Science of consciousness. [Archive]

Yahweh

13th October 2003, 06:09 PM

Originally posted by hammegk
Yeah, they don't have human consciousness. However, that is not necessarily the problem some see with materialism. ;)
Feel free to enlighten me.

Now quarks, who knows? Leptons anyone? :D Ah, the Higgs boson, huh?
"Math is stupid, when am I ever gonna use fractions in real life"... Failure to understand the way a science (or math) works isnt a reason to dismiss it as flimflam.

There is a very nice Mormon girl who sits behind me in my Physics class. Physics comes very easily for me (I dont expect to learn too much from a highschool physics class... oh well...). The Mormon girl could recite the entire Book of Mormon off the top of her head, she's failing the Physics class. She tells me "there are just some things that we know exist in the world but cant be explained by science". Do you understand the significance of this little anecdote ;) ?

While I couldnt tell you much about Leptons, Muons, Hadrons, or anything at all about Elementary and Theoretical Particle Physics, I think I would be correct in assuming it wouldnt be the right direction to go in calling the stuff "bunk" without having a redumentary understanding of the stuff. I'm sure QuarkChild and Stimpy could teach us volumes.

Feel free to pick and defend the life/non-life boundary. Once you have "life", consciousness seems to increase with complexity -- whether provided by chance or by design -- at any rate.
Ah, the "irreducibly complex" arguement.

A fern isnt conscious, mice are, rocks arent, neither is water, insects (there conflicting views to whether they have any cognitive ability - Its my opinion that they dont or there ability is extremely limited - but no one doubts they are alive... unless you found a dead bug), protists and bacteria are considered living, my computer is not alive.

Usually, I would go into the differences between a virus (which is considered to be non-living in biology) and viroid (smaller than a virus, consists solely a single string of RNA, but is [I think] considered to be "living" in biology), but I dont really have the patience to list their differences.

Science is fun!

Upchurch

13th October 2003, 08:57 PM

Originally posted by Yahweh

Ah, the "irreducibly complex" arguement. I've never heard that one. Or rather, I probably have since you've applied it to hammegk's argument, but I've never heard it called that before. Do you have a reference I could read?

Yahweh

13th October 2003, 09:21 PM

Originally posted by Upchurch
I've never heard that one. Or rather, I probably have since you've applied it to hammegk's argument, but I've never heard it called that before. Do you have a reference I could read?
Heres something from TalkOrigins:
http://www.talkorigins.org/faqs/behe/icsic.html
(Its a long read...)

In a nutshell, its basically an arguement that reads "That is so remote/there are too many 'factors', that it didnt happen", its a common logical fallacy that has a habit of ignoring accepted science althogether. Some irreducibily complex arguements are phrased "well, that and that had to happen, that and that too, all to perform this one task, they couldnt have come together through small changes over time" (if you've ever heard a creationist mention "the 'eye' arguement" when "refuting" Evolution). Its not considered an arguement at all.

Q-Source

14th October 2003, 10:39 AM

Originally posted by Upchurch
I thought about posting this in Science, but there's been a lot of talk of this topic in terms of materialism/immaterialism lately, so I thought I'd post it here.

The show (http://www.npr.org/programs/totn/)

How do biology, emotion and cognition give rise to our sense of self? This week, a University of Utah conference tries to answer that question. We'll take an interdisciplinary look at the science of consciousness.

Hey Upchurch,

I thought that Science had already answered that question... :roll: :rolleyes:

Yes, Science is still trying to explain how matter gives rise to our sense of self, but those damn scientific materialists find it soooooo difficult to understand it. I wonder why. :rolleyes:

Q-S

neutrino_cannon

14th October 2003, 11:32 AM

Originally posted by Q-Source

Hey Upchurch,

I thought that Science had already answered that question... :roll: :rolleyes:

Yes, Science is still trying to explain how matter gives rise to our sense of self, but those damn scientific materialists find it soooooo difficult to understand it. I wonder why. :rolleyes:

Q-S

What's so difficult about conscienceness as being a completely materialistic entity? I'm sure most animals look quite interesting from the inside of thier skulls.

hammegk

14th October 2003, 11:48 AM

Originally posted by Yahweh

Feel free to enlighten me.
Sorry, but you will have to check with one of our Illuminators; I have no interest in persuading you or anyone to accept my viewpoint. I'm more curious as to how you can sustain yours.

"Math is stupid, when am I ever gonna use fractions in real life"... Failure to understand the way a science (or math) works isnt a reason to dismiss it as flimflam.

There is a very nice Mormon girl who sits behind me in my Physics class. Physics comes very easily for me (I dont expect to learn too much from a highschool physics class... oh well...). The Mormon girl could recite the entire Book of Mormon off the top of her head, she's failing the Physics class. She tells me "there are just some things that we know exist in the world but cant be explained by science". Do you understand the significance of this little anecdote ;) ?
Yes. Do you?

While I couldnt tell you much about Leptons, Muons, Hadrons, or anything at all about Elementary and Theoretical Particle Physics, I think I would be correct in assuming it wouldnt be the right direction to go in calling the stuff "bunk" without having a redumentary understanding of the stuff. I'm sure QuarkChild and Stimpy could teach us volumes.
Well, at least you can read & regurgitate.

Ah, the "irreducibly complex" arguement.
Actually, no. We could I suppose discuss the boundary conditions of the Higgs Field, assuming that it exists.

A fern isnt conscious, mice are, rocks arent, neither is water, insects (there conflicting views to whether they have any cognitive ability - Its my opinion that they dont or there ability is extremely limited - but no one doubts they are alive... unless you found a dead bug), protists and bacteria are considered living, my computer is not alive.

Usually, I would go into the differences between a virus (which is considered to be non-living in biology) and viroid (smaller than a virus, consists solely a single string of RNA, but is [I think] considered to be "living" in biology), but I dont really have the patience to list their differences.
Yeah, you could collect stamps too. Neither will provide answers to some questions.

Science is fun!
So is life. Which science text are you using for your morals & ethics?

Psydox

14th October 2003, 11:50 AM

I agree with what is being said but how does being aware or having the capacity to be aware relate to the ability to feel ? I don't mean the kind of feel like when you experience it though sensory perception such as touch. I mean the kind of feel like you get when you get dumped in a relationship and you get what feels like pain in your heart (hence the word heartbreak). The thing is, how was it that you felt it if it did not come as the result of say something like someone literally sticking a knife in your chest.

Yeah one might say it is the chemical reaction going on but what is chemical reaction due to ?.... electromagnetic fields. So then when we throw our computer away, why doesn't it feel that perception of heartbreak to ?...that's what I'm not grasping yet.

It makes me think of Data from Star Trek. He was aware and yet he did not have responses such as this. Yeah I know Data was a fictional character on TV however, this raises another question for me...in talking about using the silicon for brain transplant, and depending on where the source of feeling like I described above comes from could that then not present the risk of losing the ability to feel ?

Franko

14th October 2003, 12:23 PM

The Scientific Method states that only that which can be empirically observed and verified is considered “Scientific” (or logical, provable, testable).

So what is the first thing that a Materialist does in the morning when he gets out of bed …?

… Why, he urinates all over the scientific method by assuming that “Matter” exist independently of observation. This is the foundational premise of the Religion of Materialism. It cannot be verified, tested, or observed. You simply have to take it on Blind Faith. Of course the big problem with making this assumption is that if it happens to be wrong (and there is empirical evidence that it is wrong) than all subsequent conclusions drawn from this premise will be similarly flawed in some fundamental way.

I lack-a-belief in the Religion of Materialism.

I am an Amaterialist.

(of course the Imtheists tend to call me an immaterialist)

Pahansiri

14th October 2003, 12:35 PM

hammegk

14th October 2003, 01:04 PM

Originally posted by Pahansiri

Do you really believe that a planet that is so far off that only in the last year due to better and better technology we have been able to see, did not exist until the second the scientist saw it?

Damn, do interpretations of words differ.

So far as I know, F has never said anything that would imply he holds such a stance.

Pahansiri

14th October 2003, 01:45 PM

Originally posted by hammegk

Damn, do interpretations of words differ.

So far as I know, F has never said anything that would imply he holds such a stance.

Hello Franko I thought you would use this hammegk to respond rather then really conduct a conversation.. :(

But just to help please read your post again, well OK hammegk read Franko’s ( wink wink) post again

… Why, he urinates all over the scientific method by assuming that “Matter” exist independently of observation. This is the foundational premise of the Religion of Materialism. It cannot be verified, tested, or observed.

if you remember you said in our last conversation you said :

So you are claiming that the Truth is the Truth independent of observation?

That sounds more like an unsupported and untestable assertion.

and

Here you I mean Franko did respond in a way on another thread but mainly avoided the main point but did say I would say that I do not believe the planet you are referring to exist.

Perhaps my friend you do not read “Franko’s” post well enough but I forgive you and wish you well.. :rub:

Dancing David

14th October 2003, 03:47 PM

There are plenty of fine answers to the questions that UpC has asked, what i notce though is the following.

When I have discussed the chain of biological events that lead a person percieving a color, I am told that they are still irreducable.

If you discuss the components of consiousness in a scientific sense, then you are told that they are irreducable.

So the issue as I see it is not that science has not made steps towards describing consiousness, it is just that the A-materialists will go and say it doesn't matter.

So while we can talk about the biological basis of life, they will just not listen to our viewpoint, even when we say that there could be other forms of awareness but that we haven't ben able to study them.

The real problem is this: the immaterialists can not prove anything, they can not prove that there is anomolous cognition, they can prove that there is a soul that transmigrates, they can come up with all these cool theories and speculations but they can't prove anything!

This being the philosophy forum I have to say that philosophy is a very use ful tool, and yes we should question the nature of reality.
But it doesn't amtter, a thousand years from now , we will have better medicine, better houses and hopefuly a better world, all care of the materialists who studied the world and found out it's patterns. Wether they are material or mind. What will the immaterialists have to point to?

I suppose that we will still have 'healing touch' and no proof of anything.

But hey, eletricity is a grand thing as is the flush toilet.

Dancing David

14th October 2003, 03:59 PM

Originally posted by Franko
The Scientific Method states that only that which can be empirically observed and verified is considered “Scientific” (or logical, provable, testable).

So what is the first thing that a Materialist does in the morning when he gets out of bed …?

… Why, he urinates all over the scientific method by assuming that “Matter” exist independently of observation.

No this is not an assumption of science at all, although it is a belief held by many scientists. Science does merely explore the world that can be observed and does not ask the ontological questions. Instead, can you suggest anything that might demostrate your POV?
Also the mothods of science point in the direction of matter having a very long life time, I think the current half life of a proton is way up there. Based on observation. So does the fluid in the detectors just go away when there is no human there?

This is the foundational premise of the Religion of Materialism. It cannot be verified, tested, or observed.

Could you point me in the direction of any contrary evidence. When I go outside at night, my eyes when see the light of stars that i believe are very far away. Are you saying that the light just appears because I step outside? Or are you saying that you don't have eyes?

You simply have to take it on Blind Faith. Of course the big problem with making this assumption is that if it happens to be wrong (and there is empirical evidence that it is wrong)

dear Franko, what evidence is that?

than all subsequent conclusions drawn from this premise will be similarly flawed in some fundamental way.

[B] It doesn't matter if matter is particles, faeries or little monkeys on motor scooters, the results of scientific observation will still approximate the behavior of the little buggers

I lack-a-belief in the Religion of Materialism.

I am an Amaterialist.

(of course the Imtheists tend to call me an immaterialist)

WooWho

I got my head checked by a jumbojet!

Okay, Franko what evidence is there?

Oh, solopism, that old worn out argument.

It doesn't matter at all to the scientist if the world is the product of matter or the product of mind. It is the ability to make and test predictions.

*(and there is empirical evidence that it is wrong)*

*(and there is empirical evidence that it is wrong)*

*(and there is empirical evidence that it is wrong)*

You haven't even got a pair of twos in that hand Franko, I raise you and call!

hammegk

14th October 2003, 05:10 PM

Originally posted by Pahansiri

quote Franko:
--------------------------------------------------------------------------------
So you are claiming that the Truth is the Truth independent of observation?

That sounds more like an unsupported and untestable assertion.
--------------------------------------------------------------------------------

quote Franko:
--------------------------------------------------------------------------------
I would say that I do not believe the planet you are referring to exist.
--------------------------------------------------------------------------------

How do you think this adds up to implying what you ask:

quote:
--------------------------------------------------------------------------------
Originally posted by Pahansiri

Do you really believe that a planet that is so far off that only in the last year due to better and better technology we have been able to see, did not exist until the second the scientist saw it?
--------------------------------------------------------------------------------

I fail to see the relationship.

Yahweh

14th October 2003, 06:17 PM

Originally posted by Franko
The Scientific Method states that only that which can be empirically observed and verified is considered “Scientific” (or logical, provable, testable).
WRONG!

You make yourself look very bad when you make up "facts" that are clearly not facts.

Franko, it'd be more helpful if you just gave up all together.

Pahansiri

14th October 2003, 06:42 PM

Originally posted by hammegk

How do you think this adds up to implying what you ask:

I fail to see the relationship. :rub: I'm sure you do.:rub:

sorgoth

14th October 2003, 07:37 PM

Here's my take: We can look at other people's minds, we can take psychology courses, we can observe their behavior, but we can never really experience what they are experiencing(How do I know if your red is the same as my red?, and questions like that), and can thus never really understand their conciousness. The only conciousness we can really be aware of is our own, yet, by necessity, our mind is more complex than we can imagine (Since it would require us to imagine our imagination, and then some, which we all know is impossible due to it's infinite loop status).

To put it simply, though it is midly frustrating to ponder, I think our mind is simply not equipped to view itself. Much like insects can never understand mathematics, as they are not evolved to be capable of it, our minds are lacking the ability to ponder themselves. We are capable of many things that have allowed us to come as far as we have (And for much, much farther), language and mathematics and a host of other skills that define human intelligence. Alas, we are not angels or Gods, and thus our boundaries of knowledge are limited. Let this not burden us, and move on to things that can be explained by mathematics and language (The two mediums that transmit information best).

Feedback, anyone?

Yahweh

14th October 2003, 08:50 PM

Originally posted by Franko
… Why, he urinates all over the scientific method by assuming that “Matter” exist independently of observation. This is the foundational premise of the Religion of Materialism. It cannot be verified, tested, or observed. You simply have to take it on Blind Faith. Of course the big problem with making this assumption is that if it happens to be wrong <div style="background:#FFFFDD">(and there is empirical evidence that it is wrong)</div> than all subsequent conclusions drawn from this premise will be similarly flawed in some fundamental way.
Style note: Contradicting yourself (claiming "the big problem with making an assumption is that if it happens to be wrong", then stating "empirical evidence that is wrong" is self-defeating) isnt a good way to present an arguement... unless I've misunderstood you.

You seem to be one who believes "I know at least I exist because I am experiencing consciousness". You dismiss urination, although the person performing the act is very much experiencing sensations (sight, feeling, sound, and even smell... possibly taste if they have terrible aim), why would you doubt your experiences, or is sensasation like that an illusion? (Yahweh knows how to use that circular Solipsistic reasoning also, the question is now will you make one of 3 replies I can think of that doesnt contradict one or another of your beliefs.)

Yahweh

14th October 2003, 08:57 PM

Originally posted by sorgoth
Here's my take: We can look at other people's minds, we can take psychology courses, we can observe their behavior, but we can never really experience what they are experiencing(How do I know if your red is the same as my red?, and questions like that), and can thus never really understand their conciousness.

...snip...

Feedback, anyone?
Well, unfortunately I cant go diving into another person's "mind" and experience everything they experience, but I can say with reasonable certainty that the "red" I see is the same as the "red" another person sees (assuming both of us are normal and healthy with no vision problems). Both our eyes look and function the same, the "wiring" in our brain processes visual stimuli in the same way, I wouldnt know a reason why we wouldnt "see the same red" as one another.

(Its not really a question Philosophy can answer too well, its better suited for general biology. One of my Philosophies is: Keep Philosophy and Science seperate, otherwise you'll get nothing accomplished.)

Yahweh

14th October 2003, 09:00 PM

Originally posted by hammegk
So is life. Which science text are you using for your morals & ethics?
Morality and Ethics have nothing to do with Mechanical Physics, those are best left to Philosophy. However, if that answer isnt satifying enough, I would say Sociology, Psychology, and other social sciences are the only things I could give you that would best tackle intangible concepts such as morals and ethics.

Peter Soderqvist

15th October 2003, 01:07 AM

TO JET GRIND

You wrote 10-14-2003 12:13 AM: As for anyone who tells you that materialism can't be true because individual neurons are not self-aware, tell them that by that argument water cannot exist as individual hydrogen and oxygen atoms are not wet.

Soderqvist1: I think that a computer or a Turing Machine is partly analogous to human mind, the analogous part is described by you, so I don't need to elaborate it further than this; random strings or letters like; U F L M I D N, are meaningless, but these meaningless strings in a correct pattern can give us; MINDFUL, so the pattern is the key, not its component parts!

You wrote further the more I read in the fields of cognitive neuroscience and evolutionary psychology, the more convinced I am that this hypothesis is true. I have my prejudices as computer tech-head, but I see no ontological difference between the functions of your neural-network and a silicon micro-processor (or a series of them). Such has become consensus among cognitive science and AI. researchers.

Soderqvist1: I have read 5 books (Daniel Dennet 's Darwin's Dangerous Idea, The Mind's I, by Dennet & Hofstadter, The Fabric of Reality by David Deutsch, Gödel, A life of Logic, Paradigms lost, and its sequel, Paradigms regained, by John L. Casti! None of them has seen any problem between incompleteness theorem and hard human AI, but on the other hand, I have never seen my question formalized, or answered by them either! Casti 's was the last one I read, and he has said that Godel's theorem doesn't apply to computers, because they have only finite storage units, they cannot deal with uncountable numbers, which needs infinite!

A recipe is a theorem, baking is its proof sequences, and its end product let's say; a chocolate cake is the proof that the theorem is consistent and truth! But there are abstract cakes which have no recipes, because our theorems are incomplete! David Deutsch has said something similar, namely; A Universal Virtual Reality Machine is some kind of Universal Turing Machine, and is thus able to rend every possible physical environment into virtual reality, but there are abstract mathematical environment which cannot be rend into virtual reality, and he has coined these abstract environments as Cantgotu (Cantor, Godel, Turing) environments!

So my point of view is that; whatever amount of strings we use as input to the computer, Gödel 's incompleteness theorem will never be its output, and it follows from that, that a computer cannot simulate AI hard human cognitive state of Kurt Gödel, nor any other mathematical human mind! So I think Roger Penrose was on to something in his book, The Emperor's New Mind, when he said that; a computer cannot simulate a non-computational-mathematical insight, therefore; AI hard human is false to fact!

Nagel and Newman, Gödel 's Proof!
Given any consistent set of arithmetical axioms, there are true mathematical statements that cannot be derived from the set... Even if the axioms of arithmetic are augmented by an indefinite number of other true ones, there will always be further mathematical truths that are not formally derivable from the augmented set.

Hofstadter, Gödel, Escher, Bach
Gödel showed that provability is a weaker notion than truth; no matter what axiom system is involved. http://www.miskatonic.org/godel.html

Upchurch

15th October 2003, 06:42 AM

Originally posted by Q-Source

I thought that Science had already answered that question... :roll: :rolleyes: Yeah, Q. Whenever a scientific breakthrough happens, the first place a scientist goes is NPR.
:rub:
Yes, Science is still trying to explain how matter gives rise to our sense of self, but those damn scientific materialists find it soooooo difficult to understand it. I wonder why. :rolleyes: And immaterialists have it all wrapped up, right?

No matter how much we know about something, there is always more questions to ask. Science is a process.

hammegk

15th October 2003, 07:27 AM

Originally posted by Pahansiri
:rub: I'm sure you do.:rub:
Think about it. Maybe you can fashion an answer to my question.

In case you've forgotten:

You asked

Do you really believe that a planet that is so far off that only in the last year due to better and better technology we have been able to see, did not exist until the second the scientist saw it?

Why do you think Franko would believe that to be a true statement?

If you can't answer, what is your point?

Originally posted by Yahweh

Morality and Ethics have nothing to do with Mechanical Physics, those are best left to Philosophy. However, if that answer isnt satifying enough, I would say Sociology, Psychology, and other social sciences are the only things I could give you that would best tackle intangible concepts such as morals and ethics.
Thanks, but I do fine with my basis for ethics & morals (imo, of course ;) ). Which knowledge do think will best provide you a satisfying life; math-engineering-science, or a good working basis for your ethical & moral values? For your spouse, kids, family, society?

No answer required, thanks anyway.

Peter Soderqvist: Do you consider yourself a dualist or an idealist/monist? BTW, no matter how many times our materialists/atheists/scientists read your words, they do not understand them; why is that?

Pahansiri

15th October 2003, 08:01 AM

LOL my friend hammegk..

You write Think about it. Maybe you can fashion an answer to my question.

I answered your question and as is the case most times with you under all your personas you ignored it. I do find it ironic you make such a statement when you will not answer questions and in fact said just yesterday in this same thread, to Yahweh when they asked you to prove or explain something you said.

Originally posted by Yahweh

Feel free to enlighten me.

Originally posted by hammegk.
Sorry, but you will have to check with one of our Illuminators; I have no interest in persuading you or anyone to accept my viewpoint. I'm more curious as to how you can sustain yours.

I believe the proper translation of that statement was “ I can’t explain what I said or believe I don’t really know”

In case you've forgotten:

As I demonstrate I forget little such proof being using your own post to contradict your statements.

But I will review for you again.

Franko ( wink wink) said

Originally posted by Franko:
So what is the first thing that a Materialist does in the morning when he gets out of bed …?

… Why, he urinates all over the scientific method by assuming that “Matter” exist independently of observation. This is the foundational premise of the Religion of Materialism. It cannot be verified, tested, or observed.

Here clearly saying materialist are wrong and wetting themselves ( you, or Franko lol can be so 8th grade) for believing that matter exist without being observed.

I responded and showed his belief to be illogical and wrong:

Franko I tried to get you to respond to this before perhaps now.

Do you really believe that a planet that is so far off that only in the last year due to better and better technology we have been able to see, did not exist until the second the scientist saw it?

As you see it can be verified, tested, or observed.

You then responded:

Hammegk said : Damn, do interpretations of words differ.

So far as I know, F has never said anything that would imply he holds such a stance.

As we know I then went on to prove you wrong posting what you, I mean Franko said.

Example 1

Originally posted by Franko:
So what is the first thing that a Materialist does in the morning when he gets out of bed …?

… Why, he urinates all over the scientific method by assuming that “Matter” exist independently of observation. This is the foundational premise of the Religion of Materialism. It cannot be verified, tested, or observed.
Example 2

So you are claiming that the Truth is the Truth independent of observation?

That sounds more like an unsupported and untestable assertion.

And 3:

I would say that I do not believe the planet you are referring to exist.

For one being truthful they will see that yes Franko truly believes that matter does not exist until it is observed. You really do make this too easy my friend.

Why do you think Franko would believe that to be a true statement?

If you can't answer, what is your point?

Lol read the above again, stop and repeat.

It is clear truth and facts mean little to you when it comes to your beliefs or this game you play.

Come on now I know you can be honest if you really try.

hammegk

15th October 2003, 08:38 AM

Your lack of understanding hinges on your answer to the question: "What is an "observer?". You appear to be off the path.

As for "enlightening" 14 yr olds, go for it should you feel you wish to expend the effort. ;)

Pahansiri

15th October 2003, 08:48 AM

Originally posted by hammegk
Your lack of understanding hinges on your answer to the question: "What is an "observer?". You appear to be off the path.

:rub: as I said do not allow facts to get in your way my friend. :rolleyes:

As for "enlightening" 14 yr olds, go for it should you feel you wish to expend the effort. ;) Could you say this in English?

Franko

15th October 2003, 09:32 AM

Franko:
Why, he [the Imtheist] urinates all over the scientific method by assuming that “Matter” exist independently of observation.

Dancing David:
No this is not an assumption of science at all, although it is a belief held by many scientists.

Is it a “scientific” belief, or a dogmatic (religious) one?

… Because a “scientist” who holds a non-scientific fundamental assumption about “science” has ceased to be a scientist, and instead has become a priest.

Could you point me in the direction of any contrary evidence?

You believe that something exist independent of empirical observation or verification, and you want me to explain (or prove) why your unsupported, unverifiable, unfounded, unproveable, untestable claim is scientifically invalid???

Sure, I’ll be happy too. But first you have to explain your understanding of “the scientific method”.

Oh, solipsism, that old worn out argument.

Yes, I guess solipsism isn’t much of a problem when the solipsist can simply pretend that the “matter” is more real than the solipsist. Unfortunately the solipsist can attest to his own independent existence, but not to the independent existence of the “matter”.

It doesn't matter at all to the scientist if the world is the product of matter or the product of mind. It is the ability to make and test predictions.

That is absolutely correct.

So why do so “many” imtheists want to claim that this is NOT the case? I guess one can only attribute it to complete and utter hypocrisy.

According to your worldview it would seem that it is more “parsimonious” (and “logical”) to make a primary foundational unsupported assumption than it is to NOT make that assumption.

hammegk

15th October 2003, 09:41 AM

Originally posted by Pahansiri

:rub: as I said do not allow facts to get in your way my friend. :rolleyes:
I still wait for you provide a "fact"; your answer to "Who is the "observer" some of us refer to?" Take a guess. Or ask dao.

Could you say this in English?

It was English, and it stated my opinion of the "Yahweh" personna.

Pahansiri

15th October 2003, 09:55 AM

Originally posted by hammegk

I still wait for you provide a "fact"; your answer to "Who is the "observer" some of us refer to?" Take a guess. Or ask dao.

Could you say that in English? I still wait for you provide a "fact";?? :eek: :roll:

As to the Question as to “who” is the observer, the statement is yours ( well the Franko “personna” which is spelled persona in English ) about your Goddess etc being the “Observer” in your dance and word games so the burden is yours to
1- Provide who YOU believe this “Observer”
2- Prove the existence of this “Observer”

You make this too easy.

Remember your or Franko’s statement was

Originally posted by Franko:
So what is the first thing that a Materialist does in the morning when he gets out of bed …?

… Why, he urinates all over the scientific method by assuming that “Matter” exist independently of observation. This is the foundational premise of the Religion of Materialism. It cannot be verified, tested, or observed.

Here you see he attacks a Materialist for believing not believing as he/you believe in that matter must be observed to exist.

You see the Materialist does NOT believe ( nor do I ) in your Goddess etc so the observer I and they refer to is us the thing we can prove exist.

You REALLY make this too easy to show you as being silly.
:rub:

Franko

15th October 2003, 10:02 AM

Pahansiri, my barely coherent little friend, are you a Materialist -- Yes or No?

Pahansiri

15th October 2003, 10:11 AM

Originally posted by Franko
Pahansiri, my barely coherent little friend, are you a Materialist -- Yes or No?

oops Franko you were supposed to post this post under your hammegk handle…lol You are too easy.

Supposed to post this post under your hammegk handle…lol You are too easy.

As you see your Goddess does not control you, I do.

Franko

15th October 2003, 10:22 AM

As you see your Goddess does not control you, I do.

Well I am glad you have finally come to your senses and acknowledged that we are just figments of your imagination, of course I’ve been telling you that all along.

It's a long way down little discordian ...

Pahansiri

15th October 2003, 10:28 AM

Originally posted by Franko

Well I am glad you have finally come to your senses and acknowledged that we are just figments of your imagination, of course I’ve been telling you that all along.

It's a long way down little discordian ...

LOL Franko you are a fine dancer.

As you know I have already disproved your stance as to you being a figments of my imagination but nice try to use this to avoid answering questions or supporting any statements of yours.

By the way It's a long way down little discordian ... I am sure you were trying to spell discordant. You spell very poorly under both your handles when you become angry.

:rub:

hammegk

15th October 2003, 11:01 AM

Originally posted by Pahansiri

Could you say that in English? ??
I did. What is your first language?

As to the Question as to “who” is the observer, the statement is yours ( well the Franko “personna” which is spelled persona in English ) about your Goddess etc being the “Observer” in your dance and word games so the burden is yours to
1- Provide who YOU believe this “Observer”
2- Prove the existence of this “Observer”

You make this too easy.

Naw, you still don't get it do you? Who do you think is "the observer".

Que pasa, dao didn't answer? Try pounding sand; relieve some of your tensions. ;)

Pahansiri

15th October 2003, 11:29 AM

Originally posted by hammegk

I did. What is your first language?

Really?
This is English?

I still wait for you provide a "fact"; your answer to "Who is the "observer" some of us refer to?" Take a guess. Or ask dao.

You see in English as far as what I was thought in school what the sentence would read is Example:
I still wait for you to provide a fact ( or facts) concerning who is the "observer" that some of us refer to." Take a guess. Or ask dao.

Who is dao? You do not mean a man who is dead, do you? LOL How can I ask him anything... HELLOOOO

By the way his name is/ was Lao Tzu not "dao" and I am Buddhist not really Daoist.. Do you ever get anything right?

This is what a more proper English sentence should be. But perhaps English is not your first language.

Also as I pointed out here in your statement It was English, and it stated my opinion of the "Yahweh" personna.

You misspelled persona. Perhaps in the country of your origin you spell in the poor fashion you do and I respect that.

Naw, you still don't get it do you? Who do you think is "the observer".

I know you are dancing as fast as you can it must make you very dizzy.

As I pointed out, yes I know this is truth and facts and you clearly are bother by such but I will post again in hope you can grow to understand. Perhaps even muster an honest answer.

As to the Question as to “who” is the observer, the statement is yours ( well the Franko “personna” which is spelled persona in English ) about your Goddess etc being the “Observer” in your dance and word games so the burden is yours to
1- Provide who YOU believe this “Observer”
2- Prove the existence of this “Observer”

You make this too easy.

Remember your or Franko’s statement was

Originally posted by Franko:
So what is the first thing that a Materialist does in the morning when he gets out of bed …?

… Why, he urinates all over the scientific method by assuming that “Matter” exist independently of observation. This is the foundational premise of the Religion of Materialism. It cannot be verified, tested, or observed.

Here you see he attacks a Materialist for believing not believing as he/you believe in that matter must be observed to exist.

You see the Materialist does NOT believe ( nor do I ) in your Goddess etc so the observer I and they refer to is us the thing we can prove exist.

You REALLY make this too easy to show you as being silly.

Que pasa, dao didn't answer? Try pounding sand; relieve some of your tensions. ;)

LOL, such a hypocrite, you will not answer any questions

One example being you have not answered any of mine or this

Originally posted by Yahweh

Feel free to enlighten me.

ally posted by hammegk.
quote: Sorry, but you will have to check with one of our Illuminators; I have no interest in persuading you or anyone to accept my viewpoint. I'm more curious as to how you can sustain yours.

Also your childish Try pounding sand; relieve some of your tensions. is the same silliness you posted to me some time back under your Franko handle.. LOL You make this just too easy.

Of course I feel no tensions but it is clear you for from such silly statements.

Try this conduct a mature respectful logical factual conversation. Answer questions ask of you as we do answer yours, be honest and mature and your anger will ease and your spelling will also improve.

:rub:

hammegk

15th October 2003, 11:48 AM

Thanks for your concern over my spelling & grammar. Do you recall something about timbers in some helpful person's eye vs. motes in the eye of another?

You could perhaps generate the courage to respond: 'I will not answer your question as to 'Who is the "observer"?'. Or would you care to go with an answer to "What moves? Wind, Flag, or Mind?".

And I'd thought pounding sand would an exercise you would find restful. ;)

Q-Source

15th October 2003, 12:08 PM

Originally posted by Upchurch
No matter how much we know about something, there is always more questions to ask. Science is a process.

My contention is not against Science, it is against scientific materialists that cannot understand that Science is a process and (within its own limitations) it is still trying to figure it out how consciousness and awareness arise. :rolleyes:

You see?, materialists are quick to make conclusions about consciousness that Science does not make.

Q-S

Pahansiri

15th October 2003, 12:12 PM

Originally posted by hammegk
Thanks for your concern over my spelling & grammar.

You are welcome. I as we all do make mistakes but I do not attack others. I.e. personal attacks so when someone attacks another by way of personal attacks I do point out their mistakes both in belief and in spelling.

You see my friend you are so often calling others names inferring they are dumb etc simply because they do not believe as you do. So often when you do this your spelling is so very poor, so I guess who is the dumb one?

But the fact is I do not believe you are dumb really in fact as I have said I believe you are intelligent. I believe as to beliefs you are not very honest but do believe you are an honest person. Your anger allows you to lose control and name call and spell poorly because you do not think clearly being driven by emotion and not logic.

That is what I believe.

Do you recall something about timbers in some helpful person's eye vs. motes in the eye of another?

Yes that is from the Christian Bible and I post it often to Christians who do what you are doing. I can post the passages if you like.

I assume you are saying I have misspellings? I am sure I do but can you post them for me rather then just accuse?

You could perhaps generate the courage to respond: 'I will not answer your question as to 'Who is the "observer"?'. Or would you care to go with an answer to "What moves? Wind, Flag, or Mind?".

My friend again you are
1; Dishonest. This being because I have answered several times and you know it. Rather then address my statement and facts and YOU answering you pull this silly trick. Do you really anyone falls for it?
2: More personal attacks, inferring I do not have “courage”. As we all know I address every single said to me and answer every question asked of me. You simply do not under this handle of the Franko handle.

Of course you out your “Franko-ism” more every post as you call me a coward again as you have done under the Franko handle in the past..

Immature silly games from people who can not answer a question as it relates to their beliefs or statements.

When will you answer any questions? The fact is as so many have demonstrated you really do not know what you believe.

And I'd thought pounding sand would an exercise you would find restful. ;)

A good example of when you can not say something intelligent say something stupid.:rolleyes:

jan

15th October 2003, 12:40 PM

Originally posted by Peter Soderqvist
Soderqvist1: I have read 5 books

I'm very impressed.

Originally posted by Peter Soderqvist
A recipe is a theorem, baking is its proof sequences, and its end product let's say; a chocolate cake is the proof that the theorem is consistent and truth!

Well, one could say, a theorem is like a cake, a proof is like a recipe how to make it.

Or one could say that a theorem is like the moon, mirrored in a lake in the autumn...

Now let's get serious. You have a claim:

Originally posted by Peter Soderqvist

So my point of view is that; whatever amount of strings we use as input to the computer, Gödel 's incompleteness theorem will never be its output, and it follows from that, that a computer cannot simulate AI hard human cognitive state of Kurt Gödel, nor any other mathematical human mind! So I think Roger Penrose was on to something in his book, The Emperor's New Mind, when he said that; a computer cannot simulate a non-computational-mathematical insight, therefore; AI hard human is false to fact!

I would say this point of view is refutated again and again by at least two of the five books you have read. "Gödel, Escher, Bach" is all about showing that you are wrong (think of it, Hofstaedter refuted you even before you made your claim).

But you even failed to state what you probably wanted to claim in a convincing manner.

First of all, it is a quite trivial task to make a computer output whatever Gödel has written. Since Gödel is dead and his work finite, this doesn't require much sophistication. Just output a constant string literal, and you are done.

There is a theorem Gödel has proved that uses the construction of a specific sentence within the formal framework of the Principia Mathematica (and this formal sentence is not one of Gödel's theorems, it is just used in one of his theorems). Gödel showed that is is possible to construct a similair sentence for any formal system that is similair to the formal system he was discussing. But this construction, once again, doesn't require infinite sophistication; in fact, I guess it would be rather trivial to mechanize this construction for several kinds of formal systems. Fortunately or unfortunately, there are many different kind of formal system, so it would be difficult to write a program that could "gödelize" any arbitrairy formal system with sufficient strength to contain Arithmetics. But note that Gödel also never formaly proved that all formal systems are incomplete: he only showed it for the Principia Mathematica in a formal manner, and it is obvious, but it has never been formally demonstrated, that a similair thing can be done for any other similair formal system.

But I assume that this is still not what you attempted to claim. I guess what you really wanted to claim is that a computer programm, as a formal system, can't prove all true mathematical sentences.

But what makes you think you can?

Franko

15th October 2003, 12:56 PM

But note that Gödel also never formaly proved that all formal systems are incomplete

Do you have an example of a formal system that is not incomplete as per Godel's theorem?

Dancing David

15th October 2003, 01:52 PM

Originally posted by Franko

Is it a “scientific” belief, or a dogmatic (religious) one?

Be;ief is belief, and something tha the scientific method can not really predict, is a mistaken scientific belief as invalid as a mistaken religous belief, of course ,belief is something that occurs in the abcense of knowledge.

… Because a “scientist” who holds a non-scientific fundamental assumption about “science” has ceased to be a scientist, and instead has become a priest.

Or like all people they hold beliefs not supported with evidnce.

You believe that something exist independent of empirical observation or verification, and you want me to explain (or prove) why your unsupported, unverifiable, unfounded, unproveable, untestable claim is scientifically invalid???

You were the one that siad you had the evidence, so where is it? You claimed that there was evidence to disprove materialism.

So you show your proof, I didn't make that claim.
[/B]

Sure, I’ll be happy too. But first you have to explain your understanding of “the scientific method”.
[/B] Already have, observable results leading to verification, say I make a trip and make notes of the location that I mark a tree on. My hypothesis is that if I give you an adequate description of the location of the tree that you can see my mark, and make one of your own.
If the tree is of mind or matter is not a question that the scientific method can answer. Either way, you can verify my experimental trip to the tree.

Yes, I guess solipsism isn’t much of a problem when the solipsist can simply pretend that the “matter” is more real than the solipsist. Unfortunately the solipsist can attest to his own independent existence, but not to the independent existence of the “matter”.

Do you know any tree, they are really nice and forgiving about the marks. They don't care if are thier dream or they are yours.

That is absolutely correct.

So why do so “many” imtheists want to claim that this is NOT the case? I guess one can only attribute it to complete and utter hypocrisy.

I guess the same sort of mechanism that makes them believe that protons have a very long halflife, it is subject to verification that an object existed prior to my observation of it, or at least it behaves that way.

According to your worldview it would seem that it is more “parsimonious” (and “logical”) to make a primary foundational unsupported assumption than it is to NOT make that assumption.
Now you act like Ian, and put words on my keyboards, I have my reasons to believe that matter exists and is subject to change, if it si a product of mind or impatial forces is moot.[/B]

Franko

15th October 2003, 02:17 PM

Dancing David:
Already have, [Scientific method equals(=)] observable results leading to verification.

What are the observable results leading to verification that “matter” exist independent of observable results?

You Discordians are so cute when you dance. ;)

Franko:
a “scientist” who holds a non-scientific fundamental assumption about “science” has ceased to be a scientist, and instead has become a priest.

Dancing David:
Or like all people they hold beliefs not supported with evidence.

No, no, no, my friend, we are not talking about a mere belief (like chocolate ice cream being better tasting than vanilla ice cream) we are talking about a fundamental assumption about the nature of science (reality/existence/the universe). And ANY person who claims that his “truth” is THE TRUTH (scientific or logical truth [metatruth]) yet bases all his assumptions on that initial unverifiable, untestable, unproveable assumption is no scientist … he’s a priest!

I guess the same sort of mechanism that makes them believe that protons have a very long halflife, it is subject to verification that an object existed prior to my observation of it, or at least it behaves that way.

Yes, but prior to Your observation does not mean that it existed prior to TLOP’s (“God’s”) observation.

Did this universe come into existence before or after The Laws of Physics (TLOP)?

Is it possible that the “big bang” happened first, and then TLOP came along afterwards? I don’t see how that could be? Perhaps you can explain it to me?

Franko:
According to your worldview it would seem that it is more “parsimonious” (and “logical”) to make a primary foundational unsupported assumption than it is to NOT make that assumption.

Dancing David:
Now you [edit] put words on my keyboards, I have my reasons to believe that matter exists and is subject to change, if it is a product of mind or impartial forces is moot.

But wait just a minute there cowboy!

You have failed to address the actual issue. If you have no logical reason or empirical evidence to suggest that “matter” exist independently of all (or any) observation then why on earth would you leap to such an utterly unfounded and untestable assumption??? Especially in light of the fact that this is the initial foundational premise upon which your entire worldview seems to rest?

I wouldn’t even stoop to calling that sloppy science … I would simply call it religious fanaticism and arrogant, hypocritical, blind faith.

Perhaps you can straighten me out, and help me to see the “light”?

Upchurch

15th October 2003, 02:47 PM

Originally posted by Q-Source

My contention is not against Science, it is against scientific materialists that cannot understand that Science is a process and (within its own limitations) it is still trying to figure it out how consciousness and awareness arise. :rolleyes: Q,

When you refer to science, who do you think it is you are refering to? Scientists study the properties and dynamics of the physical world: physics, chemistry, biology, etc. Which of these exist without the assumption of materialism? Scientists are materialists, Q. They study the material world.

And yes, I do realize it is an assumption, but I also realize that it is a perfectly valid assumption based on the apparent consistancy and dependability of the material world.
You see?, materialists are quick to make conclusions about consciousness that Science does not make.Just about as quick as immaterialists are to deny the existance of the material world. Why? Based on what? Why claim that some of your senses are feeding you illusions and others aren't?

hammegk

15th October 2003, 02:59 PM

Originally posted by Pahansiri

A good example of when you can not say something intelligent say something stupid.:rolleyes:

LOL. Pot:Kettle:Black. ;)

After pounding sand you are still tense, huh? :confused: Try again -- remember to use the mindfulness & meditation parts this time. :) I would hate to have to begin referring to you as Pahansilly.

No comment on flag, wind, mind? Not even "I, Pahansiri, refuse to answer."?

Franko

15th October 2003, 03:17 PM

Upchurch: (to Q-Source)
When you refer to science, who do you think it is you are referring to? Scientists study the properties and dynamics of the physical world: physics, chemistry, biology, etc. Which of these exist without the assumption of materialism?

They all do in a slightly altered and more realistic form.

Scientists are materialists, Q. They study the material world.

No … True Scientists are people who consistently rely on the scientific method, from beginning to end.

True Scientist are not inconsistent regarding the scientific method by making unfounded, untestable initial assumptions, deciding only later down the chain to adopt the scientific method when they think it suits them. That isn’t a scientist – that’s just a religious nitwit.

And yes, I do realize it is an assumption, but I also realize that it is a perfectly valid assumption based on the apparent consistancy and dependability of the material world.

Yeah, apparently according to Upchurch everyone gets a one time pass when it comes to the scientific method (or logic). This is his definition of “consistency”.

Just about as quick as immaterialists are to deny the existance of the material world.

What in the heck is the “material world”? I’m an immaterialist by your definition, but I don’t deny the existence of the universe … just your precious magically unverifiable “matter” (i.e. your “God”).

Why? Based on what? Why claim that some of your senses are feeding you illusions and others aren't?

Who’s talking about senses? We are talking about logical consistency. Why don’t you just explain why you believe it is sometimes “logical” to believe in things which cannot be observed or empirically verified? Why is it okay for you to make such a leap of faith, especially in light of your arrogance and contempt for anyone else who you perceive as committing a similar “sin”?

Upchurch

15th October 2003, 03:26 PM

Originally posted by Franko
True Scientist are not inconsistent regarding the scientific method by making unfounded, untestable initial assumptions, deciding only later down the chain to adopt the scientific method when they think it suits them. That isn’t a scientist – that’s just a religious nitwit. That's right. No True Scotsman wears anything but his kilt. (Please ignore all those Scottish nationals wearing pants)

edited to add: Boy, he couldn't have walked into that one any better if I'd scripted it for him.

Pahansiri

15th October 2003, 03:30 PM

Originally posted by hammegk

LOL. Pot:Kettle:Black. ;)

Yet another Unfounded, Unsubstantiated, Unsupported statement..

Care to post from one of my post, my words something that will prove your statement?

You see I always prove using your words what I am saying you, well just make Unfounded, Unsubstantiated, Unsupported statements.:rub:

Just the facts please. You do know what facts are, right?

After pounding sand you are still tense, huh? :confused:

How old are you? Have I been talking to a pre-teen all this time?

Try again -- remember to use the mindfulness & meditation parts this time. :) I would hate to have to begin referring to you as Pahansilly.

:rolleyes: More childish silly statements, the very same one you used sometime back under the Franko handle if I remember correctly…lol

Do you not believe that people find you and your beliefs meaningless when you respond in such an immature way when asked to answer questions concerning your beliefs and statements, when asked for proof and facts?

No comment on flag, wind, mind? Not even "I, Pahansiri, refuse to answer."?

LOL more demanding answers to quiestions when 1- you offer none and 2- after I give them already.

As to Or would you care to go with an answer to "What moves? Wind, Flag, or Mind?".

I looked back and while I answered the point I did not answer this directly and being I am mature and have nothing to fear or hide as it seems you do here is my response to your silly question..

"What moves? Wind, Flag, or Mind?".

The flag is moved by the wind. The wind is the air moved by other conditions. As to the “mind moved” how do you mean “moved” can you point to mind, show me mind and demonstrate how it which I do not believe is matter as you know can be moved if it is not comprised of matter.

If you mean “moved” as to thought I and or to some greater or lesser extent Causes and conditions effect thought.

Demands if one does not seek to control thought and allows emotion to control thought, well as your actions demonstrate.

I will be waiting for your proof as I asked for above…I know I know don’t hold my breath…LOL

Pahansiri

15th October 2003, 03:31 PM

Originally posted by Upchurch
That's right. No True Scotsman wears anything but his kilt. (Please ignore all those Scottish nationals wearing pants) :roll:

hammegk

15th October 2003, 03:39 PM

Originally posted by Pahansiri

If you mean “moved” as to thought I and or to some greater or lesser extent Causes and conditions effect thought.

One of the most meaningful & intelligent things you've ever posted. Mature you may be. With understanding? Not that you've ever demonstrated here. Parrots can show your level of "understanding".

How many times do you usually walk into a wall before you seek a doorway? :)

Pahansiri

15th October 2003, 04:03 PM

Originally posted by hammegk

One of the most meaningful & intelligent things you've ever posted. Mature you may be. With understanding? Not that you've ever demonstrated here. Parrots can show your level of "understanding".

How many times do you usually walk into a wall before you seek a doorway? :)

Hmmm ask for him to support his Unfounded, Unsubstantiated, Unsupported statements.

and you get

Yet another Unfounded, Unsubstantiated, Unsupported immature statement ..

LOL.. do you ever even try to prove what you say or believe?
:rolleyes:

jan

15th October 2003, 04:19 PM

Originally posted by Franko

Do you have an example of a formal system that is not incomplete as per Godel's theorem?

Trivial. But I assume you mean a formal system that can be used to formalize at least Arithmetics. Gödel did show that all these systems are incomplete (in a certain, technical sense), and I never intended to imply that there is reason to doubt this. But he didn't showed it using a formalized proof. He published a strict metamathematical proof that the Principia Mathematica are incomplete, but even this proof was not a formalized proof, in the strict sense as a proof within the formal framework of the Principia Mathematica is formalized.

I still fail to see the relevance of Gödels theorems for the science of consciousness. I assume that there are only finite many mathematical sentences that fit into a human brain, so what is this all about anyway?

hammegk

15th October 2003, 04:38 PM

Originally posted by Pahansiri

LOL.. do you ever even try to prove what you say or believe?

Only when I run across someone who appears to have an actual interest in it. ;) You give no indication of that.

For the umpteenth time, my real interest is why you(or anyone who is not an idealist) believes what you(they) do; unfortunately most don't like to share their beliefs, the only actual belief being "the objective material world exists".

Just what I believe .....

What DO you believe???? Nothing, apparently.

Dancing David

15th October 2003, 04:51 PM

Originally posted by Franko

What are the observable results leading to verification that “matter” exist independent of observable results?

I can't prove that the world existed prior to the 'first observation' but I have reason to believe that the photons that come from the Andromeda galaxy have travelled a long time prior to my observation of them.

And it doesn't matter if the matter existed before a human first observed it, it seems to behave as though it does. There are the layers of vesuvius and the fact that I can make a mark on a tree that seems to exist before another observes it.

You Discordians are so cute when you dance. ;)

Yeah yeah, I can really swing too, but this weekend I am calling so I just watch, I don't dance, except for two waltzes with my wife.

No, no, no, my friend, we are not talking about a mere belief (like chocolate ice cream being better tasting than vanilla ice cream) we are talking about a fundamental assumption about the nature of science (reality/existence/the universe). And ANY person who claims that his “truth” is THE TRUTH (scientific or logical truth [metatruth]) yet bases all his assumptions on that initial unverifiable, untestable, unproveable assumption is no scientist … he’s a priest!

Again I can make a mark on a tree that another observer can check on, if you don't like the evidence that the world is very old, then so be it. You don't have to assume anything about nature other than it having isotropy.

The ontology of the observable is not something I can discuss, nor can it be tested. Would you like to see a tree that I marked, just for you!

The assumption of science is isotropy, and not that it exists, just that it can be observed.

My humble POV, I am not responsible for others and thier strange beliefs.

Yes, but prior to Your observation does not mean that it existed prior to TLOP’s (“God’s”) observation.

More speculation, can't be tested, is moot. Great fiction however.

Did this universe come into existence before or after The Laws of Physics (TLOP)?

My guess is that the LOP came about as they are observed from the music that the Big Band played. Parts of lop became fixed at the time of time.
So some lop prior and some lop at the time the band started.
More speculation

Is it possible that the “big bang” happened first, and then TLOP came along afterwards? I don’t see how that could be? Perhaps you can explain it to me?

I don't know, if I understand Guth's book right, it is possible that some of the particles which clanged out in the early universe may be the fields that we see today. So some laws prior , some laws at the time the dance began, and some laws after the music started.

Cool question though.

But wait just a minute there cowboy!

You have failed to address the actual issue. If you have no logical reason or empirical evidence to suggest that “matter” exist independently of all (or any) observation then why on earth would you leap to such an utterly unfounded and untestable assumption??? Especially in light of the fact that this is the initial foundational premise upon which your entire worldview seems to rest?

My world view is probably more varied than you think! I base my own beliefs upon certain experiences I have had, if they are a product of mind or matter is moot! I can bury a walnut where you can find it!

But my worldview is a little more chaotic than some materialsts, i am an animist and a nihilist, so I really don't care which method I use, it is the results that I care about.

I wouldn’t even stoop to calling that sloppy science … I would simply call it religious fanaticism and arrogant, hypocritical, blind faith.

I would say that there are those who have beliefs unsupported by evidence. They come in many shapes and sizes too.

Perhaps you can straighten me out, and help me to see the “light”?

Ah, but you can look at Andromeda yourself, if the light travelled thirty million years to get to your eye that is real cool, if it is all just a program in the Mtrix then that is cool too.

All equaly true and all equaly false.

Pahansiri

15th October 2003, 05:05 PM

Originally posted by hammegk

Only when I run across someone who appears to have an actual interest in it. ;) You give no indication of that.

For the umpteenth time, my real interest is why you(or anyone who is not an idealist) believes what you(they) do; unfortunately most don't like to share their beliefs, the only actual belief being "the objective material world exists".

Just what I believe .....

What DO you believe???? Nothing, apparently.

Only when I run across someone who appears to have an actual interest in it. You give no indication of that.

Silly and meaningless way to avoid answering a question or posting facts and proof to support your beliefs or statements, but we all know why you will not, don’t we..wink wink

For the umpteenth time, my real interest is why you(or anyone who is not an idealist) believes what you(they) do; unfortunately most don't like to share their beliefs, the only actual belief being "the objective material world exists".

1- Prove I or others here, by name are idealist.

An idealist is one who makes statements of belief and will not support them with facts, I have supported all I have said with facts or logical conclusion. You have not, you are the idealist.

Tell me what belief and or statements that I have expressed that I have not supported.
I can hear the crickets warming up.

unfortunately most don't like to share their beliefs, the only actual belief being "the objective material world exists".

Really?
1 Care to name them?
2- Your statement is of course like many of your statements unfounded and self contradicting. You say unfortunately most don't like to share their beliefs then contradict that in the every next few words saying the only actual belief being "the objective material world exists".

Really do you think about what you say?

2- What is the numerical value of umpteenth? lol

Just what I believe .....

I know what you believe all the ever changing beliefs I just wish for once you support them with facts, just once. But you can not supply what you do not have.

What DO you believe???? Nothing, apparently.

This is of course silly and immature statement.

1- I have over and over said what I believe and supported it with facts and or logical conclusion. You should try it.
2 How can someone believe “nothing”? What a silly statement. Because as you know I believe your statements are silly and I prove it just as one example.
3 If someone believes something it denoted thought and that denoted free will, silly boy. As I have said over and over if your Goddess or TLPO controlled all then all thought would be the same.

You make this too easy and only make yourself look foolish.

You say people are wrong for believing "the objective material world exists".. OK for the, well I am not sure but it is a large number.

Prove it does not.

hammegk

15th October 2003, 05:13 PM

Keep bumping into the wall if such pleases you. And you purport to be a buddhist! LOL is correct. Enough for me, here, now.

Just what I believe ....

Pahansiri

15th October 2003, 05:18 PM

Originally posted by hammegk
Keep bumping into the wall if such pleases you. And you purport to be a buddhist! LOL is correct. Enough for me, here, now.

Just what I believe ....

Translation: “Dear Pahansiri you are right you exposed that I can not support anything I say or believe and do not attempt to. You and most here have punched holes in my beliefs and that makes me mad so I will just launch meaningless personal attacks rather then conduct a logical ,respectful mature debate. I will use this childish statement Pahansilly Pahansiri Parrot

Keep bumping into the wall if such pleases you. And you purport to be a buddhist! LOL is correct. Enough for me, here, now.

Just what I believe ....

Because as you pointed out I have nothing of substance to say.”

hammegk

15th October 2003, 05:22 PM

word

Pahansiri

15th October 2003, 05:31 PM

Originally posted by hammegk
word :rub:

hammegk

15th October 2003, 06:04 PM

Thank you, Pahansilly Pahansiri Parrot.

Pahansiri

15th October 2003, 06:32 PM

Originally posted by hammegk
Thank you, Pahansilly Pahansiri Parrot.

As you wish.
May you be well and happy my friend.

hammegk

15th October 2003, 06:36 PM

Lo mismo, mi amigo.

Peter Soderqvist

16th October 2003, 01:10 AM

TO HAMMEGK

You wrote 10-15-2003 02:27 PM: Peter Soderqvist: Do you consider yourself a dualist or an idealist/monist? BTW, no matter how many times our materialists/atheists/scientists read your words, they do not understand them; why is that?

Soderqvist1: I consider myself a human being with wishful thinking!
Since I have a strong predilection for consciousness as the collapser of wave function, and so matter is a epiphenomenon of consciousness, but I am not alone in my humanness, since there are other here with predilection for the opposite namely; longings for materialism! I firmly believe in the philosophy of Occam 's Razor, and experiments in order to separate fictions from facts! There are lot of various theories about the origin of life, and quantum mechanical interpretations, they all have more or less the potential to be truth, but they all together cannot be truth, so again, I feel a tentative confidence in our inferences from what scientific experiments have revealed, and I am more or less critical regarding everything else!

There is an endless debate going on here, it is much more constructive to decrease the amount of spamming, and in stead read many of your opponent's books, and examine each other! As a starter; the professor of physics at the Oregon University, Amit Goswami' s book, The Self-Aware Universe, how Consciousness Creates the Material World, versus David Deutsch book, The Fabric of Reality, and Carl Sagan 's book, The Demon-Haunted World, Science as a Candle in the Dark, Chapter; The marriage of Wonder and Skepticism, as a thoughtful moderator! I have read the two first books, and I am in the end of Sagan 's book! The books can be reached at Amazon COM! http://www.amazon.com/exec/obidos/tg/browse/-/283155/ref%3Dtab%5Fgw%5Fb%5F3/104-2636015-9805502

What have the general visitor to say about my solution to the endless debate? ;)

Peter Soderqvist

16th October 2003, 05:47 AM

TO JAN

You wrote 10-15-2003 07:40 PM: Well, one could say, a theorem is like a cake, a proof is like a recipe how to make it.

Soderqvist1: But what about abstract cakes "mathematical truths" which is not derivable from any axioms? The cake-bible is forever doomed to incompleteness whatever axiomatic systems involved! See my earlier link to Kurt Gödel!

Or one could say that a theorem is like the moon, mirrored in a lake in the autumn...

Sodreqvist1: what about Cantgotu moons?

Now let's get serious. You have a claim: I would say this point of view is refuted again and again by at least two of the five books you have read.

Soderqvist1: All five has alleged so!
I have a new book here by the famous Steven Rose, Making of Memory, from Molecules to Minds he disagrees with them, and so does Roger Penrose with other, he (Penrose) is one of the world's greatest mathematical-physicists! I have also read another book by Susan Greenfield; The Human Brain, she is Peter Atkins wife, and Atkins and Richard Dawkins are colleagues at the University of Oxford! She is a Parkinson, and neurological disease researcher at Oxfords University! Algorithms, recipes, theorems are analogous!

Neuroscientist Professor Susan Greenfield is the first woman director of the prestigious 200 year old Royal Institution of Great Britain. She leads a team dedicated to finding out how the brain works and whose latest work has been to look at the connection between Parkinson's and Alzheimer's disease.

Something that occupies the imagination a lot for the future, and this is the dream of many people including Marvin Minsky, is that we will dispense with the biological squalor altogether and have conscious computers. Now how realistic is that? Let's look at the possibility. I would just like to indicate why biological brains are currently not like current artificial systems. First we have non-algorithmic processes, that is to say we have commonsense and intuition, we don't necessarily think in a step by step algorithmic process. Moreover we've just seen that events in the brain are chemically based. Now this gives you a huge extra dimension, as well as on off and modulating processes. It explains why morphine gives you a different type of consciousness from LSD, gives you a different type of consciousness from Ecstasy or Prozac. Because each of these agents work in a different way on different chemicals in the brain. And until that is factored in to artificial systems, I myself am very leery about just how faithfully they are modeling the human brain.
http://www.abc.net.au/rn/science/ss/stories/s137294.htm

"Gödel, Escher, Bach" is all about showing that you are wrong (think of it, Hofstadter refuted you even before you made your claim).

Soderqvist1: I have this book, but I have not yet read it!
I have read what Hofstadter has said in the Minds' I, and I have seen various rebuttals there about neither a machine nor human mind can represent themselves totally, so Godel's incompleteness theorem limiting both, and thus humans are not supreme in that sense! But I have not seen any clear-cut description about it!
As far as I know, computers computes with algorithms, and Godel's incompleteness theorem is not an algorithm, it is a contradiction in terms, if a computer's computational procedure can show that Godel's incompleteness theorem is a computational procedure! It follows from that; what Godel had in mind 1931 regarding his incompleteness theorem was not something computable, therefore; a computer cannot model Godel's mind! Suppose that for the sake of simplicity, Godel or some other human has a Cantgotu moon in his mind how can a computer model that when a "Cantgotu moon" have no algorithms?

But you even failed to state what you probably wanted to claim in a convincing manner.

Soderqvist1: I am not a Computer scientist, nor any mathematician!
Maybe you can show me a simple rebuttal?

First of all, it is a quite trivial task to make a computer output whatever Gödel has written. Since Gödel is dead and his work finite, this doesn't require much sophistication. Just output a constant string literal, and you are done.

Soderqvist1: granted!

There is a theorem Gödel has proved that uses the construction of a specific sentence within the formal framework of the Principia Mathematica (and this formal sentence is not one of Gödel 's theorems, it is just used in one of his theorems). Gödel showed that is possible to construct a similar sentence for any formal system that is similar to the formal system he was discussing. But this construction, once again, doesn't require infinite sophistication; in fact, I guess it would be rather trivial to mechanize this construction for several kinds of formal systems. Fortunately or unfortunately, there are many different kind of formal system, so it would be difficult to write a program that could "gödelize" any arbitrary formal system with sufficient strength to contain Arithmetic. But note that Gödel also never formally proved that all formal systems are incomplete: he only showed it for the Principia Mathematica in a formal manner, and it is obvious, but it has never been formally demonstrated, that a similar thing can be done for any other similar formal system.

But I assume that this is still not what you attempted to claim. I guess what you really wanted to claim is that a computer program, as a formal system, can't prove all true mathematical sentences.

Soderqvist1: Yes, the countable numbers are only an infinitely small subset of the set of uncountable numbers! There is no transformation rules, or algorithms for uncountable numbers as far as I know!

But what makes you think you can?

Soderqvist1: I have never alleged that either!
But I have alleged that David Deutsch knows that Cantgotu environments cannot be rending into virtual reality by a Universal Virtual reality machine, which is a kind of a Universal Turing Machine! There is no algorithm for that; therefore Deutsch concept cannot be modeled by a thing, like a computer, which uses algorithms! Therefore Strong AI is false to fact!

Ian wrote 10-15-2003 11:19 PM: Franko: Do you have an example of a formal system that is not incomplete as per Godel's theorem?

Ian: Trivial. But I assume you mean a formal system that can be used to formalize at least Arithmetic s. Gödel did show that all these systems are incomplete (in a certain, technical sense), and I never intended to imply that there is reason to doubt this. But he didn't showed it using a formalized proof. He published a strict meta mathematical proof that the Principia Mathematica are incomplete, but even this proof was not a formalized proof, in the strict sense as a proof within the formal framework of the Principia Mathematica is formalized.

Soderqvist1: A meta-mathematical proof is something an observer can say about a system, when he looks into it, which the systems proof sequences doesn't say anything about! He used lines of countable numbers and described how we can increase one number on each line, the first place on the first line, and the second place on the second line, and the third place on the third line, and so on, this give a meta-mathematical diagonal line with uncountable numbers!

I still fail to see the relevance of Gödel' s theorems for the science of consciousness. I assume that there are only finite many mathematical sentences that fit into a human brain, so what is this all about anyway?

Soderqvist1: see earlier!

Dymanic

16th October 2003, 10:02 AM

I still fail to see the relevance of Gödel' s theorems for the science of consciousness.
I see it as relevant to the science of anything, because all science ultimately reduces to mathematical logic.

Squires, in Conscious Mind in the Physical World

In any finitely describable formal system that is consistent and that is rich enough to contain the rules of arithmetic, there are true statements that are not theorems. What this means is that there cannot exist a complete logical basis for all the results of arithmetic, let alone all of truth.

In other words, it will always be necessary at some point to base our understanding on some unprovable assumptions.

Franko

16th October 2003, 11:19 AM

Dynamic:
In other words, it will always be necessary at some point to base our understanding on some unprovable assumptions.

I'm not sure that I agree with this, my friend.

... at least not in an absolute sort of way.

In terms of Godel, the system may be incomplete, but once you discover a Truth that cannot be proven it is a fairly straightforward process to modify (or amend) the system in such a way that you retain all the conventions (rules/laws) of the original, and yet remove the specific incompleteness in regard to the aforementioned unproveable truth.

Dymanic

16th October 2003, 11:39 AM

Originally posted by Franko

In terms of Godel, the system may be incomplete, but once you discover a Truth that cannot be proven it is a fairly straightforward process to modify (or amend) the system in such a way that you retain all the conventions (rules/laws) of the original, and yet remove the specific incompleteness in regard to the aforementioned unproveable truth.
Precisely what Gödel showed is that you cannot do this.

System n being incomplete, we amend it to form System n+1, which is also incomplete, so we amend it to form System n+2...

If Gödel were that easy to defeat, you would never have heard the name.

Franko

16th October 2003, 11:53 AM

Do I know you Dynamic? Have we chatted before? You seem very familiar …

Dynamic:
Precisely what Gödel showed is that you cannot do this.

System n being incomplete, we amend it to form System n+1, which is also incomplete …

Yes, but it is less incomplete than the original System-n, that was my only point here.

If Gödel were that easy to defeat, you would never have heard the name.

Ohhh, believe me I have nothing but respect for Uncle Kurt. The same goes for the notions of recursion and reiteration. My hunch is we probably are saying the same thing, but I think it probably best if I (we) do not have this discussion here.

You’re not an Atheist?

Dymanic

16th October 2003, 02:40 PM

Originally posted by Franko

Do I know you Dynamic? Have we chatted before? You seem very familiar...
If this sounds familiar, it may only be because this is such a well-worn path. I don't do socks, if that's what you mean.
My hunch is we probably are saying the same thingI'm not sure if we are or not. What I'm saying is that everything that passes for knowledge is based on some fundamental assumptions, and that various standards may be applied in choosing those assumptions. Beyond a shadow of a doubt is not among the available options. Beyond a reasonable doubt is a good as it gets. In some areas, we'll have to settle for a preponderance of the evidence.
but I think it probably best if I (we) do not have this discussion here.
Doesn't matter much to me one way or the other.
You’re not an Atheist?
Oh, I am. Absolutely.

Franko

16th October 2003, 02:51 PM

Okay … what the hell. I’m almost out of Time anyway …

Dynamic:
I'm not sure if we are or not. What I'm saying is that everything that passes for knowledge is based on some fundamental assumptions …

i.e. Axioms from the particular “formal system”.

… and that various standards may be applied in choosing those assumptions.

“various standards”? I was under the impression that Godel was very specific about what constituted a “formal system”.

Beyond a shadow of a doubt is not among the available options. Beyond a reasonable doubt is a good as it gets. In some areas, we'll have to settle for a preponderance of the evidence.

I’m not sure I see the connection to Godel?

Godel’s theorem states that within a given formal system (i.e. a logically self-consistent system) that there are certain propositions, which are obviously true yet cannot be proven by the axioms of that system. However, when one encounters such an unproveable proposition there is a mechanism (and I’m not implying this is part of Godel’s theorem) by which the axioms of the system can be amended so that the original unproveable proposition is now proveable within the new expanded system.

Would you concur, or do you take issue with this?

Oh, I am. Absolutely.

very strange …

Dymanic

16th October 2003, 04:17 PM

Originally posted by Franko

I’m not sure I see the connection to Godel?
I wasn't actually proposing one, but speaking in a more general sense. Formal systems really exist only within mathematics, but elsewhere much disagreement seems to center around what standard of evidence is appropriate.

Before Gödel, it was once hoped that powerful formal mathematical systems could be devised that were both complete and consistent, giving us at least that one area where human understanding could have access to perfection, and where (to the extent that they could be mapped to such systems) concepts could be be tested for truth against this perfect logic. Since Gödel proved this wrong, we are forced to accept that any area of human thought must include some fundamentally unprovable assumptions. Those who would throw this stone at their opponents would do well to remember that their own houses are made of glass as well.

...when one encounters such an unproveable proposition there is a mechanism... ...by which the axioms of the system can be amended so that the original unproveable proposition is now proveable within the new expanded system.
I would agree with that, as far as it goes, but it must be understood that attempting to employ such a method to produce a complete and consistent system would require an infinite iteration of this process; some true propositions will be unreachable by each new system.
very strange...
You have no idea.

Tip: to get the ö character, enter 148 from the numerical keypad while holding down the Alt key.

jan

16th October 2003, 05:39 PM

Originally posted by Peter Soderqvist

Soderqvist1: But what about abstract cakes "mathematical truths" which is not derivable from any axioms? The cake-bible is forever doomed to incompleteness whatever axiomatic systems involved! See my earlier link to Kurt Gödel!

Those are the cakes nobody knows how to bake.

Originally posted by Peter Soderqvist

he (Penrose) is one of the world's greatest mathematical-physicists!

I agree that he had some wondeful mathematical ideas, and I would also agree that his ideas about consciousness are more clever than the usual Dualist weirdness; but why do I smell an appeal to authority here?

Originally posted by Peter Soderqvist

Soderqvist1: I have this book, but I have not yet read it!
I have read what Hofstadter has said in the Minds' I, and I have seen various rebuttals there about neither a machine nor human mind can represent themselves totally, so Godel's incompleteness theorem limiting both, and thus humans are not supreme in that sense! But I have not seen any clear-cut description about it!

If you are interested in this problem, you should read GEB as fast as possible (have some fun!). The usual materialistic view is that since the human brain is some kind of soft computer, any principle limitation of computers aply to human brains.

Originally posted by Peter Soderqvist

As far as I know, computers computes with algorithms, and Godel's incompleteness theorem is not an algorithm, it is a contradiction in terms, if a computer's computational procedure can show that Godel's incompleteness theorem is a computational procedure! It follows from that; what Godel had in mind 1931 regarding his incompleteness theorem was not something computable, therefore; a computer cannot model Godel's mind! Suppose that for the sake of simplicity, Godel or some other human has a Cantgotu moon in his mind how can a computer model that when a "Cantgotu moon" have no algorithms?

Gödels theorems apply to formal systems, with axioms and rules of inference. An algorithm is not strictly the same, although you can use an algorithm to get al valid inferences of a certain formal system.

I am not certain if I understand you, but it seems to me the "what Gödel had in mind" is a different problem (problem of Qualia), that has nothing to do with the work of Gödel. Still, to output Gödel's writings is a trivial task. And you could also work out some kind of formal system so Gödel's writings could be constructed within this system.

Originally posted by Peter Soderqvist

Soderqvist1: Yes, the countable numbers are only an infinitely small subset of the set of uncountable numbers! There is no transformation rules, or algorithms for uncountable numbers as far as I know!

Sorry for being that pedantic, but if you identify "a mathematical truth" with "a true finite english sentence about a mathematical topic", then the number of mathematical truth is countable (a subset of the countable set of finite english sentences).

Uncountable sets have some meaning in algorithm theory, but they are not terribly relevant in the discussion of formal systems.

Originally posted by Peter Soderqvist

Soderqvist1: I have never alleged that either!
But I have alleged that David Deutsch knows that Cantgotu environments cannot be rending into virtual reality by a Universal Virtual reality machine, which is a kind of a Universal Turing Machine! There is no algorithm for that; therefore Deutsch concept cannot be modeled by a thing, like a computer, which uses algorithms! Therefore Strong AI is false to fact!

I am tempted to ask you to explain that a bit more, but perhaps I will have to read myself.

Originally posted by Peter Soderqvist

Soderqvist1: A meta-mathematical proof is something an observer can say about a system, when he looks into it, which the systems proof sequences doesn't say anything about!

This is not strictly true. In fact, Gödel showed how a formal system could talk about itself and it's own abilities (in fact, he constructed something like "I can't be proven within this formal system.", just a bit more roundabout).

Originally posted by Peter Soderqvist

He used lines of countable numbers and described how we can increase one number on each line, the first place on the first line, and the second place on the second line, and the third place on the third line, and so on, this give a meta-mathematical diagonal line with uncountable numbers!

Sounds more like Cantor.

----------------------

Originally posted by Dymanic

I see it as relevant to the science of anything, because all science ultimately reduces to mathematical logic.

In other words, it will always be necessary at some point to base our understanding on some unprovable assumptions.

I fail to see how all science ultimately reduces to mathematical logic.

And Gödel's theorems do not show you that you have to base your understanding on some unprovable assumptions. If you use a formal language, you use unproven axioms to begin with, so a formal system can give you just relative truths anyway.

And if you encounter a formally undecidable sentence in real life, the most natural reaction would be to try to change the formal framework and to look for stronger principles. If you fail to find any, you would say you can't prove or refutate the sentence; you don't use it as a base for further explorations (or at least, as in the case of, say, Axiom of Choice, you use strong warning sings "uses Axiom of Choice! Don't trust it!").

Originally posted by Dymanic

What I'm saying is that everything that passes for knowledge is based on some fundamental assumptions, and that various standards may be applied in choosing those assumptions. Beyond a shadow of a doubt is not among the available options. Beyond a reasonable doubt is a good as it gets. In some areas, we'll have to settle for a preponderance of the evidence.

Yes, but that is how empirical sciences work. You don't have evidence in Mathematics, you start with some convincing or bizzarre, plausible or odd axioms. If you find that those axioms are insufficient to settle a specific question, you may switch to stronger axioms. Of course, as Gödel showed, this new system will also be incomplete. But usually you are not interested in completeness, but in settling a certain question. The Zermelo-Fraenkel set of axioms is certainly incomplete in the sense that you can't decide the Axiom of Choice in it. You can add the Axiom of Choice and see what happens. Or you can say "The new system will still be incomplete, so it is not worth the trouble".

Originally posted by Dymanic

Before Gödel, it was once hoped that powerful formal mathematical systems could be devised that were both complete and consistent, giving us at least that one area where human understanding could have access to perfection, and where (to the extent that they could be mapped to such systems) concepts could be be tested for truth against this perfect logic. Since Gödel proved this wrong, we are forced to accept that any area of human thought must include some fundamentally unprovable assumptions. Those who would throw this stone at their opponents would do well to remember that their own houses are made of glass as well.

Yes, Carnap was very pissed.

But I would still say: all that can be said about empirical sciences, about consciousness, about life, the universe and everything usually can be said without refering to Gödel. I would say that quoting Gödel's theorems outside a mathematical context is a bit of a bad habit, bad taste.

Originally posted by Dymanic

Tip: to get the ö character, enter 148 from the numerical keypad while holding down the Alt key.

It is &ouml; for the standard fanatics.

Originally posted by Franko
I’m not sure I see the connection to Godel?

very strange …

Franko, let me be the first to say that I was reading your previous posts with joy. No, there is no connection to Gödel. "Gödel's Theorem" is just a buzzword, like "Quantum Leap" or "Chaos Theory", or "Heisenberg's Principle".

Dymanic

16th October 2003, 06:58 PM

Originally posted by Jan

"Gödel's Theorem" is just a buzzword
I'd say that whether or not it is just a buzzword is very context-dependent. I agree that it (and the others you mentioned) is subject to abuse by those so inclined -- but that doesn't invalidate such concepts when properly applied.
Just when I am about ready (again) to relegate Gödel's theorem to the 'interesting but not very important' bin as far as consciousness is concerned, along comes somebody giving it a key role in arguments concerned with algorithmicity, the halting problem, etc. Like Penrose (again) in: Shadows of the Mind.

Right, well, ok, so he's a mathematician; naturally he's going to attach a lot of importance to Gödel. Some of the questions he addresses have got me buggin, tho -- like how the heck do we know (obviously without applying formal methods) that a certain proposition is undecidable by such methods? How can we know (obviously without applying aglorithmic methods) that a certain problem cannot be solved algorithmically? Maybe it's just one of those things -- you either get it, or you don't.

Peter Soderqvist

17th October 2003, 01:32 AM

TO JAN

Godel used an extended version of Cantor's Diagonal argument, as part of his proof about natural number 1931! But in my reply to you the diagonal variant with uncountable numbers was used by Alan Turing, the correct term is uncomputable!
It goes something like this: suppose we list horizontally all possible computable numbers with its decimals on a list. Now we advance the first digit with one unit on the first line, say from 2 to 3, and the second digit, on the second line with one unit say 4 to 5, and the third digit on the third line, and so on ad infinitum! Since the list contains all possible computable numbers, the new number on the diagonal metamathematical line is not on the list, and is therefore an uncomputable number!
The computable numbers are only a microscopically subset of all possible numbers!

One Godel sentence is; this sentence is not provable!
We can meta-mathematically see that the sentence is truth, because it is not provable! Both humans and computers are thus limited by the incompleteness theorem, since we are unable to prove it, and every proof sequence is a computational procedure, from that follows two questions, namely:

1 how can a computational computer algorithm simulate something uncomputable Qualia of Godel sentences?

2 how can this algorithm computationally simulate a human Qualia of uncomputable numbers?

As Susan Greenfield has pointed out in my link to you, neurons have not only a binary on or off property, but also even a chemical dimension! If a computer cannot simulate these (which I firmly believe they cannot do), strong AI is false to fact! ;)

I will be back at Monday!

whitefork

17th October 2003, 07:25 AM

Short discussion of Godel here (http://host.randi.org/vbulletin/showthread.php?s=&threadid=10834)

Franko

17th October 2003, 07:51 AM

Dynamic: Formal systems really exist only within mathematics …

How about computer languages? Would a computer language be considered mathematical? Would a computer language be an example of a formal system?

Before Gödel, it was once hoped that powerful formal mathematical systems could be devised that were both complete and consistent, giving us at least that one area where human understanding could have access to perfection, and where (to the extent that they could be mapped to such systems) concepts could be be tested for truth against this perfect logic.

I agree with you up to this point.

Since Gödel proved this wrong, we are forced to accept that any area of human thought must include some fundamentally unprovable assumptions. Those who would throw this stone at their opponents would do well to remember that their own houses are made of glass as well.

But not here, and I’m not sure that Godel would either. Are temporarily unproveable assumptions logically equivalent to fundamentally unproveable assumptions?

I would agree with that, as far as it goes, but it must be understood that attempting to employ such a method to produce a complete and consistent system would require an infinite iteration of this process; some true propositions will be unreachable by each new system.

I agree. Perhaps this is what you were implying above?

I am tempted to comment further, but I think it best if I refrain.

You have no idea.

Ohhh … I like you Dynamic. I am curious as to why on Earth you would call yourself an “Atheist”? … but I don’t want to spoil the moment ...

Tip: to get the ö character, enter 148 from the numerical keypad while holding down the Alt key.

Thanks for the info, unfortunately American is my primary language. ;)

Dymanic

17th October 2003, 11:36 AM

Originally posted by Franko

Would a computer language be considered mathematical?
The term 'computer language' is itself not nearly as crisp as you might imagine. At the lowest level, a computer is a dynamic set of relationships between large numbers of transistors, each of which can be in one of two states. We think of these states as 'ones' and zeroes', but aside from this abstraction, there aren't actually any little ones and zeroes anywhere in the machine. Similarly, a protohuman who sees three bears enter a cave and sees two leave, and then concludes that it is safe to enter the cave, will be eaten -- not by a one -- but by a bear.

The usefulness of mathematics as a tool resides in isomorphism -- the way concepts about the world can be mapped to mathematical concepts, these concepts then manipulated according to well-defined rules, and the results mapped back to the real world. Especially when the mapping part seems to go smoothly, we are very likely to make the mistake of presuming that there is an actual connection between what happening in the purely mathematical realm and what happens in the real world.

So when I say that what is happening at the lowest level of a running computer is that simple logical operators (like AND, NOT, OR, XOR) are being applied to binary values, it should be understood that this already involves several mappings/remappings between actual physical events and our abstract ways of conceptualizing them. With this caveat in mind, one might say that a computer can be made to model a formal mathematical system, and a computer language might be said to be a tool for expressing human thought in terms that would be considered 'well-formed' within such a system.

Would a computer language be an example of a formal system?
That depends on the language. C, for example is pretty formal, but LISP can be pretty informal (that's a joke, son).

Are temporarily unproveable assumptions logically equivalent to fundamentally unproveable assumptions?
That's an interesting question, and worthy of further thought. I might reply to that later if I am able to formulate a response.

jan

17th October 2003, 02:06 PM

Originally posted by Dymanic

I'd say that whether or not it is just a buzzword is very context-dependent.

Yes, yes, granted.

But if all one wants to say is to say that we are unable to proof something beyond any doubt, that there will always be uncertainty, that everybody uses unproven principles, and so on, I would say there are plenty of other arguments, before we have to address Gödel.

Originally posted by Peter Soderqvist
But in my reply to you the diagonal variant with uncountable numbers was used by Alan Turing, the correct term is uncomputable!

Jan: Uncountable sets have some meaning in algorithm theory...

Peter: Uncountable sets have some meaning in algorithm theory...

Originally posted by Peter Soderqvist

One Godel sentence is; this sentence is not provable!
We can meta-mathematically see that the sentence is truth, because it is not provable! Both humans and computers are thus limited by the incompleteness theorem, since we are unable to prove it [...]

No. A meta-mathematical prove is a prove. We can prove that that sentence is true. It is just impossible to give a deduction within the formal system we are discussing.

The punch line of people like Lucas is that we are able to prove those sentences. Therefore, it seems as if we are more creative than any given formal system.

But of course our ability to prove is also limited.

Originally posted by Peter Soderqvist

As Susan Greenfield has pointed out in my link to you, neurons have not only a binary on or off property, but also even a chemical dimension! If a computer cannot simulate these (which I firmly believe they cannot do), strong AI is false to fact! ;)

A color is not just an on-or-off property, but something with steps in between, and furthermore, it has not just one dimension, but three (red, green and blue). Nevertheless we seem to be quite happy representing colors with a model that contains only 224 "true" colors, thus being made perfectly digital. I fail to see why a discrete model of the brain physiology should be insufficient.

Dymanic

17th October 2003, 03:16 PM

Originally posted by Jan

But if all one wants to say is to say that we are unable to proof something beyond any doubt, that there will always be uncertainty, that everybody uses unproven principles, and so on, I would say there are plenty of other arguments, before we have to address Gödel.
Conceded. I fear that in a manner typical of one who becomes fascinated with a particularly elegant idea, I myself may be guilty of occasionally exaggerating the explanitory power of Gödel's theorem. I appreciate your criticizm, and resolve to mend my ways.

sorgoth

18th October 2003, 12:56 PM

Originally posted by Yahweh

Well, unfortunately I cant go diving into another person's "mind" and experience everything they experience, but I can say with reasonable certainty that the "red" I see is the same as the "red" another person sees (assuming both of us are normal and healthy with no vision problems). Both our eyes look and function the same, the "wiring" in our brain processes visual stimuli in the same way, I wouldnt know a reason why we wouldnt "see the same red" as one another.

(Its not really a question Philosophy can answer too well, its better suited for general biology. One of my Philosophies is: Keep Philosophy and Science seperate, otherwise you'll get nothing accomplished.)

You make a good point...it fits into the "How do I know you exist" category, I guess. I can't know for certain, but it's better to just assume so until there's proof otherwise.

My opinion on philosophy is :It's good for thinking up questions, not so great for thinking up answers.

Peter Soderqvist

20th October 2003, 02:02 AM

TO JAN

You wrote 10-17-2003 09:06 PM: No. A meta-mathematical prove is a prove. We can prove that that sentence is true. It is just impossible to give a deduction within the formal system we are discussing.

Soderqvist1: I mean that we humans can see that the sentence is truth!
But humans or computers cannot use strings and formalize a theorem, and so show that the sentence is derivable from axioms, the metamathematical proof is uniquely human Qualia! Except in those cases when there are truth, but undecidable mathematical statements in a system, in the sense that they are neither provable, nor disprovable, but it is possible to augment the set of axioms, or increase the amount of transformation rules, and so prove through theorems that even this mathematical statement is derivable, and so proven truth in the new augmented system, yet the new system is also incomplete! Therefore the Qualia of metamathematical proof; this sentence is not provable , or uncomputable numbers is not artificial intelligence, it is genuine intelligence!

The punch line of people like Lucas is that we are able to prove those sentences. Therefore, it seems as if we are more creative than any given formal system.

Soderqvist1: I think it is oxymoron, it gives me a flavor of inconsistency to use the word prove in connection with a sentence, which has alleged it is not provable, therefore; it is rather something, which can simply be shown truth, since its meta-proof is not derivable from axioms!

But of course our ability to prove is also limited.

Soderqvist1: Yes limitedness, and inconsistency are human properties, but the cognitive state of Qualia is what makes us different from computers! :)

A color is not just an on-or-off property, but something with steps in between, and furthermore, it has not just one dimension, but three (red, green and blue). Nevertheless we seem to be quite happy representing colors with a model that contains only 224 "true" colors, thus being made perfectly digital. I fail to see why a discrete model of the brain physiology should be insufficient.

Soderqvist1: I am reading Ian Glynn's book. An Anatomy of Thought, The Origin and Machinery of the Mind! I am more interested to study, than to reply about it! Btw, I have approximately 230 –250 books in my home, I will name a few, I have all Richard Dawkins's books including his last one, namely, A Devils Chaplain! I have also 3 books by Hofstadter, the latest 7 books by Daniel Dennett, including his last one, namely: Freedom Evolves! His contention is that freedom of the will is something, which evolves by natural selection! Here is a good review!

Matt Ridley reviews Freedom Evolves, The evolution of the freest
"Either our actions are determined, in which case there is nothing we can do about them, or our actions are random, in which case there is nothing we can do about them."

Daniel Dennett to the rescue. The ebullient, pugnacious and ever pithy sage of Boston has written books on free will, consciousness and Darwinism. He now returns to free will with a remarkably persuasive new idea derived from Darwinism: that freedom of the will is something that grows, that evolves. The greater the sophistication of an organism, the greater its knowledge of the world and of itself, so the greater its ability to take charge of its own destiny. A rock has no freedom to choose; a bacterium has very little; a bird has some; a conscious primate has much more; a conscious primate inheriting a rich lode of cultural knowledge has the most of all. Determinism - the idea that a cause automatically produces an effect - is not, says Dennett, the same as inevitability. This is a surprising assertion, which he spends several chapters justifying, and I think he succeeds.
http://www.arts.telegraph.co.uk/arts/main.jhtml?xml=/arts/2003/02/09/boden09.xml&sSheet=/arts/2003/02/09/bomain.html

I have also Benjamin Libet 's book, The Volitional Brain, Towards a Neuroscience of Free Will, which is listed in the bibliography in Dennett's book, Freedom Evolves! How The Mind Works, and The Blank Slate by Steven Pinker, some books by E. O. Wilson including his Magnus Opus, Sociobiology; The New Synthesis, and his adversaries book, Not In Our Genes, By Kamin, Rose, Lewontin. S J Gould's Magnus Opus 2003, The Structure of Evolutionary Theory, on 1435 pages, and Stuart Kauffman 's Origins of Order, Adaption on The Edge of Chaos!

The Volitional Brain's Home Side!
http://www.imprint.co.uk/books/volitional_brain.html

And much, much more. So many books and so little time to read! :book:

jan

20th October 2003, 11:06 AM

Peter Soderqvist,

let G be a sentence within the formal system PM, being constructed with Gödel's method and therefore true, but undecidable within PM.

Now read it from my lips: we can prove that G is a true sentence. We don't "see" it, we prove it. If we could only "see" it, it would be completely worthless.

And you yourself have mentioned a method how to proof the truth of G within a formal system (just take PM+G).

Obviously, Gödel was using strings to proof his theorems (and to show, within such a proof, that G is a true sentence). What do you think he used? Handwaving? Photos of naked women?

The idea that a machine can't experience this or that Qualia (may it be the feeling of "seeing" a proof or the experience of seeing the color red) is a bit strange if we assume that humans are just a variety of soft machines. And I fail to see what it has to do with Gödel's sentence. If machines can't experience qualia, they can't experience qualia. If they can, they can. And Gödel's theorems are in no way special.

About the number of books you have read: I couldn't resist to make fun of your claim to have read five books. It wasn't intended to harm you, or to start some sort of pissing contests. It doesn't count how many books you have read (or at least own). As long as you have read "Prince Genji", of course.

Peter Soderqvist

21st October 2003, 12:15 AM

If we assume that G is: this sentence is not provable
Jan, can you use strings and prove that this sentence is not provable?
How do you prove that G is truth?

Hofstadter, Gödel, Escher, Bach
Gödel showed that provability is a weaker notion than truth, no matter what axiom system is involved ...
http://www.miskatonic.org/godel.html

Peter Soderqvist

21st October 2003, 05:03 AM

TO JAN

You have replied 10-17-2003 12:39 AM: Originally posted by Peter Soderqvist Soderqvist1: But what about abstract cakes "mathematical truths" which is not derivable from any axioms? The cake-bible is forever doomed to incompleteness whatever axiomatic systems involved! See my earlier link to Kurt Gödel!

Jan: Those are the cakes nobody knows how to bake.

Soderqvist1: G is cake nobody knows how to bake!
And for the sake of consistency: G is a sentence nobody knows how to make, because baking is a weaker notion than G, therefore; baking is incomplete! A Turing Machine is a theorem machine, which cannot make G, the same sentence a human can see is truth, and it follows from that; a Turing Machine cannot model a human mind's concept of G. ;)

jan

22nd October 2003, 07:24 AM

Originally posted by jan
let G be a sentence within the formal system PM, being constructed with Gödel's method and therefore true, but undecidable within PM.

Now read it from my lips: we can prove that G is a true sentence. We don't "see" it, we prove it. If we could only "see" it, it would be completely worthless.

You shouldn't read from my lips, I guess. I made a mistake. The sentence G is true only if PM is consistent, so what we really prove is "if PM is consistent, G is true". Since PM can't be used to show that PM is consistent (the other theorem), it can be tough to show that a given formal system is consistent.

But that doesn't affect my position, it's just a minor detail I explained wrong. Since we can't prove that G is true (without the assumption of the consistency of PM), we also can't "see" it. So if a machine can't prove the truth of G, we are in no better position. And since we can prove that G is true, if PM is consistent, I see no reason why a machine couldn't prove it. That is, Gödel does not demand that we "see" something we can't prove.

One could say "although we can't prove that PM is consistent, is is very, very likely that it is". Perhaps. But that is not a prove. And I can't see it.

So I still claim that there is no qualia involved which is, for purely mathematical reasons, not accessible for machines, but for human beings.

Originally posted by Peter Soderqvist
If we assume that G is: this sentence is not provable
Jan, can you use strings and prove that this sentence is not provable?
How do you prove that G is truth?

Originally posted by Kurt Gödel

1. 17 Gen r is not κ-PROVABLE. For, if it were, there would (by (6.1)) be an n such that nBκ (17Genr). Hence by (16) we would have Bewκ[Neg(SB(r17Z(n)))], while, on the other hand, from the κ-PROVABILITY of 17Genr that of SB(r17Z(n)) follows. Hence, κ would be inconsistent (and a fortiori ω-inconsistent).

2. Neg(17 Gen r) is not κ-PROVABLE. Proof: As has just been proofed, 17Genr is not κ-PROVABLE; that is (by (6.1)), (n)___nBκ(17Genr) holds. From this, (n)Bewκ[SB(r17Z(n))] follows by (15), and that, in conjunction with Bewκ[Neg(17Genr)], is incompatible with the ω-consistency of κ.

17 Gen r is therefore undecidabe on the basis of κ, which proves Theorem VI.

We can readily see that the proof just given is constructive; that is, the following has been proved in an intuitionistically unobjectionable manner: Let an arbitrary recursively defined class κ of FORMULAS be given. Then, if a formal decision (on the basis of κ) of the SENTENTIAL FORMULA 17Genr (which [for each κ] can actually be exhibited) is presented to us, we can actually give

1. A PROOF of Neg(17Genr);

2. For any given n, a PROOF of SB(r17Z(n)).

The (english) sentence "this sentence is not provable" is, of course, not a mathematical sentence, and obviously not a formal sentence of PM. It could be considered as some kind of rough translation of G. There is no mathematical proof of the incompleteness of "informal sensible reasoning using the english language". Neither is there a mathematical proof of completeness. And as a sentence of the common language, it is comparable to sentences like the well-known "this sentence is false". False? True? Undecidable? Ill-formed?

Originally posted by Peter Soderqvist
G is cake nobody knows how to bake!

Originally posted by Kurt Gödel

...17Genr can actually be exhibited...

hammegk

22nd October 2003, 08:51 AM

Originally posted by jan

I made a mistake. ............

But that doesn't affect my position, it's just a minor detail I explained wrong. ............

That statement confuses me; I'd say you bet the farm on the coin flip coming up heads & it was tails.

I thought the invocation of Godel, in English, is that any formal logical system will contain at least one axiom that cannot be proved within the system itself.

For materialists, one uprovable axiom is that "an objective physical world exists".

Dancing David

22nd October 2003, 09:57 AM

hammegk

22nd October 2003, 11:06 AM

Originally posted by Dancing David

Which I have rewritten the axiom:

The physical world behaves as though it exists in an objective fashion.

There you go again. :) What is the "physical" part of "what-is"?

If you say the world of human perception behaves as though it exists in an objective fashion, you are Scientist, but not necessarily a materialist/atheist.

It appears to me you might be classified under the naturalist label. :)

Dancing David

22nd October 2003, 04:16 PM

Originally posted by hammegk

There you go again. :) What is the "physical" part of "what-is"?

If you say the world of human perception behaves as though it exists in an objective fashion, you are Scientist, but not necessarily a materialist/atheist.

It appears to me you might be classified under the naturalist label. :)

Thou art most correct,

the world that is detected through our perceptions behaves as though it has an objective existance, wether it actualy does or not.

Perception, unfortuantely suffers from many inherent errors and fabrications.

naturalist huh, can I still wear clothes?

Peter Soderqvist

23rd October 2003, 01:34 AM

TO JAN

You wrote 10-22-2003 02:24 PM: You shouldn't read from my lips, I guess. I made a mistake. The sentence G is true only if PM is consistent, so what we really prove is "if PM is consistent, G is true". Since PM can't be used to show that PM is consistent (the other theorem), it can be tough to show that a given formal system is consistent.

Soderqvist1: Granted!

But that doesn't affect my position, it's just a minor detail I explained wrong. Since we can't prove that G is true (without the assumption of the consistency of PM), we also can't "see" it.

Soderqvist1: I Disagree!
Because I can see that the sentence: this statement is not provable is truth!
Because David Hilbert has failed to put its arithmetical counterpart on a firm axiomatic base! It was David Hilbert's dream in 1928, that the whole formal system of arithmetic should be put on a firm axiomatic base, in the sense that all its proofs or mathematical statements should be derivable from axioms, and so proven truth! But within Principia Mathematica there is a paradox labeled Epimedes Paradox, more known as the Cretan liar paradox. Godel has transformed the whole language of PM into numbers, including exhibit the Epimedes paradox into its arithmetical counterpart, in short; its gödel number: this statement is not truth , he modified it slightly into this statement is not provable . Hilbert has failed to give Epimedes paradox a theorem; therefore arithmetic is incomplete, as Kurt Godel has shown 1931!

So if a machine can't prove the truth of G, we are in no better position. And since we can prove that G is true, if PM is consistent, I see no reason why a machine couldn't prove it. That is, Gödel does not demand that we "see" something we can't prove.

Soderqvist1: how is Hofstadter 's statement compatible with your proposition?

Hofstadter, Gödel, Escher, Bach
Gödel showed that provability is a weaker notion than truth, no matter what axiom system is involved ...
http://www.miskatonic.org/godel.html

Soderqvist1: The axiomatic system of PM its provability is weaker than the truth statement G!

One could say "although we can't prove that PM is consistent, it is very, very likely that it is". Perhaps. But that is not a prove. And I can't see it.

Soderqvist1: And the punch line is?

So I still claim that there is no Qualia involved which is, for purely mathematical reasons, not accessible for machines, but for human beings.

Soderqvist1: You have no case here, because you have failed, like Hilbert to give Epimedes Paradox a theorem, so you cannot through Turing Machines model human mind's pondering about Epimedes Paradox!

The (English) sentence "this sentence is not provable" is, of course, not a mathematical sentence, and obviously not a formal sentence of PM. It could be considered as some kind of rough translation of G. There is no mathematical proof of the incompleteness of "informal sensible reasoning using the English language". Neither is there a mathematical proof of completeness. And as a sentence of the common language, it is comparable to sentences like the well-known "this sentence is false". False? True? Undecidable? Ill-formed?

Soderqvist1: Il informed? :confused:

Originally posted by Jan 10-17-2003 12:39 AM:
Those are the cakes nobody knows how to bake.

Originally posted by Peter Soderqvist
G is cake nobody knows how to bake!

Originally posted by Kurt Gödel
...17 Gen r can actually be exhibited...

Soderqvist1: Very well done gödel, you have succeeded to exhibit the arithmetical counterpart to Epimedes Paradox into its Godel number, which David Hilbert failed to give a theorem, you have shown that Epimedes Paradox is really the cake nobody knows how to bake, therefore; arithmetic is incomplete! Since both G, and its negation cannot be truth theorems, we end up inconsistent both ways, since according to the old riddle; a Cretan asserts that all Cretans lie. So, is he lying? If he lies, then he tells the truth and does not lie. If he does not lie, then he tells the truth and so lies. Both cases lead to a contradiction, or inconsistency! :)

Peter Soderqvist

23rd October 2003, 05:07 AM

One of David Hilbert's assumptions about consistency was that; both a statement and its negation could not have theorems, but Cretan's statement is paradoxically both true and false, so what truth mathematical statement can be made about the Cretan's statement?

This statement is not provable!

jan

24th October 2003, 01:45 PM

Originally posted by hammegk

That statement confuses me; I'd say you bet the farm on the coin flip coming up heads & it was tails.

I thought the invocation of Godel, in English, is that any formal logical system will contain at least one axiom that cannot be proved within the system itself.

For materialists, one uprovable axiom is that "an objective physical world exists".

What has a philosophical theory like Materialism which may or may not be metaphysical to do with a metamathematical theorem about formal systems?

Many modern versions of empirialism agree that you can't prove anything. Some things are falsifiable, therefore you can test and corrobate them, but that's not a proof that they are correct. And, by the way, you never proof an axiom.

Perhaps what you are trying to say is something like "the existence of an objective physical world is an assumption of Materialism that can't be corrobated, and is thus metaphysical". We could discuss such a claim (I think this claim is wrong), but what has Gödel to do with it?

Originally posted by Peter Soderqvist

Because I can see that the sentence: this statement is not provable is truth!

I don't see it. Prove that it is true.

Originally posted by Peter Soderqvist

Soderqvist1: how is Hofstadter 's statement compatible with your proposition?

Since you are so eager to tell me the history of mathematics, let me tell you some more.

Once upon a time, Newton and Leibnitz invented the calculus, and in a less than satisfying manner, which lead to many false proofs and theorems, which culminated in a crisis in the late 19th century. The invention of set theory made things even worse, since set theory was plagued by many contradictions. In this situation, it was very doubtful if it was able to prove anything at all.

This was the reason why Hilbert, and many others, were interested in the development of a formal foundation of mathematics.

You see, mathematics is a wild enterprise that is done in greek, arabic, german, russion and english sentences. It is based on sound reasoning, but occasionally, errors occur.

A formal system, on the other hand, is a set of axioms, together with rules of inference, that allow you to built more sentences out of the axioms. The sentences are just chains of symbols, but it is possible to give them an interpretation. If we interpret such a chain of symbols, it can be true or false.

We can try to formalize the concept of truth, by saying that a sentence is true if is in the set of obtainable sentences, that is, a deducable sentence. Since a formal deduction can be taken as a proof, we may say that a deducible sentence is also a provable sentence.

It is believed (the thesis of Church&Turing) that all mathematics can be translated in principle in formal systems, that means, any provable sentence is also deducible in an apropriate formal system.

In fact, it was hoped that it was possible to find a formal system that could replace mathematics. If we had such a system, and if this system would be consistent, and if every true sentence would be deducible, we would never be in the situation that we have to wonder whether a certain given proof is valid: all we have to do is to replace that proof with a formal deduction. Indeed, we could settle any mathematical question. All we would have to do is to mechanically produce all possible deductions of the axioms, and wait untill our questionable sentence or its negation appears.

This project failed, for three reasons. Tow of these reasons are well kown, while the third reason is the only important one.

1. If we formalize mathematics, we can't proof the consistency of this formalisation (we would need stronger principles than those formalized, but we formalized all we know). Proved by Gödel.

2. Even if we assume that our formal system is consistent, it is then not complete (the other famous theorem of Gödel).

3. Doing mathematics in a formal language is incredibly roundabout. It does not help you to check whether a certain sentence is valid. If you want to check whether a certain sentence is valid, it is just a pain in the ass to give a formal deduction, and nobody ever does that. And it also turned out to be completely unnecessairy, since it turned out that calculus and set theory and probability theory and any other doubtful theory can be reorganized in a way that makes most of the former problems vanish.

To prove 1. and 2., Gödel considered a formal system P and a sentence 17Genr within that system ("17Genr" is just an abbrevation; since it is a very, very long and roundabout sentence, nobody has ever written it out), and showed that this sentence is undecidable.

If we interpret this sentence, it is something like "I cannot be deduced within P", and since this is true, that means, that 17Genr is a true sentence (and it is no problem to show, to demonstrate, to prove that it is true).

Now consider the sentence "This statement is not provable". Let's call it S. Now is S true? Provable? Whatever? I have absolutely no idea. It is just a plain english statement with doubious character.

We have shown that 17Genr is true, but not deducible withing P. Therefor, if we hope to identify mathematical truth with deducibility in any given formal system, our hope is vain. And that is just what Hofstadter said. You see, there are some important, but unfixed terms, and it is a good thing if you can give them precise meanings. So if it would have been possible to identify truth and deducibility, this would have made much clearer what truth is. But the attempt failed.

Originally posted by Peter Soderqvist

You have no case here, because you have failed, like Hilbert to give Epimedes Paradox a theorem, so you cannot through Turing Machines model human mind's pondering about Epimedes Paradox!

See, deducibilty is a technical aspect of sentences of formal systems. That's why it is able to talk about deducibility within P. You can't talk about truth within P, since this is a concept that belongs to the interpretation of the sentences of P. Therefore, there is no way to formalize the Epimenides Paradox within P. And 17Genr is not a formalized version of the Epimenides Paradox. It is talking about not being deducible with the means of P. It is not talking about being false.

You may claim that a Turing Machine can't ponder about anything. But if it can ponder about something, I still fail to see why it shouldn't ponder about Epimenides Paradox.

You see, the Epimenides Paradox is just an english sentence. You can write programs that parse english sentences and output other english sentences. Such a program is not bound to be an attempt to model a formalized version of mathematics. Inespecially, if we want to simulate or model a human being, such a system may produce sentences being vague, doubtful, or flat out wrong.

As mentioned above, the reason why formal system have been such a big name was that humans sometimes made errors. I guess a machine that models a human being will also make errors. Try to apply Gödel here.

Dymanic

24th October 2003, 06:56 PM

Originally posted by Jan

I guess a machine that models a human being will also make errors.
Something interesting here. I'm currently trying to digest Penrose's conclusion that human reasoning is made more powerful by its ability to make mistakes; for instance, by liberal use of the enthymeme (a deductive argument which omits some propositions), answers can be reached which are algorithmically unsolvable, thus avoiding what I think of as 'pathological precision'. But...but... you can't explicitly code such a thing, because that would be algorithmic...

It's driving me a little nuts.

jan

25th October 2003, 05:18 AM

Sounds interesting. I would like to add that there are several attempts to model human thinking outside the restrictions of formal deductive systems, for example, fuzzy logic or neural networks. All those attempts can be in principle simulated with ordinary algorithms, but usually they are far away from error-free reasoning. And the "in principle", in practical terms, often is another way of saying that it is not possible. A formal system is not a model of a real mathematician, but an attempt to model the ideal mathematician. Often you are not interested in a system that always gives you right answers, but in a system that gives you fast answers.

It seems quite obvious that human beings, as products of evolution, are not designed to always give correct answers, but to give likely answers fast.

Peter Soderqvist

26th October 2003, 11:03 PM

I am too bored to reply!

UndercoverElephant

27th October 2003, 03:12 AM

Pahansiri,

I do not understand how you could think that hammegk is Frankos sockpuppet. It is a preposterous idea.

:)

Geoff.

Upchurch

27th October 2003, 06:47 AM

Originally posted by JustGeoff
I do not understand how you could think that hammegk is Frankos sockpuppet. It is a preposterous idea. Having been here a month, I find it odd that you would jump to such a conclusion. I mean, what kind of experience are you basing it being a preposterous idea on?

Dancing David

27th October 2003, 06:48 AM

The algorithims would be different from what people may normaly think of a logic. The brain does a number of interesting things, the most power full is to creat and look for associations. It finds patterns and creates patterns.

I feel that the algorithims people contemplate are nor organic enough, especialy when we start talking about goedel's theorem, I would assume from the start that we are trying to make something that approxiamtes the brain, not an exact duplicate.

whitefork

27th October 2003, 07:46 AM

Originally posted by Upchurch
Having been here a month, I find it odd that you would jump to such a conclusion. I mean, what kind of experience are you basing it being a preposterous idea on? I guess you missed the post where JustGeoff said that he was the former UndercoverElephant and Jester (it's pretty clear from the writing style too).

Anything he has to say about the Sage has a high liklihood of being correct.

Dymanic

27th October 2003, 08:29 AM

Originally posted by Peter Soderqvist

I am too bored to reply!
I'm not bored, but I am rather busy today, so I won't reply either.

jan

27th October 2003, 02:08 PM

Originally posted by Peter Soderqvist
I am too bored to reply!

All your claims are belong to us.

http://www.click-smilies.de/sammlung0903/aetsch/cheeky-smiley-031.gif

Upchurch

27th October 2003, 03:40 PM

Originally posted by Kullervo
I guess you missed the post where JustGeoff said that he was the former UndercoverElephant and Jester (it's pretty clear from the writing style too). Now that you mention it, that does ring a bell. Ah, well. They say the memory is the first to something something....

hammegk

27th October 2003, 03:41 PM

Originally posted by jan

Perhaps what you are trying to say is something like "the existence of an objective physical world is an assumption of Materialism that can't be corrobated, and is thus metaphysical". We could discuss such a claim (I think this claim is wrong), but what has Gödel to do with it?
Yeah, I'd buy that. "Godel" gets invoked by me for that reason alone.

BTW, I'd like to know why you think the claim is wrong.

You may claim that a Turing Machine can't ponder about anything. But if it can ponder about something, I still fail to see why it shouldn't ponder about Epimenides Paradox.

..... Try to apply Gödel here.
"Ponder" seems a bit too open ended for a Turing Machine don't you think? As to Godel, what unprovable axioms might get involved in your defense of the "ponder" assertion?

Peter Soderqvist

28th October 2003, 01:02 AM

Originally posted by Dymanic

I'm not bored, but I am rather busy today, so I won't reply either.

Soderqvist1: that doesn't mean all your claims belong to me!

Peter Soderqvist

28th October 2003, 01:05 AM

TO JAN

Originally posted by jan

All your claims are belong to us.

http://www.click-smilies.de/sammlung0903/aetsch/cheeky-smiley-031.gif

Soderqvist1: There is a one-to-one correspondence between the logical language of PM, numbers, and meaning, or semantics! Isn't pondering about The Cretan Paradox underivable from axioms? A process must be computable if a Turing Machine shall be able to generate its theorem! One theorem derives the truth statement that "all Cretans are liars" and another theorem derive that the Cretan has said the truth, and so this Cretan is not a liar! These theorems are not consistent, because at least this Cretan is not a liar, and if he is not a liar, he has still tell a lie anyway, because he has said that all Cretans are liars, this endless loop is undecidable whatever axiomatic system involved, because the Cretan paradox is simply not provable; this statement is not provable is a truth mathematical statement which is not derivable from axioms! You have no case here until you can show, how a Turing Machine can simulate a non-computational mathematical insight, and my following truth statement; the Cretan's statement is not provable, without ending up in an endless loop, known as the "halting Problem"!

A Turing Machine is stuck in this endless loop, but humans "can mentally jump-out" from the system, and so from an external point of view, see that the system is undecidable!

A wordy reply will not help your case, my Swedish razor below can tell you why! :rolleyes:

UndercoverElephant

28th October 2003, 06:20 AM

Originally posted by Upchurch
Having been here a month, I find it odd that you would jump to such a conclusion. I mean, what kind of experience are you basing it being a preposterous idea on?

Upchurch,

You are talking to UndercoverElephant. I am intimately familiar with the views of Pahansiri, hammegk and the Frankmonster.

;)

Dymanic

28th October 2003, 08:42 AM

Originally posted by Peter Soderqvist

A Turing Machine is stuck in this endless loop, but humans "can mentally jump-out" from the system, and so from an external point of view, see that the [problem?] is undecidable!

Well, a human can conclude -- perhaps reasonably -- that further work on a particular problem is not likely to produce fruitful results, but this is much weaker than proving that no solution exists.

Plus, the halting problem as it relates to hopeless attempts at solving unsolvable problems is not quite the same as falling into an unproductive hard loop. Epimenides-paradox-type problems (my personal favorite being: "This statement contains too errors") result in endless unproductive repetitions of the same state, and on that basis can be easily identified as hopeless.

But a different type of halting problem results when a Turing machine attempts to solve a problem such as: "Find an even number not expressible as the difference between two odd primes". As successively higher numbers are tested, it might appear that progress is being made, but whether or not this is actually the case depends entirely on whether a solution actually exists.

One might invoke multiple Turing machines running in parallel, giving one the power to pull the plug on another, but (even overlooking the fact that taken together, these might be expressed as a single Turing machine) how can we be sure the plug won't be pulled on a process that does have an actual solution, just one requiring a huge number of steps to reach -- say finding the factorial of a large number?

How the heck are we humans able to simply look at a problem and make even a reasonable guess as to whether it has a solution? This is about the closest thing to real magic I've seen yet!

jan

28th October 2003, 12:59 PM

Originally posted by hammegk

"Ponder" seems a bit too open ended for a Turing Machine don't you think? As to Godel, what unprovable axioms might get involved in your defense of the "ponder" assertion?

The word "ponder" was used in response to Peter Soderquist. You may replace it with stronger claims.

Perhapy we may consider this: a robot being able to think, experience qualia, have feelings, being self-conscious and so on, but being unable to experience the qualia of "seeing" the truth of a sentence like 17Genr. Maybe we should call such a being a "g-Zombie", since Gödel is supposed to forbid such a g-zombie to experience such states. Do you think such a g-zombie is possible? Or utter nonsense?

Originally posted by jan

Perhaps what you are trying to say is something like "the existence of an objective physical world is an assumption of Materialism that can't be corrobated, and is thus metaphysical". We could discuss such a claim (I think this claim is wrong), but what has Gödel to do with it?

Originally posted by hammegk

BTW, I'd like to know why you think the claim is wrong.

Short answer: old-fashioned Materialism is about the substance the world is made of. That is a metaphysical claim. Modern Materialism is about mental states being caused by physical states (without special assumptions about the metaphysical nature of those physical states). That is an empirical and falsifiable claim.

Long answer: if you want to, we may start a new thread, since discussing such a claim could be considered as derailing (besides this thread being pretty derailed quite now).

Originally posted by Peter Soderqvist

There is a one-to-one correspondence between the logical language of PM, numbers, and meaning, or semantics! Isn't pondering about The Cretan Paradox underivable from axioms? A process must be computable if a Turing Machine shall be able to generate its theorem! One theorem derives the truth statement that "all Cretans are liars" and another theorem derive that the Cretan has said the truth, and so this Cretan is not a liar! These theorems are not consistent, because at least this Cretan is not a liar, and if he is not a liar, he has still tell a lie anyway, because he has said that all Cretans are liars, this endless loop is undecidable whatever axiomatic system involved, because the Cretan paradox is simply not provable; this statement is not provable is a truth mathematical statement which is not derivable from axioms! You have no case here until you can show, how a Turing Machine can simulate a non-computational mathematical insight, and my following truth statement; the Cretan's statement is not provable, without ending up in an endless loop, known as the "halting Problem"!

I will try to be brief: "this statement is not provable" is not a mathematical sentence.

Originally posted by Peter Soderqvist

A Turing Machine is stuck in this endless loop, but humans "can mentally jump-out" from the system, and so from an external point of view, see that the system is undecidable!

Even briefer: my faithful sidecick Dynamic refuted this. (Sorry Dynamic for calling you "my faithful sidecick" :cool: )

Originally posted by Peter Soderqvist

A wordy reply will not help your case, my Swedish razor below can tell you why! :rolleyes:

Peter Soderqvist's signature:

A simple explanation with few explanation grounds is to prefer, except when you need to hide your flaws!

I would prefer a true explanation.

If Gödel's theorem is so simple and obvious and trivial, then why do you think it took so long untill someone discovered it? Perhaps the case is just a bit more complicated than the Cretan paradox.

Dymanic

28th October 2003, 01:11 PM

Originally posted by Jan

(Sorry Dynamic for calling you "my faithful sidecick")
No prob. Just watch the spelling.

jan

28th October 2003, 01:30 PM

Grrr, I even looked it up, and I nevertheless messed it.:bricks:

hammegk

28th October 2003, 02:19 PM

Originally posted by jan

The word "ponder" was used in response to Peter Soderquist. You may replace it with stronger claims.
I thought "ponder" captures the essence of things.

Perhapy we may consider this: a robot being able to think, experience qualia, have feelings, being self-conscious and so on, but being unable to experience the qualia of "seeing" the truth of a sentence like 17Genr. Maybe we should call such a being a "g-Zombie", since Gödel is supposed to forbid such a g-zombie to experience such states. Do you think such a g-zombie is possible? Or utter nonsense?
Er, yes, I believe we are discussing a topic that bears on those questions. My position remains "utter nonsense".

Short answer: old-fashioned Materialism is about the substance the world is made of. That is a metaphysical claim. Modern Materialism is about mental states being caused by physical states (without special assumptions about the metaphysical nature of those physical states).
Love the circularity -- we'll call "mind" and "matter" physical states and physical may be mind, matter, or both, but in any case "physical" exists. Stimpy likes that answer too. ;)

That is an empirical and falsifiable claim.
If I count a sheep's tail as a leg, how many legs does it have?

Even briefer: my faithful sidecick Dynamic refuted this.
I speculate Dymanic is dynamic, but who is Dynamic? :D

And I would say his comment re "magic" is closer to my position of idealism than the position of a naturalist (=mind or matter or both, who cares?).

Dancing David

28th October 2003, 03:10 PM

Gotta agree with Stimpy: the ontology of the physical world does not exclude the verifiablity of observations made through perception. (Whew, did I say it right that time?)

Dymanic

28th October 2003, 03:14 PM

Originally posted by hammegk

I speculate Dymanic is dynamic
AND manic. Get it? Actually, it started with a typo that occurred while writing a program in QuickBasic. Now in QB, '$Dynamic is an in-line compiler instruction; a 'meta-command', having to do with the way stuff is handled in memory. It is one of the quirks of QB that such metacommands are prefaced by ' or REM, which means that if you booger the command, it will simply ignore it. Like to drove me crazy before I finally figured it out. Lately, one of my fingers has decided that it is cute to substitute a zero for a capital 'O' here and there. That also makes for really hard-to-spot bugs.
And I would say his comment re "magic" is closer to my position of idealism than the position of a naturalist
How come every time I make a statement, along comes some philosopher ready to throw some kind of 'ist' or 'ism' net over it?

jan

28th October 2003, 03:44 PM

Originally posted by hammegk

Er, yes, I believe we are discussing a topic that bears on those questions. My position remains "utter nonsense".

Why? Because you don't believe a robot could be built that thinks and feels (hint: no Gödel needed here)? Or because you believe such a robot would be able to see the truth of 17Genr (hint: Gödel not helpful here)?

Originally posted by hammegk

Love the circularity -- we'll call "mind" and "matter" physical states and physical may be mind, matter, or both, but in any case "physical" exists. Stimpy likes that answer too. ;)

I am not too embarrassed if my views are shared by Stimpy.

I suggest two possible versions of Immaterialism. Pick one or suggest a third.

i) The Laws Of Physics are more or less correct, it is just the metaphysical interpretation of Physics of Materialism that should be questioned.
ii) Physics is crap since it talks about a nonexisting material world.

Originally posted by hammegk

I speculate Dymanic is dynamic, but who is Dynamic? :D

Yeah, yeah, cick a falling man. :bricks: :bricks:

hammegk

28th October 2003, 03:51 PM

Originally posted by Dymanic

How come every time I make a statement, along comes some philosopher ready to throw some kind of 'ist' or 'ism' net over it?

:D

Er, was that a yes, no, or maybe? :confused:

jan: #1. *I* am not a Turing Machine; i.e. no such robot possible.
#2. i).
#3. Who, me? Cick someone?

DD: Agreed, but did the question disappear?

Dymanic

28th October 2003, 09:35 PM

Originally posted by hammegk

Er, was that a yes, no, or maybe?
Actually, it was more of a "mu".

Peter Soderqvist

29th October 2003, 01:43 AM

TO JAN

You wrote 10-28-2003 07:59 PM: I will try to be brief: "this statement is not provable" is not a mathematical sentence.

Soderqvist1: Do this sentence have an analogous counterpart in arithmetic, yes, or no?

hammegk

29th October 2003, 06:50 AM

Originally posted by Dymanic

Actually, it was more of a "mu".

:)

jan

29th October 2003, 10:04 AM

Originally posted by hammegk

#1. *I* am not a Turing Machine; i.e. no such robot possible.
#2. i).
#3. Who, me? Cick someone?

#1. So I assume you can show this without quoting Gödel.

#2. So what's wrong with using physical terms and claiming that certain physical phenomenons have a certain relationship to certain other phenomenons?

Originally posted by Peter Soderqvist

"this statement is not provable"
Do this sentence have an analogous counterpart in arithmetic, yes, or no?

No.

Dancing David

29th October 2003, 11:11 AM

Originally posted by hammegk

DD: Agreed, but did the question disappear? [/B]

No, but I am not sure which question you are addressing, it could have answers but it might not. ;)

Peter Soderqvist

29th October 2003, 10:59 PM

TO JAN

Originally posted by Peter Soderqvist
TO JAN

Soderqvist1: Do this sentence have an analogous counterpart in arithmetic, yes, or no?
Originally posted by jan

"this statement is not provable"

No.

Soderqvist1: Wrong!
3. Godel Sentence: Show that the sentence 'This statement is unprovable' has an arithmetical counterpart, its Godel sentence G, in every conceivable formalization of arithmetic. http://homepages.which.net/~gk.sherman/baaaaab.htm

Btw, I have just read the page 17 – 18 in Hofstadter 's Godel, Escher, Bach, An Eternal Golden Braid, that Godel has transported The Epimenides Paradox into arithmetic!

hammegk

30th October 2003, 07:20 AM

Originally posted by jan

#1. So I assume you can show this without quoting Gödel.

Sorry, no. Feel free to "prove" it one way or the other with or without Godel.

#2. So what's wrong with using physical terms and claiming that certain physical phenomenons have a certain relationship to certain other phenomenons?
Huh? When did I ever say something that would support that statement? If I did, it was a mistake; of course perceived-as-physical phenomena obey "rules" that bind them to other perceived-as-physical phenomena. TLOP can be considered the current math/physics expression of The Way Things Are.

jan

2nd November 2003, 09:12 AM

Peter Soderqvist and hammegk,

Due to the birth of my second daughter today, it may take a few days/weeks/whatever untill I will be able to play with you again, so don't hold your breath for my answer, but of course I deny everything you say.

ceptimus

2nd November 2003, 11:29 AM

Set up the Turing machine so that it does not tell lies, then ask it:

1. Are you conscious?

Of course, it might reply no. But if it replies yes, then surely it is as conscious as the rest of us?

Dancing David

2nd November 2003, 02:55 PM

This points right to the heart of the debate,
I say that you could make a machine to emulate and conciousness, you don't need to have an exact model of the brain either, because the brain is not an exact model to begin with.

Behaviorists would say, if it behaves as though it is consious then it is.

Then the immaterailist will give you some emotional reason or some 'logic' reason that it can't be consious.

Which is why p-zombies are an absurdity, if it acts consious, then it might as well be!

jan

11th August 2004, 02:53 PM

Sorry for the delay...

Originally posted by jan
Due to the birth of my second daughter today, it may take a few days/weeks/whatever untill I will be able to play with you again, so don't hold your breath for my answer, but of course I deny everything you say.

...and here we go...

Some terms have a technical meaning, and some terms lack such a technical meaning. For example, "real number" is a term with a strict mathematical definition (in fact, there are several different definitions of this term, and it can be shown that they all define the same term). Such a definition uses other terms, like the term "set". Such a term usually gets its meaning using axioms to describe how a set should behave.

A term like "number", on the other hand, lacks a strict definition like "real number". Usually, real numbers are considered to be numbers, octonions are considered to be numbers, but members of an arbitrary symmetry group are usually not called "numbers", and there is no general rule to decide what entities are to be considered to be numbers. Therefore, the word "number" is used in talks about mathematics, but it is not part of mathematical theorems, unlike the word "real number".

The words "proof" and "proving" are similar to the word "number". What mathematicians are doing is proving, but "proof" is not a mathematical term like "real number". If you want to talk about proofs, and if you want to talk about proofs within mathematics, you have to replace the terms "proof" and "proving" with terms having a strict meaning and a technical definition. So instead of talking about mathematics, mathematicians and proving, you can start talking about formal systems, formal sentences and deducibility. The sentence "formal sentence G is deducible within the formal system P" has a strict meaning and can be investigated with mathematical means.

Now compare these two sentences:

S1: This sentence has no proof.
S2: This sentence has no proof within P.

Both are informal sentences and need to be translated. S2 can be translated into some formal sentence G of the formal system P, such that G has the semantic meaning that is expressed by S2 (what we really translate is S3: "This sentence is not deducible within P" (or some sentence S4: "A sentence that is equivalent to this sentence is not deducible within P")). Now we have two possibilities: i) G is deducible within P. Since G has the meaning that G is not deducible within P, this means that G is false, and that a false sentence is deducible within P ii) G is not deducible within P, and therefore true.

If we assume that P doesn't allow the deduction of false sentences (an assumption I forgot to mention earlier), then possibility i) is ruled out, so only ii) remains, and that means that we can proof that G is true.

On the other hand, I don't know how sentence S1 could be transformed in some kind of formal sentence. This is just some kind of English sentence, like, for example, "this sentence is false" or "chocolate ice-cream tastes better than strawberry ice-cream", sentences that can be discussed, but that are not mathematical sentences and sometimes lack a proper truth-value. Since S1 is not a mathematical sentence, it lacks a mathematical proof. I have no idea whether this sentence should be considered true or false, similar to the other two sentences I mentioned. Maybe it is just a nonsensical sentence, who knows? If you happen to see the truth of this sentence, congratulations. But perhaps you should check your visions.

jan

25th August 2004, 09:28 AM

Thinking over that wikipedia coding again...

With this system, it is impossible to distinguish a number that is an encoding of a sequence of sequence of sentences from an encoding of a sequence of sentences from an encoding of a sentence from an encoding of a single letter. Unfortunately, the page claims that it is. But I think it is possible to construct a Gödel sentence even with this coding, if it is carefully ensured that it is always possible to determine whether a sentence or a sequence of sentences or whatever is expected.

For example, let a be the encoding of a sequence of sentences, and b be the encoding of a sentence. a could also be the encoding of a single sentence, or of a single letter. Now assume that PROOF(a,b) is a sentence within P that says something like "the sequence of sentences as encoded in a is a deduction within P for the sentence encoded in b", of course in arithmetic terms. Obviously, a is to be understood as the encoding of a sequence of sentences, so the ambiguity of the encoding can be considered as harmless (I guess).

I assume that all this was clear for Soderqvist all along, but he didn't cared to mention it. Gee, do I really have to do all his homework?

epepke

25th August 2004, 04:02 PM

Originally posted by jan
Thinking over that wikipedia coding again...

With this system, it is impossible to distinguish a number that is an encoding of a sequence of sequence of sentences from an encoding of a sequence of sentences from an encoding of a sentence from an encoding of a single letter.

It's trivial.

I mean that.

jan

26th August 2004, 10:09 AM

I admit I (probably) made another mistake. I came to the conclusion that I could built a formal system using the symbols mentioned in the wikipedia article which would be able to formalize all arithmetic sentences, and that I probably would be able to apply Gödel's method using the suggested coding (although I won't be doing it, since it is "trivial").

I still hold my other claims. Of which the most important currently are:

- There is no Supergödel sentence S which is undeducible in all formal systems.

- The English sentence "This statement cannot be proven" is not a proper translation of the formal sentence Gödel constructed.

- Gödel's incompleteness theorems do not prove that it is impossible to built a machine with consciousness.

Gestahl

26th August 2004, 12:10 PM

Originally posted by jan
[b]I still hold my other claims. Of which the most important currently are:

- There is no Supergödel sentence S which is undeducible in all formal systems.

No, but all formal systems have such a statement. This statement, translated from the system to English, is the one given below. I would agree with this statement.

- The English sentence "This statement cannot be proven" is not a proper translation of the formal sentence Gödel constructed.

Yes, it is. Try this.

godelize(x) = Translate the mathematical statement into a number.
quine(x) = replace every variable 'a' in a formal sentence x with godelize(x)
isTheorem(x) = Returns whether or not this godelized statement has a proof in the FS.

Lemma: Formal systems follow typographical rules. There are equivalent mathematical functions to produce new godel numberings. If the math functions are set correctly, they mirror the typographical functions.

Lemma: isTheorem(x) === (is equivalent) to 'the is a theorem within the FS'. This is a computable function, since all rule productions in the FS can be reduced to numerical computations.

Let sentence A = !isTheorem(godelize(quine(x)))

In English: "The quine of x is not a theorem, for some sentence "x"."

Let sentence B = !isTheorem(godelize(quine(A))

This is the tricky part. Notice these sentence are precisely the same, excepth for the free variable used. Follow me here:

The function quine inserts a sentence's godel number into its free variable, making it about itself. Remember, in all ways, godelizing and numerical manipulation of the results are precisely isomorphic to theorems and the rules of the formal system.

Sentence A therefore means: "Making a sentence about itself results in a non-theorem." It's truth or falsity depends on what 'x' is.

Sentence B, and this is tricky, says:

"Making "making a sentence about itself results in a non-theorem" about itself results in a non-theorem.

The indirection is the key here, because that phrase in the middle is the sentence itelf, both in English *and* mathematically!

Reducing, we get:

"Making this sentence about itself results in a non-theorem".
"Making this sentence about itself is not provable in FS."
"This sentence is false."

Not rigorous, but Q.E.D.

Which part do have an issue with? What would you suggest the proper translation is?

- Gödel's incompleteness theorems do not prove that it is impossible to built a machine with consciousness.

That I will agree with. However, *if* the universe is axiomatic, we will never be able to express all truths within any framwork. In fact, this theorem strengthens my hope for AI, because it means that, formally, we can make things operate on themselves, which is the key to consiousness. This comes with a price, however, in that there are some things about which a system *cannot* decide on within itself.

jan

26th August 2004, 01:21 PM

Ah, fresh flesh...

Originally posted by Gestahl
No, but all formal systems have such a statement.

No.

[Split Hairs]

There are formal system that are inconsistent, and for which we can show that they are inconsistent, and in which every meaningful sentence can be deduced.

There are other formal system for which we can show that they are complete and consistent. Unfortunately, they are too weak to express all mathematical truths.

There are also formal systems being complete and consistent and rich enough to express all mathematical truths (at least all mathematical truths with regard to arithmetic, but that should be pretty much the same), but unfortunately, there is no practical way to decide which sentences are axioms, and which are not.

So the formal systems having such a sentence are a special case.

[/Split Hairs]

But this shows me that I can make an even stronger claim:

- There is no Supergödel sentence S which is undeducible within every formal system that is consistent, rich enough to express every statement about arithmetic, and for which there is a recursive method to decide whether a given statement is an axiom or not.

Wow, how bold I am.

Which part do have an issue with? What would you suggest the proper translation is?

Any translation must be imperfect. The degree of imperfection depends on what your main issue at hand is. I would say that my second claim is an immediate consequence of my first claim: a certain Gödel sentence G makes sense only with regard to the special formal system in which it is expressed and for which it is constructed.

To make this clear, if "P" is the name of the formal system we are talking about, a better translation would be "This statement cannot be proven within P".

If, for example, the issue at hand is that you can't quote a sentence within itself, a better translation might be "\"is not provable if quined\" is not provable if quined". And if both concerns about possible misunderstandings are an issue, an even better translation would be "\"is not provable within P if quined\" is not provable within P if quined". If you are more concerned in expressing that G doesn't talk about sentences, but numbers, another possible translation could be "there is no number such that this number and the number of the coding of this sentence form an Arithmetic-P-Proof-Pair." And so on and so on.

The sentence "This statement cannot be proven" is just a hint what the sentence G is supposed to say; depending on context, this hint can be rather misleading.

If I understand you correctly, you want to say that Gödel's construction can be repeated, but this time using plain English as its "formal system". But that doesn't work: English, or sensible reasoning within English, is not a formal system. I see no way how you could give a finite set of rules to decide whether a certain sequence of English sentences constitute a proper proof within the English language, and which doesn't.

Consider this:

"There are finite things. Every finite thing must have a cause. Therefore, either an infinite thing exists, or an infinite chain of finite things."

Obviously, this is a sequence of three english sentences. I do not doubt that you could translate that into numbers (for example, use the ASCII-codes to translate it into a string of bytes). But is it a valid proof within the English language? Are the first two sentences valid axioms? Is the conclusion sound? I doubt it. But is there a mechanical way to decide whether this sequence of English sentences is a proof?

Unless you show me such a method to decide mechanically whether a certain sequence of sentences is a proper proof within the English language, I would say you failed to define the function isTheorem(x) for the English language.

"Making \"making a sentence about itself results in a non-theorem\" about itself results in a non-theorem."

I suppose this is intended as a Gödel sentence for the English language. Another shorter version could be

"\"is unprovable if quined\" is unprovable if quined"

I fail to see why you need all your definitions to construct this sentence. Why not just write it down?

Soderqvist used to say that such sentences are unprovable, and therefore true. If they are "therefore" true, then they are provable: which means that they are false. I would say they are just a variation of the Liar-paradox:

"\"is false if quined\" is false if quined"

True? False? Or just a hint that the English language and sensible reasoning within the English language is not a formal system?

That I will agree with. However, *if* the universe is axiomatic, we will never be able to express all truths within any framwork. In fact, this theorem strengthens my hope for AI, because it means that, formally, we can make things operate on themselves, which is the key to consiousness. This comes with a price, however, in that there are some things about which a system *cannot* decide on within itself.

Due to our finite ressources, we will never be able to express all truths anyway.

epepke

26th August 2004, 05:57 PM

Originally posted by jan
Due to our finite ressources, we will never be able to express all truths anyway.

I can:

.*

There.

Oh, you didn't want any falsehoods? Well why didn't you say so!

jan

27th August 2004, 04:40 AM

So I have to admit my third error. :D

Perhaps I should focus on gun threads, those philosophical threads are way too complicated for my simple mind.

Gestahl

28th August 2004, 12:56 PM

Originally posted by jan
Ah, fresh flesh...

<Snipped out nit-picking over definitions that I assumed were givens in the context of the conversation, but that are correct. Jan's foo is stronger than mine.>

- There is no Supergödel sentence S which is undeducible within every formal system that is consistent, rich enough to express every statement about arithmetic, and for which there is a recursive method to decide whether a given statement is an axiom or not.

Wow, how bold I am.

You are correct, for a very simple reason. If such an S existed, you could add it as an axiom, and you would have a complete and consistent language. However, we are speaking still within the formal system here. There is an S, it is just in English, with *varying modes of interpretation for each formal system to which we wish to apply it.*

Any translation must be imperfect. The degree of imperfection depends on what your main issue at hand is. I would say that my second claim is an immediate consequence of my first claim: a certain Gödel sentence G makes sense only with regard to the special formal system in which it is expressed and for which it is constructed.

The sentence "This statement cannot be proven" is just a hint what the sentence G is supposed to say; depending on context, this hint can be rather misleading.

Absolutely. Formal systems don't really say anything. We do. We assign the meanings to the symbols as we are wont.

If I understand you correctly, you want to say that Gödel's construction can be repeated, but this time using plain English as its "formal system".

Nope. I was not claiming that. I was just walking through the math to English translation, and wondering where in the process you believe I mis-translated.

Unless you show me such a method to decide mechanically whether a certain sequence of sentences is a proper proof within the English language, I would say you failed to define the function isTheorem(x) for the English language.

Of course you cannot, because no human language has a strict meaning of symbols, even when taken into context with all of English. This is because meaning is dependent upon the listener/reader. Something about isTheorem not being finite even in number theory pops into my head about now.

"Making \"making a sentence about itself results in a non-theorem\" about itself results in a non-theorem."

I suppose this is intended as a Gödel sentence for the English language. Another shorter version could be

"\"is unprovable if quined\" is unprovable if quined"

I fail to see why you need all your definitions to construct this sentence. Why not just write it down?

Because there are others reading. I wanted to make the most concise, intuitive understanding of the construction of G, both from a mathematical standpoint, and an English one. The only thing I am missing is a short little paragraph on numbering, which I forgot to put in. My whole point in the post was "why do you disagree that the "English translation" is correct"?

Soderqvist used to say that such sentences are unprovable, and therefore true. If they are "therefore" true, then they are provable: which means that they are false. I would say they are just a variation of the Liar-paradox:

"\"is false if quined\" is false if quined"

True? False? Or just a hint that the English language and sensible reasoning within the English language is not a formal system?

Provability is a weaker notion than truth. I cannot prove I exist, but it is true. Readers of GEB should remember that the author's answer to this is "mu." I.e. "this question has no answer due to the assumptions made in asking it."

Provability implies truth, but unprovability implies neither truth nor falsehood. The Epimenides/Liar's paradox (above, they are just different version of indirection) is Godel's sentence for English. I would not say that English is a formal system, but it does fall to Godel's ability. We just don't need as many indirective steps as he does.

Due to our finite ressources, we will never be able to express all truths anyway.

Agreed. As a side note, I believe that the human mind's operation is a formal system. Therefore no human can self-analyze itself with consistent and truthful results. Consequently, we can debate philosophy eternally, and psychiatrists and psychologists will always have a job ;-).

Something to think about... can *another* formal system always be able to construct a G for another given formal system?

jan

28th August 2004, 04:16 PM

I agree with most of what you have written, Gestahl. Obviously I misunderstood the middle section of your previous post as an attempt to mirror Gödel's construction within the English language as closely as possible.

I would prefer to restrict the use of the term "Gödel Sentence" to formal systems, and since true and provable are different things, I would also doubt that the Epimenides sentence is a Gödel sentence for the English language (or the greek language). But that's a dispute about names and definitions, and therefore not particular exciting.

I would agree that the human brain is a kind of machine and that the human consciousness is a product of that machine. But the programm of this machine differs from the formal systems mathematicians study: it doesn't seem to be very consistent, follows a weird and arbitrary logic and behaves quite random. That doesn't make life easier for psychologists or psychiatrists (or, depending on viewpoint, it ensures that they have and always will have a living), but I doubt that they should worry too much about Gödel's construction.

A related problem would be: it is obvious that a description how the human brain works on a neuron-per-neuron basis would be much too roundabout to be of any practical value. But is it possible to shortcut such an explanation? Perhaps the brain works in such an intricate and complicated manner that any more general explanation has to be too fuzzy to be of much practical value either. But this I really don't know.

Dymanic

28th August 2004, 11:44 PM

Originally posted by jan

A related problem would be: it is obvious that a description how the human brain works on a neuron-per-neuron basis would be much too roundabout to be of any practical value. But is it possible to shortcut such an explanation? Perhaps the brain works in such an intricate and complicated manner that any more general explanation has to be too fuzzy to be of much practical value either. But this I really don't know.That quite nicely expresses how I view the situation. Bottom-up investigations into activities within the brain, aided by rapid advances in technology, produce better and better information all the time. The difficulty in interpreting that data, however, seems to become more difficult as a product of the increase in volume. Anything remotely resembling an answer comes accompanied by a host of previously un-asked questions.

The less exacting top-down approach naturally has a longer history, and while error-prone often to the point of absurdity, evidence of its practical value might be presented as the simple observation that we are here. We are all psychologists in a sense, each descended from ancestors who were at least minimally successful at making reasonable guesses about what was going on inside the heads of other humans (often a matter of life-or-death, even today). I am convinced that it is the adaptive value of this ability more than any other that explains the phenomenal capabilities of the modern human brain. It is ironic then that, while understanding the human brain may be the most important task the human brain evolved to perform, the human brain remains the most difficult of mysteries to solve!

We don't even know how to measure our progress. For example, there is now evidence that face recognition is (normally) performed in a specific region of the brain. We can observe and measure changes in electro-chemical activity in that region. We can observe the activities of individual neurons. We have absolutely no clue how the brain actually accomplishes face recognition.

I'd love to see where we're at with it about 500 years from now.

jan

29th August 2004, 04:48 AM

Originally posted by Dymanic
We are all psychologists in a sense, each descended from ancestors who were at least minimally successful at making reasonable guesses about what was going on inside the heads of other humans (often a matter of life-or-death, even today). I am convinced that it is the adaptive value of this ability more than any other that explains the phenomenal capabilities of the modern human brain. It is ironic then that, while understanding the human brain may be the most important task the human brain evolved to perform, the human brain remains the most difficult of mysteries to solve!

I would like to add that we not only became advanced psychologists because it has an important adaptive value to be able to tell how all the other humans around us spin: but also we learned how to trick and cheat the other humans around us, and that makes things so complicated.

That is to say, our brain is the typical product of an arms race: we developed a complicated brain to be able to crack the brains of the others, and we had to develop a complicated brain so our own brain coulnd't be cracked by the others quite so easily. I think such an arms race could explain a very fast evolution of the brain ("fast", of course, only compared to other evolutionary changes).

Gestahl

30th August 2004, 07:21 AM

Originally posted by jan

I would agree that the human brain is a kind of machine and that the human consciousness is a product of that machine. But the program of this machine differs from the formal systems mathematicians study: it doesn't seem to be very consistent, follows a weird and arbitrary logic and behaves quite random.

To me, that is the mystery of a multi-level system. How can an obviously finite, discreet, and fairly deterministic brain model lead to such a phenomena as indecision, being wrong, and emotions. My answer is that all of the constructs live above the neuron model, while being dependent upon it (think cell layer versus the protien, etc. chemical layer it depends on, but exists on a different level than). We are missing the crucial "middle level" of how neuron's bring about these traits. Due to the complexity, I don't think we ever will until we build a working imitation somehow.

Dymanic

30th August 2004, 11:25 AM

Originally posted by Gestahl

How can an obviously finite, discreet, and fairly deterministic brain model lead to such a phenomena as indecision, being wrong, and emotions.
Being wrong is an interesting concept in itself.

To any given problem there must be an infinite number of wrong answers. One thing that makes humans fun is that even when they are wrong they are usually at least part right, and the parts that are wrong are often wrong in some interesting way.

In a sense, it might be considered that a computer is capable of only one type of error, that being the sort that occurs when some hardware component malfunctions (any other error should really be considered human error by electronic proxy). Such malfunctions would be expected to occur unpredictably, possibly producing errors of sufficient magnitude to send the whole system careening out of control. But the nature of human error does not suggest this sort of malfunction as its cause. The usuallyPartRightNess that characterizes human error suggests 'soft' errors; errors in semantics rather that syntax; shifted frames; operations performed properly, but on data flawed in some way.

Under formalism, I don't see how any such thing as an error could be considered to even exist. A formal system, as an abstraction, has no substrate which could support a 'hard error'; there is no way it can violate its own rules. Its theorems are considered not to have any meaning independent of the system itself, and therefore cannot be evaluated as intrinsically 'right' or 'wrong' on any extramathematical basis.

jan

31st August 2004, 09:38 AM

I don't know how to program a program with emotions; but it is trivial to program a program that produces errors.

Furthermore, I guess that most biological models of neurons don't assume them to behave discreet and deterministic. But that, I think, is not the main source of trouble: even if the elementary pieces would work on a discreet and deterministic basis, I would expect the result to be pretty unpredictable and fuzzy.

A mathematical formal system is, usually, designed to produce true and only true sentences. The human brain is, so to speak, designed to help its owner to survive. Those are quite different tasks. We can search the truth, but as far as I see, we are not optimized for doing that.

For example, I would say that homo sapiens comes with a built-in tendency to be a bit paranoid: it is very important for us to detect patterns (like the stripes of the tiger in the grass), so we tend to see patterns everywhere, even patterns in the random distribution of the stars in the sky. That surely is useful to survive; but it comes with the burden of a built-in tendency to cultivate many superstitions. If you ever wondered why there are so many kinds of superstitions: it's because we are not designed as machines to produce as much true sentences about arithmetic as possible.

If I got it right, Gödel himself, Lucas or Soderqvist assume that human beings have a special ability to "see" the truth of some sentences with the help of some kind of paranormal ability. That would, indeed, surprise me. But I see no evidence for such an ability. Human beings are quite good when it comes to wild guesses, but that's pretty much what I would expect from a kind that has been optimized by many generations of adaptive selection to be good with guesses. But we do make mistakes. And, in fact, our ability to guess becomes quite weak when it comes to realms we have no every-day experience with.

Dymanic

31st August 2004, 01:42 PM

Originally posted by jan

I guess that most biological models of neurons don't assume them to behave discreet and deterministic.
There is a lot of interesting back-and-forth over this. I'd say that most biological models of neurons assume provisionally that they behave deterministically, pending the introduction of evidence to the contrary. Whether or not you consider that they behave discretely seems to depend on whether you are considering the actions of neurons individually or collectively. I agree with Gestahl: "...all of the constructs live above the neuron..."

An understanding of the structure of cognition -- of the way neurons act in concert -- has not emerged from detailed study of individual neurons. Even assuming that neurons do act discretely and deterministically, this is not surprising, since it is probably a more diffcult challenge, by orders of magnitude, than it would be to (say) reconstruct the source code for Windows XP by observing activity at the level of individual registers. Some kind of working imitation (as Gestahl goes on to suggest) may be as close as we will ever get.

it is very important for us to detect patterns (like the stripes of the tiger in the grass), so we tend to see patterns everywhere, even patterns in the random distribution of the stars in the sky.
Perhaps even more important (and even harder to explain) is our ability to detect patterns which occur at higher levels of abstraction, to distill them down to their most fundamental essences, and to identify correlates to them against completely unrelated conceptual backgrounds (i.e: "How shall I compare thee to a summer's day?").

If I got it right, GÃ¶del himself, Lucas or Soderqvist assume that human beings have a special ability to "see" the truth of some sentences with the help of some kind of paranormal ability.
I would add Penrose to that list. I think what they are saying is that mathematical space includes some statements which, though true, cannot be reached from any given starting point in any finite number of logical steps. Under formalism, such statements would be considered false by definition (or at least disregarded) solely on the basis of that unreachability. Yet we can somehow see them as true nonetheless, which forces us to seek explanations elsewhere (something nondeterministic, whatever). I'm not sure it necessarily leads us immediately to 'the paranormal'. I'm still trying to work my way through Penrose's discussion on microtubules; that's one idea.

epepke

31st August 2004, 02:38 PM

Originally posted by jan
And, in fact, our ability to guess becomes quite weak when it comes to realms we have no every-day experience with.

It's actually not so hot even when dealing with realms where we do. Consider this: http://www.ritsumei.ac.jp/~akitaoka/saishin-e.html And for that matter, the rest of the optical illusions.

jan

1st September 2004, 09:47 AM

I think that's a striking example that "adapted" does not necessarily means "has very complicated and well functioning organs". In many cases, it just means "cheap". To perfect a certain skill usually requires to pay a price: a larger brain requires more resources, and a more complicated brain is perhaps less tolerant to small errors. The phrase "survival of the fittest" is, in the German language, often translated with something that would backtranslate as "survival of the strongest": but that is obviously nonsense. The most successful life form are the bacteria, and they are neither strong nor smart. So we not only have troubles to grasp Quantum Physics, but we also have troubles to estimate which one of two lines is longer. To quote Monty Python: to give us the "Albert Einstein Super Silver Brain Deluxe" would have been too costly and error-prone, so we have to stick with our "Curry's".

Dymanic

1st September 2004, 02:29 PM

Originally posted by jan

I think that's a striking example that "adapted" does not necessarily means "has very complicated and well functioning organs". In many cases, it just means "cheap".Yes. Well said. Biologists talk about 'r-strategy' and 'k-strategy'. In organisms that use r-strategy (like oysters, and aphids) the reproductive cycle is kept as short as possible; large numbers of offspring, minimum possible embryonic development time, offspring reach reproductive age as quickly as possible. With k-strategy, (like cheetas, and humans) more developmental resources are devoted to each offspring (possibly including extended periods of parental care) resulting in fewer, but better equipped young.

Which strategy plays out better depends on environmental conditions. If there is plenty to eat, little danger from predators, etc, even the weakest, blindest, stupidest organism may have little trouble surviving and breeding; what counts the most is: who breeds fastest? When resources are scarce, the deciding factor will tend toward the greater frequency with which important contests will be won by organisms equipped with the developmentally expensive special features.

So we not only have troubles to grasp Quantum Physics, but we also have troubles to estimate which one of two lines is longer. To quote Monty Python: to give us the "Albert Einstein Super Silver Brain Deluxe" would have been too costly and error-prone, so we have to stick with our "Curry's".But all humans are k-selected; we all have the Albert Einstein Super Silver Brain Deluxe! At least... whatever it was about Einstein brain that made it different from anyone else's, it is very unlikely that it had anything to do with a difference in size, embryonic development time, or gross structure -- or with the way his brain processed visual input. One thing that is demonstrated by optical illusions is that much of the information recieved by our eyes is 'pre-processed' before being handed off to the brain (depending on what you want to call 'the brain'). It could be argued that this preprocessing is part of what qualifies the human eye as a 'very complicated and well functioning organ' within the context of the types of problems it was designed to solve (which optical illusions, by their very design, are not). It could even be argued that it is optimization of the way the brain works together with the eye (ear, middle ear, etc) to create a model of the world that makes it so difficult for the brain to grasp quantum mechanics, relativity, non-Euclidean geometry, and the like.

Yet there was something different in the way Einstein's brain worked (Ramanujan, Von Neumann, and others also come to mind, as do the strange abilities sometimes seen in persons with autism). Such rare individuals often exhibit an apparent ability to 'leap' directly to solutions to complex problems. Their results can be verified by painstaking step-by-step methods, but they themselves appear to have arrived at their solutions by some other path. I don't believe in magic. There must be an explanation.

jan

27th September 2004, 03:18 PM

Perhaps a bit late again, but I found another way to demonstrate why the notion of seeing the truth of sentences machines fail to prove can be troublesome. Take this sentence:

"Soderqvist can't see that this sentence is true."

If we assume that Soderqvist can only see the truth of true sentences, then this sentence must be true. And can be inferred within any system that has this sentence as an axiom.

Alan Turing has explained it short and concise:

Computing machinery and intelligence (http://www.abelard.org/turpap/turpap.htm)

The short answer to this argument is that although it is established that there are limitations to the powers of any particular machine, it has only been stated, without any sort of proof, that no such limitations apply to the human intellect. But I do not think this view can be dismissed quite so lightly. Whenever one of these machines is asked the appropriate critical question, and gives a definite answer, we know that this answer must be wrong, and this gives us a certain feeling of superiority. Is this feeling illusory? It is no doubt quite genuine, but I do not think too much importance should be attached to it. We too often give wrong answers to questions ourselves to be justified in being very pleased at such evidence of fallibility on the part of the machines. Further, 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. In short, then, there might be men cleverer than any given machine, but then again there might be other machines cleverer again, and so on.

Gestahl

28th September 2004, 03:58 PM

Originally posted by jan
Perhaps a bit late again, but I found another way to demonstrate why the notion of seeing the truth of sentences machines fail to prove can be troublesome. Take this sentence:

"Soderqvist can't see that this sentence is true."

If we assume that Soderqvist can only see the truth of true sentences, then this sentence must be true. And can be inferred within any system that has this sentence as an axiom.

Precisely, Jan. Assuming something has the ability to tell truth from non-truth gets you in trouble logically every time. What might this mean in relation to religious dogmatism? ;-).

On a side note, think about this statement. The problems of truth/provability are all about context. In fact, the class of computation below a Turing machine is called a push-down automata, and can compute things that are context independent in a recursive manner. Turing machines can compute non-nested contexts (like we can). Formal systems, etc. cannot "jump out of themselves" like we seemingly can when working with a system. And here is the crux of it all... can the human mind "jump out of itself"... i.e. can it make distinctions about itself free of the context of its own being? I think not...

1) Can you tell if you are delusional, e.g. can a schizophrenic tell the difference between his delusions and reality without being told?

2) Can you force yourself out of a (chemically induced) bout of depression mentally?

3) Can you truly change your underlying personality consciously... i.e. make yourself more honest, without external feedback from others?

I think 3 is the most vexing question, and while I do not hesitate to answer 1 and 2 with a no, 3 bothers me immensely, since it seems to follow from generalization from the first two. Are humans fundamentally (no pun intended) limited?