David C. Ullrich <firstname.lastname@example.org> 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.