Mikhail Gorelkin wrote: > I would like to return to that Chaitin lesson:
Well, the problem with focusing on the Chaitin talk is that there were many things said in the talk, not all of which point in the same direction. So, it would be better if you would single out a specific aspect of the talk that bears discussion. > it seems that a full > and correct definition of mathematics is *impossible*... like a full > axiomatization of arithmetic. Mathematics is so complex that an > accurate definition of it is equal to doing math (no compression in > Chaitin's terminology). It means that all our descriptions are just > *references* to discussed subjects. --Mikhail Hmmm. I maintain my claim that math is a living language by which we describe aspects of reality. That means I agree completely that a complete and consistent definition of math is impossible. But I disagree that an accurate definition of math is equal to doing math. Because I believe math is a language, defining math is linguistics (and anthropology and history). Granted, to be specific about the actual language, one has to know and do some math. After all, describing, say, the history of the concept of "infinity" requires enough mathematical understanding to follow the historical thread. But such "doing math" is a side-effect of the linguistic work. I suspect that, in defining math, the linguist only has to about the same amount of math as a linguist has to do when defining, say, French or Swahili. Then I again agree that all our descriptions are just references to discussed objects, because that's the fundamental role of languages. They provide us with the ability to _refer_ to things (albeit the "things" that can be referred to may not actually exist or they may be an artifact of the language being used). So, I'm in the odd position of having to agree with the beginning of your argument, disagree with the middle, and agree with the end. [grin] -- glen e. p. ropella, 971-219-3846, http://tempusdictum.com ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
