Originally Posted by
MoeBlee
P.S. What is especially annoying to me is that more and more there are people (I'm not at all saying you are one of them) who habitually cite Wikipedia (for mathematics) while not also getting a more integrated perspective. What happens is that you have people with these dangling, out of context, notions about this and that and they end up basically just throwing Wikipedia quotes at one another rather. And since the articles are not integrated or even uniformly edited in any way, quotes (especially definitions) from one article don't always line up with those from other articles. And worst are people who demand things like "You're not right unless you can show me in Wikipedia." So, in general, as I said at first, (regarding mathematics) I do dislike that people more and more turn to Wikipedia RATHER THAN better, more integrated, more careully edited, more carefully conceived books and articles.
Even more fundamentally, it's interesting to me that I do very much appreciate hyperlinking, the "network" nature of our knowledge (refer even to Quine's notion of Neurath's ship built at sea), but that it doesn't always suit mathematics very well. I mean, I feel that it is better to learn certain mathematical subjects from the BEGINNING, adding definition and theorem along the way, in the traditional way, as opposed to working BACKWARDS to learn definitions and theorems and then learn the definitions and theorems that were used in regress. And Wikipedia is used too much by people in that backwards way. A made up example: What's the definition of "cardinal"?, so then have to look up the definition of "ordinal", so then have to look up the definition of "well ordered", so then have to look up the definition of "leastness", etc., rather than starting with the primitives and working FORWARD, which is much more EFFICIENT and intellectually organized.