there), it would be useless because there would be no way to know it was trustworthy (unless you too enjoyed those infinities). So a "being knowing all mathematical truths" is NOT an idealised human (by my view of what humanity is), and is NOT useful for testing algorithms versus humans.

Apparently, the use of an "ideal human knowing all mathematical truths" is no longer necessary to your arguments. At least, that's what your final paragraph suggests (to me). If so, good - I don't think it exists, you don't use it, we're both happy (just make sure you don't use it). If not, bad - we seem to have a fundament disconnect on what an ideal human is, and disagree on mathematical issues.


Topic: Godel verus algorithms

My stance: for a given algorithm, you can find a statement that is not provable by the algorithm. You can also find an algorithm that will prove the statement.

Ian' stance: ???


Indeed, although I do not recall anybody denying this; certainly it has absolutely nothing whatsoever to do with my paragraph that you are responding to.

We all know this, why don't you address the argument that the execution of an algorithm cannot simulate a mind??

[QUOTE]

Reminder: I'm saying that a sentence that is unprovable by a given algorithm can always be proven by another one. Just add the proper premise, and you're set. Ian agrees.

To quote Ian in the "paragraph (I am) responding to": "But we know they're not because we can always understand some Godelian sentance which cannot be derived from any given specific algorithm, no matter how complex."

So which is it? Name the sentence that is impossible to derive, and I'll write an algorithm that gets it. Seems relevant to me...


[QUOTE]
you insinuated that consciousness is no more than the execution of algorithms.



So far, I believe I've been trying to make sure that (to the limits of my knowledge) the maths being tossed about are roughly correct. If you choose to interpret correct mathematics as an argument for consciousness being an algorithm, it's your call, not mine.


Topic: square circles

My stance: In Euclidian space, a square and a circle are distinct. In other geometries, they can easily be seen to be identical. This illustrates how an intuitive "truth" can be false, or correct, depending on the setting.

Ian's stance: a square is not a circle because I say so.



A square does not have a diameter.



Nothing that you have said implies in the remotest that a square and a circle can be and one the same thing. It is logically impossible by virtue of what we mean by circle and square i.e a certain characteristic visual appearance. I believe I understand what you mean though; we just need to draw a square on some sphere to see what you're getting at. But as I said, it's not relevant. To understand this forget your mathematical definitions of squares and circles, and think in terms of qualia.



It certainly is not another truth as I don't think anything about space; I have no (or little) physical knowledge of space. Sure, we can check if we live in Euclidean space by drawing a huge triangle in space to see if the angles are less or greater than 180 degrees. But this has nothing to do with a circle or square drawn on paper.

If you're operating on paper, you're operating in Euclian space (or a good simulation thereof).

I dispute your logic. In my proofs, I used the "characteristics of squares and circles". I also used unusual geometries in which to apply these characteristics, but until, and unless, your logic states "in Euclidian space" there is no rule saying I have to limit myself to such.

Your proof is "we all know what I meant, so I must be right." Where is the logic therein? I'm ready to learn. Please - give me a logical proof that a square is not a circle. No "It is obvious that", no "anyone can see that", just proofs. Then I'll give you one that a square *is* a circle, using a different geometry.

Which proof is correct? Well, we can prove both, and they contradict each other, so we need to be careful. My solution: "In Euclidian geometry, a square is not a circle". What is yours?

If it's the same (using "paper" as a substitute for "Euclidian") then you should realise that what is obvious to most (and under normal conditions, I won't confuse a square and a circle) is not necessarily True in the mathematical (or logical, or whatever) sense. Hence our ability to "know" "truth" is suspect, because the "truths" we "know" are obvious.

If not, show me the logic. Please?

[RussDill]

I think a good example to use here is the halting problem. Basically says that no turing machine can determine if another turing machine will halt, or run forever. Many people would chalk this up to the limitation of the machine, and would point out that someone could write a proof, showing which machines halt, and which do not.

However, machines can write proofs too. In fact, via brute force, they can write ever single proof down. Which indicates that humans have no special powers over machines in this particular case. Only an infinitely long proof would suffice, which humans are not capable of producing.

Others have pointed out that turing machines cannot do parallism, which is untrue, parallel execution is easily modeled with a single excecution thread, producing the same output.

Randomism and QM have been mention thoughout the thread. Any result obtained by a machine with random input is also possible to obtain by a machine with no random input. Each time a random input must be taken, simply fork, and do each possibility.

[Interesting Ian]

Originally posted by MESchlum
To quote Ian in the "paragraph (I am) responding to":

II
"But we know they're not because we can always understand some Godelian sentance which cannot be derived from any given specific algorithm, no matter how complex."

MESchlum
So which is it? Name the sentence that is impossible to derive, and I'll write an algorithm that gets it. Seems relevant to me...



I really don't know how often I need to repeat myself. You need to name a specific algorithm, and then we can show that it falls short in not being able to recognise some truth that an appropriate mind can. Replace that algorithm with another so it understand that truth, and there will be some other truth which the algorithm cannot derive, but that mind can. And this process never stops. Therefore as that mind cannot be modelled by an algorithm, it is therefore not an algorithm.

And that is the very last time I present the proof.

[RussDill]

Originally posted by Interesting Ian
I really don't know how often I need to repeat myself. You need to name a specific algorithm, and then we can show that it falls short in not being able to recognise some truth that an appropriate mind can. Replace that algorithm with another so it understand that truth, and there will be some other truth which the algorithm cannot derive, but that mind can. And this process never stops. Therefore as that mind cannot be modelled by an algorithm, it is therefore not an algorithm.

And that is the very last time I present the proof.

...and what about an algorithm to generate, test, and evolve new algorithms?

[Interesting Ian]

MESchlum

Your proof is "we all know what I meant, so I must be right." Where is the logic therein?


This comment regarding my assertion that it is logically impossible for an object to be simultaneously both a cube and a sphere.

No MESchlum, my proof does not consist in that. It consists in the fact that spheres and cubes do not look like each other, and are very easily visually distinguished to all those who are not virtually blind; they do not feel like each other (one has sharp edges and the other is uniformly smooth); and they do not have the same affect on the environment. If I threw them both at your head, you're more likely to shout "ouch" with the cube as it's corner pierces your skin.

Now, talking about higher dimensions, and the geometry of the space-time continuum has absolutely nothing to do with the truth or falsity of my assertion. Just read the above paragraph and take it in.

[Peskanov]

Hello Hammegk, I got caught in the eternal metaphysic debate again...

The naturalist Master Control Program, or the idealist 'conciousness' would seldom be needed if the body (for the idealist perceived-as-body) is processing normally.

Do you find acceptable this idea of the soul creeping silently into the brain from time to time to touch some buttons?
Maybe my sense of wonder about the complexity of the brain is blinding me, but I have a hard time in finding that idea plausible. I have the feeling that this hypothesis is highly artificial, a bit like that old one about the nature of fire, the "phlogiston" element.

[Peskanov]

Ian,

You need to name a specific algorithm, and then we can show that it falls short in not being able to recognise some truth that an appropriate mind can. Replace that algorithm with another so it understand that truth, and there will be some other truth which the algorithm cannot derive, but that mind can. And this process never stops

By the same nature of you sentence, "And this process never stops", you have said both entities have the same deductive power.

[hammegk]

Originally posted by Peskanov


Do you find acceptable this idea of the soul creeping silently into the brain from time to time to touch some buttons?

Nope. That's some interactive form of dualism. An idealist's stance is there exists nothing but "soul", although words fail me here.

*I* have a perceived-as-material body that provides I/O, and is a damn fine machine needing little assistance from "soul" to keep chuggin' along (as we would perceive from our different 1st person viewpoints).

[Peskanov]

Jorghnassen, the example I posted is the most advanced (and still comming from credible scientist) I have seen, but no, I don't have new information about the team.
Most teams in the field make much more modest experiments. Recently one team acomplished a nice success making natural neurons grow in an electrical grid, and trained it to "pilot a plane" (in reality, to balance some inputs and outputs).
In the other hand, there is a company in silicon valley with a big budget who tries to emulate a whole human brain using a net of computers, but in my opinion it is just a sophisticated hoax.
About your bold text "No one understands how the hippocampus encodes information", it's true. But it's even worse than you think. Fully artificial neural nets, which are commonly trained for lots of uses (from visual reckoning to data compression), are also not understood.
The principle of neural nets is a bit like Fermat's theorem was, a theorical construction which seems to work in all the tests, but lacks a demonstration.
Still, all the parts of an artificial neural net are deterministic and known, and behave as any other machine. What the team claims is to have build an artificial neural net which replicates correctly the activity of a natural one, in this case the hippocampus. The meaning of the information which runs through is, as they admit, unknown. But the same could happen to any other part of the brain; one day we could replicate correctly the area that holds the key to consciousness without even knowing it.
A note: the hippocampus is related to the codifying of memories which will be stored for long term. It does not memorize anything, it just preprocess the information. Search for long and short memory term if you don't understand what I mean.

[drkitten]

Originally posted by Interesting Ian
I really don't know how often I need to repeat myself. You need to name a specific algorithm, and then we can show that it falls short in not being able to recognise some truth that an appropriate mind can.

Fair is fair. If I need to name a specific algorithm, you need to name a specific mind that can recognize the truth.

At this point, it's rather trivial to produce a truth that the algorithm will recognize as true, but that the specific mind cannot. (Just make it something that will take more than 150 years to prove.)

Alternatively, if you are not going to talk about a specific mind, but instead about an idealized mind of infinite capacity, then I get to present an idealized algorithm of infinite capacity.

Since algorithms of infinite capacity are not axiomatizable, they are not subject to Godel (or Turing) limitations, and in fact, an infinitely long program can solve the halting problem (using nothing more than a huge set of if/then statements, in fact).

Your whole argument is nothing more than an elaborate begging of the question. You assume an infinite capacity on the part of the human mind, an assumption never to be reached in any sort of practice and completely at odds with what we know about human capacities --- and an assumption that demonstrably implies that human intellect cannot be algorithmic. You then triumphantly present this assumption as a "proof" that human intellect cannot be algorithmic.

[Interesting Ian]

Originally posted by new drkitten
[B]Fair is fair. If I need to name a specific algorithm, you need to name a specific mind that can recognize the truth.



An immortal and idealized me will do. BTW, as I keep repeating, you can name any algorithm you like, and if it fails to model me, you can keep changing it for as long as you like. until it does. But if it never does, then my mind cannot be modelled and thus I am not a machine.



At this point, it's rather trivial to produce a truth that the algorithm will recognize as true, but that the specific mind cannot. (Just make it something that will take more than 150 years to prove.)



So what? The algorithm is supposed to be modelling me, not vice versa. Read Lucas's papers.



Alternatively, if you are not going to talk about a specific mind, but instead about an idealized mind of infinite capacity, then I get to present an idealized algorithm of infinite capacity.



No, I used the word unlimited. It is not an infinite mind, but a sufficiently great mind. If a sufficiently great algorithm (but not infinite) can model a sufficiently great mind (but not infinite), then my argument has lost.

[RussDill]

Originally posted by new drkitten

Since algorithms of infinite capacity are not axiomatizable, they are not subject to Godel (or Turing) limitations, and in fact, an infinitely long program can solve the halting problem (using nothing more than a huge set of if/then statements, in fact).


An infinitely long program will already take an infinitely long amount of time to run. It might be better to just make a short program that runs for an infinitely long amount of time.

[MESchlum]

Originally posted by Interesting Ian
I really don't know how often I need to repeat myself. You need to name a specific algorithm, and then we can show that it falls short in not being able to recognise some truth that an appropriate mind can. Replace that algorithm with another so it understand that truth, and there will be some other truth which the algorithm cannot derive, but that mind can. And this process never stops. Therefore as that mind cannot be modelled by an algorithm, it is therefore not an algorithm.

And that is the very last time I present the proof.

I see... it's a better mousetrap, basically.

Begin with a system X, and an algorithm 1 that follows X to derive true statements only.

System X is analysed (by you (human)), you (human) apply Godel, and derive (from Godel's method) a statement A that cannot be proven in X.

Algorithm 1 will never find A (or non-A).

So you create system Y, which is X and A (or X and non-A).

You write an algorithm 2, that contains X and A (or X and non-A), and derives true statements only. Algorithm 2 will easily find A (or non-A).

System Y is analysed (by you (human)), and you (human) apply Godel, and derive (from Godel's method) a statement B that cannot be proven in Y.

Algorithm 2 will never find B (or non-B).

Repeat.


This is Godel. Not human. I could write an algorithm that does this (take X, use Godel to get a statement A, create X+A, use Godel to get B, create X+A+B...). I can even use this to prove that the mind is less than algorithms.

Watch:

Start with system X, and algorithm 1. Apply a meta-algorithm to (X,1) (it's an algorithm that writes algorithms. Quite feasible).

Does the mind understand X? If not, algorithm 1 is better than the mind.

The mind understands X. The meta-algorithm applies Godel to find something that is not provable in X, and creates system Y, and algorithm 2.

The mind still understands Y? So does algorithm 2, so they're even. But the meta-algorithm can create Z...

The mind will never catch up (just like, in your premise, algorithms never will).


So where does this leave us? By my estimate, roughly nowhere. Proof dismissed.

To my view, the weakness in your "proof" is that you're secretly updating the mind (it is the same mind, and understands everything - another point I dispute) so that it understands every new system. Meanwhile, every new algorithm has to openly update, so it's "inferior".

I just switched the roles - but a meta-algorithm like the one I mentionned *can* be written. And the truths it gets after a few levels of execution are going to be far beyond you (and me). Witness what happens when you play with geometry (and that's using things we understand - the Godel sentence for geometry is probably not Euclid's parallel postulate, for instance).

[MESchlum]

Originally posted by Interesting Ian
This comment regarding my assertion that it is logically impossible for an object to be simultaneously both a cube and a sphere.

No MESchlum, my proof does not consist in that. It consists in the fact that spheres and cubes do not look like each other, and are very easily visually distinguished to all those who are not virtually blind; they do not feel like each other (one has sharp edges and the other is uniformly smooth); and they do not have the same affect on the environment. If I threw them both at your head, you're more likely to shout "ouch" with the cube as it's corner pierces your skin.

Now, talking about higher dimensions, and the geometry of the space-time continuum has absolutely nothing to do with the truth or falsity of my assertion. Just read the above paragraph and take it in.

Right. "The fact that" "You can tell" "It is obvious".

No logic.

A Euclidian sphere is not a Euclidian cube

I can prove it (with math, and so, presumably, a form of logic).

A non-Euclidian sphere is a non-Euclidian cube

I can prove it (with math in the proper non-Euclidian space, and so, presumably, a form of logic).

Accept my definitions and proofs (say Euclidian, come on, it's just a word), or give your own - until then, don't say you're using logic.

Or maybe what I'm saying is a mathematical truth that even an idealised and immortal Ian can't grasp? I can write an algorithm to prove it, though...

[Robin]

Originally posted by Interesting Ian
I really don't know how often I need to repeat myself. You need to name a specific algorithm, and then we can show that it falls short in not being able to recognise some truth that an appropriate mind can. Replace that algorithm with another so it understand that truth, and there will be some other truth which the algorithm cannot derive, but that mind can. And this process never stops. Therefore as that mind cannot be modelled by an algorithm, it is therefore not an algorithm.

And that is the very last time I present the proof.
So don't repeat yourself - answer the question that this argument raises. I have already asked you for this.

Exactly how does the appropriate mind recognise truth? You have already said that it is not through a logically valid process, so how do you know that the human has recognised truth? Unless this can be stated the proof is useless.

Every example Lucas gives in this and other articles shows the human recognising truth through some logical process - like modus tollens or proof by contradiction, which are of course easy to implement in a computer.

We just need to ask - can a computer implement more than one axiomatic system? Can it use one axiomatic system to evaluate statements about other axiomatic systems? I can see no reason why this should not be possible.

So Godel is irrelevant to the case.

[Interesting Ian]

I certainly understand Lucas's frustration. MESchlum, it is quite clear you have neither read his argument, nor my paraphrasing of it in this thread. No wonder he complains about people not turning the page! They're simply not bothering to read his argument (or mine).

[Robin]

Originally posted by Interesting Ian
I certainly understand Lucas's frustration. MESchlum, it is quite clear you have neither read his argument, nor my paraphrasing of it in this thread. No wonder he complains about people not turning the page! They're simply not bothering to read his argument (or mine).
Yes people are reading his and your argument. You are ignoring them. You are busy trying not to notice the huge crack in the middle of this argument, ie "on what basis do you assert that humans can recognise truth, if not a logically valid one?".

You have said it yourself - if Lucas means that humans understand the truth through some logically valid process, as in all his examples, then any algorithm could do the same.

[Interesting Ian]

Originally posted by Robin
Yes people are reading his and your argument. You are ignoring them. You are busy trying not to notice the huge crack in the middle of this argument, ie "on what basis do you assert that humans can recognise truth, if not a logically valid one?".

You have said it yourself - if Lucas means that humans understand the truth through some logically valid process, as in all his examples, then any algorithm could do the same.

I told you. People just see the truth. There is no process involved. They just know by an immediate intuitive understanding. Maybe their minds simply see the Platonic forms.

[jay gw]

Part of what gives people (most people) their self awareness is the physical form they are in. Everyone can perceive that they are distinct entities, separate from everything else.

How exactly does a machine come to see itself as an independent "thing"?

[Robin]

Originally posted by Interesting Ian
I told you. People just see the truth. There is no process involved. They just know by an immediate intuitive understanding. Maybe their minds simply see the Platonic forms.
Intuition can be wrong so it does not qualify as a method of knowing the truth.

But you are still not seeing the nature of the objection.

Lucas' entire argument critically hinges on this premise that a human can know something that a machine can't. And it comes down to a bald unsupported statement - "People just see truth".

Do you not think it is possible for someone to "just know" something and be wrong? Didn't Aristotle just know that the natural state of a body was at rest? Didn't a lot of people just know that the sun went round the earth? What about someone who says "I just know I will win the lottery this time"?

How do you distinguish between someone who believes that they see the truth and are wrong, and somebody who believes that they see the truth and do see the truth?

Lucas uses the example of someone capable of understanding Godel's theorems and using them to come to a logical conclusion:
We now construct a Gödelian formula in this formal system. This formula cannot be proved-in-the- system. Therefore the machine cannot produce the corresponding formula as being true. But we can see that the Gödelian formula is true: any rational being could follow Gödel's argument, and convince himself that the Gödelian formula, although unprovable-in-the-system, was nonetheless----in fact, for that very reason---true.
Note he says "... follow Godel's argument..." ie follow some logically valid process. Then your own admission:
I've read 2 of his articles. He explicitly states he does not mean this. After all, if it were a process, then an algorithm could simulate it. Which indeed you proceed to point out. Do you really think that Lucas is so dim as to not understand this?
So I have shown you where he explicitly states that the human knows the truth of the formula through a logically valid process. You have not shown me where he states anything else, explicitly or otherwise. So by your own argument above, Lucas' contention is refuted.

[Robin]

Originally posted by jay gw
Part of what gives people (most people) their self awareness is the physical form they are in. Everyone can perceive that they are distinct entities, separate from everything else.

How exactly does a machine come to see itself as an independent "thing"?
Easy - all our sense organs have artificial equivalents - cameras, microphones, machines for detecting odors, flavours - you could easily mimic touch. Then these are sent as signals through to the computer and it can work out the nature of reality as well as any human can.

But even if you could do all that and have an artificial intelligence that convinced people that it was conscious - if it was algorithmic it would not be conscious.

Suppose you take the machine code of your artificially intelligent machine and print it out, then get someone to run the algorithm manually - as you can with any algorithm. The results would be the same (albeit vastly slowed down). In this case can anybody still assert that a consciousness exists?

If not then how could you assert the same when the algorithm is run on some machine?

[Jorghnassen]

Originally posted by Robin
Easy - all our sense organs have artificial equivalents - cameras, microphones, machines for detecting odors, flavours - you could easily mimic touch. Then these are sent as signals through to the computer and it can work out the nature of reality as well as any human can.


Actually, human sensory perception is really non-trivial to emulate. One big advantage of the humain brain is blocking tons of unnecessary input that computers can't weed out so easily, even with fancy algoritms. Working out the nature of reality as well as any human is not for today...

[Robin]

Originally posted by Jorghnassen
Actually, human sensory perception is really non-trivial to emulate. One big advantage of the humain brain is blocking tons of unnecessary input that computers can't weed out so easily, even with fancy algoritms. Working out the nature of reality as well as any human is not for today...

But the question I was answering did not say "as well as any human" did it? An artificially intelligent machine would not need to process information in exactly the same way as a human to get self-awareness.

A computer can do a great deal of what a human mind does with sense data and what it does is probably enough to become aware of itself.

[jay gw]

A computer can do a great deal of what a human mind does with sense data and what it does is probably enough to become aware of itself.

It's possible that given the power of computers in the future, the amount of data coming in wouldn't be a problem.

AI has one definite advantage over humans - the lack of emotions to 'confuse' or distort it's judgment! Emotions may work to help thinking, but they can also really create false ideas/perceptions.

A machine will never invent 'god' to explain anything!

[Robin]

Originally posted by jay gw
It's possible that given the power of computers in the future, the amount of data coming in wouldn't be a problem.

AI has one definite advantage over humans - the lack of emotions to 'confuse' or distort it's judgment! Emotions may work to help thinking, but they can also really create false ideas/perceptions.

A machine will never invent 'god' to explain anything!

An artificially intelligent machine might well have machines, especially it works using processes similar to those in animal brains. And it might well decide to believe in God!

[Jorghnassen]

Originally posted by jay gw
It's possible that given the power of computers in the future, the amount of data coming in wouldn't be a problem.

AI has one definite advantage over humans - the lack of emotions to 'confuse' or distort it's judgment! Emotions may work to help thinking, but they can also really create false ideas/perceptions.

A machine will never invent 'god' to explain anything!

If emotions and religion weren't useful in some way, they wouldn't exist (one can argue the former is much more useful than the latter, but anyway). Now who is to say emotions aren't required for self-awareness?

[T'ai Chi]

Originally posted by jay gw

A machine will never invent 'god' to explain anything!

Unless it starts to think about where it came from, where its designers came from, or what the ideal computer is. ;)

[Robin]

A machine will never invent 'god' to explain anything!

In fact if you think about it an artificial intelligence will be able to see the gods (gods given that there will probably have been a design team) and have a chat with them. The AI may well then ask, "so tell me, who designed and built you guys?"

[Jorghnassen]

42.

/you all knew this was coming...

[Interesting Ian]

Originally posted by Robin
Intuition can be wrong so it does not qualify as a method of knowing the truth.

But you are still not seeing the nature of the objection.

Lucas' entire argument critically hinges on this premise that a human can know something that a machine can't.



This is true. Obviously if people deny this, then the Goedelian argument fails. Argue about this with Lucas then. He says that there is something we can see to be true which a machine cannot i.e a Goedelian sentence. Why don't you and the other people on here email him and argue it out?? I don't know if this is true or not. I simply say that any other argument that people have come up with is irrelevant. They have either not read Lucas and my contributions to this thread, or they have not understood.

But as I say, if you simply baldy assert that there are no Goedelian sentances which computers cannot see to be true, or in as much as they truly cannot see some sentence is true, then neither can we, and everyone agrees with this apart from Lucas, Penrose, and almost certainly Goedel then what is the purpose of this thread???




And it comes down to a bald unsupported statement - "People just see truth".



Yes of course they can!



Do you not think it is possible for someone to "just know" something and be wrong?



They didn't know it then did they?? :rolleyes:


Didn't Aristotle just know that the natural state of a body was at rest? Didn't a lot of people just know that the sun went round the earth? What about someone who says "I just know I will win the lottery this time"?


Yeah, mystical experiences is like when some fool says he knows he will win the lottery. :rolleyes:

Look, I've had enough of the inane arguments on this thread. I'm going.


Note he says "... follow Godel's argument..." ie follow some logically valid process. Then your own admission:

So I have shown you where he explicitly states that the human knows the truth of the formula through a logically valid process. You have not shown me where he states anything else, explicitly or otherwise. So by your own argument above, Lucas' contention is refuted. [/B]

No! "Follow" does *not* necessarily mean a logically valid process. He simply means that the commuincator has effectively communicated what he wanted to convey!

That's it. I've had enough.

[69dodge]

Originally posted by Interesting Ian
This is true. Obviously if people deny this, then the Goedelian argument fails. Argue about this with Lucas then. He says that there is something we can see to be true which a machine cannot i.e a Goedelian sentence.A Goedelian sentence is one which is so constructed as to be true if and only if the machine in question cannot prove it. Or, less precisely but perhaps more understandably, it is one which says, "the machine cannot prove me." Therefore, if the machine can "prove" it, it is necessarily false. And so, if we assume that the machine cannot prove any false statements, the Goedelian sentence is necessarily unprovable by the machine and therefore true.

Lucas is trying to demonstrate that he is different from the machine. Naturally, in the course of his demonstration, he may not assume that he is different from it; that would be circular reasoning. But if he allows for the possibility that he is identical to it, how can he correctly claim to see unconditionally that the Goedelian sentence is true? If he "sees" that it's true, and he happens to be identical to the machine, then the machine also can "see" that it's true. But that would make it false!

If he does not wish to "see" anything as true which might turn out actually to be false, and if he does not simply assume that he is different from the machine, then he cannot claim to see that the Goedelian sentence is true. But then his entire argument falls apart.

[jay gw]

If emotions and religion weren't useful in some way, they wouldn't exist (one can argue the former is much more useful than the latter, but anyway). Now who is to say emotions aren't required for self-awareness?

But emotions can't be given to machines.

The idea of god may hit the AI at a certain point, but it's my opinion that culture is responsible for 90 percent of religious beliefs.

That being the case, machines don't have a church or a god that looks like C3P0.

[Donks]

Originally posted by jay gw
But emotions can't be given to machines.

Hmmm, how do you know?

[drkitten]

Originally posted by jay gw
But emotions can't be given to machines.

So you assert. I have yet to see a demonstration one way or another.

And I have seen a lot of emulations of emotions in an effort to get realistic "human-like" behavior. Oddly enough, the usual effect of these emulations is to make the machine's behavior less intelligent, by an objective criterion, than before. Which, of course, fits in with our observation of humanity -- when in the grips of strong emotions, people make mistakes they otherwise wouldn't.

[Robin]

Interesting Ian
But as I say, if you simply baldy assert that there are no Goedelian sentances which computers cannot see to be true, or in as much as they truly cannot see some sentence is true, then neither can we, and everyone agrees with this apart from Lucas, Penrose, and almost certainly Goedel then what is the purpose of this thread???

But I didn't baldly assert it did I? I made a logical refutation to Lucas' argument which you agreed with. You just didn't agree with my understanding of his argument.

"Follow" does *not* necessarily mean a logically valid process
But "argument" does. Particularly "Godel's argument". If Godel had only clearly communicated his ideas then nobody would remember him.

I don't think you can co-opt Godel into the debate - he was a convinced dualist, yet apart from a single statement he did not use his theorems to support the notion. He probably realised the futility.