The wavefreak conjecture ...
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Any strictly material model of knowledge and cognition leads to incompleteness.
Note that this is a conjecture, not a claim so no proof will be offered. I will offer some observations on what leads me to this and ask some questions.
Formal logic has the Godel Incompleteness Theorem, computational theory has Turing's Halting Problem and formal semantics has Tarski's Indefinabilty Theorem. What strikes me as really profound is that it appears that any sufficiently structured system of knowledge representation runs into some type of fundamental barrier about what it can express. They are ulimately incomplete is some way. A materialistic model of cognition seems limited to some kind of mapping of concepts and processes to discreet brain states. All of the above theorems are based on discrete states in some fashion or another. So it seems like a not unreasonable conjecture to think that a theorem similar to those mentioned can be derived regarding cognitive models.
First question, is materalism even relevant? In my mind it is materialism that drives the cognitive models to discreet states and hence the core issue.
Second. Is the conjecture itself so outlandish that it isn't worth investigating?
Third. Does anybody know of any related essays or things?
Fourth, this seems the stuff of a PHD thesis. And since I am not in any PHD program, I suspect I am blowing smoke up the ass of god and just inventing shit to talk about.
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Oh boy, another fellow misusing Godel's theorems.
Huh?
I suggest you read the following book:
This book will clear up alot of the nonsense you're spouting. Remember, all these results are about formal systems. Since when is the mind a formal system? Godel's Theorem's say nothing outside of mathematics. More specifically, they say are only applicable in arithmetic that contains plus, minus and multiplication operators.
Not in any way.
Godel's Theorems are about formal systems such that one proves theorems from the axioms of number theory. Do you really think the mind is formal proof machine? Do you honestly believe that the mind checks every mathematic proposition to see if it is either a tautology or follows by modus ponens?
Investigate. Start with the book I recommended.
No, its the stuff of the trash heap...
"In the high school halls, in the shopping malls, conform or be cast out" ~ Rush, from Subdivisions
Here is your error.
There's no barrier of expression - most of the proof is showing that the unprovable statement can be expressed. The limit is to what can be proved through computational methods.
I'll ignore you now.My Artwork
Computational methods is the key phrase. The brain appears to be some sort of computational engine.
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A good call, I think. It seems to me that the only satisfaction that less-than-prodigious intellectuals have is caustically pointing out the errors in thought of others.
I apologise if I was talking over your head. Now be a good boy and return to your sandbox and let adults discuss these matters.
"In the high school halls, in the shopping malls, conform or be cast out" ~ Rush, from Subdivisions
I hope he will recover the deep psychological damage done by me "caustically" point out his errors. If he needs theraphy, perhaps he ought to consult todangst.
Let me know when the two of you stop crying like little babies and actually have something of value to say.
"In the high school halls, in the shopping malls, conform or be cast out" ~ Rush, from Subdivisions
It's funny how self-important you can make yourself feel by just acknowledging the fact that you know a little more than someone else.
Mediocrity is a plague among scientists, it seems.
Yes. That why 'no computational method of proof' means that proof is impossible. Your argument depends on the existence of something non-cognitive. You've proved that a proof of the Godel sentence or a halting algorithm would be non-cognitive but all that means is that neither of these things can exist.
First, let me remind everyone that I did NOT claim any of the results of the theorems mentioned had any direct correlation to the way knowledge is represented and processed in the brain. There is a similarity in different formal systems that is in escapable.
And I was so deeply offended by ChaosLord that I felt compelled to pull my copy of Godel's proof off my bookshelf and read it again. Godel makes me feel stupid. ChaosLord makes me feel, hmmm ... whats a good word, oh - that's right he doesn't make me feel much of anything at all.
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I didn't prove anything. I stated at the beginning that no proof was offered, it was only conjecture.
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Are we going to return to the issue? I really don't care what you think of me. What I do care about, and what I was hinting at, was that we get back to the issue. Presumably, the issue was on various mathematical results being applied to human cognition. However, it is evident that your only concern is attacking me. Now, I assumed you were intellegent enough to get subtle hints to get back on track. I guess I need to spell things out. Now pay attention: Can we get back on track? Can we get back to the topic at hand? FYI, attacking me isn't the topic.
Just a sidenote, but I find it funny that you accuse me of mediocrity, given that you don't know me. Furthermore, it is especially ironic coming from a theist.
"In the high school halls, in the shopping malls, conform or be cast out" ~ Rush, from Subdivisions
I perhaps didn't read it carefully enough.
I'll have another go.
Incompleteness in what way?
In Godel's theorem incompleteness means that there are some statements that cannot be proved through a computational method.
Tarski's theorem showed that truth cannot be defined mathematically. (which I don't see as a problem as the concept ought to be necessary for there to be definitions in math rather than a definition within it.)
I think you need to explain what you mean by cognitive model.
If you mean a materialistic theory of how our minds process knowledge then I can't see how such a theory would be subject to the axioms of arithmetic. If you mean a theory of knowledge as in what we can know (including the 'truths' of arithmetic) then the incompleteness would apply to all models - materialism/immaterialism would be irrelevent.
PS. The work of these logician's is one of Chaoslord's specialties.
If he's too offended to comment then that's a sign that you've seriously butchered them!
Can we return to the issue at hand? Or are going to continue to pout like a three year old? if the latter, please return to your sandbox.
"In the high school halls, in the shopping malls, conform or be cast out" ~ Rush, from Subdivisions
Since you, Strafio have actually taken the time to not only become familiar with these issues, but actually digest them, I will respond to you in a non-condesending way.
You have the general idea, but for sake of completeness (yes, I recognize the pun), it needs to be amended. Godel's first theorem*, doesn't say that there are some statements that cannot be proven, for any consistent system has this feature. I mean, if I can prove P, then I cannot prove ~P if the system is consistent. The key, is that Godel showed that there are some true statements, that you could formulate within an sufficiently robust formal system that you could not derive. I assume you already knew this. Moreover, Godel doesn't say that number theory is consistent, simply that IF it were, there would be some proposition represented by a godel number that could not be proven.
I am glad you pointed out that Godel's results applied only to computational methods. Now, the mind is of course not a computational machine in this sense. The mind is more of a heuristic learning machine.
As a side note, Godel's Theorem's are interesting, but overall, not that significant.
Close. Tarski's theorem, like Godel's theorem, is a metatheorm about a formal system. Taski showed that given classical logic, any formal theory T cannot contain within T, a truth predicate. He used the liar paradox to illustrate this. The result says that you can only talk about truth from outside the system. Then we get into his whole hierarchy of truth predicates...which I will not get into.
As a side note, Tarski's theory does not hold in three valued logic, as illustrated by Saul Kripke. Kripke showed how three valued logic can contain a truth predicate and still be consistent.
You give me to much credit. But thanks anyway.
All I ask is that people understand the concepts they are working with. Do you think Roger Penrose got respect when he presented a paper applying Godel's theorems the the Philosophy of Mind? Even though Penrose is a distinguished physicist and mathematician, his work ws greated with scorn from the philosophical community, percisely because he did not understand the basics of Godel's argument.
Perhaps more illuminating, is how biologists handle creationists. Creationists don't understand evolutionary theory, and they get treated with contempt, for the same reason as above.
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*I will use the Godel's Theorem to include the work of Rosser, who showed that regular consistency, not just omega consistency was sufficient for incompleteness.
"In the high school halls, in the shopping malls, conform or be cast out" ~ Rush, from Subdivisions
Hear, hear! The biologist raises his glass in acknowledgement of this truth. I belong to the PZ Myers school of thought, which says that all creationists suffered a tragic form of mental retardation in utero, which blocks the capability for coherent thought.
"Physical reality” isn’t some arbitrary demarcation. It is defined in terms of what we can systematically investigate, directly or not, by means of our senses. It is preposterous to assert that the process of systematic scientific reasoning arbitrarily excludes “non-physical explanations” because the very notion of “non-physical explanation” is contradictory.
-Me
Books about atheism
First, none of this has anything to do with atheism or theism.
Let me start over, concentrating on just on piece of my statement.
The Relevancy of Materialism
Materialism tells us that every concept exists as a physical thing in our brain. The concept for the number "one" does not float around out there in some immaterial concept space. It ONLY exists as states in our brains. The symbols used to write representations of the concept "one" on paper are nothing more than meaningless marks until somebody perceives it and invokes whatever processes in the brain are necessary to instantiate the states for awareness of "one". If follows from this that ALL knowledge is nothing more than states in our brain. There are no Platonic Forms. There is nothing but the physical structures and processes in our heads.
From this, we MUST conclude that in order for Turing to conceive of his little machines and derive his proofs, that a Turing Machine actually existed in his brain. What ever the human brain is, it allows for the assembly, manipulation, analysis, and meta-analysis of Turing Machines within its physical structure. Alan Turing was not just thinking about Turing Machines, he had a real Turing machine operating in his head. In order for me to thik about Turing Machines, I must construct one, a real one, in my head.
For Kurt Godel to create a proof about a production system of formula and rules of inference that was capable expressing core elements of Principia Mathematica, this actual production system had to exist in his head. To deny this is to deny materialism.
Whatever our brains are, some subset of its states and processes are capable of constructing actual Turing Machines and formal logic systems. These are not floating around out there, they actually exist as brain states.
Materialism is not only releveant, it is the ONLY thing we have. And, further, the ONLY things we can know are things that can be instantiated in the states and processes of our brains. From this it follows that if there are other senteint beings in this universe, it is s distinct possibility that the structure of whatever physical substrate that encodes their knowledge knows things that we CANNOT know because it cannot be encoded onto our structure. And, there would be things we know that this other entity CANNOT know has well.
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Wavefreak: you might be seeking to substantiate points that (1) can't be substantiated without a huge argument about, for example, the application of Godel and (2) trying to substantiate points that aren't necessary for your argument anyway and (3) trying to substantiate points that other people have already made for you.
You don't need Godel or Pinrose to demonstrate that symbolic systems break when you turn them on themselves. Structuralists and semioticians have already done this work for you. By skipping the formal logic and going directly to the hermeneutics, you can avoid the (justified) objection of logicians that the brain does not work that way. You might even consider abandoning the Turing machine angle (I don't think your position on this part is supportable) and go research how brains and hermeneutics actually work.
Also you don't need to go as far as aliens to find a brain that is very different structurally from human brains. Birds, apparently, have brains that do some things the way that human brains do, but they use an entirely different set of structures to do that work. Looking into the brains of non-human earth creatures is probably plenty to work with.
<tangent>Franzen's criticism of Hofstadter seems to me like nitpicking about semantics. My recollection of Hofstadter is not that he was claiming Godel's theorem proved anything about the nature of intelligence, but rather that the way the theorem works in formal systems suggests an analagous dynamic in hermeneutic systems. I don't agree that this is an "abuse" of the theory any more than I'd agree that Hofstadter's use of Bach to illustrate certain points is an abuse of Bach's music.</tangent>
"After Jesus was born, the Old Testament basically became a way for Bible publishers to keep their word count up." -Stephen Colbert
No comments about my materialsm observations? IS there anything wrong with what I said?
Well, if you can't get anybody to agree with your basic premises and/or your positions as presented look unsupportable, then yes there's something wrong with what you said.
Personally I'm inclined to agree that the conclusions could be right; just that there are problems with how you got there.
"After Jesus was born, the Old Testament basically became a way for Bible publishers to keep their word count up." -Stephen Colbert
Well I treid to peel it back to just the materialism part. I was hoping that anybody with objections might state them. I could conclude that there are no objections. But that's not too helpful.
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Two objections. The first one is simply that since the mind is not a formal proof machine, your argument doesn't apply. The second objection is more of a question. These arguments are employed against materialism. Now, assume you're correct. How does dualism escape your argument? I don't see how it does. If materialism is in trouble because of Godel and Turing, then so is the dualist. Substitute "immaterial mind" where you have "brain" and you ought to be able to see this.
"In the high school halls, in the shopping malls, conform or be cast out" ~ Rush, from Subdivisions
Who said anything about dualism? I'm bound by materialism. Supernatural is a broken concept. I'm speculating about properties of materialism.
I didn't claim that the mind is a proof machine. I said that materilaism requires the existence of a proof machine within the brain. The proof machine would be a subset of whatever the mind is.
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I think this from Textom came the closest to actually answering your question.
"You don't need Godel or Pinrose to demonstrate that symbolic systems break when you turn them on themselves. Structuralists and semioticians have already done this work for you. By skipping the formal logic and going directly to the hermeneutics, you can avoid the (justified) objection of logicians that the brain does not work that way."
The brain is partly a computational machine but it isn't 'locked' into a formal system the way a computer is. If it were, you would lock up and die of starvation the first time someone asked you to supply the value of pi.
So, no disagreements to the claim that a consequence of materialism is when thinking of a Turing Machine, an actual Turing Machine exists in the brain?
For now, I'm putting Godel's works aside as Turing Machines are easiear to work with.
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Ooh, now you're gonna get the computer scientists!
Not an ACTUAL Turing Machine, the REPRESENTATION of one. Also, not the entire machine at once either. Brains are a bit like flashlights in this respect; they can only think about a small part of something at one time.
In the case of a turing machine, the thought process probably went something like this:
1. Information can be stored on a tape.
2. Information can be manipulated electronically.
3. If I had an infinitely long tape. . .
and so forth.
I like the idea though. I wish more creationists would accept evolutionary simulations, such as those use to invent several useful patented devices, as actual evolution. That'd make life really easy.
Are you going for fideism then?
"Materialism has incoherencies too so it's all a matter of faith!"
I guess the materialist does have a duty to defend the coherence of their worldview. It has been put forward that the mind is a turing machine but that is not the only materialist/physicalist conception of the mind. It is only one version of functionalism.
I have heard that the brain has various parts to it that involve quantum behaviour e.g. in synapses. That would mean that the brain is physical/material without being determined by classical physics, and even if it was determined by classical physics, that doesn't mean it runs as a turing machine.
Not trying to "get" anybody.
So what's the difference between a representation of a Turing Machine on paper and a representation in our brain? When does a Turing Machine actually exist? If I can only think of part of a Turing Machine, what happens to the rest of it? Do I only know what I am currently thinking? That sounds absurd. Perhaps we can only focus on part of a Turing Machine but the rest still exists in the brain somewhere.
Electronics is not necessary. A simple Turing Mchine can be calculated in the head. A more complex one on paper.
I'm hoping your not thinking I am a creationist.
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Bueler?