Caffeine? Nicotine? Opium? Coca? Betel?
Or how about alcohol?
DOH!
Pixy Mesa! Yes you are correct and I appreciate the correction. Don't know what I was thinking! See that's what happens when you post late at night after a few beers.
Caffeine? Nicotine? Opium? Coca? Betel?
Or how about alcohol?
Bubblefish said:Ok. I should point out here that Godel was a logician; so talking about Godel in terms of systems theory is speculation. It makes sense if the universe can be described as a computer (you had a link to a couple of physicists who argue that). If it can, then Godel (via Turing, who used his theorems to define computability) becomes relevant to discussions of how simple systems might create complexity in the physical world, not just the logical world. Because logic is about creating axiomatic systems; physics is about finding the one that fits reality.
First off, I want to say how nice it is to have to spend time with a comment so I can digest it. A real treat. Your an excellent communicator and I appreciate how comprehensive you appear to conceptualize and frame things. Respect. [Bubblefish does an Ali G]
Okay, I follow that, but a question I have, and the answer to this question to me is my big unknown. Does it matter the system of logic? Does this apply to ternary logical systems? That's where I am intrigued by Godel. What happens when Godel meets ternary? Anything interesting happen or is it the same old news?
When I get this answer, I may need to grill you on it a bit if you do not mind. Wiling to offer special prizes for ideas that assist my own transcendence![]()
According to Godel, a [sufficiently complex axiomatic] system generates many statements that are provable within the system; however, it also generates some statements that are true (evaluated outside the system), but not provable (within the system).
Okay, this is directly what I am referring to in my model. To me, this is how I understand the relationship between bivalent and ternary logical systems.
To humanize this meaning a bit, to me it's summarized in a very old Hebrew saying, which I will paraphrase since I forget it's original incarnation; "Telling the truth to someone who is unable to comprehend it is the same thing as lying to them."
Does any of this make any sense what so ever to you?
Now, as long as it's consistent (free of contradiction), one statement the system generates will say that it's consistent, but it won't be able to prove it (if it's inconsistent, otoh, it will be able to prove both that it's inconsistent and consistent). So, systems that tell the truth can't tell the truth (or lie) about themselves; whereas systems that lie can both tell the truth (admit they lie) and lie (swear they don't) about themselves! (Hardly seems fair, but that's logic). It's thanks to Godel's theorems we can see this paradox from outside the system, even distinguish true systems from false (inconsistent); we just can't evaluate it within the system (because to do so yields a contradiction).
Again, this rings true to me when I evaluate bivalent and ternary systems interacting with each other.
I hope I'm not completely lost here because how can I explain that your making such sense to me?![]()
It may be implicit in the axioms (rules for generating statements) of the system if it's sufficiently complex (can number its statements). Not sure if that's what you mean.
I'm gonna phrase the question in my own language, you tell me how you roll with it?
You have a bivalent system [0/1] and a ternary system [0/1/2]. Does one emerge from the other and how can you tell which?
Umm, well... even as I may be stretching Godel's wings a little [a lot?] too far with the systems theory talk, you may be trying to fit him into too narrow a pigeonhole (re your idea of dialectical, transcendent truth). I think that's my fault for using similar language to engage the concepts and make the grand argument. So warning: they may sound similar, but they're not necessarily the same.
Oh, I definitely see that they are not the same, and I definitely see now that they are similar (was insecure about that). Now that they are similar, I want to know or define what they share in common for them to be similar. That is the question!
Maybe a cat.![]()
How about a gecko? (where is the appropriate smiley when you need it?)

His Incompleteness Theorems apply to all axiomatic systems. Including ternary (three-valued) logics. Why? Well, the classic Godel proof uses a version of the liar paradox: "this sentence is false". When you evaluate a paradox, you get a contradiction: if "this sentence is false" is false, it's true; if "this sentence is false" is true, it's false. Let's say we add a third sentence value: true, false, and unknown. What does this do to the liar paradox? If "this sentence is false" is unknown, it's false (claiming to be false when it's really unknown); but if it's false, then it's true; and if it's true, it's false; and so on. So ternary axiomatic systems are as vulnerable as binary to Godel.
Wait, so the ternary logical system assumes that (X is unknown) --> ~(X is false) AND ~(X is true)? Why is this required? Can't we have a system where (X is unknown) doesn't imply this?
And there are so-called paraconsistent logics (sort of workarounds for Godel Incompleteness) which allow for overlap between true and false: statements that are both true and false having a distinct truth value, for example.
Our ability to think has long been considered central to what makes us human. Now research suggests that our bodies and their relationship with the environment govern even our most abstract thoughts. This includes thinking up random numbers or deciding whether to recount positive or negative experiences.
"Advocates of traditional accounts of cognition would be surprised," says Tobias Loetscher at the University of Melbourne in Parkville, Australia. "They generally consider human reasoning to involve abstract cognitive processes devoid of any connection to body or space."
Until recently, the assumption has been that our bodies contribute only to our most basic interactions with the environment, namely sensory and motor processes. The new results suggest that our bodies are also exploited to produce abstract thought, and that even seemingly inconsequential activities have the power to influence our thinking.
Ahem....Pixy Mesa and co
http://www.newscientist.com/article...-thinking.html?DCMP=OTC-rss&nsref=online-news
Lakoff says that if intelligent aliens exist, they may have very different bodies and therefore have developed very different abstract thought - even perhaps a different mathematical system. "People assume that mathematics is objective and that everybody will have the same math," says Lakoff. "But there is no reason to believe that."
Ahem....Pixy Mesa and co
http://www.newscientist.com/article...-thinking.html?DCMP=OTC-rss&nsref=online-news
Can I suggest something, BF? Maybe if you didn't try to categorise me and others so much and just stayed with what we're saying. What do you think?
Something I feel I have been trying to point out to you pretty much throughout this thread is that the whole shamanic perspective is flawed. Believing yourself to be a self in need of healing is only one of the perspectives materialism affords. If you understand the true nature of the self, on a personal level, the truth about "healing" is laid bare. But because you can't grasp materialism, at least to the point where you can see the so-called "hard problem" for what it truly is, you can't grasp just what I'm talking about. With all your judgments and categorising, BF, you completely overlook what is right in front of you.
Nick
Sure. In this case your middle value would be something like the "unknown" discussed above. The hearer doesn't know whether your proposition is true or false because he can't understand it (and if nobody, even the teller, understands it, it really is unknown; though that's no guarantee of deep truth: it may be wrong, or nonsense).
Logic is pretty dry stuff, but some of the results, like Godel Incompleteness, are handy metaphors that we can shape to our own sense and taste. Mindful we're doing poetry, and not logic, of course.
Mmm... not out of classical logic systems. Make them programs, throw in a genetic algorithm, you might see ternary logic evolved as a variation on binary. Not sure it would be superior, though. Ternary has one more value than binary logic, but fewer axioms. In a way, it's more flexible (about truth), but less powerful (for proof).
I don't have much of an answer, I'm afraid. Maybe a joke?
Godel Incompleteness shows, among other things, that there is meaning in the system that can only be evaluated outside the system.
I think that's a nice metaphor for transcendence. Zen teaches a third value between yes and no: mu. A student who always expects complete answers, gets a mu answer. Or a bamboo stick to the head (same thing). In theory, by finally accepting incompleteness he transcends it. But in practice, he often just ends up with a sore head.
He'd freeze his geck off.![]()
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The article is reinforcing materialism. Thinking is a physical process.
Nick
I thought this bit was interesting: Lakoff says that if intelligent aliens exist, they may have very different bodies and therefore have developed very different abstract thought - even perhaps a different mathematical system. "People assume that mathematics is objective and that everybody will have the same math," says Lakoff. "But there is no reason to believe that."
.
And there are so-called paraconsistent logics (sort of workarounds for Godel Incompleteness) which allow for overlap between true and false: statements that are both true and false having a distinct truth value, for example.
I'll continue to lurk a little and comment here and there if that's all-right BF. I've noticed you kind of like saying, "I want to continue talking to this person, but not that person," and I can respect that.
Heh, I have two leopard geckos and two cats. I ain't got me no fish tho, bubble or otherwise.![]()
Er. maybe not such a great idea. However, Topamax is by far the best anticonvulsant for severe childhood epilepsy, so a lot of children HAVE been exposed for long periods of time to a medication that has at least one of the same major effects as ayahuasca (serotonin agonism as the 5HT2A receptor.) Actually, topiramate is the best all-around AE drug, hands down. Nothing works as well. But the side effects can be appalling (kidney functioning-related,mostly) so it's not a first-line med.
I read some of those weird ayahuasca experiences... not exactly what I'd call controlled studies, but I will say, for whatever it's worth, that in this anecdotal context, at least, the people who had psychological problems after taking it certainly seemed as if they would have had them anyway.
You're not considering my ideas fully. I am not, nor have I ever said or suggested, that thinking was not a physical process. It's the experience of thinking, and the experience of the ideas that arise (maybe from?) thinking - that I am referring to.
And this article was posted to highlight more what I was suggesting to Pixy Mesa, that 'attention' happens NOT just in the brain, but in the whole body. Our entire being is computational, not just the brain. Or that is my suggestion and what makes sense to me based on over 15 years experience and study on the matter.