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.

• Category

  People & Blogs

[idunnononame]

Actually no; He rather doesn't know what he's talking about...

[idunnononame]

You don't appear to know what you are talking about..

Have you looked at any of the ACTUAL proofs for incompleteness?

[yaboibangs]

The infinity you refer to in the abominable phrase "Infinity and it's (sic) unknowableness" means something very precise in mathematics...and it almost certainly isn't what you think it is.

You need to have a more precise idea of what they actually ARE trying to say before you criticise it like that.

But then again, it's not like you've spent your entire professional life studying advanced mathematics or anything...

[Shotsy Greene]

well that sounds more like common sense! to me - if common sense is still a virtue in this discombobulated day & age!

[lucy1lucy1]

i found this very helpful. thanks!!

[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]

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