Monday, July 04, 2005
Gödel And The Nature Of Mathematical Truth
“Gödel mistrusted our ability to communicate. Natural language, he thought, was imprecise, and we usually don't understand each other. Gödel wanted to prove a mathematical theorem that would have all the precision of mathematics—the only language with any claims to precision—but with the sweep of philosophy. He wanted a mathematical theorem that would speak to the issues of meta-mathematics. And two extraordinary things happened. One is that he actually did produce such a theorem. The other is that it was interpreted by the jazzier parts of the intellectual culture as saying, philosophically exactly the opposite of what he had been intending to say with it.” – 'An interview with Rebecca Goldstein', Edge.
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4 comments:
Thank you for posting that interview. Anything on Godel is always very much appreciated. I will read it in its entirety shortly.
Craig
Not a problem. Will keep an eye out.
I'm not entirely sure what was the foundation for Godel's faith in mathematical realism. I do understand that at least in mathematics, specifically arithmatic, there is little or no ambiguity, and a clearly defined logical structure, things that are lacking in english at least. Considerations like this are what is behind the drive to develop synthetic languages such as Lojban (look it up on wikipedia, also I'll put a link on my page) which sought to bring the precision and logical nature of mathematics to a human language. It is a facinating project and worth looking at if you are interested in that sort of thing. It is intersting to note, in relation to Godel, that this language allows the use of meta-discursive operators, ie you can say "this sentence is false" in lojban without it automatically generating a paradox. However at this time it seems that there is no Godel sentence in Lojban, though some people are working on how it might be done.
Here is a good place to start.
Lojban
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