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 Limits to Our Understanding

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PostSubject: Limits to Our Understanding   Tue 13 Mar 2012, 4:05 pm

I've posted this full length video in the thread on Kurt Godel & Mathematic's Shortcomings. I am reposting the entire video here, and subming new postings that include several imporant clips from the talk, all ofwhich I believe also have a significant impact on philosophical discussions.

Full Length Discussion at World Science Festival




http://worldsciencefestival.com/videos/the_limits_of_understanding

About This Video

This statement is false. Think about it, and it makes your head hurt. If it’s true, it’s false. If it’s false, it’s true. In 1931, Austrian logician Kurt Gödel shocked the worlds of mathematics and philosophy by establishing that such statements are far more than a quirky turn of language: he showed that there are mathematical truths which simply can’t be proven. In the decades since, thinkers have taken the brilliant Gödel’s result in a variety of directions—linking it to limits of human comprehension and the quest to recreate human thinking on a computer. In this full program from the 2010 Festival, leading thinkers untangle Gödel’s discovery and examine the wider implications of his revolutionary finding.

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PostSubject: Re: Limits to Our Understanding   Tue 13 Mar 2012, 4:08 pm

Gödel's Lasting Legacy (Limits of our Understanding clip #1)

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PostSubject: Re: Limits to Our Understanding   Tue 13 Mar 2012, 4:40 pm

Incompleteness and Complexity
http://worldsciencefestival.com/videos/incompleteness_and_complexity


About This Video
Most people assume that mathematics lead to absolute certainty, but Kurt Gödel’s incompleteness theorems deny that result. Gregory Chaitin explains his own attempts to make sense of Godel’s incompleteness theorems. By looking for mathematical scenarios where the truth must look accidental, Chaitin hopes to gain insight to “what’s going on” in mathematical logic. Recorded June 2010; Posted October 2010

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PostSubject: Re: Limits to Our Understanding   Tue 13 Mar 2012, 4:42 pm

Gödel’s Incompleteness Theorems
http://worldsciencefestival.com/videos/godels_incompleteness_theorems


About This Video
What is the nature of mathematics? Mathematics is an a priori discipline, meaning its proofs arise from first principles. The early 19th-century logician Kurt Gödel wrestled with this notion in forming his landmark ideas known as the incompleteness theorems. Philosopher Rebecca Newberger Goldstein explains how Gödel demonstrated that in any formal system, such as mathematics, there will arise some true propositions that cannot be proven within the system—a paradox that still inspires philosophers, mathematicians, and scientists today.
Image courtesy of the Kurt Gödel Papers, The Shelby White and Leon Levy Archives Center, Institute for Advanced Study, Princeton, NJ, USA, on deposit at Princeton University; Recorded June 2010; Posted October 2010

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