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

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.

Simon
A contigency is a statement that cannot be deduced trough logic, that is, there's not enough applications to reduce all abstractions. Btw haven't you said once that abstractions do not exist, or that abstractions cannot be percepted? Here's an example of a tautology:
not (p and not p)
this is an abstraction because of the variable p, however if we apply any p we see that we can reduce it to true. Because its true for any p, the whole statement is true, and thus a tautology.
p and q
is a contigency because its an abstraction with two variables p and q, and it cannot be deduced to true. However if we choose a p and a q we can deduce it either to true or false.


Suppose that the universe consisted of two entitities, you and a turing machine representing the universe.
The only way of communication between you and the universe is, that you ask a yes/no question and the UTM answers either yes or no. Also UTM cannot answer yes and no on the same question.
for instance:
MIND: p="I see a cat", is p true? --> | <-- Yes : UTM

now how do i formulate the gödel sentence if UTM is unknown, simple, we assume that you will get the answer if UTM exists.

MIND: g="do I not get the answer yes" is g true? --> | <--... : UTM
MIND: f="ah I see that g is true" is f true? --> | <--Yes : UTM

It looks like UTM is incomplete, but couldn't it be that the question never passed the barrier | in between? | denoting the interface between UTM and MIND that allows this communication.
In the next question you ask if you see that g is true, and UTM answers yes, this means that you think g is true, but UTM doesn't say if its true nevertheless, it lets you think that its true. This suggest that MIND is inconsistent, however MIND is not a turing machine, it does not emmit information to UTM, it only percepts information from UTM, it only asks UTM questions, not state anything. The fundamental difference between MIND and UTM is that MIND asks and UTM answers.

Now lets make a set of questions that MIND can ask. We'll make a lamda function that takes any of these questions and returns an answer. Note that MIND cannot ask if a contigency is true, because the truth of contigencies cannot be percepted, only tautologies. Why is this?

We have assumed that all of MIND's perceptions are Yes/no answers to MIND's questions, in other words we cannot experience anything else. Thus its possible to experience f but not possible to experience g.

MIND cannot do any information processing on its own, it can only experience the deduction trough UTM, and f is not a deduction, it could be called intuition, but its still an experience which UTM offers. Its similar to the experience you mentioned about the cat, you saw what seemed to be a cat but later on you were certain that you were delusional.

My point is that UTM is not UTM unless it can stand for all of your experiences, including the intuitive truth of gödel's sentence. Btw I do not experience it at all, it must only go for certain minds. I for instance haven't seen dogs that i first though were cats either.

Kedaman

It is occurring to me that we have a fundamental difference in the way we view our consciousness (and the way it interacts with everything else).

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MIND cannot do any information processing on its own, it can only experience the deduction trough UTM, and f is not a deduction, it could be called intuition, but its still an experience which UTM offers. Its similar to the experience you mentioned about the cat, you saw what seemed to be a cat but later on you were certain that you were delusional.

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In my opinion, our minds do process information. Indeed, it is our minds that turn raw data into informaiton.

When we ask if we see a cat, the turing machine doesn't give us an answer. We are supplied with raw, observational data which we extrapolate meaning from. We interpret the data and generate an answer to the question.

In your view, the observer and the information processor are seperate entities. In my view, they are one and the same entity. In addition there is an entity that I call "reality".

We are each splitting our universe into two entities but in different places.

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My point is that UTM is not UTM unless it can stand for all of your experiences, including the intuitive truth of gödel's sentence.

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Then the UTM cannot be a formal system...

Simon
perhaps if you could try to understand my point of view, you'd see that there isn't anything that is inconsistent or incomplete?

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perhaps if you could try to understand my point of view, you'd see that there isn't anything that is inconsistent or incomplete?

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Well, I thought I was trying to. Am I way off the mark though?

Simon
What is consciousness?
In Object Oriented Programming, you refer data and algoritms contained in objects and messages sent between them, this is more or less also how Realists view the universe.
However there are several good reasons why mathematicians wants to separate data and algorithms, mainly because of distringuishing abstraction from actual data.
In Functional Programming, or even better, purely functional languages you distinguish data from algoritms and thus abstraction just becomes a model, not a law. Instrumentalists view the universe entirely subjectively and treats the universe like a mathematician treats a function, or a programmers treats a functional programming language.
The mistake realists often do is define consciousness as an object with data and algoritms, that is they think it can contain certain known data and as well perform private operations on this data. Their universe looks like this:
---------------------------------------------
| Your data <|> rest of the universe data
| Your algoritms <|> rest of the universe algoritms
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This structuring is meaningless though to anyone else, there's always an algoritm that applies on all data, and anyone can use it without concerning of where the data is stored in which medium, only if the algoritm is known.
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| algoritms ( data)
---------------------------------------------
well this looks much nicer, the instrumentalist only needs to know an universal algoritm to obtain any data.
These two views are both turing complete models, the latter reminds of lamda calculus and the previous of turing machines, however only the latter puts consciousness in a role as a pure observer. Now its obvious the consciousness cannot be a turing machine, it can only be aware, not process data, thats the point of the UTM, to process the data.

Instrumentalists eliminate the medium, they eliminate the object which encapsulates data and algorithms, they only take into account relevant information. They see relations between observations, not interactions between you and objects.

In practice what you call mind and anything else are never the same because the process to initiate the observations is unkown, we only know that these events actually happens, while a turing machines generate observations only when initiated.

Now what is it that you observe? Without any concept about these algoritms, you observe certain things, while not other things, we call this a state of an event space. Lets define a small event space:
{see cat, see dog, hear music, smell food}
imagine you're a very simple being that can only be aware of these four things. This is thus your universe, you can only percept 2^4 sets of information, for instance if you only see a dog and hear music, but don't smell anything, you have just observed (0,1,1,0).
The universe could be annotated as a cartesian product of boolean values, containing 2^n sets of information. This already can be represented by a turing machine.
Now it seems to happens in {see cat, see tail} that tail can be seen when cat is seen. This is because you have defined this relation tail Ícat, meaning that the set of observations that you see a cat in is contained in the set of observations you see a tail in (or just simply cats have tails)
Now you have succesfully reduced the complexity of universe just a little bit. namely there are only 3 sets of information instead of 4 {{tail, cat}, {tail, no cat} {no tail, no cat}}
Its possible to do all these reductions with the same operator Í, although there are other operators in boolean calculus. This is equivalent with the universe you have defined including the abstract axioms, and can also be represented by a turing machine.
Now theres one more thing, all these observations are contigencies, because otherways you wouldn't need any information to answer them, that is not need to observe. What makes you an observer is the following things:
1. You have defined the relationships, the contigencies that constitutes a universe, in an event space
2. You observe by recieving the information from the UTM.

Now lets add another dimension into the event space, namely time, because we know that we cannot observe a cat and no cat at the same time. To make it really simple, we only define two points of time, yesterday and today, so we have:
{saw cat yesterday, saw cat today}
(You can extend this to any point of time and any space dimensions you want, and any sorts of cats or dogs or whatever you want, but the idea is still the same)
This makes the universe well defined because lets say that you didn't see a cat yesterday but see a cat today, there is only one set of information now {saw no cat yesterday, saw cat today}. So its possible to define the whole universe! Now this would mean that there is only one set of information, and this, this is what you observe, and the configuration of relations Í is our UTM, which is a turing machine.

Kedaman

You say that consciousness mere observes and does not process but what about the act of defining relations between observations? Isn't that a kind of information processing?

For instance, how would I define the relationship that all cats have tails merely by making observations of cats and tails at the same time?

A purely passive activity of observation wouldn't define anything, would it?

Simon
To define is not to process, to define a relation is also a way of observing a general pattern, an "abstraction". If you're confused on who does what, then maybe you could say that its you're doing all the processor as well, but then you're a solipsist :)
But actually you're right about one thing, it doesn't matter who processes as long as its being processed, and that would put me and the solipsist in the same cage after all.

Kedaman

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To define is not to process, to define a relation is also a way of observing a general pattern, an "abstraction". If you're confused on who does what, then maybe you could say that its you're doing all the processor as well, but then you're a solipsist

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Perhaps I do some of the processing but not all of it? Why is it an all or nothing?

Simon
I guess you could say, that a process has no owner.

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I guess you could say, that a process has no owner.

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But if I instigate and control a process, then I own it.

whoops ... a metaphysical conundrum :)

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Originally posted by simonm
But if I instigate and control a process, then I own it.

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have you read Asimov's Foundation series? In far future a galatic empire is about to fall due to its costly complexity. A mathematician Hari Seldon predicts this fall and that it cannot be prevented, however he comes up with a plan to minimize the peridod til the next empire can take over, virtually this constituting of a group of scientists working on an ecyclopedia, called foundation. 500 years later when the galactic empire have deteriorated the foundation has grown strong enough to start expanding on its own. Unknown to the galaxy including the foundation, a second foundation was setup to watch over the progress of the first, which had certain mental ability to control other individuals, so in case anything didn't go as predicted they could correct the error preserving the plan. A politician Trevize and a historician Pelorat from the foundation is sent out on a mission to find Earth, the root of the civilisation, of which all information has been hidden from the former empire. They however encounter with an isolated planet called Gaia, where all people, animals and non-lifeforms share consciousness. Gaia has in fact arranged this situation, gathering both representants from the foundation as well as from the second foundation, in order to decide on an issue in which only Trevitze can give the answer to (this happens to be his amazing intuition).
The issue was which of the three were best suited for the task to control the second empire, the first, the second foundation or Gaia. Tretzie chose Gaia, or rather the galactic organism, and the representants from the other organisations continued as if they thought he chose them. Why? Because none was leaved their post, and thus thought they'd control the galaxy, while in fact the foundation was doing so under the invisible administration of the second foundation, while Gaia in fact could keep control over them all.

So who had control over the second empire in the end? All of them thought they had.
The answer is that process has no owner, you can only be aware of a process as much as you think its your own. Hari Seldon was certain that this would have happened, even without him.

Kedaman

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have you read Asimov's Foundation series?

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No I haven't.

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So who had control over the second empire in the end? All of them thought they had.
The answer is that process has no owner, you can only be aware of a process as much as you think its your own. Hari Seldon was certain that this would have happened, even without him.

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Not attall. The only process they were aware of is their own administration procedures. The wrongly attributed the effects to their control process but that is a different issue. The actual process they had control over cannot be disputed.

Simon

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Not attall. The only process they were aware of is their own administration procedures. The wrongly attributed the effects to their control process but that is a different issue. The actual process they had control over cannot be disputed.

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What do you mean wrongly attributed? I have a feeling you're misconcepting my analogue.

Kedaman

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What do you mean wrongly attributed? I have a feeling you're misconcepting my analogue.

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I don't think I am. There are two distinct entities here. The process and the effects of the process.

With the second foundation, each of the organisations is correctly sensing control over it's own administrative process. They are wrongly attributing the observed effects with their administrative process.

Consider an analogy to your analogy:

Three people, oblivious of each other's presence are sitting infront of a machine for which they must press the button when the robot arm moves above the cuddly toy. Each presses the button at the same time but only one is actually controlling the arm. They are each aware of the process of pushing the button and they each observe the effect of the arm grabbing the cuddly toy.

The point is, they are not actually aware of the process of the arm grabbing the cuddly toy. They are only aware of the effect. Thus there is a distinction between processes that they own and processes which they do not own.

Simon
I don't think you are capable of making such a distinction. I don't even think this distinction exist, and there's no reason to introduce this distinction because it adds more complexity to an already complete model, when asking the question about consciousness this causes even more confusion.

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Perhaps I do some of the processing but not all of it? Why is it an all or nothing?

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All: Solipsist
Something in between: You
Nothing: Me
In the end, all models work. Yours is most complex and confusing, the solipsist is totally impractical, while mine is most practical. This is because of Occam's razor.

Kedaman

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I don't think you are capable of making such a distinction. I don't even think this distinction exist, and there's no reason to introduce this distinction because it adds more complexity to an already complete model, when asking the question about consciousness this causes even more confusion.

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Actually, I think that there is a very good reason to introduce this distinction. I say "introduce" but really this distinction is thrust upon us as some processes we appear to have control over and some we don't.

Why should such a distinction become apparent itself if it does not exist? Yes, your "Foundation" example illustrates when that this sensation of control may be misplaced but it certainly does not imply that it is always be misplaced.

So, in actual fact, you would assume that we can make the distinction until there is good reason to believe other wise. And you would assume this by occam's razor if you decide that our sensation of control is misplaced, you must provide some convuluted example (such as the foundation series) to explain it away.

Once again, your argument comes down the the principle that we should not believe in reality merely because our beliefs are sometimes misplaced.

Simon

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Why should such a distinction become apparent itself if it does not exist? Yes, your "Foundation" example illustrates when that this sensation of control may be misplaced but it certainly does not imply that it is always be misplaced.

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When did I ever mention misplacement?
The point in my foundation example is that, all of them experience control, while there is no obvious initiator nor controller, not even Hari Seldon that invented the plan, he said anybody could have done that in this situation, and somebody else would have taken his place if he didn't make it. Who knows what all entities experiences control of the things you think you do other than yourself? I could give any finite list of conscious indivduals, it makes no difference. This has nothing to do with misplacement of experience, but the mechanical process is selfowned and does not need a conscious initiator/controller to be operational. For instance, replace any entity in the foundation example with am equivalent turing machine, according to the turing thesis the mechanical output of the operation is equivalent.

The imperative in Occam's razor is to reduce complexity, and by realizing that consciousness, including sense of control, have no mechanical effect on the universe, we make no distinction based on it, when defining the universe. If you want it your way we could introduce any finite amount of observers for each process, that wont change anything, just make the theory meaninglessly complex.

Kedaman

I guess we will just have to accept that we cannot agree on this one. I think the simpler answer is that we do have control and you think the opposite.

All your foundation example does is demonstrate the possibility of having a false sense of control. But it is a highly complex and contrived situation. What is the likelyhood that there is another entity controlling our body in just the same way as we are trying to control it?

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Originally posted by simonm
Kedaman

I guess we will just have to accept that we cannot agree on this one. I think the simpler answer is that we do have control and you think the opposite.

All your foundation example does is demonstrate the possibility of having a false sense of control. But it is a highly complex and contrived situation. What is the likelyhood that there is another entity controlling our body in just the same way as we are trying to control it?

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Agreed. It certainly goes against Occam's razor.

The Foundation example illustrates an unnatural evolution towards three groups hijacking all individuals inherent capability of self determination. However, it is purely an artifice, since if all three groups were eradicated, then everyone would be free again.

BTW, interesting example, since the whole Foundation occurance was initiated by R. Daneel, an AI.

-Lou

Simon
You know, a while ago I though we had agreed on a common goal here, consistency/completeness, a theory that can explain everything. Now if it was the case that you were happy with your model of universe, then why are we pursuing this discussion?
Turing couldn't explain the mind, Penrose can't explain the mind, who can? I think you want to know but you're afraid to let something go. Why does Penrose think the mind is not logical? I think he is afraid.

There is a logical explanation simon, you're just not letting me explain it.

Kedaman

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You know, a while ago I though we had agreed on a common goal here, consistency/completeness, a theory that can explain everything. Now if it was the case that you were happy with your model of universe, then why are we pursuing this discussion?

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I am all for trying to understand your point of view but I get the feeling that you are not resiprocating. You know the truth and if I don't see it, it's just because I'm not opening my mind up enough to your arguments. :rolleyes:

No, I am not happy with my model of the universe but I am yet to be convinced that your alternative offers any kind of advantage.

If it is worth continuing this discussion, it will be because we are both trying to understand each other's point of view and not being so convinced of one's own correctness.

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There is a logical explanation simon, you're just not letting me explain it.

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How am I stopping you? Perhaps I am failing to understand you but I am certainly not standing in your way.

It might help if you weren't so convinced of your own righteousness.

NOTLKH

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Agreed. It certainly goes against Occam's razor.

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Thankyou, at least I know I'm not t he only one seeing a problem with Kedaman's interpretation...

Both you and Lou have now misunderstood my intention with the analogy, in other we don't see the same analogy. I wanted to emphasise the nonrelevance between sense of control and effect. You both think i'm trying to emphasise misplacement of control.

My point is that placement of control has no mechanical relevance and thus is unnessesary complexity according to Occam, meanwhile you think I'm arguing there is misplacement and thus think I'm adding complexity. How can I argue that there is misplacement when I don't think placement matters at all?

If this is not what you're trying to say then I apologise for my ignorance.

Simon
Why do you think I know the truth? Especially when I've told you uncountable times that I don't believe in an objective reality. I'm presenting a model here, not stating my beliefs.

Kedaman

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Both you and Lou have now misunderstood my intention with the analogy, in other we don't see the same analogy. I wanted to emphasise the nonrelevance between sense of control and effect. You both think i'm trying to emphasise misplacement of control.

My point is that placement of control has no mechanical relevance and thus is unnessesary complexity according to Occam, meanwhile you think I'm arguing there is misplacement and thus think I'm adding complexity. How can I argue that there is misplacement when I don't think placement matters at all?

If this is not what you're trying to say then I apologise for my ignorance.

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You may see it as irrelevant but to me, it is very important. Whether or not I am in control of my actions is of great importance to most people.

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Why do you think I know the truth? Especially when I've told you uncountable times that I don't believe in an objective reality. I'm presenting a model here, not stating my beliefs.

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That's what you say but it does not come across in the way you say it.

Simon
Why is it important to you? What exactly makes having control any different?

Because being in control of one's own life is motivation to change it.

What is the point if we have no control? Why not lie down in the road and wait to be run over...what could you have done about it anyway? You had no control...

Simon
You know thats not an argument. I'm asking for practical differences, for instance if cats didn't have tails, then they'd not be able to keep their balance as well. Having control or no control of a process doesn't change a thing, however I think the sensation of control does motivate you in life.

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Having control or no control of a process doesn't change a thing, however I think the sensation of control does motivate you in life.

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I want more than the mere sensation of control. I want to know that I am actually in control.

If there is no control, there is no point to life (as far as I am concerned). I want to do more than just watch a movie. I want it to be interractive.

Simon

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I want more than the mere sensation of control. I want to know that I am actually in control.

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What is our goal here in this discussion? I have a feeling your pragmatic self is starting to awake. Til now it was pure scientific interest. Now you want like an instrumentalist alter perception.

Instrumentalist: Do you want to know something?
Realist: Yeah of course, I want to know everything.
Instrumentalist: You don't have control.
Realist: Thats not true!
Instrumentalist: Why not?
Realist: Because I want to have control!

Ask yourself. Does your wants really make an argument in testing a model? In that case there's no use of science at all.

I'm not saying that because I want to know that I have control, it means that I do. I know that's not a valid supportive argument.

But you're saying that it's unimportant and that's what I disagree with. It's of utmost importance as far as I'm concerned.

Tell me, if we don't have control over our observed actions, what is the point in the scientific pursuit of knowledge? Why bother? Infact, "bother" becomes a meaningless word. You don't have a choice. You will just do whatever it is you will do.

Simon
Unimportantness means there are lack of practical implications.

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Tell me, if we don't have control over our observed actions, what is the point in the scientific pursuit of knowledge?

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Ask yourself. Does your wants really make an argument in testing a model? In that case there's no use of science at all.

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Looks like you're out of options. Unless you want to become a instrumentalist of course :)

Kedaman

I'm not following you I'm afraid...

SImon

Realist: I believe there is an objective universe that we exist in.
Instrumentalist: I don't believe in such nonsense.
Realist: Why not?
Instrumentalist: Because its like locking yourself at home for the rest of your life and watch TV.
Realist: No. We do have control over our lives.
Instrumentalist: I don't think so, you just want to know the truth.
Realist: Of course we do, thats our interest in life.
Instrumentalist: And yet you admit that you can never reach it.
Realist: We can come closer and closer though.
Instrumentalist: The scientific method? The only thing it does is reduce the amount of channels to watch on your TV.
Instrumentalist: Do you want to know something?
Realist: Yeah of course, I want to know everything.
Instrumentalist: You don't have control.
Realist: Thats not true!
Instrumentalist: Why not?
Realist: Because I want to have control!
Instrumentalist: Then you will have to become an instrumentalist.
Realist: Why?
Instrumentalist: Because only instrumentalist can do whatever they want. That is our methodology, not pursue a truth like you do.

Here's my version of the conversation:

Realist: I believe there is an objective universe that we exist in.
Instrumentalist: I don't believe there's any value in making such an assertion.
Realist: Why not?
Instrumentalist: Because doing so does not make you better able to predict future observations we make.
Realist: On the contrary, it is only by comparing the explanatory power of two (as yet unfalsified) rival theories that we are able to select the best one.
Instrumentalist: But why is one theory better than another if it's predictive power is no greater?
Realist: Because if one theory raises more unanswerable questions than the other (by making more untestable assertions), it effectively increases our ignorance.
Instrumentalist: So do you believe that you have control over your own actions?
Realist: Yes. At least I would like to think so.
Instrumentalist: I don't think so, you just want to know the truth.
Realist: Of course we do, that's what motivates us to understand reality.
Instrumentalist: And yet you admit that you can never reach it.
Realist: We can come closer and closer though.
Instrumentalist: The scientific method? The only thing it does is reduce the amount of channels to watch on your TV.
Realist: So what? I only want to watch true channels (or at least channels that have not yet been falsified).
Instrumentalist: Do you want to know something?
Realist: Yeah of course, I want to know everything.
Instrumentalist: You don't have control.
Realist: Why do you say that?
Instrumentalist: Because believing that you do have control brings nothing to the party. It does not help you select better theories. It is an unecessary irrelevence. An untestable assertion that (by your own words) increases your ignorance.
Realist: But if we don't have control, what is the point to anything? I would like to believe we are in control of our own actions otherwise there is no point to anything anyway.
Instrumentalist: Then you will have to become an instrumentalist.
Realist: Why?
Instrumentalist: Because only instrumentalist can do whatever they want. That is our methodology, not pursue a truth like you do.
Realist: But perhaps we do have control. If that is the truth then it is a legitimate concern for realists. Indeed, if we do not have control, it should worry you instrumentalists as well because there is little point to finding the most predictive theory either. It wouldn't matter in either case. If we do not have control over our own information processing functions, there is no point to either the realists or the instrumentalists.

You're missing the point simon, Instrumentalists are not interested in truth, they want to change their perception to meet their needs, while Realists are interested in truth, they want to find the correct perception no matter if it matches their needs or not. This includes Lack of Control.

Those calling themself realists, claiming that they have control, just because they want to cannot be realists, they don't follow the scientific method. They're instrumentalists, because they let their needs interfer.

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Those calling themself realists, claiming that they have control, just because they want to cannot be realists, they don't follow the scientific method. They're instrumentalists, because they let their needs interfer.

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The point is there's no reason not to believe we do have control. It's not just that realists want to have control, they see no reason to believe otherwise.

In addition, I am not saying I believe we do have control because I want it to be the case, I am saying that if we don't have control, everything becomes meaningless.

Simon

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The point is there's no reason not to believe we do have control. It's not just that realists want to have control, they see no reason to believe otherwise.

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its unnessesary complexity and answers no further questions.

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Originally posted by simonm
In addition, I am not saying I believe we do have control because I want it to be the case, I am saying that if we don't have control, everything becomes meaningless.

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I think you feel that your life is meaningless for the simple reason that you feel lack of the sensation of control.

Kedaman

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its unnessesary complexity and answers no further questions.

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It's not unnessary. Indeed, if I am not in control, that raises further questions. Why do I have the sensation of control if I don't? What is it that is controlling my actions?

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I think you feel that your life is meaningless for the simple reason that you feel lack of the sensation of control.

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Why do you think that? I do have the sensation of control? It is because I feel in control that there is a purpose to living.