Incompleteness: A Personal Perspective

Google Tech Talks
November 4, 2008

ABSTRACT

Our aim is to present a personal view of Gdel's incompleteness. We will focus on interesting/natural concrete independent sentences, on the source of incompleteness, and on how common the incompleteness phenomenon is. Some open questions will be briefly stated.

Speaker: Cristian Calude
A lifelong researcher in algorithmic information theory and a close friend of Gregory Chaitin, Dr. Calude has written and edited dozens of books and hundreds of articles on computability and incompleteness.

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[sbergman27]

@tatsumakisempyukaku The Incompleteness Theorem does not apply to individual theorems, but to logical systems. Since it has been proven, we know (obviously) that it is one of the provable statements. Many people would have preferred it to have been unprovable. But its proof is air-tight.

[jeffrussell777]

the truth is subjective to the observer and its conscious awareness..... what is truth to one is a lie to another that breeds a new observation by both ....to be all knowing and almighty / 1 needs another 1 to prove its self true ....like god needed lucifer like Adam needed eve..... like you need me

[eveningstarnm]

It's interesting how someone who admits that they are not an expert feels qualified to say that an expert is wrong. That phenomenon is becoming far too prevalent in our society. Arrogance replaces respect for knowledgeable authority and a willingness to listen. Thus, we end up with people like Sarah Palin, who is the epitome of ignorant arrogance, rising to national prominence. Our educational system is a dismal failure. P.S. Christian Calude is brilliant.

[harvestingStarlight]

@tatsumakisempyukaku Hey, I'm no expert so don't take me as gospel but Godel's theorem is a statement about formal system's, but is not itself a formal system. So it doesn't have to prove itself within itself if that makes sense. I feel like Hofstader in Godel, Escher, Bach (lectures are online) gives an easier to understand presentation of this theorem. Also a language is not a formal system in the same way as Peano Arithmatic (it cannot be algorithmically generated in the same way)

[tatsumakisempyukaku]

I suppose one can hope that there's a corespondence to the noumena. But again the noumena or the thing itself inaccessible to experience is what language attempts to refer to

[tatsumakisempyukaku]

Me again. Does godel's theorem have to apply to ALL propositions or is it limited to a certain type? I realized, that G's theorem must be true of languages. You can never reach "ultimate reality" or never confuse ultimate reality with the symbol of it. How does the words redness give any meaning to a blind person? It can't. So of course language has it's limits.

[tatsumakisempyukaku]

I'm no mathematician. That said, is godel's theorem also incomplete or inconsistent or contradictory. That is, does godel's theorem hold up to godel's theorem?

[HecklerBoy7]

@sirwizardoflight Hey dumbass. Give it a break. This theorem has been proved time and time again. So shut your fucking pie-hole. You're not smart.

[sirwizardoflight]

How would a formal system hold out on the surface of a black hole? This is a question for astrophysicists, not mathamaticians working in local space. This is either stupidity at its finest, or just plain chicanery. This is like the guy who argues that god must exist because the universe is infinite. But in that case, the green and yellow polkadotted talking half-rat with a star-shaped eye and a tail 5000 thousand feet long also exists.

[sirwizardoflight]

Incompleteness is an appropriate name for this BS. They create sentences like "I am lying", and say it proves certain things can't be completely proven. It is simply an error of omission. It says nothing about what they would be lying about, it's not a complete thought, yet then they say that a conclusion can be hatched out of it. They base their arguement on infinity and it's unknowableness. But these are same the clowns who assume they can define and use infinity in their equations.