Kedaman & Simonm Reality Debate (and anyone else brave enough to enter)

Kedaman

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A definition assigns meaning to a word, this is done by declaring its practical implications.

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Substituting one word or phrase with another does not explore it's practical implications.

Some would argue that you explore the meaning of a word by looking at how it is used rather than by providing a generalised definition. Look at examples in which it is used to glean an understanding of it's meaning.

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If a statement wasn't analytical, you can't derive meaning from it, and thus the statement is meaningless, you don't call these statements, you call them phrases. Phrases that have meaning are called statements though.

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Since you make no distinction between observations gained from the external world and observations gained from the internal world, you would naturally be incapable of grasping the distinction between analytical and synthetic statements.

Since you are operating on the Solipsist premise, you believe that we are not qualified to speak about anything other than our own perception, it is no suprise that you dismiss all other kinds of statements as meaningless.

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What do you mean by external to our own perception? I'm not sure where we are in disagreement now, Thoughts are percepted, otherways we wouldn't be aware of them, correct?

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Thoughts are snapshots of our perception, yes, but they are observations when they are fueled by sensual data.

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What is this internal versus external business? How do you distinguish internal from external reality?

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As I went on to explain, it is both the lucidity of our mental image and the control we have over it that is indicitive of an external "reality".

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Your will is an observation, I think if there's anything you'd probably confuse for self-awareness then it must be will, however it could be argued that you just sense that will, and think of it as your own, when in fact its just something you observe.

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You can argue that free-will is an illusion (and you may be right) but you cannot deny that there is (at the very least an illusion of) a distinction between thoughts that we control and those that we don't. Whether or not it is an illusion is not relevent to the point I am making.

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Substituting one undefined word or phrase with another does not explore it's practical implications.

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my turn now, as you can see you wont have meaning unless you put it there in the first place, and logic is a way to express meaning - practical implications.

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Some would argue that you explore the meaning of a word by looking at how it is used rather than by providing a generalised definition. Look at examples in which it is used to glean an understanding of it's meaning.

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Those are practical implications, btw a generalised defintion is equal to all the examples - Axiom Extensionality.

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Since you make no distinction between observations gained from the external world and observations gained from the internal world, you would naturally be incapable of grasping the distinction between analytical and synthetic statements.

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My point exactly, reason why I asked you of an explicit observable distinction.

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Thoughts are snapshots of our perception, yes, but they are observations when they are fueled by sensual data.

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By sensual data you talk about your biological senses?

Btw what is Lucidity?

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You can argue that free-will is an illusion (and you may be right) but you cannot deny that there is (at the very least an illusion of) a distinction between thoughts that we control and those that we don't. Whether or not it is an illusion is not relevent to the point I am making.

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free-will is not an illusion, its an observation, whether its your own or not is not the question, its that you are aware of it. The only distinction I can see that has any practical difference is when things that i wasn't aware of become clear to me, even if only vaguely, there is information transmitted into your awareness, extending your consciousness, similarly when things slip back into your subconscious you lose the concept of it.

Kedaman

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Those are practical implications, btw a generalised defintion is equal to all the examples - Axiom Extensionality.

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I understand what you're saying here. That a generalised concept is equal to all the infinite possible instances of it, however, that does not apply to language. No two words are exactly alike or always used in an identical fashion.

The point I am making here is that it is more useful to uncover the meaning of a word to see examples of how it is used rather than attempt to substitute it with another word.

If you cannot assume I share your understanding of the word "observation", why should you assume that I share your understanding of the phrase "perceived information"?

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By sensual data you talk about your biological senses?

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Yes.

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Btw what is Lucidity?

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I mean vividity. My experiences in a dream are not as vivid as when I am awake. They are of a greater intensity.

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free-will is not an illusion, its an observation, whether its your own or not is not the question, its that you are aware of it.

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It is critically important to the notion of free-will whether or not we are in control or merely passively observing (with the false impression that we are in control).

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The only distinction I can see that has any practical difference is when things that i wasn't aware of become clear to me, even if only vaguely, there is information transmitted into your awareness, extending your consciousness, similarly when things slip back into your subconscious you lose the concept of it.

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Do you regard that as an entirely passive affair? Do you not make any distinction between that which is familiar to you and that which you have not seen before?

When I close my eyes, I can form vague images in my mind which I have complete control over. When I open my eyes, I have extremely vivid images that unfold before me and which I have no control over. I can interact with it, but not control it.

Isn't this a distinction that has practical implications?

simon

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I understand what you're saying here. That a generalised concept is equal to all the infinite possible instances of it, however, that does not apply to language. No two words are exactly alike or always used in an identical fashion.

The point I am making here is that it is more useful to uncover the meaning of a word to see examples of how it is used rather than attempt to substitute it with another word.

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ok, I get your point. But as we are talking about languages, all languages are derived from lamda calculus. The word substitution doesn't describe the flow of information in natural languages quite well agreed, but thats not the point in lamda calculus either, the process of reduction is merely a computational tool, and in natural languages we seek for meaning which is largely dependent on the context in scope ranging from the current sentence to the whole discussion. The diversification of meaning using the same word is in programming languages called ad-hoc polymorphism, in mathematical languages its avoided at all costs, because ad-hoc polymorphism makes a language if not vague and ambigous then unnessesarily complex.

Even though we'll get around this by just being descriptive enough, wont we?

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It is critically important to the notion of free-will whether or not we are in control or merely passively observing (with the false impression that we are in control).

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How so? I don't feel any difference, assuming either is true. Both theories are equally explanative for the same phenomenon but being a pure observer is more mathematically correct (Occam's razor), which is why I adopt it. Your definition of relying on biological matter is restrictive, we both know that we're more than mere lifeforms.

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Do you not make any distinction between that which is familiar to you and that which you have not seen before?

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My memories, even though they are observations are naturally closer to me than most information, even though many of my memories are lost in my subconscious, because I don't need to keep track of them. However other than that they're information as much as anything else.

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Do you regard that as an entirely passive affair?

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Wheter or not we're merely watching a movie or not seems critical to you as an issue of restriction. Ask yourself what exactly is control? If it was essential to your consciousness, then what is it? The actions you take, the control you have over your thoughts, what is this power over information? You know your brain is a logical circuitry and you know your thoughts follow something you want to call your own intelligence, the more intelligent you are the more sense you can derive from your environment, and make intelligent decisions. This is the information, that is closest to you, that you are aware of most of the time, maybe less when you're sleeping but when you're awake these are the main information highways to your awareness empire, without these you'd have very limited vision and control (and control here is the ability to expand or withdraw your awareness.) By observing control (the circuitry that processes information) you naturally get the feeling of lucidity as these link most of your awareness empire together as well as guard your awareness perimeters from your subconscious.

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When I close my eyes, I can form vague images in my mind which I have complete control over. When I open my eyes, I have extremely vivid images that unfold before me and which I have no control over. I can interact with it, but not control it.

Isn't this a distinction that has practical implications?

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Your eyes are one of your biological senses, and biology is the gateway to a world in your subconscious where you lack control, but seek to expand, you can experience control even outside your bilogical senses, for instance social power and control over mechanisms like your car, your computer etc.. that expand your senses as well. But often the world seems out of your hands, things act their way not your way, and some things like gravity, are so deep in your subconscious that there is no way of digging them up without digging the rest of the world up from there.

Kedaman

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ok, I get your point. But as we are talking about languages, all languages are derived from lamda calculus.

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I don't agree with that. Natural language preceeded lamda calculus. I doubt that natural language is anywhere near as logical and structured as lamda calculus is either.

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The word substitution doesn't describe the flow of information in natural languages quite well agreed, but thats not the point in lamda calculus either, the process of reduction is merely a computational tool, and in natural languages we seek for meaning which is largely dependent on the context in scope ranging from the current sentence to the whole discussion. The diversification of meaning using the same word is in programming languages called ad-hoc polymorphism, in mathematical languages its avoided at all costs, because ad-hoc polymorphism makes a language if not vague and ambigous then unnessesarily complex.

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This goes deep into the question of how we actually aquire knowledge. How do we come to understand concepts? I don't think that anybody really knows.

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Even though we'll get around this by just being descriptive enough, wont we?

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I guess we have no choice...

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It is critically important to the notion of free-will whether or not we are in control or merely passively observing (with the false impression that we are in control).

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How so? I don't feel any difference, assuming either is true. Both theories are equally explanative for the same phenomenon but being a pure observer is more mathematically correct (Occam's razor), which is why I adopt it. Your definition of relying on biological matter is restrictive, we both know that we're more than mere lifeforms.

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I disagree. By Occam's razor, we would eliminate the theory of illusion because there isn't any reason to believe that it is an illusion.
Since you agree that the possibility of our free will being an illusion equally as explanatory as it not being an illusion, we would eliminate the theory that it is an illusion as that contains the additional complexity of why we have that illusion attall.

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My memories, even though they are observations are naturally closer to me than most information, even though many of my memories are lost in my subconscious, because I don't need to keep track of them. However other than that they're information as much as anything else.

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But what about new information? Information that you have never perceived before. When that enters your awareness, could that not to be said to come from an external source (i.e. an external reality)?

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...control here is the ability to expand or withdraw your awareness.

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Ah, but it's more than that. It's the ability to determine how I interact with my perceived information.

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By observing control (the circuitry that processes information) you naturally get the feeling of lucidity as these link most of your awareness empire together as well as guard your awareness perimeters from your subconscious.

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I don't understand why observing the control (information processing) centres in my mind should empower me with the sensation of being in control if I am not.

Besides, the vividity of my experiences and my sensation of being in control of my thoughts are two different entities and not to be confused.

Simon

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I don't agree with that. Natural language preceeded lamda calculus. I doubt that natural language is anywhere near as logical and structured as lamda calculus is either.

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What are you saying? Lamda calculus is a tool to represent any language, its not just a tool to verify grammar, but can be used to derive meaning and perform any computation, just like you do. Lamda calculus is agreed, not an observer, its a processor, its the ultimate tool for computation as well as expression of information, its proven that all natural languages are subsets of lamda calculus.

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This goes deep into the question of how we actually aquire knowledge. How do we come to understand concepts? I don't think that anybody really knows.

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Is that of any importance? My theory of information explains at least what and why, the how part is just to extend control, the process of computation, which has only one function: to work. In any practical issue you end up with the question what anyway.

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I disagree. By Occam's razor, we would eliminate the theory of illusion because there isn't any reason to believe that it is an illusion.
Since you agree that the possibility of our free will being an illusion equally as explanatory as it not being an illusion, we would eliminate the theory that it is an illusion as that contains the additional complexity of why we have that illusion attall.

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I didn't say free-will is an illusion, in thats a word that doesn't exist in my theory, its a word only for realists. If you want to eliminate something because of illusions then eliminate the theory of reality.
You argue that we should use our biological senses as physical limits to what is observable or not, I think this is way too restrictive, You do know that there are mechancial arms for patients that have lost them that transmit sensory information to your nerv system? I don't see how mechanical eyes would be impossible. The question should arise to you that where exactly could you cut the information stream and inhibit it with other data without making any difference to your conscious self. If you cannot answer this then your theory isn't explanatory enough, because mine does. My definition for observation is more generic and can be used in context that aren't dependent on biology.

Btw do you know why math is purely abstract? Yes, its to reduce complexity.

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But what about new information? Information that you have never perceived before. When that enters your awareness, could that not to be said to come from an external source (i.e. an external reality)?

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It is said to be from an external reality, it does however not make any difference, our subconscious is more generic and explanatory and if as you say that information can escape reality and enter your consciousness then that reality will naturally be a subset of your subconscious.

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Ah, but it's more than that. It's the ability to determine how I interact with my perceived information.

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As said, all your interactions are mere observations. I've also explained why they are so close to you, they do determine how to handle information perceieved from for instance your biological senses.

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I don't understand why observing the control (information processing) centres in my mind should empower me with the sensation of being in control if I am not.

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Being aware of the process, is experiencing control over it. Again this is the definition of consciousness, nobody could explain why you observe, just what you do.

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Besides, the vividity of my experiences and my sensation of being in control of my thoughts are two different entities and not to be confused.

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I'm not confusing the vividity of your experiences with your sensations of being in control of your thought. Your experiences are mere sensory information, while your sense of control derives from processing that information, they're both very closely linked though as one trigger the other.

Kedaman

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What are you saying? Lamda calculus is a tool to represent any language, its not just a tool to verify grammar, but can be used to derive meaning and perform any computation, just like you do. Lamda calculus is agreed, not an observer, its a processor, its the ultimate tool for computation as well as expression of information, its proven that all natural languages are subsets of lamda calculus.

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Perhaps you could provide a link to more information on the subject because I'm not convinced. I need more than your say so that all natural languages are a subset of lamda calculus. As far as I was aware, all attempts to reduce natural language to formal logic had failed miserably.

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Is that of any importance? My theory of information explains at least what and why, the how part is just to extend control, the process of computation, which has only one function: to work. In any practical issue you end up with the question what anyway.

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It is of importance to those who study epistimology. There is no logical basis to explain how we gain understanding of concepts. Somehow we do.

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I didn't say free-will is an illusion, in thats a word that doesn't exist in my theory, its a word only for realists. If you want to eliminate something because of illusions then eliminate the theory of reality.

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If we have the sensation of control and yet do not, it is an illusion. What else would you call it?

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You argue that we should use our biological senses as physical limits to what is observable or not, I think this is way too restrictive...

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I wouldn't argue that attall. I cannot observe light at infrared wavelengths but I can build a machine (well, not me personally) to sense them so I know they exist. They are observable even though not by my own biological senses.

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The question should arise to you that where exactly could you cut the information stream and inhibit it with other data without making any difference to your conscious self. If you cannot answer this then your theory isn't explanatory enough, because mine does. My definition for observation is more generic and can be used in context that aren't dependent on biology.

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Your theory encapsulates all without actually explaining anything, in my opinion.

No I cannot explain the mystery of consciousness but neither does your theory (as far as I can see).

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It is said to be from an external reality, it does however not make any difference, our subconscious is more generic and explanatory and if as you say that information can escape reality and enter your consciousness then that reality will naturally be a subset of your subconscious.

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I don't think information "escapes reality by entering our consciousness" attall. I think an external reality leaves impressions on our perception.

If you believe that conjuring up this mystical black box that you call our "subconsciousness" solves anything, then I fail to see why. Perhaps it's more generic, but it doesn't demystify anything.

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Being aware of the process, is experiencing control over it. Again this is the definition of consciousness, nobody could explain why you observe, just what you do.

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Sorry, but I'm not convinced of this. I am aware of many different processes but I am not labouring under the impression that I am in control over it.

Simon

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Perhaps you could provide a link to more information on the subject because I'm not convinced. I need more than your say so that all natural languages are a subset of lamda calculus. As far as I was aware, all attempts to reduce natural language to formal logic had failed miserably.

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I didn't say it has been done, but Its theoretically possible, in practice natural languages are way too complex and destandardised for this task to be easy. I will try to look up a reference saying that. If not I'll try to find one that says lamda calculus is capable of of everything a turing machine is.

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It is of importance to those who study epistimology. There is no logical basis to explain how we gain understanding of concepts. Somehow we do.

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I think the question is similar to why we observe at all, why are we conscious? There's no need to answer such question imo. I'm always willing to hear your reasoning.

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If we have the sensation of control and yet do not, it is an illusion. What else would you call it?

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Control, information processing, being conscious about it is to be in control, not an illusion of having it. You are contradicting yourself here.

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Your theory encapsulates all without actually explaining anything, in my opinion.

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Here's something else I don't understand. If I can encapsulate everything, then I can also explain everything.

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No I cannot explain the mystery of consciousness but neither does your theory (as far as I can see).

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Consciousness is a set of information that you are aware of. The answer to the question is that you can cut it everywhere, there is no internal "secure" area where information is guaranteed to be "known", if you know what i mean.

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I don't think information "escapes reality by entering our consciousness" attall. I think an external reality leaves impressions on our perception.

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That sounds like the same thing to me, if reality leaves impression on your perception then surely the information is transmitted from reality to you?

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If you believe that conjuring up this mystical black box that you call our "subconsciousness" solves anything, then I fail to see why. Perhaps it's more generic, but it doesn't demystify anything.

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It definitely demystifies everything that at least I can think of is mystic.

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Sorry, but I'm not convinced of this. I am aware of many different processes but I am not labouring under the impression that I am in control over it.

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Mention any process you think you are aware of.

You've entered ... the Twilight zone *tumdidumdidum*

Kedaman

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Control, information processing, being conscious about it is to be in control, not an illusion of having it. You are contradicting yourself here.

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The bit that is processing information is not the bit that is doing the observing, is it? If so, that is selfawareness.

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Here's something else I don't understand. If I can encapsulate everything, then I can also explain everything.

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In order to achieve a theory that is consistant with all your observations and free of any doubt, you have retracted as many assertions as possible. You only retain the assertions that you can hold with certainty but you are saying less.

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Consciousness is a set of information that you are aware of.

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If the "set of information" is empty, is it still consciousness? What is it that has become aware? The information itself? If not, what?

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That sounds like the same thing to me, if reality leaves impression on your perception then surely the information is transmitted from reality to you?

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Information doesn't leave reality. It doesn't transmit anywhere.

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Mention any process you think you are aware of.

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Anything you care to name. Every object that moves before my eyes is a process. I am aware of it but I do not feel in control.

Simon

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Every object that moves before my eyes is a process.

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Well here's misconception #1. I have said before objects obrain their movement vector til an external net force alter its course. This is an example of why you can't be aware of a process, you only observed its results, and believe that there is a mechanism behind it, in this example there was none. In any example it could be anything. A process that you are aware of is for instance thinking, or ordering pizza, or post in this thread, because in all those you sense control, you are aware of each step in the process, not just the result. Eating, walking and breathing are for processes that you can be both aware of and not, when you walk you're usually not concentrating on how exactly your leg muscles should be moved, this process is automated, in other word sent back into your subconscious, but whenever you feel like doing something else with your legs, you gain control over them again. Before you were just aware of the results: you were going forward. But now you can move your legs the way you want, you become conscious over the process. Say an object is moving before your eyes, you could stop it from doing that by putting your hand in the way, this is a conscious process. A reflex is not a conscious process, its done without your attention. You don't observe it before its done, say you touch something that burns, and move away your hand, still you observe the result. Your heartbeat is totally automated, you can't control your heart muscles, even though they're part of your biological self, this process is much deeper into your subcoscious.

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In order to achieve a theory that is consistant with all your observations and free of any doubt, you have retracted as many assertions as possible. You only retain the assertions that you can hold with certainty but you are saying less.

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That's true, yet I argue that this is all the answers you need. Let's compare my strategy with the realists. The realist push forward a line of theories that is possibly true and leave the falsified ones behind. Yet I have a an argument that falsfies all their theories. This strategy is meaningless. My strategy however concentrates on giving answers to the questions concerning your needs, in the end you wont ask for something you don't need.

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If the "set of information" is empty, is it still consciousness? What is it that has become aware? The information itself? If not, what?

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In math you have the empty set, and its still a set. If you call it consciousness, then it must be conscious of nothing. When you become aware of something it enters your consciousness.

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Information doesn't leave reality. It doesn't transmit anywhere.

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What I meant is, is the source of information your reality?

Kedaman

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Well here's misconception #1. I have said before objects obrain their movement vector til an external net force alter its course. This is an example of why you can't be aware of a process, you only observed its results, and believe that there is a mechanism behind it, in this example there was none. In any example it could be anything. A process that you are aware of is for instance thinking, or ordering pizza, or post in this thread, because in all those you sense control, you are aware of each step in the process, not just the result.

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OK...I see what you're saying here but I'm not sure I'm convinced...

Am I trully aware of "each step in the process" when I move my leg? I am not really aware of the nerve impulse travelling down my leg and my muscles contracting in just the right way. All I really do is observe the results. What makes me feel in control of the action is that I was aware of my intention to move my leg before it happened.

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That's true, yet I argue that this is all the answers you need. Let's compare my strategy with the realists. The realist push forward a line of theories that is possibly true and leave the falsified ones behind. Yet I have a an argument that falsfies all their theories.

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You don't falsify scientific theories with arguments. You falsify them with empirical evidence.

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This strategy is meaningless. My strategy however concentrates on giving answers to the questions concerning your needs, in the end you wont ask for something you don't need.

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You speak as if realists advocate meaningless theories. Theories that do not meet our needs. This is just false.

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In math you have the empty set, and its still a set. If you call it consciousness, then it must be conscious of nothing. When you become aware of something it enters your consciousness.

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OK, that answers the first part of my question. What about the next part? What is the it that is doing the observing?

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What I meant is, is the source of information your reality?

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Yes.

Simon
Here's a couple of references btw:

http://www.geocities.com/SoHo/Square...ounphrase.html

As you well know, the turing machine is a finite state machine that generates one output per input, while a finite state machine can be used to recognize languages, a turing machine can be used to process languages, for instance translating them into other languages or derive mathematical or any meaning out of them.

http://www.cs.yorku.ca/Courses97-98/...mbdaNotes.html

Lamda calculus is equivalent in computing power to a Turing machine - thus it is possible to represent all languages in Lamda calculus. This is the approach Squirrel is deriving.

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OK...I see what you're saying here but I'm not sure I'm convinced...

Am I trully aware of "each step in the process" when I move my leg? I am not really aware of the nerve impulse travelling down my leg and my muscles contracting in just the right way. All I really do is observe the results. What makes me feel in control of the action is that I was aware of my intention to move my leg before it happened.

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Most of the information supporting the process is deep inside your subconscious, I shouldn't have said "each step in the process" the actual difference is that when you are aware of a process your intention initialize the process, and thus have control over it, while you observe the result of process you are not aware of, you cannot be sure which process is behind it, only have a range of possible theories, these remain in your subconscious. You know the process ordering a pizza, even if it fails, its still a process you are aware of, when it fails though, you're not aware of the process behind the failure, even though you've observed that you've been left without pizza. Its fully possible to be aware of the whole process including all details, for instance the turing machine, and the lamda calculus.

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You don't falsify scientific theories with arguments. You falsify them with empirical evidence.

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fine then, call it empirical evidence.

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You speak as if realists advocate meaningless theories. Theories that do not meet our needs. This is just false.

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Why?

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What is the it that is doing the observing?

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I think i've answered this too. You do.

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It is said to be from an external reality, it does however not make any difference, our subconscious is more generic and explanatory and if as you say that information can escape reality and enter your consciousness then that reality will naturally be a subset of your subconscious.

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I don't think information "escapes reality by entering our consciousness" attall. I think an external reality leaves impressions on our perception.
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That was what I meant, sorry for the confusion.

Kedaman

Thanks for providing links to Lamda Calculus.

Whilst I do accept that a Lamda calculus is equivillent to a Turing machine, I am not convinced about it's capacity to fully encasulate human language (and thought).

Indeed, those (Such as Roger Penrose) argue that human thought (and therefore language) are not computable by turing machines:

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Penrose seems to suggest that human thinking is non algorithmic, and that a machine is not capable of human thought. He bases this on the fact that a Turing machine cannot predict when it will halt, but by insight a human can because we are
outside of the system.

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For a more detailed looked at how Penrose uses Godel's incompleteness theorems to dispute the Turing/Church conjecture, see here: http://www.turing.org.uk/philosophy/lecture1.html

I'm not saying that Penrose has proven Turing wrong, but the jury is still out on the matter.

Simon
I get a bad gateway DNS lookup error following that link, is it just me?

I don't think truth exist outside Boolean calculus. Boolean calculus is the theory about consistency, and all "truth"'s human can think of are arbitrary, or as you want to call it "empirical". If Penrose thinks there is a practical implication that would differ human thought from turing machines, then i'm certain he is wrong.

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Originally posted by kedaman
Simon
I get a bad gateway DNS lookup error following that link, is it just me?

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Nope, its not just you.
I get it too.

Oops I seem to have strayed into Dorksville !

:D ;)

Hmmm...I don't know why the link isn't working for you two...it's ok for me? :confused: There's too much text to reproduce here so I won't bother.

Kedaman

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I don't think truth exist outside Boolean calculus. Boolean calculus is the theory about consistency...

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Fair enough. That is what you believe. As I have already stated, I believe boolean calculus is a human construct that we have created with the intention of encapsulating truth. Whether or not it is sufficient, I don't know.

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...and all "truth"'s human can think of are arbitrary, or as you want to call it "empirical".

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Please don't confuse arbitary "truths" with empirical ones...you may not make a distinction but I do. "Empirical" is more than just my word for "Arbitary".

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If Penrose thinks there is a practical implication that would differ human thought from turing machines, then i'm certain he is wrong.

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Well, you wouldn't be alone in that sentiment. He has not yhet convinced the mainstream of the scientific comunity of his ideas but I have read books by scientists/mathematicians who are not yet convinced of his ideas but are keeping their minds open to the possibility that he might be right.

One extract that I will produce from the link:

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This Turing thesis marks the essential point on which Penrose parts company from Turing. To summarise Penrose's views: Gödel's theorem tells us that we can see the truth of statements which cannot be proved by the application of a formal system of rules. Using Turing machines, this argument can be put in the form of showing minds able to perform uncomputable operations. Gödel also took this view of the mind's power, but unlike Gödel, Penrose insists on a materialist or physicalist base for mental faculties and deduces that there must be uncomputable elements in physical law which the brain exploits when it performs the uncomputable work of seeing the truth. Penrose locates these elements in the as yet unknown laws governing the reduction of the wave-function in quantum mechanics. Hence Penrose explicitly contradicts 'Turing's Thesis' in the form he has given.

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It is also worth noting that Turing, for most of his career, was convinced that there must exist part of the brain which is non-mechanisable:

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Turing's 1938 Princeton Ph.D. thesis, work conducted in close cooperation with Church, was entitled Systems of logic defined by ordinals, and published as (Turing 1939). Predominantly the work consisted of highly technical developments within mathematical logic. However the driving force lay in the question: what is the consequence of supplementing a formal system with uncomputable deductive steps? In pursuit of this question, Turing introduced the definition of an 'oracle' which can supply on demand the answer to the halting problem for every Turing machine. Turing gave his subject-matter an interpretation which described the mathematician's 'intuition' in theorem-proving, and Newman (1955) effectively identified the uncomputable 'oracle' with intuition. This was perhaps going too far since the 'oracle' is capable of far more than any human being; nevertheless Newman had a unique status as Turing's collaborator at this period and must reflect the tenor of Turing's discussions. In any case, Turing makes it clear that the 'intuition' being discussed is related to the human act of seeing the truth of a formally unprovable Gödel statement. To summarise, it is notable that Turing's 1938 work focussed on the same issue as Penrose now raises: the interpretation of uncomputable deductions.

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Simon

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Fair enough. That is what you believe. As I have already stated, I believe boolean calculus is a human construct that we have created with the intention of encapsulating truth. Whether or not it is sufficient, I don't know.

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Everything is a human construct, I'm not saying that I believe in anything, I'm defining truth in terms of boolean calculus, after all the truth is not an element itself, it has practical implications of everything consistent (have a look at the link to see how you encode true as a function in lamda calculus)

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Please don't confuse arbitary "truths" with empirical ones...you may not make a distinction but I do. "Empirical" is more than just my word for "Arbitary".

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There's only truths that are axiomatic, and those that can be derived from those axioms, whether you want to call the axioms empiricall or not is your decision, but I don't see any practical difference.

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It is also worth noting that Turing, for most of his career, was convinced that there must exist part of the brain which is non-mechanisable

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The brain is just a tool, remember the question I asked you about your biological senses, what determines the certain interface towards your observations? At what stage is it possible to replace your sensory information with generated information? The answer is at any stage. There's no way you can say for sure that any information isn't generated, making the internal/external theory redudant. Thus its possible to replace the brain with a turing machine. It doesn't change anything.

Btw in your quotation from the page, "human intuition" I think Isaac Asimov defined it as the ability to draw conclusions with insufficient data. This just doesn't make sense, there's a logical explanation for this too, and that is that intuition isn't a direct deduction, its a long process that could be taking into account probabilities, feelings or exactly anything that feels right. Its not logical, its just nonsense that might work.

Kedaman

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Everything is a human construct, I'm not saying that I believe in anything, I'm defining truth in terms of boolean calculus, after all the truth is not an element itself, it has practical implications of everything consistent (have a look at the link to see how you encode true as a function in lamda calculus)

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OK, I see what you're saying here. There is no external truth. Truth is whatever we define it to be. I don't agree with you but I hear what you're saying.

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At what stage is it possible to replace your sensory information with generated information? The answer is at any stage. There's no way you can say for sure that any information isn't generated, making the internal/external theory redudant.

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Aha! This is the crux of our disagreement and underlies our different opinions. This identifies you, pretty conclusively, as a solipsist.

You see, we both agree that there's no sure fire way to discriminate between sensory and generated information. Where we go from there is where we differ.

Because we cannot be absolutely certain which information is sensory and which is generated, you say that, rather than take the risk of occaisionally being wrong, we should reject the notion of any distinction whatsoever (and therefore the notion of an external reality). That way, we can never be wrong because we can only make statements about our own perception.

However, I say that, just because we can't be absolutely certain of a distinction, we can still be right most of the time. We can make statements about an external reality and, if we're careful, usually be correct. We can take steps to minimise that uncertainty.

Why do I think my approach is better? Because it allows us to assert more. I can make assertions beyond my own perception. The only danger is that I must forever hold onto the knowledge that I might be wrong. As long as I don't forget that, there's no real danger.

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Btw in your quotation from the page, "human intuition" I think Isaac Asimov defined it as the ability to draw conclusions with insufficient data. This just doesn't make sense, there's a logical explanation for this too, and that is that intuition isn't a direct deduction, its a long process that could be taking into account probabilities, feelings or exactly anything that feels right. Its not logical, its just nonsense that might work.

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Perhaps, but it's undeniably useful. And it's what a Turing machine would need to resolve the "halting" problem. It's what enables us to see the truth of the Godel sentence even though we cannot proove it.

Despite the fact that intuition can often be wrong, it is also a useful tool that a turing machine does not have.

Simon

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This identifies you, pretty conclusively, as a solipsist.

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How so? I thought solipsists had the belief that everything is projected from your mind. I'm pretty much the other way around, everything is projected into your mind.

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Why do I think my approach is better? Because it allows us to assert more. I can make assertions beyond my own perception. The only danger is that I must forever hold onto the knowledge that I might be wrong. As long as I don't forget that, there's no real danger.

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You know, I thought we agreed on that intersubjectivity is subjective because after all, you do observe that the others tell you what they observe, correct? We use the same analogy again, the "imaginative perceptions" you argue to have, are also your observations, everything imaginative is observed equally much as anything else. I can pretty much do all the assertions you do, its just a matter of observing.

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Perhaps, but it's undeniably useful. And it's what a Turing machine would need to resolve the "halting" problem. It's what enables us to see the truth of the Godel sentence even though we cannot proove it.

Despite the fact that intuition can often be wrong, it is also a useful tool that a turing machine does not have.

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When I think about it, I wouldn't want to call a turing machine that halts, a turing machine, as much as I don't want to call a phrase that is self referential a statement. I don't think even humans can grasp self referential statements, they're misunderstanding them and find meaning in them. I think Gödel's sentence is widely misunderstood. Its not a statement.

Kedaman

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How so? I thought solipsists had the belief that everything is projected from your mind. I'm pretty much the other way around, everything is projected into your mind.

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Doesn't that pretty much amount to the same thing?

The way I see it, there are three possibilities:

1. 100% of our experiences are generated
2. 100% of our experiences are sensory
3. We experience a mixture of sensory and generated information (the exact balance unknown).

If either 1 or 2 is the case, there is no point in trying to make a distinction between generated or sensory information.

If 1 is the case, there is no reason to expect any kind of consistancy in our experiences. If 2 is the case, there is no reason to expect any kind of inconsistancy in our experiences (unless reality is itself inconsistant).

I do seem to experience inconsistancies so that would rule out No. 2 unless I am prepared to accept that reality is not consistant. Despite the fact that I do experience inconsistancies, there does appear to be some patterns of consistancy. Why should that be the case if No. 1 was true? In other words, I do not perceive completely consistant nor completely inconsistant experiences. It is some mixture of both.

Therfore, I conclude that No. 3 must be the case. If No. 3 is the case, then it stands to reason that we would seek to distinguish between generated and sensory information.

Whether you put yourself in category 1 or 2, there is no point in seeking such a distinction as I do. In either case, you are left with the difficult question of explaining apparant consistancies/inconsistancies.

Whereas I can explain away inconsistancies by assuming that I became confused in the distinction between a particular set of generated and sensory information.

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You know, I thought we agreed on that intersubjectivity is subjective because after all, you do observe that the others tell you what they observe, correct? We use the same analogy again, the "imaginative perceptions" you argue to have, are also your observations, everything imaginative is observed equally much as anything else. I can pretty much do all the assertions you do, its just a matter of observing.

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Your assertions do not go beyond statements about the nature of your own perceptions. Mine do.

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When I think about it, I wouldn't want to call a turing machine that halts, a turing machine, as much as I don't want to call a phrase that is self referential a statement. I don't think even humans can grasp self referential statements, they're misunderstanding them and find meaning in them.

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Well, it wouldn't be a turing machine. It would be something more. If humans can do something more than a turing machine, it stands to reason that we are more than a mere turing machine.

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I think Gödel's sentence is widely misunderstood. Its not a statement.

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You mean universally misunderstood by the entire mathematical community? Well, that's very bold of you, I must say.

You insist that all statements can be generated by a Turing machine but Gödel says there are statements that a turing machine cannot compute. If you dismiss those statements as invalid merely because they cannot be generated by a Turing machine then you are merely using circular logic to prove your original assertion.

Simon

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Doesn't that pretty much amount to the same thing?

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Nope, the Solipsists takes for granted that its you that generate the information. I take for granted that I revieve information.

Whether our experiences are generated or sensory does not matter in my theory. Information cannot be inconsistent, it cannot answer both yes or no to the same question, thats not information. Thus its by the definition not possible to experience inconsistent information.

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Your assertions do not go beyond statements about the nature of your own perceptions. Mine do.

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When I say assertions, I mean essentially anything a instrumentalist needs, and my theory is such that by adopting it you wont be constrained in any way, achieving these needs.

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Well, it wouldn't be a turing machine. It would be something more. If humans can do something more than a turing machine, it stands to reason that we are more than a mere turing machine.

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I still don't think humans can grasp self referential phrases. Such express no information.

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If you dismiss those statements as invalid merely because they cannot be generated by a Turing machine then you are merely using circular logic to prove your original assertion.

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thats the purpose of axioms, as soon as you add a contradiction, you can contradict the whole system. The idea with consistency is that you only have axioms that don't contradict each other and the rest is just plain illogical. self referential phrases are illogical.

Kedaman

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Nope, the Solipsists takes for granted that its you that generate the information. I take for granted that I revieve information.

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As I went on to demonstrate, in terms of practical implication, they amount to the same thing.

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Information cannot be inconsistent, it cannot answer both yes or no to the same question, thats not information. Thus its by the definition not possible to experience inconsistent information.

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But one piece of information may contradict another, right? That is what I mean by inconsistant.

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I still don't think humans can grasp self referential phrases. Such express no information.

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But I can make and understand statements about myself, can I not? "I am angry" is a self-referential statement when I say it. It is the self refering to itself.

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thats the purpose of axioms, as soon as you add a contradiction, you can contradict the whole system. The idea with consistency is that you only have axioms that don't contradict each other and the rest is just plain illogical. self referential phrases are illogical.

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But how can you know whether a formal system contains contradictory axioms? It may not be immediately obvious. Indeed, Godel has proved that it is impossible to prove the consistancy of any formal system (that is powerful enough to compute arithmetic).

You can never be sure that your axioms do not contradict. As long as you are unaware of a contradiction, your formal system is incomplete (true statements that cannot be proven). Completeness implies inconsistancy.

Simon

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But one piece of information may contradict another, right? That is what I mean by inconsistant.

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The axiom of non contradiction is not (p(x)^not p(x)) - the statements contradicts itself, not other statements. Two statements in conjunction that implies yes and no to the same question is a contradiction, without the conjunction they're either

1. both contigencies
2. one of them is an axiom, the other is a disproved theorem.

but not

3. both of them axioms.

what i'm trying to say, that its not possible to assume that something is incosistent, because that would answer yes and no on the same question and thus not make any sense, if you percept something that doesn't make any sense, then there's obviously lack of information. Contradicting statements doesn't contain information. Information is defined as everything that answers yes or no to a question, that is exclusively yes or no in logical terms. What you are doing is asking these yes or no questions, and what you experience is the answers to these yes or no questions.

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But I can make and understand statements about myself, can I not? "I am angry" is a self-referential statement when I say it. It is the self refering to itself.

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"this is false" is a self referential phrase, because you can't substitute this with the whole phrase as you will end up with another this to substitute each time. "I am angry" is a contigency angry(x) with x="I". What you experience is this:
1. You ask the question "am I angry?"
2. You recieve the answer "Yes"
3. Conclusion: You have observed that you are angry.
This is not a self referential statement as you clearly observed your "own" angriness, whether its actually yours or not doesn't matter. However "this is false" is definitely a self referential phrase.

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It may not be immediately obvious. Indeed, Godel has proved that it is impossible to prove the consistancy of any formal system (that is powerful enough to compute arithmetic).

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if there is a inconsistency in aritmethic math then the whole system will automatically be a contradiction and is not in fact a logical system at all. Gödel is wrong, if there are systems that doesn't contradict each other because they don't contain the arithmetic flaw then that doesn't prove that all systems are inherently inconsistent.

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But how can you know whether a formal system contains contradictory axioms?

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It implies a contradiction - meaning it can be deduced using its axioms.

Kedaman

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The axiom of non contradiction is not (p(x)^not p(x)) - the statements contradicts itself, not other statements. Two statements in conjunction that implies yes and no to the same question is a contradiction, without the conjunction they're either

1. both contigencies
2. one of them is an axiom, the other is a disproved theorem.

but not

3. both of them axioms.

what i'm trying to say, that its not possible to assume that something is incosistent, because that would answer yes and no on the same question and thus not make any sense, if you percept something that doesn't make any sense, then there's obviously lack of information. Contradicting statements doesn't contain information. Information is defined as everything that answers yes or no to a question, that is exclusively yes or no in logical terms. What you are doing is asking these yes or no questions, and what you experience is the answers to these yes or no questions.

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The inconsistancy I'm talking about are multiple observations that contradict each other. You might try to dismiss one observation as being incomplete information but that doesn't wash in your solipsist idea of perception.

If we do not generate any information ourselves, if we only receive information from reality (an external source) that is consistant and it is not subject to internally generated distortions, why should we ever experience inconsistant observations? Incomplete observations do not explain it. If I only percieve half a circle, it does not contradict with the later observation of a complete circle, does it? The later observation contains the first observation as a subset.

However, the nature of our experiences is that observations we make sometimes completely falsify previous observations. You have not explained, at least to my satisfaction, why such inconsistancies would occur if 100% of our observaions are sensory.

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if there is a inconsistency in aritmethic math then the whole system will automatically be a contradiction and is not in fact a logical system at all. Gödel is wrong, if there are systems that doesn't contradict each other because they don't contain the arithmetic flaw then that doesn't prove that all systems are inherently inconsistent.

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He didn't say that all systems are inherantly inconsistant. He said that all systems are incomplete (cannot prove some true statements). We can only make a complete formal system by introducing a contradiction.

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But how can you know whether a formal system contains contradictory axioms?

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It implies a contradiction - meaning it can be deduced using its axioms.

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But you cannot immediately see all possible theorems just by looking at a formal system's axioms. You do not know it is inconsistant until you finally stumble across a theorem that is a contradiction of an axiom.

Simon

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The inconsistancy I'm talking about are multiple observations that contradict each other. You cannot both see a cat and not a see a cat.

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Multiple observations cannot contradict each other. You can't both see a cat and not see a cat.

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However, the nature of our experiences is that observations we make sometimes completely falsify previous observations. You have not explained, at least to my satisfaction, why such inconsistancies would occur if 100% of our observaions are sensory.

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Give me an example.

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He didn't say that all systems are inherantly inconsistant. He said that all systems are incomplete (cannot prove some true statements).

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And he proved that using invalid axioms :rolleyes: who couldn't do that with any invalid axioms?

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We can only make a complete formal system by introducing a contradiction.

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Now thats what I call a contradiction.

Kedaman

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Multiple observations cannot contradict each other. You can't both see a cat and not see a cat.

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Yes I can! I might see, what at first glance looks like a cat (Say it was from a distance and only a quick glance). On subsequant inspection (and more carefully), I observe that it is a dog.
Because I have a cat at home and am used to seeing cats all the time, the first thing that popped into my head was cat when I saw that four legged animal. My preconception prevented, what would have been enough under normal circumstances, me from recognising the animal for what it was.
Note, this is not just a case of incomplete information, it was enough but it was distorted by my preconceived ideas (generated information). An experienced inconsistancy. One which I resolve afterwards by dismissing my first experience as false.

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And he proved that using invalid axioms who couldn't do that with any invalid axioms?

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The only axioms he used were those we all use for elementary number theory. Peano's arithmetic. If those axioms are invalid, then so is our arithmetic.

And, in regards to what you said a while back regarding the Godel sentence being invalid as it can't be represented in Lamda calculus...think again! Here is a page that shows you how Godel's proof can be demonstrated in LISP (an implementation of lamda calculus): http://www.cs.auckland.ac.nz/CDMTCS/...wable/ch3.html

First he demonstrates how you handle self-reference in LISP, then how to use that to demonstrate Godel's incompleteness theorem.

Does that convince you?

Simon

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Yes I can! I might see, what at first glance looks like a cat (Say it was from a distance and only a quick glance). On subsequant inspection (and more carefully), I observe that it is a dog.

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nope, because here you also observe that your first observation wasn't careful enough and thus you dismiss the theory that its a cat. Your axioms will be consistent during both instants. Btw, a dog could look like a cat, if not even be both a cat and a dog by definition (in analogue with multiple inheritance in OOP).

Note that with the time dimension in your observations, you only observed the cat during an instant, not troughout eternity. Observing a door that is open one instant and closed another instant, doesn't trouble you, but observing a door being both closed and open at the same instant is nonsense.

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And, in regards to what you said a while back regarding the Godel sentence being invalid as it can't be represented in Lamda calculus...think again! Here is a page that shows you how Godel's proof can be demonstrated in LISP (an implementation of lamda calculus): http://www.cs.auckland.ac.nz/CDMTCS...owable/ ch3.html

First he demonstrates how you handle self-reference in LISP, then how to use that to demonstrate Godel's incompleteness theorem.

Does that convince you?

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I don't know LISP and how it evaluates functions. I know however very well that you can write functions in most programming languages that recurses infinitely and will compile and run as long as they're not called, when they will oveflow the stack. Even in lamda calculus the Y operator does the job.
My point is that Gödel didn't bother checking if the Gödel Sentence was valid statement before checking if the its not provable, neither does the compilers check for infinite recursion.

Kedaman

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nope, because here you also observe that your first observation wasn't careful enough and thus you dismiss the theory that its a cat. Your axioms will be consistent during both instants.

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It is only my later experience that forces me to invalidate my earlier experience. In order to rationalise two conflicting experiences, I will simply declare I was mistaken on the occaision of minimum verification. My desire for a rational and consistant understanding of reality forces me to overide a perceived experience.

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Note that with the time dimension in your observations, you only observed the cat during an instant, not troughout eternity. Observing a door that is open one instant and closed another instant, doesn't trouble you, but observing a door being both closed and open at the same instant is nonsense.

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It is the natural function of a door (in a consistant universe) that it may be open one minute but closed the next. It is not a natural function for a cat to transform into a dog.

The whole point I'm making here is that our experiences can be contradictory. OK, we often put that down to incomplete analysis but it is undeniable that our own perception shapes the way we perceive. Our experiences are shaped, even sometimes distorted beyond recognitian, by what has gone before. What was sensory information once is used to determine how future sensory information will be interpreted.

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I don't know LISP and how it evaluates functions. I know however very well that you can write functions in most programming languages that recurses infinitely and will compile and run as long as they're not called, when they will oveflow the stack. Even in lamda calculus the Y operator does the job.

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The point is that self reference is not invalid in lamda calculus (as you previously claimed) and Godel's proof can be demonstrated using lamda calculus.

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My point is that Gödel didn't bother checking if the Gödel Sentence was valid statement before checking if the its not provable, neither does the compilers check for infinite recursion.

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Why is it that you, and nobody else, has decided that the godel sentence is invalid? Why is it that everyone else (who cares to) recognises that as a valid statement, can evaluate it's verisimillitude?

Out of interest, do you disagree with both incompleteness theorems? Do you agree with the first that stated no formal system could prove it's own consistancy? Is it only the second one you disagree with?

Simon
I think I understand what Gödel Is saying now. However Penrose is misconcepting the whole thing imo. I don't agree with you that its possible to observe inconsistent information - Its an inconsistent act in it self and cannot be done.

The observer does only recieve information (this is equivalent with ask for information), all information is percepted from a generator. The generator by definition can provide any information, thus the observer cannot percept information outside the generator.

The turing machine can only generate information, if asked a yes/no question answer either yes or no, or return a contigency. Contigencies are turing machines themselves, and have to be questioned further for an answer.

Now lets say there's a set of all turing machines, any two consistent turing machines is a turing machine too. During any instant, the observer will be asking a certain amount of yes/no questions, and get either yes/no answers or a contigency in return from only one turing machine. All of these are in fact turing machines themselves, but the questions will be directed to only one.

So lets say that the observer asks a certain turing machine the gödel sentence, the machine should fail to answer, and be classed as incosistent. However the answer the observer will get is a turing machine true, that is reduced from another turing machine containing the negated inconsistent one.

While, there is no turing machine you could ask the question without making it inconsistent, there is anyways always a turing machine that says that it is incosistent in the set of all turing machines. Whenever you ask this or any question it will be directed to a turing machine.

Now lets call this turing machine U (as in universe), that will always give the answer, because we know that at least one will always and we call it U. If you were to ask U the gödel's sentence the fundamental error is yours, because the recieved answer will not come from U, the contradiction is that you asked the question in first place. If we advocate consistency then this question cannot be asked to other than turing machines contained as negated inconsistencies inside U. In fact once a question is asked to a turing machine the fundamental assumption is that the turing machine is consistent. If you assume that its incosistent, then the question is actually asked a turing machine that contains the negated inconsistent one, and this is like saying you're asking a question to someone you're not talking to - it cannot be done.

Similar to that there is no largest integer, there is no Universal turingmachine, even though there is always a larger integer, and there is always a turing machine that answers all your questions. So while Gödel is correct, that its not provable, this proof is provided by a turing machine, and the sentence cannot be conceived to be true, because this question cannot be asked an universal turing machine, as it doesn't exist.

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It is the natural function of a door (in a consistant universe) that it may be open one minute but closed the next. It is not a natural function for a cat to transform into a dog.

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Maybe not, if you want to put it that way, its a dog that looked like a cat at first sight. consistency isn't about what is natural, its what prevents a question from being answered both yes and no.

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The point is that self reference is not invalid in lamda calculus (as you previously claimed) and Godel's proof can be demonstrated using lamda calculus.

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Its valid, its just that it cannot be evaluated. Gödel's sentence cannot be evaluated either, quite meaningless actually, because they are theories that cannot answer any questions and should be dismissed by Occam's razor.

Kedaman

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I think I understand what Gödel Is saying now. However Penrose is misconcepting the whole thing imo.

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Well, that's something at least. Penrose's ideas are far from universally accepted amoung his contemporaries but he is still working on the problem and many have reserved judgement until his work is complete. I'm not even saying that I agree with Penrose, I'm just saying that he may be right, I just don't know.

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The observer does only recieve information (this is equivalent with ask for information), all information is percepted from a generator. The generator by definition can provide any information, thus the observer cannot percept information outside the generator.

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It is not clear to me how you arrive at your final conclusion above. How do you know there is not more than one generator?

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So lets say that the observer asks a certain turing machine the gödel sentence, the machine should fail to answer, and be classed as incosistent.

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No, that is not the case. The machine, by failing to answer the question will be classed as incomplete. It would be inconsistant if it did answer.

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However the answer the observer will get is a turing machine true, that is reduced from another turing machine containing the negated inconsistent one.

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You can overcome the incompleteness of a formal system by adding the unproveable godel sentance to the system as another axiom but that just generates a new godel sentence.

However, we see the truth of the godel sentence, not because we are told that by another turing machine that contains the old one as a subset. We see the truth by consulting a non-mechanisable part of the mind that Turing called the "oracle" and what Penrose calls intuition.

We do not get stuck in an infinitely recurring loop as we try to validate the truthfullness of the godel sentence. We step outside of the loop and this process must be non-mechanisable (as proved by Turing himself).

Simon

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It is not clear to me how you arrive at your final conclusion above. How do you know there is not more than one generator?

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I didn't say that, two generators is one generator by definition, they both generate information.

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No, that is not the case. The machine, by failing to answer the question will be classed as incomplete. It would be inconsistant if it did answer.

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Nope, thats not what i meant. A machine can't answer that doesn't exist. But a machine that is capable to answer and fails to answer is inconsistent (as in contradictory) and thus doesn't exist.

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However, we see the truth of the godel sentence, not because we are told that by another turing machine that contains the old one as a subset. We see the truth by consulting a non-mechanisable part of the mind that Turing called the "oracle" and what Penrose calls intuition.

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So are you agreeing with penrose now or just saying that this is a possibility?

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We do not get stuck in an infinitely recurring loop as we try to validate the truthfullness of the godel sentence. We step outside of the loop and this process must be non-mechanisable (as proved by Turing himself).

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And this somehow is true because of what?
You know, if you want to listen I could prove that a infinitely recurring statement does not generate information.

Kedaman

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Nope, thats not what i meant. A machine can't answer that doesn't exist. But a machine that is capable to answer and fails to answer is inconsistent (as in contradictory) and thus doesn't exist.

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I don't understand....Why would such a machine be inconsistant if it didn't answer the question? This just doesn't follow. The point that is made here is that any machine (based on formal logic) that we did create would either be incomplete or inconsistant. It would only be inconsistant if it attempted to answer the godel question.

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So are you agreeing with penrose now or just saying that this is a possibility?

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I am saying that, at present, there is a gap in what can be stated by a completely mechanisable process. Both Turing and Penrose agree on this. What is the question here is whether we (as conscious human beings) have something additional (and non mechanisable) in our consciousness that enables us to overcome the limitations of formal systems (as demonstrated by Godel).

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And this somehow is true because of what?
You know, if you want to listen I could prove that a infinitely recurring statement does not generate information.

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Statements do not generate information attall. They may or may not contain information but I don't see how they generate information.

However, it seems we are at logger heads here and there is no way forwards.

One last piece of food for thought is that it is worth considering that all statements are ultimately infinitely recursive. If you don't start form any point of understanding, how can you finitely define any sentence?

So, would that mean that no statements generate/contain information?

Simon

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Statements do not generate information attall. They may or may not contain information but I don't see how they generate information.

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well thats not what i meant, I meant that they have no practical implications.

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One last piece of food for thought is that it is worth considering that all statements are ultimately infinitely recursive. If you don't start form any point of understanding, how can you finitely define any sentence?

So, would that mean that no statements generate/contain information?

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Why are all statements are infinitely recursive?
You're misunderstanding the purpose of statements. They're not nessesarily ways to express information, they are propositions in boolean calculus. When you ask a question you usually refer to a statement, asking if its true or not. the answer is the actual information, the statement itself is your own idea, not anyone elses, so the question is not if the statement makes sense or not, because statements are models for your senses, you either experience it or not. If you don't experience it, the statement is false, if you experience it, the statement is true.

Gödel proved that there is no UTM right? now how can the Gödel's sentence make any sense, if it refers to a UTM? he assumed that UTM actually existed, and this lead to a contradiction, thus proof trough contradiction: UTM doesn't exist. If this is true, then Gödel sentence can't make any sense.

Let me show a similar proof:
assume there is a largest integer L. This means x<L for all integers x. However by definition of integers we have, that if x is an integer then x+1 is an integer. L+1 is thus an integer and L+1<L is false. We have a contradiction. L does not exist. x<L is like saying x<infinity but this is not mathematically defined. Same goes for gödel's sentence. L is just a hypotetical notation, so is UTM.

Kedaman

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Gödel proved that there is no UTM right? now how can the Gödel's sentence make any sense, if it refers to a UTM? he assumed that UTM actually existed, and this lead to a contradiction, thus proof trough contradiction: UTM doesn't exist. If this is true, then Gödel sentence can't make any sense.

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No, he didn't prove that the UTM could not exist. He proved that any machine that was claimed to be a UTM would either be incomplete or inconsistant.

Simon

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No, he didn't prove that the UTM could not exist. He proved that any machine that was claimed to be a UTM would either be incomplete or inconsistant.

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What are you saying? That there could (or is?)an UTM which cannot be claimed to be an UTM? What exactly do you mean by incomplete?

A UTM (Universal Truth Machine) is a machine operating a system of formal logic that will evaluate True or False for every statement asked of it.

What Godel proved is that any formal system of logic used to construct such a machine would either be incomplete (true statements that it could not proove) or inconsistant (able to contradict itself).

Any such machine that was built and claimed to be a UTM would be subject to the same limitations.

Simon

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A UTM (Universal Truth Machine) is a machine operating a system of formal logic that will evaluate True or False for every statement asked of it.

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A machine operating on formal logic can't evaluate true or false for contigencies, and contigencies are statements. Are you sure Gödel's sentence is not a contigency?

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What Godel proved is that any formal system of logic used to construct such a machine would either be incomplete (true statements that it could not proove) or inconsistant (able to contradict itself).

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Why would the statements be true? I think either the mind or the machine has to be inconsistent, and I'm certain its the mind, and i'm also certain its not my mind, in other words not every mind.

Kedaman

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A machine operating on formal logic can't evaluate true or false for contigencies, and contigencies are statements. Are you sure Gödel's sentence is not a contigency?

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What do you mean by a contigency? A statement that is true or false depending on something that hasn't happened yet?

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Why would the statements be true?

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Because, if I say to the UTM, "The UTM will not say this statement is true", it will fail to answer (if it is consistant) and will be evidently true (to observers).

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I think either the mind or the machine has to be inconsistent, and I'm certain its the mind, and i'm also certain its not my mind, in other words not every mind.

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I don't know what you mean by the above statement.