jacinthebox

10

I'm sorry if I wasn't clear. *I* endorse the "cynical view" that mathematics is fundamentally symbol manipulation. Fundamental in the sense that mathematics as we currently know it can be completely described by symbol manipulation without having to resort to notions such as "intuition." Eliezer, apparently, disagrees with this philosophy on the grounds that it is robbing mathematics of something which he finds aesthetically pleasing.

00

You may have read - I've certainly read - some philosophy which endeavors to score points for counter-intuitive cynicism by saying that all mathematics is a mere game of tokens; that we start with a meaningless string of symbols like: ...and we follow some symbol-manipulation rules like "If you have the string 'A ∧ (A → B)' you are allowed to go to the string 'B'", and so finally end up with the string: ...and this activity of string-manipulation is all there is to what mathematicians call "theorem-proving" - all there is to the glorious human endeavor of mathematics.

I don't consider the post to be an emotional appeal, just the phrase "and this activity of string-manipulation is all there is to what mathematicians call "theorem-proving" - all there is to the glorious human endeavor of mathematics." I mean, there is essentially no content there. Just a rough outline of a philosophy, and then not even a legitimate attack on it, just a "if they are right, then mathematics doesn't seem glorious to me any longer!"