On Mon, 10 May 2004 16:44:17 +0000 (UTC), Marc Olschok <firstname.lastname@example.org> wrote:
>David C. Ullrich <email@example.com> wrote: >>[...] >> (i) the ability to engage in precise reasoning is very important. >> (ii) the ability to memorize definitions is relatively unimportant. >> (iii) someone whose notion of a certain definition is as above >> will not be able to engage in precise reasoning. >> >> Those three statements seem mutually inconsistent. > >As far as I have understood from following this thread, James' main >point was, that (iii) is compatible with (ii). While it is certainly >useful to have the precise definitions available _in_memory_ the >actual prerequisite from (iii) is, that they are available _at_all_. > >In fact, in my opinion the initial problems of the OP arose, because >after having read the text and memorizing some item in a distorted >version, he _never_again_ consulted the original texts with the definitions >to check what had sunk in his memory. > >So in a nutshell: it is nice to have it in memory but if not, one should >face it and grab for the reference again. > >I admit that it must be painfull to look up the definition of a vector space >more than once or twice. But after tackling a couple of problems and >exercises and after having looked it up and used it e.g. 5 or 6 times, >it sinks into memory. This is far better than trying to memorize in >isolation before one starts to tackle any problems.
Oh. Well all that's perfectly reasonable. As I think I've said at least once, "the problem" is that "they" don't believe that they need to _know_ the definitions (or what amounts to the same thing, they think they know the definitions when they're able to give garbled versions like the one a few posts up.)