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Old 04-24-2006, 08:09 PM   #1 (permalink)
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Gödel, incompleteness, unprovability, truth

im sure all the logic junkies around here have already heard of Gödel, if you have not, be sure to wiki or google him, along with the liars paradox and be sure to check out the logical law of bivalence.

now
before Gödel's theorems were published, everbody believed that not only was everything proven by mathematics true, but also that within its conceptual universe everything true could be proven
nope.
he showed there are true statements in certain mathematical systems that can not be proven.
so ppl seem to take this to mean that you cant do everything with math, there are limits to logic, and that by rational and logical thought you can not penetrate to the ultimate truth.
so for those that insist that mathmatics and science and logic will eventually answer all questions and do away with religion and put an end to foolish ideas about God and the supernatural: im sorry, it just isnt so.

there are some ppl that take Gödel and Heisenberg and Einstein together as showing that we cant ever really be sure about anything. "you cant prove shit," the lower-functining philosopher says, "so why dont you stfu?"
but just becuz something cannot be proven, that doesnt make it untrue

i am absolutely not trying to make a case for anti-logic or some kind of subversive attack on rationality. what i want to show you is something else:
there are limits to formal logic so that you cant prove some things, but there is the possibility of finding truths beyond mathmatical formalisms that are absolutely undeniable. the nature of reality is so much bigger and wider than any symbolic abstraction, filled with timeless truths that defy classification and confound bivalence, and human minds can find these truths not by following the futile methodologies of formal systems, but by taking astonishing leaps, making unusual connections, revealing hidden meanings

therefore, the reason i cannot prove some true things is that your systems of symbolic thinking and communication are not sufficient to arrive at the proof. you must achieve a higher level of consciousness to meet me at the truth, rather than demand that i show you proof of color in a black and white format.
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Old 04-24-2006, 08:36 PM   #2 (permalink)
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i dont agree with any theory that states anyone is on a different level of consciousness than anyone else.

all reality must be logical, otherwise reality would be illogical and that would be nonsense ; i think your looking for another word entirely. maybe "truth?"
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Old 04-24-2006, 08:44 PM   #3 (permalink)
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Quote:
Originally Posted by v3d4
therefore, the reason i cannot prove some true things is that your systems of symbolic thinking and communication are not sufficient to arrive at the proof. you must achieve a higher level of consciousness to meet me at the truth, rather than demand that i show you proof of color in a black and white format.
discuss
WHOA. Are you sure this is the wording you wished to relay this meaning? It appears to be rather condescending. I'll get to this after my late dinner and a joint.
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Old 04-24-2006, 08:52 PM   #4 (permalink)
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Quote:
therefore, the reason i cannot prove some true things is that your systems of symbolic thinking and communication are unable to arrive at the proof. you must adopt another system of consciousness to meet me at the truth, rather than demand that i show you proof of color in a black and white format.
discuss
Something like this. Bolded parts of course being the ones I've changed. Now, time for a joint, then to the rest of the post.
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Old 04-24-2006, 08:57 PM   #5 (permalink)
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Hey v3d4, I was wondering when someone would post in SS, thnx hun .

About levels of consciousness.. If one must reach a certain level of consciousness to meet you or anyone else at truth, couldn't the same be said for the conscious level of logic? What are your thoughts on this?
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Old 04-24-2006, 09:15 PM   #6 (permalink)
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yeah zip thats pretty good, altho i dont see why you object to "not sufficient"
you know im not talking down to anybody...

reverie,
dont be fooled, "level of consciousness" is just a metaphor not a moral judgement or qualitative measurement or anything like that. as far as "conscious level of logic" goes, i dont know exactly what that means in this context. formal logical systems (math) dont rely on consciousness to work, and neither the other way around
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Old 04-24-2006, 10:28 PM   #7 (permalink)
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Sorry for the confusion V3d4, its hard sometimes communicating through text. What do you mean by "higher levels of consciousness"? To me, when I read this I get the impression that this suggests separation. Separation, in that the way you operate is separate from the way others do (ie: the way religion functions vs. the way science does).

Imo logic is a conscious process as well this is why I brought up the relevance. Though mathematical equations are self serving on their own it takes conscious thought to formulate them and conscious activity to put them into motion. In that sense logic is like a tool- a form we use to gain understanding when we align our consciousness with it. Now this why many believe that logic is separate from faith (they are different "tools" or forms to measure understanding). To me it depends where you channel your focus ( in logic or faith), or in other words where you "align your consciousness". How we use the tools...

I personally don't believe that either focus is greater than the other because when I keep in mind that they are tools I am more aware of my conscious potential and ability. That I am not at the whim of things exterior to me because I can adapt, I can mold to the understanding I wish to achieve. Just like any other tool, it is not the item itself that is in question, it is dependant on what the person wishes to do with it. If I wish to put a nail in the wall to hang a picture and I open my tool box to see how I can accomplish this, I'm not gonna want to take the wrench to get the job done. I'm going to select the tool which compliments the situation to recieve the results I desire most effectively- the hammer.

So since the understanding gained by an individual is dependant on the focus they take on, I believe we all can experience similar "truths" given that we are flexible and mobile. Limit separation and expand further into unity and understanding.
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Old 04-24-2006, 10:39 PM   #8 (permalink)
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Cool post, I will check out that Godel dude and his work.

I do like Ziplock's reword better.
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Old 04-24-2006, 10:55 PM   #9 (permalink)
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Of course v3d4, and I was being pretty critical with that one. It's really just a personal bias of mine in regards to this topic. To me sufficient brings up a system of qualification, one being able to fulfill a particular role. When this is integrated into a system of conscious development or to the verification of proof in a statement, it vexes me in a way. Addresses a persons competency It's purely semantical of course.

This goes also for the matter of levels of consciousness. This of course being one of our symbols to explain the development of consciousness. I do choose to avoid higher and lower terminology as this implies a heirarchy of sorts. While this may align more accurately with some peoples beliefs, it does not to mine. Some may choose a higher or lower terminology, but it has to be relative to a vertical axis of sorts. What determines that vertical axis is really up to you.

So we get to the original post. Many inconsistances and perplexing circumstances arise when you attempt to have Godel's theorems apply to consciousness and the pursuit of truth. This isn't to say not accurate, we're just trying to stuff an elephant into the trunk of a VW beetle. Some of it fits, but there's a lot left hanging.
Quote:
Originally Posted by v3d4
he showed there are true statements in certain mathematical systems that can not be proven.
so ppl seem to take this to mean that you cant do everything with math, there are limits to logic, and that by rational and logical thought you can not penetrate to the ultimate truth.
so for those that insist that mathmatics and science and logic will eventually answer all questions and do away with religion and put an end to foolish ideas about God and the supernatural: im sorry, it just isnt so.
This comes to mind: "He is still hung up on his self-closing resistance, in this case anchored down to reactionary pattern, and naturally is still bound by another modified pattern and can move within its limits. He has not digested the simple fact that truth exists outside all molds; pattern and awareness is never exclusive." - Bruce Lee.

Symbolism, as you touched on, is extremely intimate with consciousness. We like to create systems of symbols, attempting to have them represent as closely as possible the reality we observe. Many have different methods in formulation and application, and we enjoy regarding one anothers methods and criticise them. This is great! It gives us the opportunities to learn other artistic techniques, to hone our craft. However, this has to of course be done in a respectable manner. You have to respect the artist, respect their choice of expression. While abstract may not be our cup of tea, it's an artform in nonetheless.

While we can engage heavily in and focus intently on this platonic game of prisoners in a cave, we have to at some time recognize that these shadows we pay so much attention to are still just that, shadows, silhouettes of the forms that cast them. The only way to penetrate that truth is to abandon the forms, and walk out of the cave. The shadows that we create are a part of existence, they're beautiful in their own way. However, you're cheating yourself and extremely naive if you think that the shadows in themselves are absolute. Every theory and belief we have in regards to reality is just that, in regards to reality. They're dependant on reality as the shadow is on the form. Without the form there is no shadow. Seek out the source of the shadow. Then the source of the light. So on and so forth.

When we commit ourselves fully to any shadow we're restricting ourselves. We have to adapt our methods of description and analyzation according to the subject. Each subject requires a different method. Logic, mathematics, these are great for certain things. When you tangible, specific phenomena that you're attempting to describe mathematics is a great way to describe them, and logic is a great way to check and verify them. Now we get to the tricky part.

When you take methods used for the tangible, specified phenomena and apply it to the intangible, abstract, symbolic nature of the individual, you get a lot of short comings. This is fine, we can still adapt these (such as demonstrated in your original post) to fit to a degree. They can aid us in determining say the location of someone's subjective existence in regards to objective reality. Or in other words, someone's beliefs, religion, etc. I can describe to you my understanding symbolically, and you can then use these as sign posts in order to determine my location. It's a game of marco polo, back and forth exchange, constant verification of position in relation to course, correcting any deviations. Like flying a plane from Boston to Los Angeles.

Now, you have the subjective, isolated, statements of opinion, constructed out of experience. These require no proof, no relative position other than to the individual in order to be held as truthful. The construction and reinforcement of these statements can lead to any number of subjective experiences. These experiences can then go to further verify and support them, a self sustaining system. It draws from it's environment (anything conscious including perceptions offered by the senses) what it requires and what is most suitable for it's growth. It's an organism of made up of conscious matter. They can be anything, you're imagination is the limit.

Knowing this, we can then make up anything we want and have it be truthful on it's own, isolated level. It's your natural ability and right to, thanks to the freedom of the imagination. Even the most seemlying absurd concepts like omnipotent invisible pink unicorns of the 32nd and 1/2 dimension, hamburger dictators, tax free living, and ewoks, are all completely true in this context. We can convince ourselves as deeply as we want of their reality. Visualization for example is a good example of this.

Due to it's intangible nature, (that is I can't percieve it directly, that'd be telepathy) it cannot be proven, but that doesn't make it untrue, as you stated. Proof has to be related to, outside of the isolated, subjective mind. It has to be something offered to compliment it. This can be provided by relating it to another's thoughts and beliefs, or towards physical occurances that would compel one to accept our chosen system. The moment you do this though, the subjective isolated truth no longer applies, and the form of truth is now a collective one.

When determining a collective truth, one must continually expose their concepts to whatever relative material they can. They must take their organisms and sit them in different environments. This, and imo your post as well, would imply that we should never seek to solidify or crystalize our forms, instead keep them changing and adapting to the environment or subject fluently like fluid. This ensures the best application. We're not restricted by the single sided approach of some blunt object. We can encompass, circle around the subject and work our way into the crevices. "Be like water making its way through cracks. Do not be assertive, but adjust to the object, and you shall find a way round or through it. If nothing within you stays rigid, outward things will disclose themselves." - Bruce Lee.

Basically, there are limits in the application of all forms based on their characteristics. One then should seek their forms to be formless and adaptive in accordance to what the form is in contact with. To become minimize ones limits, to become limitless. I enjoy forms, playing with them, holding them temporarily, but I do not hold onto them. Cage myself within them. I find it amusing when people take with so much certainty and seperation towards things like logic, faith, religions. This and that, this set outside of that set. It's really unhealthy.
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Old 04-24-2006, 11:34 PM   #10 (permalink)
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right on, my sistren and my bredren, right on!

o look at this:
http://www.sm.luth.se/~torkel/eget/godel.html
Quote:
Every day, Gödel's incompleteness theorem is invoked on the net to support some claim or other, or just to whack people over the head with it in a general way. In news, we find such invocations not only in sci.logic, sci.math, comp.ai.philosophy, sci.philosophy.tech and other such places where one might expect them, but with equal frequency in groups dealing with politics or religion, and indeed in alt.cuddle, soc.culture.malaysia , rec.music.hip-hop, and what have you. In short, whenever a bunch of people get together on the net, sooner or later somebody will invoke Gödel's incompleteness theorem.

Unsurprisingly, the bulk of these invocations covers a range from the nonsensical to the merely technically inaccurate, and they often give rise to a flurry of corrections and more or less extended technical or philosophical disputes.
Quote:
"Proof", in Gödel's theorem, is always proof in some particular formal system T. Gödel's theorem can be used to conclude that for any such T there is a true G in the language of T which is not provable in T. It doesn't follow that G is unprovable in any absolute sense. On the contrary, G is always trivially provable in some other theory T'. Whether G is provable in some more interesting sense, for example in the sense of being a consequence of axioms which we can recognize as true, is a matter that Gödel's theorem doesn't tell us anything about.

In short: Gödel's theorem can't be invoked to support the idea that there are truths that are in some absolute sense unprovable.
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Old 04-24-2006, 11:38 PM   #11 (permalink)
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p.s.
well, "higher level of consciousness" really means that you should be here smoking some of my bomb-ass weed with me, then we would all understand eachother perfectly
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Old 04-24-2006, 11:43 PM   #12 (permalink)
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Haha true that! Time for a few more hits me thinks. Stuff like this makes me wish I followed through with my mathematics more.
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Old 04-25-2006, 12:32 AM   #13 (permalink)
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whenever on 7+ grams of mushrooms i would always see geometrical patterns in nature, and even algebra problems while looking at light.

always wondered if i would have seen those without all the damn math classes i was forced to take when young.

just like i wonder if people would really see jesus in their door if they hadnt been forced through church.

questions... questions, questions, and more questions.

it doesnt really ever end, does it?

it just always has to be some big mystery, it's almost like we are looking for that.
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the goal of alchemy is to turn lead into gold. to take a substance and combine it with another substance that makes it more than it's origenal worth. in this sense, you really need to start making bronze statues of your pharmacist or local chemist, for they have made gods own medicine, morphine, and in contrast, a shiney rock doesnt seem to compete.

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Old 04-25-2006, 04:49 AM   #14 (permalink)
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There is so much written on Godel....

Here's an article I find particularly interesting....

Stephen Hawking
"Gödel and the end of physics"
http://www.damtp.cam.ac.uk/strings02/dirac/hawking/


-Hedons
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Old 04-25-2006, 07:39 AM   #15 (permalink)
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Quote:
Originally Posted by Kosh
So I ingested these yesterday...was drawing, triangles, squares, hexagons, (listening to classical music)... adding on to them to create bigger structures from the base forms...and it certainly seems like it never does end...what a mystery indeed.
Reminds me of Kepler's models.

(Those look like some freshies kosh )
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Old 04-25-2006, 10:19 AM   #16 (permalink)
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Sure you didn't see any dodecahedrons?
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Old 04-25-2006, 03:40 PM   #17 (permalink)
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As usual, I have only read bits and pieces (sue me )... here's the deal.... everyone 'is' 'at times' in the state of mind that we are referring to. We may have 'met there' may 'at times' meet there or may some day meet there. Everything that you try to say may seem condescending to someone with a different POINT OF VIEW.... another way of saying 'frame of mind' or even 'state of consciousness' is POINT OF VIEW. Now, none is RIGHT and none is WRONG... one might say that one is correct for a specific purpose. For instance, if I were asleep and dreaming and you approached my sleeping body quietly, I would never know that you were there because my point of view is in the dreaming world. We can meet here or there but we both have to be where we meet. And 'not meeting' doesn't make one right and one wrong, this is just a misperception.
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Old 04-25-2006, 07:37 PM   #18 (permalink)
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E-prime would not allow such logical fallacies. E-Prime allows for the quantum world to exist freely in our semantic dictionaries, where things can be true, false, true and false, meaningless, true and meaningless, false and meaningless, and true and false and meaningless, indeterminate, false and indeterminate, true and indeterminate, true and false and meaningless and indeterminate, false and meaningless and indeterminiate, and true and meaningless and indeterminate.

If you don't know about E-Prime, you can look it up on google.
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Old 04-26-2006, 04:30 PM   #19 (permalink)
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Haha... just started reading kosh's reply Stop reverse engineering... lol ... actually, continue... fun, fun
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