(no subject)
Aug. 25th, 2007 01:46 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
stormdogIf you were to ask me right now to name the two most important books I've read, my answer would be Douglas Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid, and Raymond Smullyan's The Tao is Silent. Reading them both in sequence might be a bit much, but having gotten through all of the latter, then reading a bit of the former, than paging through the latter again, a synergism appears.
The greatest part of Gödel's work was showing, in his analysis of the Principia Mathematica, that for any given formal mathematical system (that is, a computable axiomatic theorem), and I quote from Wikipedia here:
This turned mathematics on it's ear by proving that no system of mathematics can ever account for every mathematical possibility. For any given formal system, there must exist some mathematical concepts and expressions that cannot be accounted for by that system.
A similarity between Gödel's work and what I read in Smullyan's book becomes apparent. It seems to me that the driving principal behind zen and taoist philosophy is that no formal system of philosophical beliefs can comprise every possible philosophical idea. There must exist some forms of philosophical belief and expression that cannot be accounted for by any system of belief, yet those beliefs and expressions are not necessarily faulty. I think that that's the root of all the seemingly paradoxical or nonsensical bits that you encounter in zen philosophy. It's also why those bits should never be discarded out of hand; just because a parable or an insight does not fit in to your existing framework, or even flies in flagrant opposition to it, does not mean that it's wrong or invalid. Impossibilities, infinite recursion, and pure chaos are inescapable parts of mathematics, philosophy, art, music, and your world.
On a (probably) purely unrelated note:
Ronald: "Hamburglar is stealing all the frilly panties from the girls of McDonaldland!"
Hamburglar: "Ruffle ruffle!
=============
Ok, this is quite interesting. When I was writing that entry, I did a Google search for Raymond Smullyan and linked to his Wikipedia entry, but didn't actually read it. Now that I am reading it, well what do you know? A lot of his work in logic (instead of philosophy) centered around Gödel's incompleteness theorem. I feel kind of cool for having seen the connection prior to reading about it, especially when he doesn't mention Gödel anywhere in the book. And, Bach is one of his favorite composers. He must have read GEB at some point.
The greatest part of Gödel's work was showing, in his analysis of the Principia Mathematica, that for any given formal mathematical system (that is, a computable axiomatic theorem), and I quote from Wikipedia here:
1. If the system is consistent, it cannot be complete. (This is generally known as the incompleteness theorem.)
2. The consistency of the axioms cannot be proved within the system.
This turned mathematics on it's ear by proving that no system of mathematics can ever account for every mathematical possibility. For any given formal system, there must exist some mathematical concepts and expressions that cannot be accounted for by that system.
A similarity between Gödel's work and what I read in Smullyan's book becomes apparent. It seems to me that the driving principal behind zen and taoist philosophy is that no formal system of philosophical beliefs can comprise every possible philosophical idea. There must exist some forms of philosophical belief and expression that cannot be accounted for by any system of belief, yet those beliefs and expressions are not necessarily faulty. I think that that's the root of all the seemingly paradoxical or nonsensical bits that you encounter in zen philosophy. It's also why those bits should never be discarded out of hand; just because a parable or an insight does not fit in to your existing framework, or even flies in flagrant opposition to it, does not mean that it's wrong or invalid. Impossibilities, infinite recursion, and pure chaos are inescapable parts of mathematics, philosophy, art, music, and your world.
On a (probably) purely unrelated note:
Ronald: "Hamburglar is stealing all the frilly panties from the girls of McDonaldland!"
Hamburglar: "Ruffle ruffle!
=============
Ok, this is quite interesting. When I was writing that entry, I did a Google search for Raymond Smullyan and linked to his Wikipedia entry, but didn't actually read it. Now that I am reading it, well what do you know? A lot of his work in logic (instead of philosophy) centered around Gödel's incompleteness theorem. I feel kind of cool for having seen the connection prior to reading about it, especially when he doesn't mention Gödel anywhere in the book. And, Bach is one of his favorite composers. He must have read GEB at some point.
