# Marcus_Oz comments on Mysterious Answers to Mysterious Questions - Less Wrong

72 25 August 2007 10:27PM

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Comment author: 11 November 2014 06:59:23AM *  1 point [-]

Hi Capla - no that is not what Godel's theorem says (actually there are two incompleteness theorems)

1) Godel's theorems don't talk about what is knowable - only about what is (formally) provable in a mathematical or logic sense

2) The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an any sort of algorithm is capable of proving all truths about the relations of the natural numbers. In other words for any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency.

3) This doesn't mean that some things can never be proven - although it provides some challenges - it does mean that we cannot create a consistent system (within itself) that can demonstrate or prove (algorithmically) all things that are true for that system

This creates some significant challenges for AI and consciousness - but perhaps not insurmountable ones.

For example - as far as i know - Godel's theorem rests on classical logic. Quantum logic - where something can be both "true" and "not true" at the same time may provide some different outcomes

Regarding consciousness - I think I would agree with the thrust of this post - that we cannot yet fully explain or reproduce consciousness (hell we have trouble defining it) does not mean that it will forever be beyond reach. Consciousness is only mysterious because of our lack of knowledge of it

And we are learning more all the time

we are starting to unravel how some of the mechanisms by which consciousness emerges from the brain - since consciousness appears to be process phenomena rather rather than a physical property

Comment author: 11 November 2014 04:34:36PM 0 points [-]