Kurt Gödel: Modern Dev. of the Foundations Of Mathematics In Light Of Philosophy (Complete w/music)

A great Book on Kurt Gödel: http://www.amazon.com/dp/0262730871?tag=gargecsguitot-20&camp=14573&c...

http://garygeck.com/?page_id=42 for an mp3 this video for your iPod.

A version of this vid w/out musical soundtrack is here (if you find it distracting): http://www.youtube.com/watch?v=CgZ_9gQfitc

Hello, this is Gary Geck of Gary Geck.com. Kurt Gödel has been called the greatest logician since Aristotle and A Genius at odds with the Zeitgeist.

The following is my reading of Kurt Gödel's 1961 lecture called "The modern Development Of The Foundations Of Mathematics In The Light Of Philosophy". As was typical of Gödel's very private philosophical work, the lecture was never delivered. I now will read it in its entirety on youtube or in an mp3 (found at http://garygeck.com/?page_id=42).

It should become very clear that Gödel was a lone voice in his age of logical positivism, skepticism and analytical philosophy such as Harvard's Dr. Willard Quine's variety. Quine of course called the higher reaches of Set Theory mere mathematical recreation...a view clearly at odds with Gödel's. According to Dr. Richard Tieszen of San Jose University, "The three philosophers Gödel found most congenial to his own way of thinking were Plato, Leibniz and Husserl." In fact Gödel saw much of Western Thought as being on the wrong path since it had strayed from the influence of Leibniz in the 18th Century. It is surprising that Gödel promotes Kant (albeit in a modified form) with much enthusiasm in this lecture when Kant certainly helped to hasten the demise of Leibnizianism. Kant once called Plato' work 'babble'.

On an interesting note "His few interests were in surrealist and abstract art, his favorite writers included Goethe and Franz Kafka, he enjoyed light classics and some 'pop' music and Disney films, especially Snow White." [source: http://www.bookrags.com/biography/kurt-godel/ ]

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[kano26]

This video is truly amazing. Wish i could hear more modern ones that indulge the philosophy of mathematics more elaborately. Want to see how we have changed our perspective of such abstract and intuitive field of reasoning throughout time.

If anybody know of some good ones plz send link.

[GaryGeckDotCom]

@kano26 thanks for the interest. Gödel didn't see philosophy advancing much since Leibniz, hegel, Kant and Husserl. So if it hasn't advanced much since Gödel's time, that isn't much of a surprise. Mathematical logic does continue to have advances however..very profound ones...i just don't think we have been able to keep up with the philosophical implications of these discoveries...

[volpotmakmak]

"This is Gary Geck and I am druuuuunk."

[GaryGeckDotCom]

A version of this vid w/out musical soundtrack is now linked to from the description above towards the top...or in the video itself as an annotation...or just go to my videos channel.

[umbalaba]

Wow Gary, that was very interesting indeed!

I love how you draw directly on source material and state your sources so clearly.

[docerex]

Thank you very much for the visual contexts, and the musical contexts. I don't think I would have had the patience to parse the structure of Godel's arguments to fully appreciate what he was expressing; and yet I am such a fan of his work. I have spent years trying to understand his theorems in addition to understanding his seemingly surprising position against the current Zeigeist.

[docerex]

Thanks for this. I am going to have to watch this several more times obviously. If I understood correctly, our current Zeitgeist has certainly headed even further into the direction that Kurt Godel is warning us against and it seems anyone arguing outside of empiricism are branded as intellectual heretics. It is refreshing to hear an intellectual giant arguing in favour for that vague something extra that is missing beyond mechanical thinking (insight, intuition)

[GaryGeckDotCom]

@astroboomboy I have not undertaken a study of minksy but if you can point me to one select paper by minsky i will read it and comment. I don't get your reference as a result, but by 'shortcuts' do you mean like how we humans (and machines also) never write the infinite 0s in front of a number like we really should? I'd rather comment on a specific paper.

[GaryGeckDotCom]

@astroboomboy Turing machines have limitations. Because they enumerate, ALL real nums are out of reach. It can enumerate any given real num though (ex. pi).

Turing machines can make infinite strings...they just can't make all infinite strings. Diagonalization demonstrates this intuitively. I see it as very well defined in terms of combinatorics.

Whether the mind is only a universal Turing machine is an open question still so you can say it can be or it can possibly not be the case too.

[astroboomboy]

@GaryGeckDotCom I think we have to be careful in taking Gödels theorems outside of mathematics and projecting them onto the real world. And it actually may be so that there are infinite ways of looking at the universe, and our minds are only capable of certain interpretations that are approximations of the things in themselves (as Kant would put it). And as Kant would also state, time and space are the conditions of our faculties, not something "real" and so reality will always evade us somewhat

[astroboomboy]

@GaryGeckDotCom There are many who criticize the idea that the Turing machine makes it impossible to create AI, and that the human mind has to be more than a turing machine. You have probably read Minsky, but his critique seems to be rather plausible, that even though turing machines can't make infinite strings there are shortcuts, and our mind uses such shortcuts to do these things.

[astroboomboy]

@GaryGeckDotCom The theories and critiques of Turing machines are very subtle and seems to me misunderstood. Like the ability of a Turing machine to conceptualize infinity, or make infinite conceptual strings, something we humans seem to be able to (although this is not well defined nor demonstrated). I think the theories are too subtle to actually say anything about the human mind, computers, and it seems to me that the mind can be universal and a turing machine.