Someone needs to go back & re-read the thread... Assumptions can also bite your bum!
Someone needs to go back & re-read the thread... Assumptions can also bite your bum!
Never doubt there is Truth, just doubt that you have it!
Actually, the thing I should have done from the start is write a disclaimer to this topic, in order avoid this kind of confusion. Well, better late than never! Here it goes...
Disclaimer: This idea is subject to change at any given moment (don't worry, not the subtractive kind of editing, but the additive kind; oh YEAH!) and whatever is written in this topic is abstract in nature, so, interpret it as you like, we are all probably right about what we think anyway, so... That pretty much settles everything!
Math and science are not all about hard work. It's a lot of fun, actually! I mean, I don't know how you all came to learn math and science, but I had a good time! It's like art. It's so creative! Read Godel's Incompleteness Theorem, please. In fact, I changed my mind! OK, new disclaimer! Here I go, again...
Disclaimer: Godel's Incompleteness Theorem is the disclaimer. LEARN IT! It will dispel all confusion!
Godel's Incompleteness Theorem would probably make a reasonable disclaimer if what you are attempting to convey were arithmetical in nature. But trying to understand the structure of the causal & non-physical universes would not seem to fall within the 'arithmetic' definition.
There are those who think maybe Godel's theorems can be applied in a wider context but from what I've seen over the years, Godel didn't make that connection himself.
It is disputable whether the presence of Consciousness within the Causal Universe would then remove it (the universe) from the province of Godel's Theorems.
My personal thought is to wonder if the theorem can be applied to anything in real life at all, given real life systems are intermeshed so much. It talks about systems that are standalone, while we have to deal with enmeshed systems that are never standalone.
Never doubt there is Truth, just doubt that you have it!
Well, you know, Godel didn't think of everything... And besides, he was talking about axiomatic systems as well, sooo... It's not restricted to just arithmetic. His theorems are known as "general theorems", that they are theorems that apply to all branches of math, not just arithmetic! Besides all that, all branches of math are defined by their axioms, so, yeah, I would say Godel was takling about all math, not just arithmetic!There are those who think maybe Godel's theorems can be applied in a wider context but from what I've seen over the years, Godel didn't make that connection himself.
Nope. Why should it? One way or another, you're going to form some abstraction about it, so... one way or another you're going to think about it in a particular fashion. In fact, you probably already have! I know I have! And whatever it is that we abstract from this phenomena of the physical and astral worlds, and consciousness, it's going to be working within some kind of logic, whether it be intuitive and simple, or more rigorous and complex. And, yes, Godel's Incompleteness Theorem would cover that as well! Before you can talk about the phenomena you experience, you must understand that what you think of the phenomena isn't the phenomena you experienced! Language has its limits, and we must work within those limits! That's all that Godel was bringing people's attention to. There can be nothing that is %100 logically consistent. And, Godel even goes on to state that if there was a system that was %100 consistent, that it was impossible to prove that!It is disputable whether the presence of Consciousness within the Causal Universe would then remove it (the universe) from the province of Godel's Theorems.
I guess maybe what I'm suggesting or imagining here, is that one day, our thinking will catch up with the physical world. Sure, the physical world is incredibly complex, but anything constructed or generated with such attention to detail and complexity will defy our pattern recognition skills initially! With time, though, and patience, we could crack that illusion of incomprehensibility. So, if that ever happened, it would be covered by Godel's Incompleteness Theorem. I think there's enough phenomena to exhibit the physical universe as being designed and created, and therefore, an abstraction as well. A HUGE abstraction, but an abstraction nonetheless, which would be accounted for in "GIT".
So, yeah, I guess I'm one of "those who think maybe Godel's theorems can be applied in a wider context". YEAH! I don't understand; what do you mean by "wider context"? More like, ALL context!!
Again, it is quite clear Godel is talking about a singular system that includes arithmetic concepts.
Originally Posted by Godel's First TheoremIt is crystal clear he is talking arithmetic systems & reasonably clear he is talking about single systems. You might like to extend it beyond where he intended but you shouldn't claim you're using his theorems as justification for your ideas. Nowhere in the theorems does he mention axiomatic systems.Originally Posted by Godel's Second Theorem
What he's saying is you can't prove a system from within itself - so his theorems simply don't apply if the system is enmeshed, such as with consciousness, which, as it defies definition within the current physical models, would seem to be from outside the system. Thus Godel's theorem will not apply here, even if you ignore his insistence on ARITHMETIC systems.
Never doubt there is Truth, just doubt that you have it!
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