[No Music Version] Kurt Gödel: Modern Dvmt of the Foundations Of Mathematics In Light Of Philosophy

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

This is a version without a musical soundtrack for those who For the original version with a soundtrack please go to http://www.youtube.com/watch?v=cG7MyZtGSB0

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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[SarahStarmer]

When defining the rules of chess, why worry about the truth or otherwise of the rules and pieces. In my mind numbers are no more true than chess pieces.

[GaryGeckDotCom]

@SarahStarmer right, but once the rules of chess are defined, universal mathematical principles determine the combination of possible moves. It is at this level that mathematical "platonic" reality lies. You don't decide how many combinations of moves are possible once you set the rules, something universal takes over that is out of your power.

[GaryGeckDotCom]

@GaryGeckDotCom we can come up with games but when we take a really far asway birds eye view, we realize even our games are on the back of something universal..not our arbitrary whims...we can define games that are truly arbitrary where every possible move is a unique arbitrary rule but such a game is absurd.

[SarahStarmer]

I like it without the music.

I prefer truth through definition to grand spiritual truths because I want to be the creator of my own truths. If I want to define rules by which numbers can be manipulated no one can stop me.

[GaryGeckDotCom]

@SarahStarmer i don't think you can do this because you can come up with arbitrary rules, but ultimately you need to fall back on something universal such as addition or else the entire system is purely arbitrary and useless...or can you explain how i'm wrong?

[docerex]

@SarahStarmer Consistency is an aesthetic that is central to truths, and yet mathematicians must persevere without that safety net in many branches of mathematics. I like Godel's position that we need something more than mechanical thinking necessary to discovering certain truths...aesthetically speaking. Insight, Intuition (what are they?). Where are the borders between Art and Science?

[docerex]

@SarahStarmer However, as you may already know, whatever axiomatic system you develop that involves a sufficient degree of number theory, there will be truths that will exist in your sandbox that you will not be able to prove. Additionally, Godel's incompleteness theorem also asserts that you will have no tools to prove your axiomatic system to be consistent.

[docerex]

I liked it with music. The material is quite heady stuff, so employing a dramatic cadence helps as guide posts when the logical bridges lead to dramatic assertions. It helps keep me a sense of orientation.

[christiaan81music]

complex :o

[KraussHelmut]

Nice upload, thanks!

[SarahStarmer]

Yes mathematical patterns are discovered not created.

[SarahStarmer]

Good answer.