Have we grasped the implications of Gödel's theorems?

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Mlw
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Have we grasped the implications of Gödel's theorems?

Post by Mlw » July 17th, 2018, 9:14 am

In my view, Gödel's theorems lead us to conclude that no perfect logical order, which relies on its own criteria, can be created. It spells demise for all philosophical systems and societal totalitarian systems, because one cannot create a "hermetically closed logical structure", even though the internal logic is perfect. It simply cannot work. It runs up against self-contradictions; so it's no use trying. Russell's and Whitehead's Principia Mathematica could not be completed for this reason.

It also means that cosmologist won't be able to create a Grand Unified Theory of all the natural laws. We will never be able to wholly understand the universe, because it cannot be built around a set of natural laws that work in harmony to create a unified and perfect whole.

It also means that we cannot create a machine capable of thinking logically on its own device. AI is a hype, created to fool politicians and institutions to contribute economically.

M. Winther | http://two-paths.com

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Mlw
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Re: Have we grasped the implications of Gödel's theorems?

Post by Mlw » July 19th, 2018, 3:13 am

It's not like a philosopher can ignore this monumentally important discovery in mathematical logic.

Gödel's Incompleteness Theorems

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Frewah
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Re: Have we grasped the implications of Gödel's theorems?

Post by Frewah » October 31st, 2018, 9:13 pm

I think not. It’s the same with the chaos theory where a very small change can have major impact after some time. The more complex a system is, the harder it is to analyse. I think people don’t understand that this is an intrinsic property rather than a speck of dust in an othetwise perfect machine and that it applies to real systems like the ones you mention.

However, I don’t think it prevents us from creating a GUT or that we won’t be able to create logical machines. We can have a system that is perfectly understandable but not forecastable. A double pendulum or a feedback system like a gibson guitar.

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ktz
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Re: Have we grasped the implications of Gödel's theorems?

Post by ktz » November 10th, 2018, 3:55 am

I agree with the previous poster that Godel doesn't logically imply that AI is a conspiracy nor does it contraindicate the possibility of a GUT regardless of what the answer to those questions may be. Godel just demonstrates the existence of true but not provable statements, and limitations to our ability to verify knowledge. This however has no bearing on knowledge that is already verifiable. The existence of self-contradictions doesn't necessarily imply that the whole thing is bunk. It just indicates a class of problems that are not answerable within its own framework. Concluding that it isn't worth trying would be to let the perfect be the enemy of the good.

On a side note, I'm currently reading Rebecca Goldstein's biography of Godel which is quite interesting, titled Incompleteness: The Proof and Paradox of Kurt Godel. I found it quite interesting that Godel is on record as rebelling against the positivists and verificationists of Wittgenstein and the Vienna Circle. I encourage anyone interested in Godel to check it out.

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